A survey -- about your research questions.
I don't normally follow unsolicited links on the Internet because of potential fishing scams no fence but I'd be happy to share my research interests here -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Some questions on ontology of dreams
I wonder what would happen to someone's mind if they were born in a white (or any color) isolation tank. What would happen as years wore on? Would the person ever hallucinate anything? It has only seen the tank for his whole life. So what would inspire him to hallucinate something? Can he hallucinate, say, a friend staring at him from across the void without ever seeing a friend or anything for that matter except the white isolation tank. Would he dream and what would he dream of? Would dreaming become one with waking? Would he even know what a dream is? He has never heard the word "dream" spoken out loud. But he knows which worlds decay faster or are more "curvy" in the world-line sense: dreams decay faster or are more "curvy" than waking events. So, locally, we usually know when it's a dream. When the event world-line is straight, that means we pretty much never know what is a dream and what is "real"? -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A mathematical description of the level IV Multiverse
Thank you everyone for responding. Please keep in mind that I wrote that when my ideas about formal systems were more naive than they are now two years ago :D On Mon, Jun 15, 2015 at 12:43 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 15 Jun 2015, at 17:15, Brian Tenneson wrote: I had forgotten I wrote this a while back, from my FB feed on this day. Seems relevant. Can truth ever be proven? That has no meaning. Truth about what? Let's start with mathematical truth. Isn't it contingent? In other words, it seems to me that theorems are considered true but aren't they only true if the axioms are true and if the rules of inference are sound? Is logic infallible? If yes, can that be proven with logic? If no, what makes logic superior to other things like intuition and faith? (I know these are false dichotomies but I thought they might trigger some interesting discussions.) Here's something I wrote in a discussion I'm having. Structure does not cause something to be non-fictional, nor does lack of structure cause something to be fictional. A theorem in one formal system might be false in another, Formal system = machine = 3p-person. yes, they have all theior on opinion, but this does not mean that some are not true or false. Ok, then, which theorems are absolutely true? (Of course the ones absolutely false would be negations of the former.) a lot like how different video games have different rules. Even if you prove something about all formal systems, that proof has been carried out in a larger formal system; Not necessarily. Formal systems can prove a lot about themselves, including their own incompleteness conditionalised on their consistency. A la Godel's theorems, right? so there is an inherent circularity, I think the one you allude to is the one solved by the diagonals of Kleene. Not the time to say much more, but I have explained this. Sorry, I don't read every post in this group. Can you give me a brief tutorial on these results of Kleene? or more accurately, an inherent interdependency. It's like being in a video game trying to prove that something is true of all video games but that meta-game proof is being conducted in one of the video games the proof is about. Thus, the concept of proof needs to be anchored to something true but by this rationale, proof is merely anchored to itself. Anchoring proof on truth leads to the first person. That sounds reasonable. So how can you describe the connection(s) between proof of truth (in mathematics say) to the 1p? Therefore, perhaps proof of truth is an unattainable goal in math. Proof of which truth. In logic, truth is defined by a model. A is true if it is the case that A in the intended model. This leads me back to the question earlier: is logic infallible? If so, is there a proof of that using logic? If not, then how can we use it with any confidence? Perhaps proof of truth is an unattainable goal anywhere. ? Well, proof of Truth, with a big T is like the proof of the existence of God: that does not exist, we have to start from something. But since Gödel we know that proof means belief, and that it can't be taken for granted. Isn't it true that once you lock in the definitions (of truth or god or Truth or God), the assumptions, what types of statements are grammatically correct, what the rules of inference are, and what constitutes proof, that conclusions are inescapable? If so, is THAT an inescapable or escapable theorem? If I were to say that both confirming and denying the statement there is no such thing as truth implies that there is truth, I am still formulating that theorem there is truth within yet another formal system which, on the surface of things, gets us nowhere. It is like inventing a two-player game with, from an outside point of view, a bizarre set of rules, and claiming that checkmating someone in that game amounts to producing not just truth but proof of truth. The people outside our fishbowl looking in on us must be very amused, just as are the people outside their fishbowl looking in on them. Ok, that is Truth with a big T, and so it needs faith. It is religion. OK. If I say, there is no absolute truth, well, that is an absolutely true statement isn't it? IOW, if there is no absolute truth is false then there is absolute truth. If there is no absolute truth is true, then it is absolutely true. However, and perhaps you can explain this better than I, I think that quirky statements in language like I always lie don't prove much unless we start doing things like assuming logic is infallible which requires faith, does it not? Formal systems show us that our usual formal systems (the ones we use to communicate, inform, and persuade in English for instance) have the same relationship to truth that Earth does to the center of the universe. No formal system is provably true and correct, though
Re: A mathematical description of the level IV Multiverse
I had forgotten I wrote this a while back, from my FB feed on this day. Seems relevant. Can truth ever be proven? Here's something I wrote in a discussion I'm having. Structure does not cause something to be non-fictional, nor does lack of structure cause something to be fictional. A theorem in one formal system might be false in another, a lot like how different video games have different rules. Even if you prove something about all formal systems, that proof has been carried out in a larger formal system; so there is an inherent circularity, or more accurately, an inherent interdependency. It's like being in a video game trying to prove that something is true of all video games but that meta-game proof is being conducted in one of the video games the proof is about. Thus, the concept of proof needs to be anchored to something true but by this rationale, proof is merely anchored to itself. Therefore, perhaps proof of truth is an unattainable goal in math. Perhaps proof of truth is an unattainable goal anywhere. If I were to say that both confirming and denying the statement there is no such thing as truth implies that there is truth, I am still formulating that theorem there is truth within yet another formal system which, on the surface of things, gets us nowhere. It is like inventing a two-player game with, from an outside point of view, a bizarre set of rules, and claiming that checkmating someone in that game amounts to producing not just truth but proof of truth. The people outside our fishbowl looking in on us must be very amused, just as are the people outside their fishbowl looking in on them. Formal systems show us that our usual formal systems (the ones we use to communicate, inform, and persuade in English for instance) have the same relationship to truth that Earth does to the center of the universe. No formal system is provably true and correct, though there are formal systems that might conform to what we perceive. Formal systems can only be proved relatively true compared to other formal systems. At least until that anchor is found. That reduces math to a grand symphony. Grand symphonies aren't inherently true or false and there is no hope in my mind of proving the grand symphony that is math to be true. Another way to look at is is a grand poem that makes up its own rules and even explicitly acknowledges that fact. The question of whether concepts referenced by the poem actually exist is to open the door to many formal systems we might walk into in order to answer the question. Moreover, it will be true in some but not others that that concept exists. A really broad interpretation of existence would be that something exists if it is referenced by a grammatically-correct statement made in at least one formal system. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A mathematical description of the level IV Multiverse
Hi Brent
On Wed, Jun 3, 2015 at 1:17 PM, meekerdb meeke...@verizon.net wrote:
On 6/3/2015 7:16 AM, Brian Tenneson wrote:
On Wednesday, June 3, 2015 at 2:16:31 AM UTC-7, Bruno Marchal wrote:
On 02 Jun 2015, at 20:10, Brian Tenneson wrote:
Grammatical systems just might be the type of thing Tegmark is looking
for that is a framework for all mathematical structures... or at least a
large class of them.
I am still exploring the idea of grammatical system induction.
I am not sure what you mean by grammatical induction. Is that not
equivalent with the omega-induction principles, like with PA?
It is described in this document:
https://docs.google.com/document/d/1amDb4Yti4egpKfcO2oLcnGAH8UpC8_tKb7ivuH3AT7A/edit?usp=sharing
A couple of points I don't understand. First, G is a set of sentences.
I'm not sure what any means.
It means that G is a subset of the set of utterances.
Does it mean G is all grammatical sentences?
G is the set of grammatically-correct utterances for the formal system
(A,G,X,I). Yes, all of them. That does not mean that G needs to be the
entire set of utterances though.
Is G assumed finite, or countable?
There are no assumptions on G other than it is a subset of the set of all
utterances using symbols in the alphabet A.
Second, why is H defined as an element of G^n (Cartesian product of sets)
instead of just a subset of G?
H is a *subset* of a Cartesian power of G, not an *element* of a Cartesian
power of G.
It is possible that a rule of inference is not defined for all of G^n, so H
is the domain of the rule of inference in question. Modus ponens, for
instance, in the FOL (first order logic) formal system is only defined so
that it is this function:
Modus ponens = {( (p, p--q) , q ) : p is in element of G, p--q is an
element of G, and q is an element of G}. Modus ponens is not defined for
all of G^2. For instance, (p,q--p) is not in the domain of Modus Ponens.
In first order logic, n is usually 1 or 2.
Third, if [H-G] is a function doesn't that implies that T(H) ends with a
unique G, which is not generally true of inferences.
Well, I checked this list of some rules of inference
http://en.wikipedia.org/wiki/List_of_rules_of_inference
ALL of them have a single conclusion, which is an element of G.
Which inference rules have multiple conclusions? We can make the minor
adjustment that T is in [H--G^m] instead of T is in [H--G]. But I don't
see why we have to.
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Re: A mathematical description of the level IV Multiverse
On Wednesday, June 3, 2015 at 2:16:31 AM UTC-7, Bruno Marchal wrote: On 02 Jun 2015, at 20:10, Brian Tenneson wrote: Grammatical systems just might be the type of thing Tegmark is looking for that is a framework for all mathematical structures... or at least a large class of them. I am still exploring the idea of grammatical system induction. I am not sure what you mean by grammatical induction. Is that not equivalent with the omega-induction principles, like with PA? It is described in this document: https://docs.google.com/document/d/1amDb4Yti4egpKfcO2oLcnGAH8UpC8_tKb7ivuH3AT7A/edit?usp=sharing I believe it can be used to provide an induction principle that allows one to prove something about all sets in ZFC (or any set theory). You will need transfinite induction. But with the usual (omega) induction, you get already Löbianity, and the self-reference logics will not been changed with addition. Applying the general grammatical system induction to formal systems, I believe there is a way to prove something about all theorems within a formal system, Yes, PA can prove that ZF proves things. For proving that a formal system does not prove something, you will need strionger systems, and by incompleteness such negative statements cannot be axiomatized in once system. perhaps providing a little insight into truth in general. Also, an induction principle applies to all proofs if one wants to prove something about all proofs in a formal system. The document in the first post has been updated to include all of this. There are some words I need to change so just notice the essence... Any feedback is appreciated! If you assume computationalism, simple (omega) induction is enough to get the machine psychology and theology, and to justify why machines will build more and more induction rules, but none will get the whole truth, which is beyond axiomatization and formalization (even assuming computationalism). You seem to try to do what the logicians have already done. You might study the little book by Torkel Franzen on the Inexhaustibility, which makes rather clear the elusive character of truth. I realized later that what I've done was done roughly in the 1930's. But no one has connected the notion of grammatical system to Max Tegmark's Level IV multiverse idea as far as I know. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com javascript:. To post to this group, send email to everyth...@googlegroups.com javascript:. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A mathematical description of the level IV Multiverse
Grammatical systems just might be the type of thing Tegmark is looking for that is a framework for all mathematical structures... or at least a large class of them. I am still exploring the idea of grammatical system induction. I believe it can be used to provide an induction principle that allows one to prove something about all sets in ZFC (or any set theory). Applying the general grammatical system induction to formal systems, I believe there is a way to prove something about all theorems within a formal system, perhaps providing a little insight into truth in general. Also, an induction principle applies to all proofs if one wants to prove something about all proofs in a formal system. The document in the first post has been updated to include all of this. There are some words I need to change so just notice the essence... Any feedback is appreciated! -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A mathematical description of the level IV Multiverse
Oh it seems all of the results in what I wrote are already known, which I actually sort of hoped for. http://bookzz.org/book/717308/5c7a03/?_ir=1 Especially 1.2 and chapter 6... Now what about the aggregate of all grammatical systems being a candidate for the level 4 multiverse? On Sunday, May 10, 2015 at 10:42:20 PM UTC-7, Brian Tenneson wrote: Hi Everyone, In the final section of the document I linked to earlier, I am trying to prove a principle that, if correct, would be a way to prove something is true for all sets in ZFC; the methods could possibly be adapted to other set theories. I still have a lot of work to do but it feels promising... https://docs.google.com/document/d/1amDb4Yti4egpKfcO2oLcnGAH8UpC8_tKb7ivuH3AT7A/edit?usp=sharing The juicy parts start on page 10-11. I'd like to be proven wrong before I go much further! Cheers Brian On Thursday, May 7, 2015 at 9:30:50 AM UTC-7, Brian Tenneson wrote: Hi Bruno, Thank you! Cheers Brian On Thursday, May 7, 2015 at 6:18:35 AM UTC-7, Bruno Marchal wrote: Hi Brian, On 06 May 2015, at 18:48, Brian Tenneson wrote: Good morning Everything List, Bruno Marchal's (sorry if I misspelled your name, Bruno!) feedback on my work has been instrumental in helping me realize when certain ideas need revision. I have been trying to figure out which mathematical entity is our external reality. Tegmark and others have suggested that the universe is an ensemble of mathematical objects, such as the ensemble of all computable structures defined in Model theory. Thanks to Bruno, I have had to go back to the drawing board several times, needing to completely scrap my ideas and start anew. And I mean that sincerely. I have been working on something I call grammatical systems. There already is a nice, neatly-formatted description of what I've got over at physicsforums.com. I would appreciate your expert opinions on what I have done so far. Now is a good time to have to scrap it and return to the drawing board as I have not yet gotten very far. Thanks in advance for any and all feedback. Here is the link: https://www.physicsforums.com/threads/a-generalization-of-formal-systems-grammatical-systems.812241/ I will take a look, and plausibly make some comments, perhaps out-of- line. Best, Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A mathematical description of the level IV Multiverse
Hi Everyone, In the final section of the document I linked to earlier, I am trying to prove a principle that, if correct, would be a way to prove something is true for all sets in ZFC; the methods could possibly be adapted to other set theories. I still have a lot of work to do but it feels promising... https://docs.google.com/document/d/1amDb4Yti4egpKfcO2oLcnGAH8UpC8_tKb7ivuH3AT7A/edit?usp=sharing The juicy parts start on page 10-11. I'd like to be proven wrong before I go much further! Cheers Brian On Thursday, May 7, 2015 at 9:30:50 AM UTC-7, Brian Tenneson wrote: Hi Bruno, Thank you! Cheers Brian On Thursday, May 7, 2015 at 6:18:35 AM UTC-7, Bruno Marchal wrote: Hi Brian, On 06 May 2015, at 18:48, Brian Tenneson wrote: Good morning Everything List, Bruno Marchal's (sorry if I misspelled your name, Bruno!) feedback on my work has been instrumental in helping me realize when certain ideas need revision. I have been trying to figure out which mathematical entity is our external reality. Tegmark and others have suggested that the universe is an ensemble of mathematical objects, such as the ensemble of all computable structures defined in Model theory. Thanks to Bruno, I have had to go back to the drawing board several times, needing to completely scrap my ideas and start anew. And I mean that sincerely. I have been working on something I call grammatical systems. There already is a nice, neatly-formatted description of what I've got over at physicsforums.com. I would appreciate your expert opinions on what I have done so far. Now is a good time to have to scrap it and return to the drawing board as I have not yet gotten very far. Thanks in advance for any and all feedback. Here is the link: https://www.physicsforums.com/threads/a-generalization-of-formal-systems-grammatical-systems.812241/ I will take a look, and plausibly make some comments, perhaps out-of- line. Best, Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A mathematical description of the level IV Multiverse
Hi Bruno, Thank you! Cheers Brian On Thursday, May 7, 2015 at 6:18:35 AM UTC-7, Bruno Marchal wrote: Hi Brian, On 06 May 2015, at 18:48, Brian Tenneson wrote: Good morning Everything List, Bruno Marchal's (sorry if I misspelled your name, Bruno!) feedback on my work has been instrumental in helping me realize when certain ideas need revision. I have been trying to figure out which mathematical entity is our external reality. Tegmark and others have suggested that the universe is an ensemble of mathematical objects, such as the ensemble of all computable structures defined in Model theory. Thanks to Bruno, I have had to go back to the drawing board several times, needing to completely scrap my ideas and start anew. And I mean that sincerely. I have been working on something I call grammatical systems. There already is a nice, neatly-formatted description of what I've got over at physicsforums.com. I would appreciate your expert opinions on what I have done so far. Now is a good time to have to scrap it and return to the drawing board as I have not yet gotten very far. Thanks in advance for any and all feedback. Here is the link: https://www.physicsforums.com/threads/a-generalization-of-formal-systems-grammatical-systems.812241/ I will take a look, and plausibly make some comments, perhaps out-of- line. Best, Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
A mathematical description of the level IV Multiverse
Good morning Everything List, Bruno Marchal's (sorry if I misspelled your name, Bruno!) feedback on my work has been instrumental in helping me realize when certain ideas need revision. I have been trying to figure out which mathematical entity is our external reality. Tegmark and others have suggested that the universe is an ensemble of mathematical objects, such as the ensemble of all computable structures defined in Model theory. Thanks to Bruno, I have had to go back to the drawing board several times, needing to completely scrap my ideas and start anew. And I mean that sincerely. I have been working on something I call grammatical systems. There already is a nice, neatly-formatted description of what I've got over at physicsforums.com. I would appreciate your expert opinions on what I have done so far. Now is a good time to have to scrap it and return to the drawing board as I have not yet gotten very far. Thanks in advance for any and all feedback. Here is the link: https://www.physicsforums.com/threads/a-generalization-of-formal-systems-grammatical-systems.812241/ Brian -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: The situation at Fukushima appears to be deteriorating
This is what they call a google bomb. Historians may think google searches represent something about the mind of humanity. So this particular google bomb might lead them to think the Fukushima reactor exploded in 2014. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Would math make God obsolete ?
Yes, some day a computer might be able to figure out that the set of rationals is not equipollent to the set of real numbers. I saw somewhere that using an automated theorem prover, one of Godel's incompleteness theorems was proved by a computer. The question I raised initially was this: will there ever be a machine or human who can correctly answer all questions with a mathematical theme that have answers? I didn't think so in my original post but now I'm starting to wonder. It's the existence of undecidable statements that would probably lead to the machine or human not being able to do it in general. This reminds me of the halting problem. The good news is we will never run out of mathematical territory to think about. On Mon, Jan 27, 2014 at 6:58 AM, Gabriel Bodeen gabebod...@gmail.comwrote: FWIW, under the usual definitions, the rationals are enumerable and so are a smaller set than the reals. I'd suppose that if people can figure that out with our nifty fleshy brains, then a well-designed computer brain could, too. -Gabe On Friday, January 24, 2014 1:23:40 AM UTC-6, Brian Tenneson wrote: There are undecidable statements (about arithmetic)... There are true statements lacking proof. There are also false statements about arithmetic the proof of whose falsehood is impossible; not just impossible for you and me but for a computer of any capacity or other forms of rational processing. We'll never have a computer, then, that will work as a mathematically-omniscient device. By that I mean a computer such that every question that has a mathematically-oriented theme having an answer truthfully can be answered by such a device. Calculators demonstrate the concept but are clearly not mathematically-omniscient: you ask the calculator what is 2+2 and press a button and presto you get an answer. What I'm talking about would be questions like is the set of rational numbers equal in size to the set of real numbers, and get the correct answer. So we will never have such a computer no matter what its capacities are, even if computer encompasses the entire human brain. Unfortunately, that means that even for humans, we will never know everything about math. Unless something weird would happen and we suddenly had infinite capacities; that might change the conclusions. -- You received this message because you are subscribed to a topic in the Google Groups Everything List group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/everything-list/xabA-SKxTHM/unsubscribe. To unsubscribe from this group and all its topics, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Would math make God obsolete ?
Some basic.questions. When you say PA, do you mean the set of all theorems entailed by the axioms of Peano arithmetic? Does this include the true (relative to PA of course) wffs that are not provable from PA alone? How can it be that PA+con(I) can prove its own consistency because it is inconsistent? Do you mean that it is consistent relative to itself but inconsistent in the metalanguage? Or else how can we have it be both consistent and inconsistent? This is probably way off the subject (hope that's ok with you): isn't all mathematical truth relative to the formal system one is operating in? all mathematical truth is relative to the formal system one is operating in is relative to the formal system I call rational discourse in which mathematical discourse and machine-level discourse are sub-systems. On Mon, Jan 27, 2014 at 7:41 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 27 Jan 2014, at 16:12, Brian Tenneson wrote: Yes, some day a computer might be able to figure out that the set of rationals is not equipollent to the set of real numbers. A Lôbian machine like ZF can do that already. I saw somewhere that using an automated theorem prover, one of Godel's incompleteness theorems was proved by a computer. Boyer and Moore, yes, but that is not conceptuallydifferent than ZF, except that the Boyer-Moore machine uses more efficient sort of AI path. Gödel discovered that PM already proves his own incompleteness theorem. All Lôbian machine proves their own Gödel's theorem. They all prove If I am consistent, then I can't prove my consistency. The question I raised initially was this: will there ever be a machine or human who can correctly answer all questions with a mathematical theme that have answers? All? No, for any machine i in the phi_i. But that is less clear for evolving machines, whose evolution rule is not part of the program of the machine. Of course, at each moment of her life, she will be incomplete, but if her evolution is enough non computable, or using some special oracle, it might be that the machine will generate the infinitely many truth of arithmetic, but not in any provable way. I didn't think so in my original post but now I'm starting to wonder. It's the existence of undecidable statements that would probably lead to the machine or human not being able to do it in general. This reminds me of the halting problem. Those are related. Undecidable is always relative. Consistent(PA) is not provable by PA, but is provable in two lines in the theory PA+con(PA). Of course PA+con(PA) cannot prove con(PA+con(PA)). What about PA+con(I), with I = PA+con(I). It exists as we can eliminate the occurence of I by using the Dx = xx method. Well, in this case PA+con(I) can prove its own consistency, but only because it is actually inconsistent. The good news is we will never run out of mathematical territory to think about. Yes indeed, even if we confine ourselves on elementary (first order) arithmetic. There is an infinity of surprises there. Bruno On Mon, Jan 27, 2014 at 6:58 AM, Gabriel Bodeen gabebod...@gmail.comwrote: FWIW, under the usual definitions, the rationals are enumerable and so are a smaller set than the reals. I'd suppose that if people can figure that out with our nifty fleshy brains, then a well-designed computer brain could, too. -Gabe On Friday, January 24, 2014 1:23:40 AM UTC-6, Brian Tenneson wrote: There are undecidable statements (about arithmetic)... There are true statements lacking proof. There are also false statements about arithmetic the proof of whose falsehood is impossible; not just impossible for you and me but for a computer of any capacity or other forms of rational processing. We'll never have a computer, then, that will work as a mathematically-omniscient device. By that I mean a computer such that every question that has a mathematically-oriented theme having an answer truthfully can be answered by such a device. Calculators demonstrate the concept but are clearly not mathematically-omniscient: you ask the calculator what is 2+2 and press a button and presto you get an answer. What I'm talking about would be questions like is the set of rational numbers equal in size to the set of real numbers, and get the correct answer. So we will never have such a computer no matter what its capacities are, even if computer encompasses the entire human brain. Unfortunately, that means that even for humans, we will never know everything about math. Unless something weird would happen and we suddenly had infinite capacities; that might change the conclusions. -- You received this message because you are subscribed to a topic in the Google Groups Everything List group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/everything-list/xabA-SKxTHM/unsubscribe . To unsubscribe from this group and all its topics, send an email to everything-list
Re: Would math make God obsolete ?
You could always just add it and its negation to the list of axioms (though not at the same time, of course) and see where that leads, if anywhere. On Mon, Jan 27, 2014 at 10:55 AM, John Clark johnkcl...@gmail.com wrote: On Fri, Jan 24, 2014 at 2:23 AM, Brian Tenneson tenn...@gmail.com wrote: There are undecidable statements (about arithmetic)... There are true statements lacking proof. Yes. There are also false statements about arithmetic the proof of whose falsehood is impossible; A proof is a FINITE number of statements establishing the truth or falsehood of something; if Goldbach's Conjecture is untrue then there is a FINITE even number that is NOT the sum of 2 primes. It would only take a finite number of lines to list all the prime numbers smaller than that even number and show that no two of them equal that even number, and that would be a proof that Goldbach's Conjecture is wrong. The real problem would come if Goldbach's Conjecture is true (so we'll never find two primes to show it's wrong) but can not be proven to be true (so we will never find a finite proof to show its correct). John K Clark not just impossible for you and me but for a computer of any capacity or other forms of rational processing. We'll never have a computer, then, that will work as a mathematically-omniscient device. By that I mean a computer such that every question that has a mathematically-oriented theme having an answer truthfully can be answered by such a device. Calculators demonstrate the concept but are clearly not mathematically-omniscient: you ask the calculator what is 2+2 and press a button and presto you get an answer. What I'm talking about would be questions like is the set of rational numbers equal in size to the set of real numbers, and get the correct answer. So we will never have such a computer no matter what its capacities are, even if computer encompasses the entire human brain. Unfortunately, that means that even for humans, we will never know everything about math. Unless something weird would happen and we suddenly had infinite capacities; that might change the conclusions. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to a topic in the Google Groups Everything List group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/everything-list/xabA-SKxTHM/unsubscribe. To unsubscribe from this group and all its topics, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Would math make God obsolete ?
There are undecidable statements (about arithmetic)... There are true statements lacking proof. There are also false statements about arithmetic the proof of whose falsehood is impossible; not just impossible for you and me but for a computer of any capacity or other forms of rational processing. We'll never have a computer, then, that will work as a mathematically-omniscient device. By that I mean a computer such that every question that has a mathematically-oriented theme having an answer truthfully can be answered by such a device. Calculators demonstrate the concept but are clearly not mathematically-omniscient: you ask the calculator what is 2+2 and press a button and presto you get an answer. What I'm talking about would be questions like is the set of rational numbers equal in size to the set of real numbers, and get the correct answer. So we will never have such a computer no matter what its capacities are, even if computer encompasses the entire human brain. Unfortunately, that means that even for humans, we will never know everything about math. Unless something weird would happen and we suddenly had infinite capacities; that might change the conclusions. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Bruno's mathematical reality
I had a question about the quote below of Edgar's. In what sense of 'compute' do you believe that something computes reality? Also, I'm wondering if Laplace's demon is relevant. http://en.wikipedia.org/wiki/Laplace%27s_demon According to the article, we have: In 2008, David Wolperthttp://en.wikipedia.org/w/index.php?title=David_Wolpertaction=editredlink=1 used Cantor diagonalizationhttp://en.wikipedia.org/wiki/Cantor_diagonalization to disprove Laplace's demon. He did this by assuming that the demon is a computational device and showing that no two such devices can completely predict each other.[5]http://en.wikipedia.org/wiki/Laplace%27s_demon#cite_note-5 [6] http://en.wikipedia.org/wiki/Laplace%27s_demon#cite_note-6 If the demon were not contained within and computed by the universe, any accurate simulation of the universe would be indistinguishable from the universe to an internal observer, and the argument remains distinct from what is observable. On Friday, December 20, 2013 3:52:54 PM UTC-8, Edgar Owen wrote: the actual math and logic that computes reality. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Rationals vs Reals in Comp
On Tue, Apr 23, 2013 at 8:53 PM, Craig Weinberg whatsons...@gmail.comwrote: On Tuesday, April 23, 2013 11:37:14 PM UTC-4, Brian Tenneson wrote: You keep claiming that we understand this and that or know this and that. And, yes, saying something along the lines of we know we understand because we care about what we understand *is* circular. No, it's not. I'm saying that it is impossible to doubt we understand. It's just playing with words. My point about caring is that it makes it clear that we intuitively make a distinction between merely being aware of something and understanding it. I'll try to explain how we know we understand because we care about what we understand is circular. Note the use of the word understand towards the left edge of the statement in quotes followed by another instance of the word understand. This is analogous to saying We are Unicorns because care about Unicorns. Doesn't prove unicorns exist; doesn't prove understanding exists (i.e., that any human understands anything). If this is all sophistry then it should be easily dismissible. And yes, playing with words is what people normally do, wittingly or unwittingly, and that lends more evidence to the notion that we are processors in a Chinese room. Still doesn't rule out the possibility that we are in a Chinese room right now, manipulating symbols without really understanding what's going on but able to adeptly shuffle the symbols around fast enough to appear functional. Why not? If we were manipulating symbols, why would we care about them. What you're saying doesn't even make sense. We are having a conversation. We care about the conversation because we understand it. If I was being dictated to write in another language instead, I would not care about the conversation. Are you claiming that there is no difference between having a conversation in English and dictating text in a language you don't understand? We care about the symbols because working through the symbols in our brains is what leads to food, shelter, sex, and all the things animals want. Or we care about the symbols because they further enrich our lives. The symbols in this corner of the internet (barring my contributions of course) are examples of that. Regarding the world, would you say there is more that we (i.e., at least one human) understand or more that we don't? I would vote 'don't' and that leads me also to suspect we are in a chinese room right now. Your coupling of caring and understanding is somewhat arbitrary. You seem to be saying we care because we understand and we understand because we care. But it is the case that even if we do understand something, we don't have to care about it. And understanding because we care doesn't follow either: I care a great deal about science, 20-21st stuff mainly, but I understand almost nothing of it. Would you say we live in a world where we are confronted daily with numerous events; are you claiming you understand most or all of these events? The less you understand the greater the chances of being in a Chinese room. We know that we're not the center of the universe or even the solar system. We know that space is almost unfathomably vast. We know humans are fallible, even when it comes time to do some math and science. So why be so shocked that we are in a Chinese room, lacking understanding of the texts? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
Re: Rationals vs Reals in Comp
On Wed, Apr 24, 2013 at 4:46 AM, Craig Weinberg whatsons...@gmail.comwrote: On Wednesday, April 24, 2013 4:31:55 AM UTC-4, Brian Tenneson wrote: On Tue, Apr 23, 2013 at 8:53 PM, Craig Weinberg whats...@gmail.comwrote: On Tuesday, April 23, 2013 11:37:14 PM UTC-4, Brian Tenneson wrote: You keep claiming that we understand this and that or know this and that. And, yes, saying something along the lines of we know we understand because we care about what we understand *is* circular. No, it's not. I'm saying that it is impossible to doubt we understand. It's just playing with words. My point about caring is that it makes it clear that we intuitively make a distinction between merely being aware of something and understanding it. I'll try to explain how we know we understand because we care about what we understand is circular. Note the use of the word understand towards the left edge of the statement in quotes followed by another instance of the word understand. You should read it as we know we understand because we care about X. My only intention in repeating the word was to make it clear that the thing that we care about is the thing that we understand. It is the caring which is a symptom of understanding. The absence of that symptom of caring in a machine indicates to me that there is a lack of understanding. Things which understand can care, but things that cannot care cannot understand. Now that isn't circular but that's a poor sign of understanding. I care very much for women but I can't say that I understand them. I understand the rules of English grammar and punctuation but care little of it. I'm sure you can think of examples. So the two are not correlated, caring and understanding. Caring is not something that can really be measured in humans while caring can be measured in machines/computers. For example, one might define caring about something means it is thinking a lot about it, where a lot means some threshold like over 50% resources are dedicated to think about something for a while (a nonzero, finite span of time). These days, we can multitask and look up the resource monitor to see what the CPU cares about, if anything. If it doesn't care about anything, it uses close to 0% and is called idle. But if I am running an intensive computation while typing this and look at my resource monitor, I can see measurements indicating that my CPU cares much more about the intensive computation rather than what I am typing. Does that mean the CPU understands what it is doing? No. Likewise with human brains: we can care a lot about something but have little to no understanding of it. This is analogous to saying We are Unicorns because care about Unicorns. No, this is analogous to you not understanding what I mean and unintentionally making a straw man of my argument. Well, be honest here, you changed a phrasing. You went from (paraphrasing) we know we understand because we care that we understand to You know we understand because we care about X. Correct me if I'm wrong. The first phrasing is meaningless because of the second use of the word understand (so you might as well be talking about unicorns). The first phrasing gives no insight into what understanding is and why we have it but computers can't. The problem with your new and improved phrasing is that it's a doctored definition of caring; you pick a definition related to understanding such that it (the definition of 'caring') will *automatically*fail for anything other than a non-apathetic human, in essence, assuming computers don't care about anything when, in fact, doing what they are programmed to do (much like a human, I might add) is the machine-equivalent of them caring about what they are told to do. Doesn't prove unicorns exist; doesn't prove understanding exists (i.e., that any human understands anything). If this is all sophistry then it should be easily dismissible. And yes, playing with words is what people normally do, wittingly or unwittingly, and that lends more evidence to the notion that we are processors in a Chinese room. The position that we only think we understand or that consciousness is an illusion is, in my view, the desperate act of a stubborn mind. Truly, you are sawing off the branch that you are sitting on to suggest that we are incapable of understanding the very conversation that we are having. Well calling a conclusion the desperate act of a stubborn mind, rather than supply some decent rejoinder, is also the desperate act of a stubborn mind, wouldn't you say? While sawing off the branch you are sitting on is a very clever arrangement of letters (can I use it in a future poem?), it falls short of being an argument at all or even persuasive. We can get along just fine by thinking that we understand this conversation. But knowing that we understand this conversation? I'd like to see that proved. Until then, I will continue to think
Re: Rationals vs Reals in Comp
I probably shouldn't be talking to someone who thinks distinguishing a sack of potatoes from a woman means understanding women. News flash: understand tacitly implies understand completely. On Wed, Apr 24, 2013 at 8:37 AM, Craig Weinberg whatsons...@gmail.comwrote: On Wednesday, April 24, 2013 10:09:44 AM UTC-4, Brian Tenneson wrote: On Wed, Apr 24, 2013 at 4:46 AM, Craig Weinberg whats...@gmail.comwrote: On Wednesday, April 24, 2013 4:31:55 AM UTC-4, Brian Tenneson wrote: On Tue, Apr 23, 2013 at 8:53 PM, Craig Weinberg whats...@gmail.comwrote: On Tuesday, April 23, 2013 11:37:14 PM UTC-4, Brian Tenneson wrote: You keep claiming that we understand this and that or know this and that. And, yes, saying something along the lines of we know we understand because we care about what we understand *is* circular. No, it's not. I'm saying that it is impossible to doubt we understand. It's just playing with words. My point about caring is that it makes it clear that we intuitively make a distinction between merely being aware of something and understanding it. I'll try to explain how we know we understand because we care about what we understand is circular. Note the use of the word understand towards the left edge of the statement in quotes followed by another instance of the word understand. You should read it as we know we understand because we care about X. My only intention in repeating the word was to make it clear that the thing that we care about is the thing that we understand. It is the caring which is a symptom of understanding. The absence of that symptom of caring in a machine indicates to me that there is a lack of understanding. Things which understand can care, but things that cannot care cannot understand. Now that isn't circular but that's a poor sign of understanding. I care very much for women but I can't say that I understand them. That's a cliche. You may not be able to understand women completely, but you are not likely to confuse them with a sack of potatoes in a dress. With a computer, the dress might be all that a security camera search engine might look for, and may very well categorize a sack of potatoes as a woman if it happens to be wearing a dress. I understand the rules of English grammar and punctuation but care little of it. Yes, you don't have to care about it, but you can care about it if you want to. A machine does not have that option. It can't try harder to follow proper grammar, it can only assign a priority to the task. It has no feeling for which tasks are assigned which priority, which is the entire utility of machines. I'm sure you can think of examples. So the two are not correlated, caring and understanding. Can you explain why the word understanding is a synonym for kindness and caring? A coincidence? Caring is not something that can really be measured in humans while caring can be measured in machines/computers. Give me a break. For example, one might define caring about something means it is thinking a lot about it You might define warm feelings by the onset of influenza but that is a false equivalence. , where a lot means some threshold like over 50% resources are dedicated to think about something for a while (a nonzero, finite span of time). These days, we can multitask and look up the resource monitor to see what the CPU cares about, if anything. That has nothing whatsover to do with caring. Does the amount of money in your wallet tell you how much your wallet values money? If it doesn't care about anything, it uses close to 0% and is called idle. Next you are going to tell me that when a stuffed animal doesn't eat anything it must be because it is full - but we have no way of knowing if we are hungry ourselves. But if I am running an intensive computation while typing this and look at my resource monitor, I can see measurements indicating that my CPU cares much more about the intensive computation rather than what I am typing. Does that mean the CPU understands what it is doing? No. Likewise with human brains: we can care a lot about something but have little to no understanding of it. Your entire argument is a defense of the Pathetic fallacy. Nothing you have said could not apply to any inanimate object, cartoon, abstract concept etc. Anyone can say 'you can't prove ice cream isn't melting because it's sad'. It's ridiculous. Find the universe. It is more interesting than making up stories about CPUs cares, kindnesses, and understanding. This is analogous to saying We are Unicorns because care about Unicorns. No, this is analogous to you not understanding what I mean and unintentionally making a straw man of my argument. Well, be honest here, you changed a phrasing. You went from (paraphrasing) we know we understand because we care that we understand to You know we understand because we care about X. Correct
Re: Rationals vs Reals in Comp
Interesting read. The problem I have with this is that in set theory, there are several examples of sets who owe their existence to axioms alone. In other words, there is an axiom that states there is a set X such that (blah, blah, blah). How are we to know which sets/notions are meaningless concepts? Because to me, it sounds like Doron's personal opinion that some concepts are meaningless while other concepts like huge, unknowable, and tiny are not meaningless. Is there anything that would remove the opinion portion of this? How is the second axiom an improvement while containing words like huge, unknowable, and tiny?? quote So I deny even the existence of the Peano axiom that every integer has a successor. Eventually we would get an overflow error in the big computer in the sky, and the sum and product of any two integers is well-defined only if the result is less than p, or if one wishes, one can compute them modulo p. Since p is so large, this is not a practical problem, since the overflow in our earthly computers comes so much sooner than the overflow errors in the big computer in the sky. end quote What if the big computer in the sky is infinite? Or if all computers are finite in capacity yet there is no largest computer? What if NO computer activity is relevant to the set of numbers that exist mathematically? On Monday, April 22, 2013 11:28:46 AM UTC-7, smi...@zonnet.nl wrote: See here: http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf Saibal To post to this group, send email to everyth...@googlegroups.comjavascript:. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
Re: Rationals vs Reals in Comp
On Tue, Apr 23, 2013 at 1:26 PM, Craig Weinberg whatsons...@gmail.comwrote: Searle wasn't wrong. The whole point of the Chinese Room is to point out that computation is a disconnected, anesthetic function which is accomplished with no need for understanding of larger contexts. How do we know that what humans do is understand things rather than just compute things? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
Re: Rationals vs Reals in Comp
On Tue, Apr 23, 2013 at 3:13 PM, Craig Weinberg whatsons...@gmail.comwrote: On Tuesday, April 23, 2013 4:31:05 PM UTC-4, Brian Tenneson wrote: On Tue, Apr 23, 2013 at 1:26 PM, Craig Weinberg whats...@gmail.comwrote: Searle wasn't wrong. The whole point of the Chinese Room is to point out that computation is a disconnected, anesthetic function which is accomplished with no need for understanding of larger contexts. How do we know that what humans do is understand things rather than just compute things? Because we care about what we understand, and we identify with it personally. Understanding is used also to mean compassion. When someone demonstrates a lack of human understanding, we say that they are behaving robotically, like a machine, etc. Questions like, How do you know you are conscious?, or How do you know that you feel? are sophistry. How do you know that you can ask that question? Sounds circular. we do understand things because we care about what we understand. The type of understanding I was referring to was not about compassion. Why is it so strange to think that we are stuck in a big Chinese room, without really understanding anything but being adept at pushing symbols around? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
Re: Rationals vs Reals in Comp
You keep claiming that we understand this and that or know this and that. And, yes, saying something along the lines of we know we understand because we care about what we understand *is* circular. Still doesn't rule out the possibility that we are in a Chinese room right now, manipulating symbols without really understanding what's going on but able to adeptly shuffle the symbols around fast enough to appear functional. If that is the case, AI might be able to replicate human behavior if human behavior is all computation-based. On Tue, Apr 23, 2013 at 8:25 PM, Craig Weinberg whatsons...@gmail.comwrote: On Tuesday, April 23, 2013 7:59:26 PM UTC-4, Brian Tenneson wrote: On Tue, Apr 23, 2013 at 3:13 PM, Craig Weinberg whats...@gmail.comwrote: On Tuesday, April 23, 2013 4:31:05 PM UTC-4, Brian Tenneson wrote: On Tue, Apr 23, 2013 at 1:26 PM, Craig Weinberg whats...@gmail.comwrote: Searle wasn't wrong. The whole point of the Chinese Room is to point out that computation is a disconnected, anesthetic function which is accomplished with no need for understanding of larger contexts. How do we know that what humans do is understand things rather than just compute things? Because we care about what we understand, and we identify with it personally. Understanding is used also to mean compassion. When someone demonstrates a lack of human understanding, we say that they are behaving robotically, like a machine, etc. Questions like, How do you know you are conscious?, or How do you know that you feel? are sophistry. How do you know that you can ask that question? Sounds circular. we do understand things because we care about what we understand. The type of understanding I was referring to was not about compassion. Why is it so strange to think that we are stuck in a big Chinese room, without really understanding anything but being adept at pushing symbols around? It's not circular, I was trying to be clear about the difference between computation and understanding. Computation is variations on the theme of counting, but counting does not help us understand. A dog might be able to count how many times we speak a command, and we can train them to respond to the third instance we speak it, but we can use any command to associate with the action of sitting or begging. We are not in a Chinese room because we know what kinds of things the word 'sit' actually might refer to. We know what kind of context it relates to, and we understand what our options for interpretation and participation are. The dog has no options. It can follow the conditioned response and get the reward, or it can fail to do that. It doesn't know what else to do. Craig -- You received this message because you are subscribed to a topic in the Google Groups Everything List group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/everything-list/bY0TNHtwNh8/unsubscribe?hl=en . To unsubscribe from this group and all its topics, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
Re: Fw: the world as mathematical. was pythagoras right after all ?
So is that a yes? If so, can you stipulate such a physical object? On Sunday, December 30, 2012 9:08:27 PM UTC-8, Brent wrote: On 12/30/2012 11:23 AM, Brian Tenneson wrote: Is there a physical object that exists physically which is not isomorphic to a mathematical object, having mathematical existence? If it exists physically then it has at least one attribute that no mathematical object has. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/qZtC-6PEXg4J. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Fw: the world as mathematical. was pythagoras right after all ?
Is there a physical object that exists physically which is not isomorphic to a mathematical object, having mathematical existence? -- You received this message because you are subscribed to the Google Groups Everything List group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/wB785ntkfK0J. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Ten top-of-my-head arguments against multiverses
Why not take the categories of all categories (besides that Lawyere tried that without to much success, except rediscovering Grothendieck topoi). I'm more interested in the smallest mathematical object in which all mathematical structures are embedded but the category of all categories will do. But if you assume comp, elementary arithmetic is enough, and it is better to keep the infinities and categories into the universal machine's mind tools. Enough for what, in what sense? To have a single mathematical object that all mathematical structures can be *embedded* would give us an object that, in a sense, contains all structures. If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects). I think that this is deeply flawed. We cannot identify the physical and the mathematical. We might try theory on the physical, or on the mental, or on the mathematical, which might suggest relation between those thing, but I doubt any non trivial theory would identify them, unless enlarging the sense of the words like mental, physical. Isn't it simpler to assume there is only one type of existence? What are the actual flaws of a mathematical universe? A physical system can be mathematically encoded by its corresponding set of world lines. This encoding is an isomorphism. A very simple example of what I mean is the nearly parabolic path taken by a projectile. The set of world lines would be some subset of R^4 or R^n if it turns out that n != 4. I am aware that indeterminacy due to Heisenberg's uncertainty principle kicks in here so we may never know which subset of R^n a physical system is isomorphic to but by a pigeonhole principle, the physical system must be isomorphic to some subset of R^n, several in fact. With computationalism, the coupling consciousness/physical is a phenomenon, person perceptible through numbers relations when they (the persons) bet on their relative self-consistency. This explains the appearance of the physical, without going out of the arithmetical. It works thanks to Church thesis and the closure of the comp everything (UD*, sigma_1 completeness). How are you defining consciousness here? It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply. I would have to fine-tune the argument to work in the case of the category C I have in mind. The n-categories might be interesting, but we don't need so rich ontology. If we are machine, the cardinality of the basic TOE is absolutely undecidable from inside. Omega is enough. Do you have an argument that proves that our minds can't transcend inside? If the cocompletion of C is the One, that which all mathematical structures can be embedded, then the parallel universe question would be a matter of logic and category theory; it would depend on how you defined the visible universe and parallel universe. You will have to define an observer, its points of view, and to take into account its many distributions in that super-mathematical structure, but you can't do that, as you will need an even bigger structure to define and study the indeterminacy. So you will have to limit your notion of observer and use some comp hypothesis (an infinite variant if you want). With comp, it is easier: you cannot really take more than arithmetic. God created the Natural Numbers, all the rest belong to the (singular and collective) number's imagination. If nature refutes this, it will still remain time to add the infinities needed. I think. How is the arithmetical structure going to give rise to a description of reality that takes into account observer, its points of view, and its many distributions without the need to study the indeterminacy? -- You received this message because you are subscribed to the Google Groups Everything List group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/XqN5TmRQ1n0J. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Ten top-of-my-head arguments against multiverses
At least in the videohttp://www.youtube.com/watch?v=FiMigmLwwTMfeature=player_detailpage#t=2594s(skip to 43:14), Tegmark estimates that our doppelgangers are 2^10^118 meters away which probably puts it past the range of direct testing and, consequently, makes it not falsifiable. Regarding (4), I think the disparity between you and Tegmark can be explained by having different definitions of universe and multiverse. Of course, if you have a metauniverse, then you'd have a metametauniverse, ad infinitum. There is only one totality of all that exists and I bet that if you were to explain what you mean by the One to him, he would agree that there is only one One. When he uses an aphorism like multiverse he may as well be saying poly mega galaxy cluster or some such. In other words I don't think Tegmark believes in multiple Ones. In his mathematical universe paper and ultimate ensemble paper, he posits that there is only one type of existence which would simplify things (a la Occam's razor). Instead of there being mathematical and physical existence, there is an identification between the two so they are seen to be one in the same. This merges the spaces mathematical objects with physical objects. He argues this in those papers (though to me sometimes it seems to be merely a plausibility argument). Now if ME=PE, then one natural question is which mathematical structure is the totality of all that exists isomorphic to? In other words, what is the One? What is the universe? Or to abuse language a bit, what is the multiverse? This is a question that I've been thinking about for a while now and I'm really not sure. The current idea is to take the category of all mathematical structures C (which is large, unfortunately), and embed that into a category of functors defined on that category (a la Yoneda's lemma), in such a way that every mathematical structure is embedded within that category of functors (called a cocompletion of C), a sort of presheaf category. To have a single mathematical object that all mathematical structures can be *embedded* would give us an object that, in a sense, contains all structures. If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects). It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply. I would have to fine-tune the argument to work in the case of the category C I have in mind. If the cocompletion of C is the One, that which all mathematical structures can be embedded, then the parallel universe question would be a matter of logic and category theory; it would depend on how you defined the visible universe and parallel universe. On Tuesday, December 25, 2012 6:34:45 AM UTC-8, rclough wrote: Hi Brian Tenneson Tegmark has many many good ideas, but I am not a believer in multiverses, which only a strict mechanistic 19th century type can believe. Multiverses defy reason. Just off the top of head: 1) For one reason because of Occam's razor: it is a needless complication, and the universe (or its Creator) does not do needless things, because IMHO the universe is purposeful. 2) Purposeful meaning that Aristotle's end causes are needed for a final collapse, as they are for life, which is not mechanistic. 3) As in life/mind/consciousness/intelligence, which are also purposeful. 4) In order for there to be multiple universes, there would have to be multiple platonic Ones. But there can only be one One. 5) Multiverses are mechanistic and so in spacetime, but consciouss life and all that other good stuff are outside of spacetime. Would the minds of multiverses be mashed together ? And all particular lifes would have to terminate at the same time. 6) There is no non-Boltzmann physics which is required for a final collapse. Time has to begin to travel backwards as things reorganize, in which case the final collapse should be a reflection of the initial creation. That would be cool. 7) But each universes being differemnt, they would not be expected to all terminate at the same time. 8) One might conjecture also that the presence of life, consciousness and intelligence (which are all individual, personal, subjective) are not mechanical and so cannot be part of a multiverse. It's each man for himself. Along these lines, because of natural selection and different worlds not being all the same, evolution would not occur in parallel. 9) Besides, there are alternate possibilities for a quantum wave collapse. 10) In a related matter, one of the multiverse sites cited William James as a proponent. Because of his pragmatism, his multiverses arise because there is no fixed
Re: Fw: the world as mathematical. was pythagoras right after all ?
What do you think of Tegmark's version of a mathematical Platoia? -- You received this message because you are subscribed to the Google Groups Everything List group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/6WzRUmWbHY0J. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Can a computer make independent choices ?
So suppose there is a choice to be made. A or B. Is there software that enables the computer to independently choose A or B. What about a neural network of many nodes and connections that has been through many epochs to the point where its outputs perfectly *resemble*pseudorandom number sequences? Or put more simply, if its behavior cannot be predicted, does that make it independent? On Tue, Sep 25, 2012 at 3:44 PM, Stephen P. King stephe...@charter.netwrote: On 9/25/2012 3:33 PM, meekerdb wrote: On 9/25/2012 12:24 PM, William R. Buckley wrote: From: everything-list@googlegroups.com [mailto:everything everything- l...@googlegroups.com] On Behalf Of Roger Clough Sent: Tuesday, September 25, 2012 5:26 AM To: everything-list Subject: Can a computer make independent choices ? Hi Stephen P. King I don't deny that a computer can optimize itself, but I deny that the operation is autonomous, meaning independent, for ultimately it is software dependent, using a program written by an outsider. True intelligence and true consciousness must be to whatever extent possible independent of outside help or perspective. Which just means the learned component of behavior should be big compared to the built-in component. Just as we don't think of animals as intelligent when they simply follow instincts but we do think them intelligent when they learn things. Brent -- Simple prejudice explains that... -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: questions on machines, belief, awareness, and knowledge
Hi Bruno On Fri, Sep 14, 2012 at 1:20 AM, Bruno Marchal marc...@ulb.ac.be wrote: Hi Brian, On 13 Sep 2012, at 22:04, Brian Tenneson wrote: Bruno, You use B as a predicate symbol for belief I think. I use for the modal unspecified box, in some context (in place of the more common []). Then I use it mainly for the box corresponding to Gödel's beweisbar (provability) arithmetical predicate (definable with the symbols E, A, , -, ~, s, 0 and parentheses. Thanks to the fact that Bp - p is not a theorem, it can plays the role of believability for the ideally correct machines. How come Bp-p is not a theorem? What are some properties of B and is there a predicate for knowing/being aware of that might lead to a definition for self-awareness? Yes, B and its variants: B_1 p == Bp p B_2 p = Bp Dt B_3 p = Bp Dt t, and others. D? B_1? B_2? B_3? btw, what is a machine and what types of machines are there? With comp we bet that we are, at some level, digital machine. The theory is one studied by logicians (Post, Church, Turing, etc.). I am also curious as to the definition of a digital machine. Is there a generic description for a structure (in the math logic sense) to have a belief or to be aware; something like A |= I am the structure A ? Yes, by using the Dx = xx method, you can define a machine having its integral 3p plan available. But the 1p-self, given by Bp p, does not admit any name. It is the difference between I have two legs and I have a pain in a leg, even if a phantom one. G* proves them equivalent (for correct machines), but G cannot identify them, and they obeys different logic (G and S4Grz). DX = xx? Finally, on a different note, if there is a structure for which all structures can be 1-1 injected into it, does that in itself imply a sort of ultimate structure perhaps what Max Tegmark views as the level IV multiverse? A 1-1 map is too cheap for that, and the set structure is a too much structural flattening. Comp used the simulation, notion, at a non specifiable level substitution. This structure I have in mind having the property that all structures can be injected into it has more structure than a set structure. See, I have revised my thoughts and put them into a fairly short document. You helped me a year or two ago to show me some flaws with my thoughts in a document. I could send it to you. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: imaginary numbers in comp
We might as well just use ordered pairs of integers or rational numbers. On Thursday, September 13, 2012 8:45:53 AM UTC-7, rclough wrote: Hi everything-list Since human thought and perception consists of both a logical quantitative or objective component as well as a feelings-spiritual qualitative or subjective components, would it make any sense to do comp using complex numbers, where the real part is the objective part of the mental the imaginary part is the subjective part of the mental ? Isn't there an intuitive mathematics ? Roger Clough, rcl...@verizon.net javascript: 9/13/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. -- You received this message because you are subscribed to the Google Groups Everything List group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/fKAoBO2j5nkJ. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Where do numbers and geometry come from ?
All numbers can be defined in terms of sets. The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King Yes, of course, but I wanted a more obvious, dramatic example. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change itself is a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. If numbers are platonic, I wonder what the presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King stephe...@charter.net *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 07:53:18 *Subject:* Re: Could we have invented the prime numbers ? Dear Roger, Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou If the prime numbers were there from the beginning, before man, then I think they were mind-created (platonic) not brain-created (human creations). Are the prime numbers an invention by man or one of man's discoveries ? I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced 6 apart, plus or minus one) Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 etc. for n5, they can be placed +-1 on a grid with a spacing of 6 That spacing seems to me at least to be a priori, out of man's control. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stathis Papaioannou stath...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 01:24:31 *Subject:* Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com%20whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Re: Where do numbers and geometry come from ?
Sure you can have sets without numbers. The popular set theory's development known as ZFC is not based on numbers. http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory Numbers are defined in terms of sets. What that means is that all numbers are sets but not all sets are numbers. I do agree that numbers are not created by man but neither are sets. On Thu, Sep 6, 2012 at 8:19 AM, Roger Clough rclo...@verizon.net wrote: Hi Brian Tenneson I'm just to establish the fact that numbers are a priori and so not created by man. Given that, it doesn't matter if sets are a priori or not. Presumably (I am not a mathematician) you cannot have sets without numbers, so the numbers rule. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Brian Tenneson tenn...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 10:28:51 *Subject:* Re: Where do numbers and geometry come from ? All numbers can be defined in terms of sets.� The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King � � Yes, of course, but I wanted a more obvious, dramatic爀xample. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change爄tself 爄s a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. � If numbers are platonic,營 wonder what the� presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. � � � Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King stephe...@charter.net *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 07:53:18 *Subject:* Re: Could we have invented the prime numbers ? Dear Roger, 牋� Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou � If the prime numbers were there from the beginning, before man, then� I think they were mind-created (platonic) not brain-created (human creations). � Are the prime numbers an invention by man or one of man's discoveries ?� � I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced� 6 apart, plus or minus one) � Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 6747%2053%2059%2061%206771 etc. � � for n5, they can be placed +-1 on a grid with a spacing of 6 � That spacing seems to me at least to be a priori, out of man's control. � Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stathis Papaioannou stath...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 01:24:31 *Subject:* Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com%20whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you
Re: Where do numbers and geometry come from ?
I couldn't agree more. On Thu, Sep 6, 2012 at 8:35 AM, Stephen P. King stephe...@charter.netwrote: Dear Roger, Why is it that people persist in even suggesting that numbers are created by man? Why the anthropocentric bias? Pink Ponies might have actually crated them, or Polka-dotted Unicorns! The idea is just silly! The point is that properties do not occur at the whim of any one thing, never have and never will. On 9/6/2012 11:19 AM, Roger Clough wrote: Hi Brian Tenneson I'm just to establish the fact that numbers are a priori and so not created by man. Given that, it doesn't matter if sets are a priori or not. Presumably (I am not a mathematician) you cannot have sets without numbers, so the numbers rule. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Brian Tenneson tenn...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 10:28:51 *Subject:* Re: Where do numbers and geometry come from ? All numbers can be defined in terms of sets.� The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King � � Yes, of course, but I wanted a more obvious, dramatic爀xample. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change爄tself 爄s a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. � If numbers are platonic,營 wonder what the� presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. � � � Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King stephe...@charter.net *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 07:53:18 *Subject:* Re: Could we have invented the prime numbers ? Dear Roger, 牋� Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou � If the prime numbers were there from the beginning, before man, then� I think they were mind-created (platonic) not brain-created (human creations). � Are the prime numbers an invention by man or one of man's discoveries ?� � I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced� 6 apart, plus or minus one) � Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 6747%2053%2059%2061%206771 etc. � � for n5, they can be placed +-1 on a grid with a spacing of 6 � That spacing seems to me at least to be a priori, out of man's control. � Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stathis Papaioannou stath...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 01:24:31 *Subject:* Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com%20whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You
Re: The All
A too much powerful God leads to inconsistency. What if reality does not always obey the laws of logic? What if reality is sometimes inconsistent? -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: What is thinking ?
Thinking implies a progression of time. So perhaps it is equally important to define time. On Thu, Aug 30, 2012 at 8:10 AM, Roger Clough rclo...@verizon.net wrote: Hi John Clark Please define the term thinking. What is thinking ? Roger Clough, rclo...@verizon.net 8/30/2012 Leibniz would say, If there's no God, we'd have to invent him so everything could function. - Receiving the following content - *From:* John Clark johnkcl...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-08-29, 16:10:20 *Subject:* Re: Two reasons why computers IMHO cannot exhibit intelligence On Tue, Aug 28, 2012 at 7:21 PM, Craig Weinberg whatsons...@gmail.comwrote: It's worth mentioning that Turing did not intend his test to imply that machines could think, only that the closest we could come would be to construct machines that would be good at playing The Imitation Game. No you are entirely incorrect, that is not worth mentioning. There is no difference between arithmetic and simulated arithmetic and no difference between thinking and imitation thinking. � I have used the example of a trashcan lid in a fast food place that says THANK YOU. And when a employee of a fast food restaurant says THANK YOU to the 47'th customer for the 47'th time in the last hour he puts about as much thought into the message as the trash can did. � John K Clark -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Re: What is thinking ?
Hi I agree with what you say about thought but the question was about thinking which to me suggests a process. The word thinking is a verb, meaning something (the thinker) is doing something (thinking). There is a dictionary-type correspondence between processes and formally-defined algorithms. The first is in the realm of the physical universe and the second is in the Platonic realm. This correspondence is like a bridge between the two. (Although Max Tegmark might say there is no essential difference between the two realms.) Thinking is a process and thoughts are the outputs of algorithms (algorithms exist in the Platonic realm and may or may not be expressible in a natural language). PERHAPS we can identify (concrete) thinking with specific (abstract) algorithms or at least encode one by the other. With that identification made I can see how thinking can be viewed as something abstract. On Thu, Aug 30, 2012 at 8:31 AM, Roger Clough rclo...@verizon.net wrote: Hi Brian Tenneson Thought itself, IMHO, is beyond spacetime. It belongs to that Platonic realm to which the circumstances of time are wholly irrelevant. But the brain is not. Perhaps it is something like a fishing line and hook waiting for something of interest or useful in the sea of thought to become esnared on it. Roger Clough, rclo...@verizon.net 8/30/2012 Leibniz would say, If there's no God, we'd have to invent him so everything could function. - Receiving the following content - *From:* Brian Tenneson tenn...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-08-30, 11:16:13 *Subject:* Re: What is thinking ? Thinking implies a progression of time. So perhaps it is equally important to define time. On Thu, Aug 30, 2012 at 8:10 AM, Roger Clough rclo...@verizon.net wrote: Hi John Clark Please define the term thinking. What is thinking ? Roger Clough, rclo...@verizon.net 8/30/2012 Leibniz would say, If there's no God, we'd have to invent him so everything could function. - Receiving the following content - *From:* John Clark johnkcl...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-08-29, 16:10:20 *Subject:* Re: Two reasons why computers IMHO cannot exhibit intelligence On Tue, Aug 28, 2012 at 7:21 PM, Craig Weinberg whatsons...@gmail.comwrote: It's worth mentioning that Turing did not intend his test to imply that machines could think, only that the closest we could come would be to construct machines that would be good at playing The Imitation Game. No you are entirely incorrect, that is not worth mentioning. There is no difference between arithmetic and simulated arithmetic and no difference between thinking and imitation thinking. I have used the example of a trashcan lid in a fast food place that says THANK YOU. And when a employee of a fast food restaurant says THANK YOU to the 47'th customer for the 47'th time in the last hour he puts about as much thought into the message as the trash can did. John K Clark -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: 0s and 1s
The universe is purely subjective. Is that statement purely subjective? Maybe you meant: other than this statement, the universe is purely subjective. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Words vs experience
This is already a consequence of computer science. All sound machines looking inward, or doing self-reference, cannot avoid the discovery between what they can justify with words, and what they can intuit as truth. What do justify and intuit mean? There are some machines out there that do not believe intuiting the truth exists; for them, if it is not justified they do not believe. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: God has no name
Yeah but you can't define what a set is either, so... On Fri, Aug 10, 2012 at 2:22 AM, Bruno Marchal marc...@ulb.ac.be wrote: Hi Roger, On 07 Aug 2012, at 11:53, Roger wrote: Hi Bruno Marchal OUR FATHER, WHICH ART IN HEAVBEN, HALLOWED BE THY NAME. Luther said that to meditate of the sacredness of God according to this phrase is the oldest prayer. In old testament times, God's name was considered too sacred to speak by the Jews. The King James Bible uses YHWH, the Jews never say God as far as I know, they sometimes write it as G*d. We have relaxed these constrictions in the protestant tradition, use Jehovah and all sorts of other sacfed names. It is the problem with the notions of God, Whole, Truth, consciousness, etc. we can't define them. You can sum up Damascius by one sentence on the ineffable is already one sentence too much, it can only miss the point. (But Damascius wrote thousand of pages on this!). Like Lao Tseu said that the genuine wise man is mute, also. John Clark said it recently too! This is actually well explained (which does not mean that the explanation is correct) by computer science: a universal machine can look inward and prove things about itself, including that there are true proposition that she cannot prove as far as she is consistent, that machine-truth is not expressible, etc. My last paper (in french) is entitled la machine mystique (the mystical machine) and concerns all the things that a machine might know without being able to justify it rationally and which might be counter-intuitive from her own point of view. The word god is not problematical ... as long as we don't take the word too much seriously. You can say I search God, but you can't say I found God, and still less things like God told me to tell you to send me money or you will go to hell. God is more a project or a hope for an explanation. It cannot be an explanation itself. For a scientist: it is more a problem than a solution, like consciousness, for example. Bruno Roger , rclo...@verizon.net 8/7/2012 Is life a cause/effect activity ? If so, what is the cause agent ? - Receiving the following content - *From:* Bruno Marchal marc...@ulb.ac.be *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-08-07, 05:37:56 *Subject:* Re: God has no name Hi Stephen, On 8/6/2012 8:29 AM, Bruno Marchal wrote: [SPK] Which is the definition I use. Any one that actually thinks that God is a person, could be a person, or is the complement (anti) of such, has truly not thought through the implications of such. [BM For me, and comp, it is an open problem. [SPK] ? Why? It's not complicated! A person must be, at least, nameable. A person has always has a name. [BM] Why? Because names are necessary for persistent distinguishability. OK. You are using name in the logician sense of definite description. With comp we always have a 3-name, but the first person have no name. Let us try an informal proof by contradiction. Consider the case where it is *not* necessary for a person to have a name. What means would then exist for one entity to be distinguished from another? By the entity itself: no problem (and so this is not a problem for the personal evaluation of the measure). By some other entity? We might consider the location of an entity as a proxy for the purposes of identification, but this will not work because entities can change location and a list of all of the past locations of an entity would constitute a name and such is not allowed in our consideration here. Sure. What about the 1p content of an entity, i.e. the private name that an entity has for itself with in its self-referential beliefs? It has no such name. Bp p, for example, cannot be described in arithmetic, despite being defined in arithmetical terms. It is like arithmetical truth, we can't define it in arithmetic language. Since it is not communicable - as this would make the 1p aspect a non-first person concern and thus make it vanish - it cannot be a name. Names are 3p, they are public invariants that form from a consensus of many entities coming to an agreement, and thus cannot be determined strictly by 1p content. You might also note that the anti-foundation axiom is every graph has a unique decoration. The decoration is the name! It is the name that allow for non-ambiguous identification. A number's name is its meaning invariant symbol representation class... Consider what would happen to COMP if entities had no names! Do I need to go any further for you to see the absurdity of persons (or semi-autonomous entities) not having names? Say that it is X. There is something that is not that person and that something must therefore have a different name: not-X. What is God's name? ... It cannot be named because there is nothing that it is not! Therefore God cannot be a
Re: Free will: a definition
So you don't know what God wants. Is that what you're saying? I hope you're not for any reason obsessed with the Bible. On Wed, Aug 1, 2012 at 9:43 AM, John Clark johnkcl...@gmail.com wrote: On Wed, Aug 1, 2012 at 12:26 PM, Brian Tenneson tenn...@gmail.com wrote: How do you know what God wants? By reading my Bible! I can't imagine a better way to figure out how the universe works than studying the myths of a 3 thousand year old bronze age tribe. Eat your heart out Large Hadron Collider. Assuming God is complete If he wasn't He wouldn't be God. it has no wants whatsoever. Yes, I would certainly think so; and yet the Bible is full of God wants this and God was displeased by that. It's a puzzle. Ancient Hebrew cosmology couldn't be wrong could it? John K Clark -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Free will: a definition
We may be overthinking things here. What's wrong with defining it as the capacity to make choices when more than one option is available? On Wed, Aug 1, 2012 at 9:17 AM, meekerdb meeke...@verizon.net wrote: On 8/1/2012 5:04 AM, Russell Standish wrote: Yes - and rationality often does not help much. In such situations, it is often better to make a fast decision than a good one. Only irrational agents can make fast decisions. Almost all real decisions (even in chess) are time constrained. How can it be rational to wait too long for your decision to matter and irrational to make a quick decision on incomplete information, on incomplete analysis? From the responses I've received on this list, I don't think people are using the term rational in the same way it is used in economics. Flipping a coin is never rational, although it may well be the best thing to do. Random moves are optimum in many games and provably so. What meaning of 'rational' are you using? Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.**comeverything-list@googlegroups.com . To unsubscribe from this group, send email to everything-list+unsubscribe@ **googlegroups.com everything-list%2bunsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/** group/everything-list?hl=enhttp://groups.google.com/group/everything-list?hl=en . -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Free will: a definition
On Wed, Aug 1, 2012 at 9:24 AM, John Clark johnkcl...@gmail.com wrote: So free will is the ability to always get what we want, after all if we don't get what we want its because something has stopped us from doing so. Thus even God doesn't have free will because He doesn't want us to sin and yet we do. John K Clark How do you know what God wants? Is that what some ancient text claimed? Assuming God is complete, it has no wants whatsoever. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Physics and Tautology.
Isn't every (alleged) proof of something's truth just a list of things (steps) implied by the previous statement until one arrives at the final statement...a tautology? Briefly: isn't every proof just a (possibly lengthy) list of tautologies? Therefore, using that notion, calling out alleged proofs of masses coming from (or not coming from) the big bang and what not specifically is, actually, redundant. On Wed, Aug 1, 2012 at 1:50 PM, socra...@bezeqint.net socra...@bezeqint.net wrote: Physics and Tautology. =. 1 Where did the masses for ‘ big bang ‘ come from ? These masses came from surrounding space. 2 Where did these masses from surrounding space come from ? These masses came from ‘big bang’. ===. Why he is poor ? Because he is stupid. Why he is stupid? Because he is poor. ===. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: truth
The thread is about the possibility of an omnipotent being being able to manipulate what is true. On Wed, Jul 4, 2012 at 7:12 AM, Platonist Guitar Cowboy multiplecit...@gmail.com wrote: Hello Everythinglisters, First post here, and seems fun to get lost reading the discussions from time to time, so here somebody contributing with a more musical tendency. It's funny how this game keeps cropping up where people want to do stuff like: 1 + 1 = 11 If people are sincere about pulling whatever sums they feel like with personal justification, then we might as well say 1 + 1 = 0, with a kind of zen logic, where everything = nothing as a fancy justification. And anybody still willing to assert this could post their bank account details and pin numbers and be freed from arithmetic dictatorship by having their account cleaned out by other everything listers that DO believe in sums, successors etc. as 0 = whatever they want, and the sum of their balance doesn't really matter, as it's only some personal belief shared by a few control freaks. Guitar and composition imho, have arithmetic overlap, albeit in a less than total sense, which is why I won't have to post my details here :) Looking forward to contributing from time to time. On Saturday, June 30, 2012 12:09:53 AM UTC+2, JohnM wrote: Bruno asked: . Is that an absolute truth? By no means. It is a word-flower, a semantic hint, something in MY agnosticism and I feel like a semantic messenger only. I accept better expressions. (Except for absolute truth - ha ha). And Teilhard was a great master of words. John M On Fri, Jun 29, 2012 at 12:32 PM, Bruno Marchal marc...@ulb.ac.bewrote: On 29 Jun 2012, at 16:21, John Mikes wrote: Brent, thanks for the appreciation! My point was simply that anybody's 'truth' is conditioned. We have no (approvable?) authority for an ABSOLUTE truth. Whatever WE accept is human. Is that an absolute truth? In my humble opinion, WE = human seems to me quite relative. When I listen to the jumping spiders or the Löbian machines, most seems to disagree. Bruno *We are not human beings having a spiritual experience. We are spiritual beings having a human experience.* (de Chardin). What is Mother Nature accepting? John M On Thu, Jun 28, 2012 at 4:09 PM, meekerdb meeke...@verizon.net wrote: On 6/28/2012 12:46 PM, John Mikes wrote: Brent: I am the 3rd kind of the two: think not in binary, just in plain peasant logic, when 1 and 1 make 11, nothing more. So Bruno's absolute truth may have even more relatives. John Or less facetiously, (The father of Kirsten)+(The father of Gennifer)=(One, me) and (one raindrop)+(one raindrop)=(one raindrop). So whether successor(x)=(x+1) depends on the applicability of arithmetic to your model. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.**c** om everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscribe@**go**oglegroups.comeverything-list%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/**group* */everything-list?hl=enhttp://groups.google.com/group/everything-list?hl=en . -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.**comeverything-list@googlegroups.com . To unsubscribe from this group, send email to everything-list+unsubscribe@**googlegroups.comeverything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/** group/everything-list?hl=enhttp://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~**marchal/http://iridia.ulb.ac.be/%7Emarchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.**comeverything-list@googlegroups.com . To unsubscribe from this group, send email to everything-list+unsubscribe@**googlegroups.comeverything-list%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/** group/everything-list?hl=enhttp://groups.google.com/group/everything-list?hl=en . -- You received this message because you are subscribed to the Google Groups Everything List group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/aa8ElOQLmdwJ. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google
Re: truth
What I was wondering, and I know this is ill-formed, is if in different parallels, different things are absolutely true. Things like 2+2=17. It may be completely impractical to imagine such parallels since there is presumably zero overlap and no means of travel to there. The basic premise is that an omnipotent being has the ability to fool computers into thinking various things are true. On Thu, Jun 28, 2012 at 12:46 PM, John Mikes jami...@gmail.com wrote: Brent: I am the 3rd kind of the two: think not in binary, just in plain peasant logic, when 1 and 1 make 11, nothing more. So Bruno's absolute truth may have even more relatives. John On Wed, Jun 27, 2012 at 5:36 PM, meekerdb meeke...@verizon.net wrote: On 6/27/2012 2:26 PM, John Mikes wrote: Dear Bruno, think about it as absolute truth: Isn't 1+1 not 2, but 11? Respectfully John Naah! It's 10. Brent There are 10 kinds of people; those who think in binary and those who don't. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: truth
What I meant is an omnipotent being being able to manipulate what is actually, absolutely true (so in a parallel 2+2 might actually be 17). Not manipulate the perception of truth. On Thu, Jun 28, 2012 at 1:11 PM, meekerdb meeke...@verizon.net wrote: On 6/28/2012 1:06 PM, Brian Tenneson wrote: What I was wondering, and I know this is ill-formed, is if in different parallels, different things are absolutely true. Things like 2+2=17. It may be completely impractical to imagine such parallels since there is presumably zero overlap and no means of travel to there. The basic premise is that an omnipotent being has the ability to fool computers into thinking various things are true. It doesn't take an omnipotent being to do that - unless you think Rush Limbaugh is omnipotent. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
truth
I have many questions. One is what if truth were malleable? -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
I will exercise my *insert gibberish here* by disagreeing. On Wed, Jun 6, 2012 at 8:53 AM, John Clark johnkcl...@gmail.com wrote: On Tue, Jun 5, 2012 meekerdb meeke...@verizon.net wrote: while you do not *always* know what you're going to do, you know your preferences most of the time. And Turing proved that some of the time a computer can tell if it will eventually stop or not, but not all of the time. The feeling of 'free will' comes from the inability retrospectively to see all the causes; so that, out of ignorance, it seems that one could have done otherwise. Yes, and unlike other definitions of free will this one is not gibberish, however when you boil it down all it's really saying is you don't know what you don't know. The highest status the philosophical concept called free will can aspire to is that of being right but trivially circular, most of the time it's not even that, most of the time it's just gibberish. John K Clark -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
Speaking of the legal aspect, Yes, Hitler exercised his *insert gibberish here* when he issued orders to kill the Jews. IF *gibberish* does not exist, then how can we hold criminals culpable in that they had no choice but to commit crime? Seems unfair to punish anyone under those circumstances. On Wed, Jun 6, 2012 at 9:05 AM, meekerdb meeke...@verizon.net wrote: On Wed, Jun 6, 2012 at 8:53 AM, John Clark johnkcl...@gmail.com wrote: On Tue, Jun 5, 2012 meekerdb meeke...@verizon.net wrote: while you do not *always* know what you're going to do, you know your preferences most of the time. And Turing proved that some of the time a computer can tell if it will eventually stop or not, but not all of the time. The feeling of 'free will' comes from the inability retrospectively to see all the causes; so that, out of ignorance, it seems that one could have done otherwise. Yes, and unlike other definitions of free will this one is not gibberish, however when you boil it down all it's really saying is you don't know what you don't know. The highest status the philosophical concept called free will can aspire to is that of being right but trivially circular, most of the time it's not even that, most of the time it's just gibberish. Aside from the philosophical concept, there is the social/legal concept of not coerced, referred to as exercising 'free will', which is what Stenger proposes just to call autonomy. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
I think people make choices from among available options many times every day and that is why the concept in question exists. On Wed, Jun 6, 2012 at 9:15 AM, R AM ramra...@gmail.com wrote: On Wed, Jun 6, 2012 at 6:08 PM, Brian Tenneson tenn...@gmail.com wrote: Speaking of the legal aspect, Yes, Hitler exercised his *insert gibberish here* when he issued orders to kill the Jews. IF *gibberish* does not exist, then how can we hold criminals culpable in that they had no choice but to commit crime? Seems unfair to punish anyone under those circumstances. Perhaps the concept of free-will exists because people think it is unfair to punish anyone under those circumstances? On Wed, Jun 6, 2012 at 9:05 AM, meekerdb meeke...@verizon.net wrote: On Wed, Jun 6, 2012 at 8:53 AM, John Clark johnkcl...@gmail.com wrote: On Tue, Jun 5, 2012 meekerdb meeke...@verizon.net wrote: while you do not *always* know what you're going to do, you know your preferences most of the time. And Turing proved that some of the time a computer can tell if it will eventually stop or not, but not all of the time. The feeling of 'free will' comes from the inability retrospectively to see all the causes; so that, out of ignorance, it seems that one could have done otherwise. Yes, and unlike other definitions of free will this one is not gibberish, however when you boil it down all it's really saying is you don't know what you don't know. The highest status the philosophical concept called free will can aspire to is that of being right but trivially circular, most of the time it's not even that, most of the time it's just gibberish. Aside from the philosophical concept, there is the social/legal concept of not coerced, referred to as exercising 'free will', which is what Stenger proposes just to call autonomy. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
The capacity (which can be defined) of an agent (which can be defined) to be able (which can be defined) to choose (which can be defined) when (which can be defined) presented (which can be defined) with a choice (which can be defined). Certainly not meaningless. On Sat, Jun 2, 2012 at 9:58 AM, John Clark johnkcl...@gmail.com wrote: On Fri, Jun 1, 2012 Brian Tenneson tenn...@gmail.com wrote: The fact that free will is debated lends credence to the notion that Free will is not meaningless. Free will has to mean something before it can be attacked. But I'm not saying free will does not exist, and I'm not attacking it because there is nothing to attack, it would be like attacking a duck's quack. I'm saying I don't know what the hell you're talking about when you type the ASCII characters free will and neither do you. I'm not saying the idea is wrong, I'm saying there is no idea there. How do I know this? Because whenever anybody talks about free will the resulting verbiage is ALWAYS a blizzard of contradictory statements, circular definitions, vague illusions, pious speeches, and just plain old idiocy; there is never any substance there. Never. John K Clark -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
FREE means being *able *to choose *any *among a number of choices. You want freedom of will to mean an agent can choose something beyond what the given choices are? That would imply free will does not exist yet, in that event, free will is still NOT meaningless. Right now I am unconcerned with whether free will exists or not. I am concerned with the statement free will is meaningless. I have given a definition, borrowed from the SEP, that is as good a definition as for any concept (outside mathematical ones). It certainly IS not meaningless and IS an identification, however not of a *FREE* will. It is a decision between given choices. Tomorrow more info may be given to us and our today's choice may be overridden. What I consider a *free will* is independent of the 'choices' we *G E T* and is solely formatted by our (pesonal? inside?) mindset (call it will?). We, however, are part of a more extended (expanded?) world, I like to call it 'Everything' (an infinite complexity of so far(?) unknowable content) and all of its influences (may) contribute to our 'decisionmaking' although we may not know about either the nature of most of those influences, nor that we ARE responding to them. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
How about define agent to be a type 4 agent as explained here: http://cs.wallawalla.edu/~aabyan/Colloquia/Aware/aware2.html On Sat, Jun 2, 2012 at 5:22 PM, meekerdb meeke...@verizon.net wrote: The hard one to define with falling into circularity is agent which is often defined as an entity with free will. To test something you need an operational definition. Agent might be defined as an entity with acts unpredictably but purposefully. But both of those are a little fuzzy. Brent On 6/2/2012 10:40 AM, Brian Tenneson wrote: The capacity (which can be defined) of an agent (which can be defined) to be able (which can be defined) to choose (which can be defined) when (which can be defined) presented (which can be defined) with a choice (which can be defined). Certainly not meaningless. On Sat, Jun 2, 2012 at 9:58 AM, John Clark johnkcl...@gmail.com wrote: On Fri, Jun 1, 2012 Brian Tenneson tenn...@gmail.com wrote: The fact that free will is debated lends credence to the notion that Free will is not meaningless. Free will has to mean something before it can be attacked. But I'm not saying free will does not exist, and I'm not attacking it because there is nothing to attack, it would be like attacking a duck's quack. I'm saying I don't know what the hell you're talking about when you type the ASCII characters free will and neither do you. I'm not saying the idea is wrong, I'm saying there is no idea there. How do I know this? Because whenever anybody talks about free will the resulting verbiage is ALWAYS a blizzard of contradictory statements, circular definitions, vague illusions, pious speeches, and just plain old idiocy; there is never any substance there. Never. John K Clark -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
Cannot comment, don't know what ASCII string free will means and neither do you. John K Clark Of course there are various degrees to which it can be free but that doesn't mean free will is a meaningless string. Freedom is defined by the observer. I note the freedom I have in choosing my beliefs. I am not bound to agree with you nor am I bound to disagree with you. The Stanford Encyclopedia of Philosophy defines free will as follows “Free Will” is a particular sort of capacity of rational agents to choose a course of action from among various alternatives. So what is the fuss about? -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
The fact that free will is debated lends credence to the notion that Free will is not meaningless. Free will has to mean something before it can be attacked. On Fri, Jun 1, 2012 at 12:30 PM, meekerdb meeke...@verizon.net wrote: On 6/1/2012 11:43 AM, Brian Tenneson wrote: Cannot comment, don't know what ASCII string free will means and neither do you. John K Clark Of course there are various degrees to which it can be free but that doesn't mean free will is a meaningless string. Freedom is defined by the observer. I note the freedom I have in choosing my beliefs. I am not bound to agree with you nor am I bound to disagree with you. The Stanford Encyclopedia of Philosophy defines free will as follows “Free Will” is a particular sort of capacity of rational agents to choose a course of action from among various alternatives. So what is the fuss about? The fuss is because the concept is thought to be fundamental to jurisprudence and social policy (it's even cited in some Supreme Court decisions). The concept of free will has been carried over from past theological and philosophical ideas. But now the concept is attacked by scientists and some philosophers as incoherent or empirically false. If they are right it would seem to imply revision of the social/legal concepts and laws derived from it. Can existing practice be justified on a purely utilitarian basis? Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
Of course it doesn't, nothing real can have anything to do with free will because free will is gibberish. http://plato.stanford.edu/entries/freewill/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
What about Gabriel's Horn or the Koch Snowflake curve? They may also contradict intuition but the results are not dependent upon the axiom of choice. On Wed, May 30, 2012 at 9:17 AM, meekerdb meeke...@verizon.net wrote: On 5/30/2012 1:45 AM, Bruno Marchal wrote: Banach and Tarski proved an amazing theorem with the axiom of choice, but it is not a paradox, in the sense that it contradicts nothing, and you can't get anything from it. Bruno It contradicts intuition. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: free will and mathematics
It doesn't take free will to prove that every even number is divisible by 2. How to prove a statement with a universal quantifier is pretty basic. On Tue, May 29, 2012 at 12:01 PM, Aleksandr Lokshin aaloks...@gmail.comwrote: *The notion of choosing isn't actually important--if a proof says something like pick an arbitrary member of the set X, and you will find it obeys Y, this is equivalent to the statement every member of the set X obeys Y* No, the logical operator every contains the free will choice inside of it. I do insist that one cannot consider an infinite set of onjects simultaneously! Instead of so doing one considers an arbitraryly chosen object. It is a very specific mathematical operation . By using operator every we construct a formalism which hides the essens of matter - the using of a free will choice. On Tue, May 29, 2012 at 10:30 PM, meekerdb meeke...@verizon.net wrote: On 5/29/2012 10:52 AMOne cannot, John Clark wrote: On Sun, May 27, 2012 Aleksandr Lokshin aaloks...@gmail.com wrote: All main mathematical notions ( such as infinity, variable, integer number) implicitly depend on the notion of free will. Because nobody can explain what the ASCII string free will means the above statement is of no value. A new approach to the Alan Turing problem (how to distinguish a person from an android) is also proposed ; this approach is based on the idea that an android cannot generate the notion of an arbitrary object. But arbitrary just means picking something for no reason or picking something just because you like it but you like it for no reason; in other words it means random. It's true that a pure Turing machine can not produce randomness, however this limitation can be easily overcome by attaching a very simple and cheap hardware random number generator to it. Or by computing psuedo-random numbers with a sufficiently long period that no one will be able to determine the algorithm. Brent Then the android could be as arbitrary as any arbitrary person, if you think being arbitrary is a virtue that is. John K Clark -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Two Mathematicians in a Bunker and Existence of Pi
There is an important distinction between the names and notations of mathematics and the objects of study of mathematics. I believe the former are inventions of humans while the latter exist independently of mankind. For example, I am saying that the symbol 0 is an invention of mankind but what is pointed to by the symbol 0 is not an invention of mankind. I can't give you absolute proof especially when we're going to assume different things (i.e., we live in different paradigms). One thing that gives me a clue about my conclusion is that mathematical objects will not exist any less if humanity were to go extinct. However, arguing that is like arguing for a particular answer to a koan. On Sun, Mar 4, 2012 at 8:12 AM, Evgenii Rudnyi use...@rudnyi.ru wrote: Yet, according to my current view, mathematics has been created by the mankind. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: comp is simply false?
Are you talking about tautology? On Thu, Feb 16, 2012 at 12:38 PM, Stephen P. King stephe...@charter.netwrote: On 2/16/2012 2:15 PM, Quentin Anciaux wrote: [SPK] All of this substitution stuff is predicated upon the possibility that the brain can be emulated by a Universal Turing Machine. It would be helpful if we first established that a Turing Machine is capable of what we are assuming it do be able to do. I am pretty well convinced that it cannot Well at least, you state now that you think comp is simply false... so it's just trolling about it, when you just reject the premices... Is there a difference between a statement being true given some context and the same sentence being true in no context whatsoever? Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: On Pre-existing Fields
Lots of interesting ideas going about. It sounds like you're pondering how many elements are in the set of all world-lines consistent with the true laws of physics (e.g., possibly, the least action principle). (Incidentally, that set oddly enough is timeless yet the bundles of world-lines that comprise our selves evidently perceive change.) Proof by throwing in an axiom isn't very satisfying but I would like to say that Banach-Tarski is no more strange than Gabriel's Horn or Cantor's hierarchy of infinities. Strangeness is of course a matter of opinion and mine is that the existence of nonmeasurable sets is not a heavy price to pay for that poof (a proof by throwing in an axiom). Cheers On Mon, Feb 13, 2012 at 6:55 PM, Stephen P. King stephe...@charter.netwrote: On 2/13/2012 5:27 PM, acw wrote: [SPK] There is a problem with this though b/c it assumes that the field is pre-existing; it is the same as the block universe idea that Andrew Soltau and others are wrestling with. Why is a pre-existing field so troublesome? Seems like a similar problem as the one you have with Platonia. For any system featuring time or change, you can find a meta-system in which you can describe that system timelessly (and you have to, if one is to talk about time and change at all). Dear Kermit, OK, I will try to explain this in detail and check my math. I am good with pictures, even N-dimensional ones, but not symbols, equations and words... Think of a collection of different objects. Now think of how many ways that they can be arranged or partitioned up. For N objects, I believe that there are at least N! numbers of ways that they can be arranged. Now think of an Electromagnetic Field as we do in classical physics. At each point in space, it has a vector and a scalar value representing its magnetic and electric potentials. How many ways can this field be configured in terms of the possible values of the potentials at each point? At least 1x2x3x...xM ways, where M is the number of points of space. Let's add a dimension of time so that we have a 3,1 dimensional field configuration. How many different ways can this be configured? Well, that depends. We known that in Nature there is something called the Least Action Principle that basically states that what ever happens in a situation it is the one that minimizes the action. Water flows down hill for this reason, among other things... But it is still at least M! number of possible configurations. How do we compute what the minimum action configuration of the electromagnetic fields distributed across space-time? It is an optimization problem of figuring out which is the least action configured field given a choice of all possible field configurations. This computational problem is known to be NP-Complete and as such requires a quantity of resources to run the computation that increases as a non-polynomial power of the number of possible choices, so the number is, I think, 2^M! . The easiest to understand example of this kind of problem is the Traveling Salesman problemhttp://en.wikipedia.org/wiki/Travelling_salesman_problem: Given a list of cities and their pairwise distances, the task is to find the shortest possible route that visits each city exactly once. The number of possible routes that the salesman can take increases exponentially with the number of cities, there for the number of possible distances that have to be compared to each other to find the shortest route increases at least exponentially. So for a computer running a program to find the solution it takes exponentially more resources of memory and time (in computational steps) or some combination of the two. Now, given all of that, in the concept of Platonia we have the idea of ideal forms, be they the Good, or some particular infinite string of numbers. How exactly are they determined to be the best possible by some standard. Whatever the standard, all that matters is that there are multiple possible options of The Forms with the stipulation that it is the best or most consistent or whatever. It is still an optimization problem with N variables that are required to be compared to each other according to some standard. Therefore, in most cases there is an Np-complete problem to be solved. How can it be computed if it has to exist as perfect from the beginning? I figured this out when I was trying to wrap my head around Leindniz' idea of a Pre-Established Harmony. It was supposed to have been created by God to synchronize all of the Monads with each other so that they appeared to interact with each other without actually having to exchange substances - which was forbidden to happen as Monads have no windows. For God to have created such a PEH, it would have to solve an NP-Complete problem on the configuration space of all possible worlds. If the number of possible worlds is infinite then the computation will
Re: Interesting paper on consciousness, computation and MWI
Thanks Bruno for patiently explaining things. It's interesting that you bring up computer science as I am doing a career change right now and am going into computer science. I eventually want to work in brain simulation. A lot of the ideas in this group are relevant. From the paper, I'll quote again (mainly for myself when I look back at this message) From page 17 It is my contention that the only way out of this dilemma is to deny the initial assumption that a classical computer running a particular program can generate conscious awareness in the first place. If the author is correct that would seem to drive a nail in the coffin for the digital generation of conscious awareness though in some way that might not prove that brain simulation is impossible. Perhaps brain simulation would occur in such a way that the simulation is never consciously self-aware but if that were the case, how good is that simulation?? If my doctor wanted to replace my brain with an artificial brain, I think I'd be scared out of my mind if LINUX wasn't an option hehe... Thanks Bruno. I know this might seem like a naive observation but the Bolshoi universe simulation recently done on a supercomputer at UC Santa Cruz in California produced some images of an early universe that had an uncanny resemblance to the human brain. It gives me hope that it is possible to simulate a brain on a classical computer. Perhaps the details would involve highly complex neural networks; the hope would be to rival the complexity of an actual brain. Here is a link that includes video http://hipacc.ucsc.edu/Bolshoi/ (Then of course we might get into some ethical quandaries regarding the personhood of a simulated brain such as can we run any experiment on it that we feel like running... is simulated suffering ethically equivalent to actual suffering... and that sort of thing.) On Thu, Oct 6, 2011 at 11:04 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 04 Oct 2011, at 23:14, Brian Tenneson wrote: Hmm... Unfortunately there are several terms there I don't understand. Digital brain. What's a brain? I ask because I'm betting it doesn't mean a pile of gray and white matter. Suppose that you have a brain disease, and you doctor propose to you an artificial brain, and he does not hide that this mean he will copy your brain state at the level of the molecules, processed by a computer. he adds that you can choose between a mac or a pc. Comp assumes that there is a level such that you can survive in the usual clinical sense with such a digital brain like you can already survive with an artificial pump at the place of the heart. Then you mention artificial brain. That's different from digital? Well, it could be for those studying an analog version of comp. But unless the analog system use actual infinities, it will be emulable by a digital machine. The redundancy of the brains and its evolution pleads for the idea that the brain is indeed digitally emulable. Is digital more nonphysical than artificial? Not a priori, at all. Sellable computers are digital and physical. Today the non physical universal machines are still free, and can be found in books or on the net. You might find a lot by looking toward yourself, but the study of computer science can accelerate that discovery a lot. Bruno On Tue, Oct 4, 2011 at 7:31 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 04 Oct 2011, at 05:33, Brian Tenneson wrote: From page 17 It is my contention that the only way out of this dilemma is to deny the initial assumption that a classical computer running a particular program can generate conscious awareness in the first place. What about the possibility of allowing for a large number of conscious moments that would, in a limit of some sort, approximate continuous, conscious awareness? In my mind, I liken the comparison to that of a radioactive substance and half-life decay formulas. In truth, there are finitely many atoms decaying but the half-life decay formulas never acknowledge that at some point the predicted mass of what's left measures less than one atom. So I'm talking about a massive number of calculated conscious moments so that for all intents and purposes, continuous conscious awareness is the observed result. Earlier on page 17... its program must only generate a finite sequence of conscious moments. I think I agree with you. I think that such a view is the only compatible with Digital Mechanism, but also with QM (without collapse). Consciousness is never generated by the running of a particular computer. If we can survive with a digital brain, this is related to the fact that we already belong to an infinity of computations, and the artificial brain just preserve that infinity, in a way such that I can survive in my usual normal (Gaussian) neighborhoods. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed
Re: Interesting paper on consciousness, computation and MWI
Hmm... Unfortunately there are several terms there I don't understand. Digital brain. What's a brain? I ask because I'm betting it doesn't mean a pile of gray and white matter. Then you mention artificial brain. That's different from digital? Is digital more nonphysical than artificial? On Tue, Oct 4, 2011 at 7:31 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 04 Oct 2011, at 05:33, Brian Tenneson wrote: From page 17 It is my contention that the only way out of this dilemma is to deny the initial assumption that a classical computer running a particular program can generate conscious awareness in the first place. What about the possibility of allowing for a large number of conscious moments that would, in a limit of some sort, approximate continuous, conscious awareness? In my mind, I liken the comparison to that of a radioactive substance and half-life decay formulas. In truth, there are finitely many atoms decaying but the half-life decay formulas never acknowledge that at some point the predicted mass of what's left measures less than one atom. So I'm talking about a massive number of calculated conscious moments so that for all intents and purposes, continuous conscious awareness is the observed result. Earlier on page 17... its program must only generate a finite sequence of conscious moments. I think I agree with you. I think that such a view is the only compatible with Digital Mechanism, but also with QM (without collapse). Consciousness is never generated by the running of a particular computer. If we can survive with a digital brain, this is related to the fact that we already belong to an infinity of computations, and the artificial brain just preserve that infinity, in a way such that I can survive in my usual normal (Gaussian) neighborhoods. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Interesting paper on consciousness, computation and MWI
From page 17 It is my contention that the only way out of this dilemma is to deny the initial assumption that a classical computer running a particular program can generate conscious awareness in the first place. What about the possibility of allowing for a large number of conscious moments that would, in a limit of some sort, approximate continuous, conscious awareness? In my mind, I liken the comparison to that of a radioactive substance and half-life decay formulas. In truth, there are finitely many atoms decaying but the half-life decay formulas never acknowledge that at some point the predicted mass of what's left measures less than one atom. So I'm talking about a massive number of calculated conscious moments so that for all intents and purposes, continuous conscious awareness is the observed result. Earlier on page 17... its program must only generate a finite sequence of conscious moments. Cheers Brian -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Mathematical closure of consciousness and computation
Self aware in what sense? On Sat, Jun 4, 2011 at 2:09 AM, Felix Hoenikker fhoenikk...@gmail.comwrote: Sorry again, but I want to add one thing: The broadest mathematical closure of the existence of computation, the observation of consciousness anywhere suggests the following, in my mind: all possible numbers (including transfinite-ones) are, in fact, self aware substructures in the mathematical universe, recursively communicating to each other by exchanging bits in an attempt to develop the algorithm which compresses themselves to a single state, which represents the number one, after which it promptly forgets and starts all over again, everywhere, and all at once. -- Forwarded message -- From: Felix Hoenikker fhoenikk...@gmail.com Date: Sat, Jun 4, 2011 at 3:03 AM Subject: The final TOE? To: Everything List everything-list@googlegroups.com Hi all, Consider the following fully general way of saying this is the following: quantum mechanics and general relativity are symmetrically the exact same theory, modulo the additional bit of information that quantum entanglement reduces net gravitational energy. This is the EXACT answer to the EPR paradox, and all paradoxes about singularities, and consistent with our picture of reality in every respect, as it necessarily must be since it follows exactly from the asssumption of 3+1 spacetime embedded within some higher dimensional structure of any form (i.e. including string theory). Since no true gravitational singularities exist, then every point in space is an apparent black hole because no point in space is an apparent black hole. Thus, at every point in space, a bit of information (or a photon) can escape from the observable universe on our scale, go into the past, and come out in the future in a symmetric manner for all observers, without considering your frame of reference in 3+1 space time. This qualitatively predicts all features of GR without QCD or QFT. However, since photons travelling through locally closed loops can look like point particles with some net entanglement coming out, then they can look like bundles that, for all intents and purposes, appear to randomly add information in some way, and in some spherically symmetric fashion, which predicts the divergence and appearance of other fundamental forces early in the inflating universe. It is often said that QM and GR differ from each other exactly by the contemplation of the singularity, and that our inability to discover the true laws of the universe has been limited by our lack of knowledge about the twin singularities: the inflationary bubble and the black hole. It follows that this fact was exactly true all along, and the laws of physics are a completely dimensionless consequences of our local geometry of space, and our civilization has, in fact, rather than been trying to discover the next laws of physics, has in fact been struggling to unlearn the concept of Indeterminacy and quantum mechanics, since QM follows from GR, the postulate of 3+1 spacetime and E = mc^2 (a nice, dimensionless equation). Einstein, in fact, was right all along, and successfully completed the fully deterministic general laws of physics. Consider then, the reason why indeterministic QM was ever suggested: the apparently subjective indeterminacy of the universe from each observer point of view (i.e. the uncertainty principle). Or actually, consider the fact that, if the universe is completely deterministic, and you for any defined you is getting non-random information from any source, then that information must, in fact, be added to you by the rest of the universe in some systematic fashion, down to the tiniest quantum of universe. This implies that there is actually, some quanta of the universe, a photon, and each photon is having information added to it from the rest of the universe, in a systematic fashion, and recursively so for every observer. This is actually a fully generic model for the universe, and the absolute generalization of QM and SR. Next, consider the fact that you are conscious and possibly indeterminstic (i.e. have subjective free will). I think I do. Therefore, I am not a quanta of information, or a bit, but it was added to me from somewhere. No, consider the mathematical closure of this observation. What does this imply about and anthropic principle and fine tuning? Does that make sense anymore. Also, does this not mean that our observable universe, for some definition of observable, from any subjective observer's point of view, is constantly being added non-random information from outside. I truly beg you all to consider this argument fully. Please let me know what you think, F.H. On Fri, Jun 3, 2011 at 7:16 PM, Felix Hoenikker fhoenikk...@gmail.com wrote: Every apparent event horizon is really a separation of two universes, where the outside universe is entangled
Re: Remarks on the form of a TOE
Those are some very interesting results, I must say. Why the letter choice of B? Does it "secretly" stand for "believes" or something else? If x is true then ~Bx seems to imply that if a hypothesis is true then science will never prove it no matter how much time you give them (barring any sort of infinite time). Is that right? I've had some exposure to Alan Watts and all I have seen is both profound and simple. Dt is a bit hard for me to understand. Would you elaborate for me? Bruno Marchal wrote: On 05 Jan 2011, at 21:45, Brian Tenneson wrote: "The Tao that can be described is not the ultimate Tao" I 3 Lao tseu, and all the taoists. There is a full chapter on Lao-tseu in the long version of my PhD(*). They were aware of the dream argument. In fact, I call the modal formula: x - ~B x (or its contrapositive Bx - ~x) with B intended for the scientific communication or proof: the Lao-Tseu Watts Valadier principle, there. Alan Watts describes indeed something similar in his book "the wisdom of insecurity", and Valadier, a french jesuit, wrote a remarkable book where it shows that making moral is immoral. Gdel's theorem (and Lb, Solovay) provides many solutions, having an arithmetical content, for such an equation. Indeed all x belonging to G* \ G obeys to that equation. With x = Dt (= ~Bf = consistency), you get Gdel's second incompleteness theorem: Dt - ~BDt. But Dt is also a solution. Most formula beginning by D (= ~B ~) are solutions. Correct machines cannot prove that they cannot prove something. Tarski's theorem provides even more insightful solutions, which are analytical, and on which the correct machine can only be mute. It led me also to a very simple theory of intelligence. A machine is intelligent if she is not stupid, and a machine is stupid if either she believes that she is intelligent, or she believes she is stupid. Aagain incompleteness provides solution. From that I showed that intelligence has a positive feedback on competence, but that competence has a negative feedback on intelligence. Interesting. I wonder if it's so. Whether or not the ultimate Tao can be described has been the object of all my research-related thinking for a while now. I finally made a breakthrough this year on the problem. I still have to manipulate what I think on it and massage the document about it. At least I can say that I'm not trying to describe the Tao. I'm trying to describe a description of the Tao. The reduced product of all structures is my candidate for my description for a description of the Tao. Perhaps Lao Tzu already put in his two cents regarding this kind of TOE. In "conscience and mechanism" I argue in detail that most of the writing of Lao-Tseu, Tchouang-Tseu, and especially (my favorite) Lie-Tseu can be interpreted by the discourse of the self-referentially correct machine. But Plotinus is closer to us. I have studied classical chinese and modern chinese, for years, to discuss on Lao-Tseu with scholars. It is difficult. Mechanism makes a bridge between Smullyan's "Tao is silent" and Smullyan's "Forever undecided". I still don't know if Smullyan would agree on this. Some remark by him makes me think he is not aware of that connection, or that mechanism favors that connection. If you like Lao-Tseu, you might appreciate Smullyan's book "tao is silent". Bruno (*) http://iridia.ulb.ac.be/~marchal/bxlthesis/consciencemecanisme.html -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
"The Tao that can be described is not the ultimate Tao" Interesting. I wonder if it's so. Whether or not the ultimate Tao can be described has been the object of all my research-related thinking for a while now. I finally made a breakthrough this year on the problem. I still have to manipulate what I think on it and massage the document about it. At least I can say that I'm not trying to describe the Tao. I'm trying to describe a description of the Tao. The reduced product of all structures is my candidate for my description for a description of the Tao. Perhaps Lao Tzu already put in his two cents regarding this kind of TOE. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
Ah, ok. Well, as your friend checked my proof, what I was/am working on is an effective theory. Bruno Marchal wrote: On 02 Jan 2011, at 18:01, Brian Tenneson wrote: Bruno Marchal wrote: On 02 Jan 2011, at 11:31, silky wrote: On Sun, Jan 2, 2011 at 8:31 PM, Brian Tenneson tenn...@gmail.com wrote: In the case of a TOE, the model IS reality. Okay, I won't reply further, this has become irrelevant noise. I suspect the traditional confusion between "model" in the sense of physicists (where model = a theory, like a toy model), and model in the sense of the logician, where model = the reality studied (like a woman serving as model for a painter, or the mathematical structure (N, +, x) for PA or RA). Logicians and physicists use the word "model" in the complete opposite sense, and this leads often to complete deaf dialog. This makes even more problem with computationalism, where an observer accept that some "theories/brains/finite-describable-objects" fits the reality. When you say "yes" to the doctor, it is because you believe that the artificial brain does capture (locally, with respect to your current environment) the real thing (your conscious you). In that case *you* are a fixed point where a model-theory correspond to a model-reality, a bit like in Brouwer fixed point theorem, where a map of a territory is shown to have a point on it matching the real point in the territory, provided the map is not ripped in two disconnected parts, but only transformed continuously. The point is that in some contexts some overlap can exist between a theory and its (or one of its) model, between description and realities, like with the painting of a painting of a pipe (cf Magritte). Things get confusing also if, like Brian, (but also logicians in some circumstances) people makes a model (a "reality") into a (non effective) theory. This can be justified for some technical reason, when working on super non effective structure, but is really out of topic, imo. Bruno What makes a theory effective? That its proofs are checkable. That its set of theorems is recursively enumerable. I'm going to be less precise given that my audience has changed in a way I do not know. We argue in an interdisciplinary field. Given a couple of assumptions, which are essentially that (1) reality is independent of humans (which will imply that a model (in the logical sense) can be a TOE as defined in this thread) and I don't see this. I prefer to use "theory" for something finitely presentable (finite or recursively enumerable). (2) a model every model can be embedded within endows that model with a universality that makes it a candidate for being reality. This is then a brief description of reality, though I couldn't hope to give all the details about reality. In that case the model (N, +, x) is the "TOE" that your are searching. It is rather a ROE (realm of everything), and the embedding relation is simulation (emulation or partial emulation). My point is that we have no choice in the matter once we assume that brains work like a digital machine at some level of description. I am also working on the hypothesis that a TOE can be given in an finite/infinite presentation such as found in ZF with axioms and axiom schemata. Question: what is the theory with no assumptions? I know that in logic, the consequent closure of the empty set of statements is the set of tautologies, which is not really what I'd call an effective theory. The set of (classical tautologies) is effective. But the empty theory as all models, the structure of which depending of the meta-theory. It is the trivial theory satisfied by all structures. But what about if we remove all assumptions? Sounds like chaos to me. This is connected to all this as I can explain. In fact, I can prove (1) on the grounds that there is no largest number. It took me a while to find this argument. "1)" follows from comp, which assumes arithmetical realism (used in "there is no largest number"). Bruno -- silky http://dnoondt.wordpress.com/ (Noon Silk) | http://www.mirios.com.au:8081 "Every morning when I wake up, I experience an exquisite joy — the joy of being this signature." http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-lis
Re: Remarks on the form of a TOE
Have you read the whole thread? silky wrote: On Sun, Jan 2, 2011 at 4:43 PM, Brian Tenneson tenn...@gmail.com wrote: We're talking about a mathematical theory about E. What relevance does this comment have? -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
In the case of a TOE, the model IS reality. Evgenii Rudnyi wrote: on 02.01.2011 08:47 silky said the following: On Sun, Jan 2, 2011 at 4:43 PM, Brian Tennesontenn...@gmail.com wrote: We're talking about a mathematical theory about E. What relevance does this comment have? I would say that a model and reality are different things. Do you mean that they could be the same? Evgenii -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
That's probably for the best. I think if you read the thread you'd understand what my point of view is, and answer your own questions towards me. You might want to look into the works of Max Tegmark for a place to start. http://arxiv.org/pdf/gr-qc/9704009 silky wrote: On Sun, Jan 2, 2011 at 8:31 PM, Brian Tenneson tenn...@gmail.com wrote: In the case of a TOE, the model IS reality. Okay, I won't reply further, this has become irrelevant noise. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
Evgenii Rudnyi wrote: I am new to this kind of thoughts, so my questions could be naive. Still, I would appreciate if you could help me to understand such a statement. In my understanding, people make models basically to become more competitive, in other words, to earn more money. From this viewpoint, the statement "the model IS reality" is a bit puzzling, as in this case the model brings actually nothing new. Say it is highly unlikely that it will help me to solve my personal problems (well, provided that I have free will whatever it means). The model is reality is something I'm following from the ultimate ensemble theory of everything in which physical existence is mathematical existence (see the M. Tegmark article I linked to in the previous post, it blew my mind). IF (big if) physical existence is mathematical existence then the model of reality is reality. It seems that people are not getting the thread in that I am trying to simplify this toe. Some time ago, I have read David Chalmers, The Matrix as Metaphysics http://consc.net/papers/matrix.pdf Let me make one citation "Importantly, nothing about this Metaphysical Hypothesis is skeptical. The Metaphysical Hypothesis here tells us about the processes underlying our ordinary reality, but it does not entail that this reality does not exist. We still have bodies, and there are still chairs and tables: it’s just that their fundamental nature is a bit different from what we may have thought. In this manner, the Metaphysical Hypothesis is analogous to a physical hypothesis, such as one involving quantum mechanics. Both the physical hypothesis and the Metaphysical Hypothesis tell us about the processes underlying chairs. They do not entail that there are no chairs. Rather, they tell us what chairs are really like." Along this lines, I would paraphrase that TOE is just Metaphysics. Do you agree with this, or you mean something else? I'm not exactly sure how I would define "metaphysics". In the hypothesis that mathematical existence is physical existence (which Tegmark puts into a -testable- theory in the paper I cited), chairs are mathematical structures which agrees with your quote. But Bruno is really the expert here. Evgenii http://blog.rudnyi.ru/2010/08/computable-universes.html on 02.01.2011 10:31 Brian Tenneson said the following: In the case of a TOE, the model IS reality. Evgenii Rudnyi wrote: on 02.01.2011 08:47 silky said the following: On Sun, Jan 2, 2011 at 4:43 PM, Brian Tennesontenn...@gmail.com wrote: We're talking about a mathematical theory about E. What relevance does this comment have? I would say that a model and reality are different things. Do you mean that they could be the same? Evgenii -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
Evgenii Rudnyi wrote: on 02.01.2011 12:07 Brian Tenneson said the following: Evgenii Rudnyi wrote: ... Some time ago, I have read David Chalmers, The Matrix as Metaphysics http://consc.net/papers/matrix.pdf Let me make one citation "Importantly, nothing about this Metaphysical Hypothesis is skeptical. The Metaphysical Hypothesis here tells us about the processes underlying our ordinary reality, but it does not entail that this reality does not exist. We still have bodies, and there are still chairs and tables: it’s just that their fundamental nature is a bit different from what we may have thought. In this manner, the Metaphysical Hypothesis is analogous to a physical hypothesis, such as one involving quantum mechanics. Both the physical hypothesis and the Metaphysical Hypothesis tell us about the processes underlying chairs. They do not entail that there are no chairs. Rather, they tell us what chairs are really like." Along this lines, I would paraphrase that TOE is just Metaphysics. Do you agree with this, or you mean something else? I'm not exactly sure how I would define "metaphysics". In the hypothesis that mathematical existence is physical existence (which Tegmark puts into a -testable- theory in the paper I cited), chairs are mathematical structures which agrees with your quote. But Bruno is really the expert here. Thank you for your answers. We could say that the Universe is made of superstrings or we could say that the Universe is made of numbers. Chalmers shows that for a human being this basically makes no difference. Would that be because superstrings are made of numbers? Evgenii http://blog.rudnyi.ru/2010/08/computable-universes.html -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
Bruno Marchal wrote: On 02 Jan 2011, at 11:31, silky wrote: On Sun, Jan 2, 2011 at 8:31 PM, Brian Tenneson tenn...@gmail.com wrote: In the case of a TOE, the model IS reality. Okay, I won't reply further, this has become irrelevant noise. I suspect the traditional confusion between "model" in the sense of physicists (where model = a theory, like a toy model), and model in the sense of the logician, where model = the reality studied (like a woman serving as model for a painter, or the mathematical structure (N, +, x) for PA or RA). Logicians and physicists use the word "model" in the complete opposite sense, and this leads often to complete deaf dialog. This makes even more problem with computationalism, where an observer accept that some "theories/brains/finite-describable-objects" fits the reality. When you say "yes" to the doctor, it is because you believe that the artificial brain does capture (locally, with respect to your current environment) the real thing (your conscious you). In that case *you* are a fixed point where a model-theory correspond to a model-reality, a bit like in Brouwer fixed point theorem, where a map of a territory is shown to have a point on it matching the real point in the territory, provided the map is not ripped in two disconnected parts, but only transformed continuously. The point is that in some contexts some overlap can exist between a theory and its (or one of its) model, between description and realities, like with the painting of a painting of a pipe (cf Magritte). Things get confusing also if, like Brian, (but also logicians in some circumstances) people makes a model (a "reality") into a (non effective) theory. This can be justified for some technical reason, when working on super non effective structure, but is really out of topic, imo. Bruno What makes a theory effective? I'm going to be less precise given that my audience has changed in a way I do not know. Given a couple of assumptions, which are essentially that (1) reality is independent of humans (which will imply that a model (in the logical sense) can be a TOE as defined in this thread) and (2) a model every model can be embedded within endows that model with a universality that makes it a candidate for being reality. This is then a brief description of reality, though I couldn't hope to give all the details about reality. I am also working on the hypothesis that a TOE can be given in an finite/infinite presentation such as found in ZF with axioms and axiom schemata. Question: what is the theory with no assumptions? I know that in logic, the consequent closure of the empty set of statements is the set of tautologies, which is not really what I'd call an effective theory. But what about if we remove all assumptions? Sounds like chaos to me. This is connected to all this as I can explain. In fact, I can prove (1) on the grounds that there is no largest number. It took me a while to find this argument. -- silky http://dnoondt.wordpress.com/ (Noon Silk) | http://www.mirios.com.au:8081 "Every morning when I wake up, I experience an exquisite joy — the joy of being this signature." http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
Also, the _expression_ "superstring are made of numbers" is unclear. If computationalism is correct the _expression_ "made of" has no sense. Things are not made of something, they are dreamed by (infinities) of computation. The physical worlds becomes the border of the "matrix", that is a first person plural reality, a partially sharable dream. I know. I'm having to decide what my audience is. What I mean to suggest is Tegmark's hypothesis in his ultimate ensemble paper that physical existence is mathematical existence. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
How can we know that? Reality is the totality of all that exists is a finite complete description. Well, that is my favorite definition of reality. But it is not a theory: you don't say what exist. RA says what exist. It says that 1 exists (Ex(x = s(0)), it says that you current computational states exists. It's not meant to be a theory, it's a description and a definition. Now I'm assuming, for the sake of argument, that totality, all, and exists have finite complete descriptions. And if these words don't, then no words do and we might as well be talking about asdjedwjef. Well, as you know, if we limit ourself to first order language, we can talk in a metaphysics-free language. With mechanism this works well for the ontology, but for the epistemology we have to give meaning to the standard model, and eventually to the full analytical truth, and beyond. To explain mechanism, we need people having a notion of consciousness, enough for doubting they can survive a digital substitution. Beyond? Interesting. So to explain mechanism there is a contingency. What I'm after is what else we can say about a TOE. Given what a TOE is, it does answer all questions written in its language. Are you not confusing the theory, and the subject of the theory. I'm not confused on this, actually. I know the difference between remarks about a TOE and the TOE itself. All my research is dedicated to remarks about a TOE, which is I think caused a big misunderstanding between us in the past. We might need to introduce an intermediate notion. Let us call that the realm. With mechanism the numbers, structured by addition and multiplication is the Realm of Everything: ROE. But that is what I called above the ontology. For a (naïve) physicalist the Realm is given by particles structured by their force (fermions and bosons, the quantum law). The epistemology will be given by higher order substructures of the ontological structure. Physical brains for the physicalist, Löbian numbers for the digital mechanist. For a mechanist, a physical brain appearance for numbers has to be justified by the numbers' structure. Ok. I'm interested in both, but moreso the digital mechanist side. Unfortunately, I know nothing of digital mechanism. Your ROE is curious. One way to describe something, a real basic way to describe something, is to form an aggregate of all things that meet that description. There may be no effective procedure for deciding whether or not A is in that aggregate, whatever. The point is that that is one way to describe something. Thus reality basically describes itself. Reality is an aggregate and as such is a TOE, a complete description of reality. But that is the trivial TOE. You are saying take the territory for map. That is all I need to show that a TOE exists. It's a trivial, brutal proof. Not elegant, I know. What is the nature of a TOE, though? I know actually finding a TOE might be difficult to say the least but we can at least say some things about the nature of a TOE. It is what unifies what we know, believe, feel, observe, guess .. into a coherent picture. I see. It makes sense, given all the data. Axiom schemata in ZF are infinitely many statements, aren't they? Oh! Take Von Neumann Bernays Gödel instead. It is more powerful than ZF, and it admits finite presentation. ZF is OK. I really meant finite or recursively enumerable theories, or theories having a finite presentation. They are (abstract ) machine or programs. I'm just saying that a very popular set theory uses infinitely many statements, as I'm sure you know. Which is why I question your belief that we 'ought' to stick to only finitely checkable proofs. Who really wants to check a proof anyway? I know, it's a required task in order to decide if someone is talking out of their butt. The thing about ZF is that it does have a finite presentation which uses infinitely many axioms (technically). SO why can't a TOE have a similar finite/infinite presentation? With mechanism: what exist basically (the true relation between numbers) is conceptually very simple, and is enough to understand that the every appearances is infinitely complex, but highly structured. Well, that's what I've been trying to prove. I guess I can stop now =) Sorry :-/ No, it's good. I can rest a bit. The facts is that if mechanism is true, I really don't see how we can escape the conclusion that elementary arithmetic is enough, and the internal epistemology of arithmetic explains all the dreams, why their are stable, why some are sharable, etc. Eventually, interpreting the ONE of Plotinus by Arithmetical truth gives back a transparent interpretation of a neopythagorean neoplatonist Theology. And my point is only that the physics of machine is already enough precise to be confronted with the
Dovetailing
I was unaware of this. Seems like it's a crucial part of Bruno's work. http://en.wikipedia.org/wiki/Dovetailing_%28computer_science%29 Trying to understand the concept here. Suppose there are infinitely many instructions of two programs. One way to run that program is to start putting green dots on a grid. (3,5) corresponds to instruction 3 of program 1 and instruction5 of program 2. http://www.youtube.com/watch?v=R7bAexWUD_c (btw, I found a formula that maps N onto Q, it's kinda neat) -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
We're talking about a mathematical theory about E. silky wrote: On Sun, Jan 2, 2011 at 12:03 AM, Brian Tenneson tenn...@gmail.com wrote: [...] One way to describe something, a real basic way to describe something, is to form an aggregate of all things that meet that description. There may be no effective procedure for deciding whether or not A is in that aggregate, whatever. The point is that that is one way to describe something. Thus reality basically describes itself. Reality is an aggregate and as such is a TOE, a complete description of reality. But that is the trivial TOE. You are saying take the territory for map. That is all I need to show that a TOE exists. It's a trivial, brutal proof. Not elegant, I know. Reality is the E of TOE. What's the point of calling it a TOE? You can't use it for anything. the TO part implies that we understand it. We don't understand of all reality, so we can't use all its properties to make predictions, so it's not useful for us as a theory and I don't see it as correct or appropriate to refer to it as such. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
On Dec 31, 1:42 am, Bruno Marchal marc...@ulb.ac.be wrote: On 29 Dec 2010, at 13:50, Brian Tenneson wrote: If a complete description of arithmetical truth is not possible, what exactly are we talking about? We, humans, have a rather good intuition of what is a true arithmetical sentence, independently of the fact that we have to recognize that it can be quite tricky to decide if this or that arithmetical proposition is true or not. But if arithmetical truth can not be described then what are we talking about? About God, or Everything, or the ONE, or the one-who-has-no- description, etc. The big thing, that is, or the big nothing ... Spot on. That's what I've been secretly themeing my paper to be about underneath the surface. What our intuition tells us? I'm still unclear as to why a complete description of reality is not possible because we apparently can know what we're talking about when we talk about arithmetical truth, despite arithmetical truth not being recursively enumerable. The proof that we cannot *know* what is arithmetical truth is related to the fact that we cannot know if mechanism is true. So we can already not know if some arithmetical relations make people or zombie. We can only know that IF mechanism is true THEN we cannot know which number(s)/machine(s) we are, etc. We can have a description of reality, but not a complete theory answering all the questions that we can formulate in the theory. So if a TOE is not recursively enumerable, it still might be captured in some finite set of statements like how arithmetic can be captured in the Peano axioms. That arithmetical truth is not recursively enumerable can somehow be derived from these first principles, right? Perhaps the same is true of a TOE. That's what I'm wondering. Accepting some hypothesis, we can make statement on 'reality'. With the hypothesis digital mechanism, we can state that reality is not recursively enumerable, neither pi_i or sigma_i for any positive integer i, etc. In particular we can know, relatively to that hypothesis, that reality does not admit any finite complete description. How can we know that? Reality is the totality of all that exists is a finite complete description. Now I'm assuming, for the sake of argument, that totality, all, and exists have finite complete descriptions. And if these words don't, then no words do and we might as well be talking about asdjedwjef. It means that the theory of everything cannot answer all question written in its language. It means that many surprises will ever attend us, and that some mystery will remain forever. But we can account epistemologically for those surprises and mysteries. What I'm after is what else we can say about a TOE. Given what a TOE is, it does answer all questions written in its language. One way to describe something, a real basic way to describe something, is to form an aggregate of all things that meet that description. There may be no effective procedure for deciding whether or not A is in that aggregate, whatever. The point is that that is one way to describe something. Thus reality basically describes itself. Reality is an aggregate and as such is a TOE, a complete description of reality. OK. But that is not an effective theory, nor a theory at all with the definition given. You talk about the model, which is what we talk about: the intended model of a theory of everything (including matter, consciousness, taxes and death, ...). What is the nature of a TOE, though? I know actually finding a TOE might be difficult to say the least but we can at least say some things about the nature of a TOE. I thought we agree that a theory has to be finite? Axiom schemata in ZF are infinitely many statements, aren't they? With mechanism: what exist basically (the true relation between numbers) is conceptually very simple, and is enough to understand that the every appearances is infinitely complex, but highly structured. Well, that's what I've been trying to prove. I guess I can stop now =) It is the overall, basic structure of what exists. The reduced product of all structures is a key to this. I am really not seeing how one can have an outside view of the ultimate reality based on what you've said. Can you explain it in more simple terms? If there were an outside to ultimate, then it wasn't ultimate to start with. You are the one invoking NF so that the universe U of sets is a set! You should be less annoyed than anyone else with the idea of an ultimate reality being an object by itself. Such U belongs to U. So that U can serve itself as an outside view of itself! But I don't need NF, because with mechanism just a diophantine degree 4 polynomial can do the trick, or any other universal ... But U is not outside U. read more » Sorry, it seems to have eaten your post here...hmm. -- You received this message
Re: Remarks on the form of a TOE
If a complete description of arithmetical truth is not possible, what exactly are we talking about? We, humans, have a rather good intuition of what is a true arithmetical sentence, independently of the fact that we have to recognize that it can be quite tricky to decide if this or that arithmetical proposition is true or not. But if arithmetical truth can not be described then what are we talking about? What our intuition tells us? I'm still unclear as to why a complete description of reality is not possible because we apparently can know what we're talking about when we talk about arithmetical truth, despite arithmetical truth not being recursively enumerable. How does one even prove that arithmetical truth is not recursively enumerable if one does not have a complete description of arithmetical truth. Take whatever level of description of arithmetical truth necessary to prove that statement and analogously take reality to be described to that level, then it no longer seems your implausibility argument based on arithmetical truth not being recursively enumerable is applicable. What I mean is that couldn't we make statements about a complete description of reality such as it is not recursively enumerable? How does that mean a complete description of reality does not exist, as you said? There is a complete description of reality, though the most evident one is infinite in length, and not recursively enumerable (since arithmetical truth isn't). What I'm after is analogous to a finite basis for a vector space over an infinite field. Can any infinite TOE be abridged into a finite document that, when provided with how to expand the finite document (like the span of a basis in my analogy), is the original infinite document? If so, that would entail that reality is somehow self-similar or, in a sense, holographic in nature. Or if there is an infinite TOE whose number of symbols is of a certain cardinality, what is the smallest cardinal that that TOE can be compressed into? IF that is provably finite then I think that would be interesting. What is the outside view of the ultimate reality? Assuming mechanism, arithmetical truth is enough. It is infinite and non algorithmically generable. It is just absolutely undecidable that there is anything more needed for the outside view. So by Occam razor ... If we are machine (survive at some substitution for some level, or are fully turing emulable with fully meaning that consciousness is preserved) then the inside knowledge view of arithmetical truth will be FAR BIGGER than arithmetical truth. Indeed, it corresponds plausibly to George Levy first person plenitude. That things is much less definable (if I can say) than arithmetical truth. There is here an analog of Skolem paradox, with the existence of a structure which looks small from outside and is immensely big from inside. How is it possible to have an outside view of the ultimate reality? By assuming mechanism. If mechanism fails the UDA test, we will know that arithmetical truth is too big or to small. Plausibly too small (for the reason that we can already conceive, apparently, arithmetical truth (but an ultrafinitist could contest this). Church thesis rehabilitates the Pythagorean Neoplatonist theology. The relation between the numbers (the true arithmetical relation or propositions) defines, by the first person indeterminacy, a differentiating flux of consciousness, which, by the non awareness of the basic UD execution time (defined by those relations), filters *in the limit* the possible and sharable infinite consistent histories. The reason why you are conscious here and now is rather easy. It depends only on the truth of one sigma_1 arithmetical sentence (asserting the existence of your computational state relatively to some universal number). But there are infinitely many equivalent sentences, both with the same universal numbers and with different universal numbers. Most relations involve pretty big numbers. What the first person indeterminacy makes complex is the relation between 'here and now', and 'there and then'. This, unfortunately depends on that infinity of universal (among others) numbers, and all those sigma_1 propositions, and actually all their proofs, which define the relative measure. Below your substitution level, an infinity of universal number compete, for proving your existence, together with all random oracles. Fortunately, the constraints of self-referential correctness for the Löbian observers are enough to shed some light on this, and to make quite plausible that the bottom physical reality will appear linear and extremely symmetrical, then self-observation break the symmetries from the point of view of the self-observing machines. You can see this as Everett spirit applied to arithmetic. Everett embeds the physicist in the quantum reality. DM
Re: Remarks on the form of a TOE
Thank you, happy new year to you, too! On Dec 27, 8:36 am, Bruno Marchal marc...@ulb.ac.be wrote: On 26 Dec 2010, at 22:51, Brian Tenneson wrote: Limits To Science: God, Godel, Gravity http://www.science20.com/hammock_physicist/limits_science_god_godel_g... Here is my comment: An important question is whether or not a TOE will be finite in length. Of course, this is a matter of definition. Indeed. I am taking 'TOE' to be, as a working definition, a complete description of reality or a complete description of everything that exists. That does not exist. Arithmetical truth is already not recursively enumerable. If a complete description of arithmetical truth is not possible, what exactly are we talking about? Then one *might* consider this program which generates a TOE to arbitrary precision to be the TOE, a compression of an infinitely long document into a finitely long document, thus showing that reality at its core does not possess the trait of Kolmogorov randomness. Being that reality contains the uncomputable, it *seems* unlikely that everything can be finitely describable. This is simply wrong. That's good! The argument is made that a TOE can be in the form of a logical structure which is a tuple consisting of an underlying set, a set of distinguished constants (like zero), functions (like successor), and relations (like less than) on this underlying set. Making the additional assumption that if there is a structure such that *all* logical structures can be embedded within it, then this type of universality endows such a structure with the same structure as reality. Thus this sort of ultimate structure would be in an intuitive sense like ultimate reality. Thus a description of this ultimate structure would be a description of reality. You have to distinguish the outside and inside view of the ultimate reality. What is the outside view of the ultimate reality? How is it possible to have an outside view of the ultimate reality? -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
Limits To Science: God, Godel, Gravity
http://www.science20.com/hammock_physicist/limits_science_god_godel_gravity
Here is my comment:
An important question is whether or not a TOE will be finite in
length. I am taking 'TOE' to be, as a working definition, a complete
description of reality or a complete description of everything that
exists. Reality is infinitely vast at least for the reason that it
contains all the integers, not to mention the vastness of the physical
multiverse. So a TOE can be an infinite document. But like the digits
of pi, perhaps this infinitely long document can be computed to
arbitrary precision in a finitely long program, set of instructions.
Then one *might* consider this program which generates a TOE to
arbitrary precision to be the TOE, a compression of an infinitely
long document into a finitely long document, thus showing that reality
at its core does not possess the trait of Kolmogorov randomness. Being
that reality contains the uncomputable, it *seems* unlikely that
everything can be finitely describable.
However, I believe that there is a TOE (complete description of
reality) whose *form* can be written down. This TOE has a shape to
it, but without specifying any more details than that. It's an
existence proof of a plausible form a TOE could be in. It is roughly
based on Tegmark's article entitled the Mathematical Universe
Hypothesis (available on arxiv.org) which can be broken down to rely
on the axiom that reality is independent of humans which is possibly
controversial.
The argument is made that a TOE can be in the form of a logical
structure which is a tuple consisting of an underlying set, a set of
distinguished constants (like zero), functions (like successor), and
relations (like less than) on this underlying set. Making the
additional assumption that if there is a structure such that *all*
logical structures can be embedded within it, then this type of
universality endows such a structure with the same structure as
reality. Thus this sort of ultimate structure would be in an intuitive
sense like ultimate reality. Thus a description of this ultimate
structure would be a description of reality.
To do this, I employ a different-than-usual set theory called NFU
which stands for new foundations with urelements as explained by
Randal Holmes' textbook on NFU. The NFU has been shown to be
consistent which cannot be said of the more famous ZF or ZFC set
theories. The NFU also has a universal set (a set containing all sets)
and a stratified comprehension theorem which essentially states that
any object of the form {x : F} where F is any stratified formula is
a set in NFU. An example of a *non*-stratified formula F is the
infamous formula used in Russell's paradox: x is not an element of x.
Thus the object considered in Russell's argument isn't a set and from
this argument, no Russell-type contradictions can be derived from the
universal set axiom + stratified comprehension.
Within NFU, it is possible to see that the object which contains *all*
structures is a set. Then one can form the reduced product of all
structures, using this set as the index set. One feature of a reduced
product is that it is a logical structure and another feature is that
every structure used to form the product (in this case, every
structure) is embedded within the reduced product.
The reduced product of all structures is the ultimate structure as
described a few paragraphs above.
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Re: A possible structure isomorphic to reality
There is evidently a weaker version of the embedding concept. http://en.wikipedia.org/wiki/Embedding#Universal_algebra_and_model_theory (No references as far as I can tell for this definition) I am looking at this definition and the flaw in my proof on page 13 and, while I will have to study it further, preliminarily, it appears that this weakened concept of embedding will work. That is to say that the theorem on page 12 will be correct if I simply remove the word elementary. The Wiki article is somewhat dubious in lacking references to this weakened version of embedding. I don't see this in Chang and Kiesler (so far). The definition given seems to, intuitively, say that A is embedded in B via h if h is 1-1, h preserves the interpretation of function symbols (I'm not sure how else to state that yet), and h preserves the truth of relations. The last bit is significantly weaker than preserving the truth of all formulas. In fact, I never needed the embedding to be elementary. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: A possible structure isomorphic to reality
Is there any first order formula true in only one of R and R*? I would think that if the answer is NO then R R*. What I'm exploring is the connection of to [=], with the statement that implies [=]. Are there any other comparitive relations besides elementary embedding that would fit with what I'm trying to do? What I'm trying to do is one major leg of my paper: there is a superstructure to all structures. What super means could be any comparitive relation. But what relation is 'good'? On Dec 9, 8:12 am, Bruno Marchal marc...@ulb.ac.be wrote: On 09 Dec 2010, at 05:12, Brian Tenneson wrote: On Dec 5, 12:02 pm, Bruno Marchal marc...@ulb.ac.be wrote: On 04 Dec 2010, at 18:50, Brian Tenneson wrote: That means that R (standard model of the first order theory of the reals + archimedian axiom, without the term natural number) is not elementary embeddable in R*, given that such an embedding has to preserve all first order formula (purely first order formula, and so without notion like natural number). I'm a bit confused. Is R R* or not? I thought there was a fairly natural way to elementarily embed R in R*. I would say that NOT(R R*). *You* gave me the counter example. The archimedian axiom. You are confusing (like me when I read your draft the first time) an algebraical injective morphism with an elementary embedding. But elementary embedding conserves the truth of all first order formula, and then the archimedian axiom (without natural numbers) is true in R but not in R*. Elementary embeddings are *terribly* conservator, quite unlike algebraical monomorphism or categorical arrows, or Turing emulations. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group athttp://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: A possible structure isomorphic to reality
On Dec 5, 12:02 pm, Bruno Marchal marc...@ulb.ac.be wrote: On 04 Dec 2010, at 18:50, Brian Tenneson wrote: That means that R (standard model of the first order theory of the reals + archimedian axiom, without the term natural number) is not elementary embeddable in R*, given that such an embedding has to preserve all first order formula (purely first order formula, and so without notion like natural number). I'm a bit confused. Is R R* or not? I thought there was a fairly natural way to elementarily embed R in R*. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Remarks on the form of a TOE
So is it impossible that there are enough redundancies in an infinitely long statement of a TOE to make it into an equivalent, finite document? -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: A possible structure isomorphic to reality
On Dec 4, 2:52 am, Bruno Marchal marc...@ulb.ac.be wrote: I just said that if M1 M2, then M1 [=] M2. This means that M2 needs higher order logical formula to be distinguished from M1. Elementary embeddings () are a too much strong notion of model theory. It is used in context where we want use non standard notions, like in Robinson analysis. Doesn't the archemedian property show that R is not elementarily equivalent to R*? I mean the following 1st order formula true in only one of R and R*: for all X there is a Y such that (Y is a natural number and XY) This is true in R but not in R*. This would appear to me to be an example of why R is not [=] to R*. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: A possible structure isomorphic to reality
I'm going to try to concentrate on each issue, one per post. Let me say again that your feedback is absolutely invaluable to my work. In an earlier post you say something that implies the following: Suppose M1, M2, and M3 are mathematical structures Let denote the elementarily embedded relation Let [=] denote elementarily equivalence (A) If M1 M3 and M2 M3 then M1 [=] M2. Consequently, one of my theorems must be wrong since all structures elementarily embedded within U implies all structures are elementarily equivalent, which is false. Firstly, is (A) implied by your statement quoted here? [quote] If they are all elementary embeddable within it [my structure U], then they are all elementary equivalent, given that the truth of first order formula are preserved. All mathematical theories would have the same theorems. So eventually there has to be something wrong in your theorem. [unquote] Secondly, I believe I can prove (A) is false, thus restoring plausibility of my theorem on page 12. I still need to prove theorem on page 12 if possible, of course fixing the flaw which might be a flaw in the way it was stated. Perhaps I can rescue the main theorem even if I weaken the theorem on page 12. However, if (A) is not implied by your remarks then I wouldn't need to try to prove it false as my proof would be a moot point. If (A) is implied by your remarks then I will show my proof that (A) is false. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Remarks on the form of a TOE
If there is a TOE, I would expect it to be pretty lengthy and complicated. The TOE would basically be a conjunction of all answers to all questions. But can this even be done in human terms? Wouldn't there be infinitely many questions (e.g., what is 1+1, what is 1+2, what is 1+3)? That would mean that TOE is infinite in length. So then the question becomes can this infinite set of answers can be abridged into a finite, yet equivalent, document? And finally, can we find a particular document with all the answers and be able to prove that is the most succinct those answers could possibly be? (IOW, can we find the shortest document that contain all answers to all questions?) Well the subject of questions and answers related to all this is given here: http://arxiv.org/abs/0708.1362 That which answers questions is called an inference device. It appears that there might be some interesting results concerning strong inference devices. It would vastly simplify things if something is considered an answer only if that answer has a finite proof. Then the question would become how many finite proofs are there? There are infinitely many different finitely long proofs. That leads me to the conclusion that TOE is not expressible in a finite document. However, if there are finitely many categories of proofs then the document would just be a summary of the categories of proofs which would make the TOE document finite. Two proofs are in the same category if their conclusions are equivalent and not in the same category if their conclusions are not equivalent, meaning that they are not merely restatements of one another. Thus, there are finitely many categories of proof if and only if TOE is a finite document. There being finitely many categories of proof implies that TOE is a finite document. There being infinitely many categories implies that TOE is an infinite document. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: A possible structure isomorphic to reality
If they are all elementary embeddable within it, then they are all elementary equivalent, given that the truth of first order formula are preserved. How would all structures be elementarily equivalent? All mathematical theories would have the same theorems. So eventually there has to be something wrong in your theorem. My friend found the error. Your theorem page 12 is wrong, and the error is page 13 in he last bullet paragraph, when you do the negation induction step for your lemma. When you say: Since it is not the case that A l= ψ(Fi (b)), it is not the case that Aj l= ψ(Fi (b)(j)) by induction. This will be true for *some* j, not for an arbitrary j. If you negate for all j Aj l= ψ(Fi (b)(j)) , it means that there is a j such that it is not the case that Aj l= ψ(Fi (b)(j)). After that your j is no more arbitrary. It took me a while to understand what you're saying but indeed I see the error of my proof at this point. I'm going to try to prove it in a different way but my hope is quite limited. Although I have nothing to show for my efforts, I do feel like I learned a bit along the way. Thanks for your feedback. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
A possible structure isomorphic to reality
I am starting a new thread which begins with some quotes by myself and to continue the conversation with Bruno. I figure this is especially of interest because of the references to Tegmark's works. From a logician's standpoint, it may be of interest that I show that there is a structure U such that all structures, regardless of symbol set, can be elementarily embedded within it. From a physicist's point of view, at least one who might subscribe to Tegmark's 4-level hierarchy of parallel universes, a structure with this property might be of interest under the hypothesis that reality is a mathematical structure. If we suppose that reality is something which is all encompassing, then the structure with the aforementioned property could be said to be all encompassing. Now that I have this structure in hand, I can try to go further by looking at the structure from a model-theoretic point of view. This task to further the investigation will be undertaken soon. Here is a link http://www.alphaomegadimension.info/media/A_Mathematical_Structure_Isomorphic_to_Reality_ver_5-12_anon.pdf Any feedback is encouraged, critical or otherwise. [quote] Let us call universe, the ultimate reality. Then I agree with this: if the universe is a mathematical object, then NF is the best tool to attempt a description of that universal object. The universe, when being a mathematical object, has to belong to itself, so we need a theory à-la Quine, instead of the usual Zermelo- Franekek or Von Neuman Bernays Gödel. In that sense it improves the raw description Tegmark makes of level 4. [end quote] Belong in the context of the paper is elementary embedding. Since every structure is elementarily embeddable within itself, there is no violation of any kind of foundation axiom and no anti-foundedness assumption is required. Also, the universal set is barely used; what's more important in my paper is the stratified comprehension theorem. The universal set is invoked in any mention of power set such as for relations. It would be nice to say something like the universal set V is what is isomorphic to reality. However, the argument presented entails that a baggage-free complete description of reality (ie, a TOE) is a mathematical structure instead of a mathematical set. Once this ultimate structure is found, I think the means to finding it (eg, NFU) are largely irrelevant in the same vain as the Dedekind cut construction of the reals is largely irrelevant when actually dealing with real analysis at least in the sense that Dedekind cuts are rarely mentioned when you do calculus. [quote] Such universal machine cannot know in which computational history she would belong, still less in which mathematical structure she belongs, but below its level of substitution, she belongs to an infinity of universal history (number relations, combinators relation, Horn clause relations) 'competing' in term of a measure of credibility. [end quote] Well if the paper is accurate, she can know that as herself, being a mathematical structure, she is elementarily embeddable within U as argued in the paper. Elementary embedding is not literally belonging as in is an element of, so I'm not sure if this directly contradicts the hypotheses you are using. However, this statement of yours is not inconsistent with my paper. I would presume that one could say that she is in a sort of intersection of all structures containing (ie elementarily embeddable within) herself, which is the smallest structure she is embeddable within. I know that intersection is vague at this point regarding math structures. For example, what is the intersection of a lattice structure and the complex number field? It would have something to do with intersecting the universes, functions, and relations involved. [quote] So with mechanism the physical is not something mathematical among the mathematical, it is a very special structure which sums on all mathematical structures is a way specified by computer science and the logic of self-references. It is based on distinction of different internal sel-referential views. [end quote] A major shortcoming of the paper appears to be the lack of explanation for the physical. Then again, this is a description of the level 4 universe, and not lower levels so one would view this as a piece of the puzzle that is meant to complete the picture painted by Tegmark in his works. In truth, it is a house of cards and if the level 4 universe does not fit, then everything in the paper falls apart as then the underlying hypotheses would be false. But that remains to be seen. [quote] Also, I am not convinced by your argument that from the premise there exists a reality completely independent of us human it follows that reality is a mathematical structure. You beg the question by identifying a baggage free description with a mathematical structure. A physicalist argues in general that baggage-free description is what him provides:
Another paper for your Comments
I figure this is especially of interest because of the references to Tegmark's works. From a logician's standpoint, it may be of interest that I show that there is a structure U such that all structures, regardless of symbol set, can be elementarily embedded within it. From a physicist's point of view, at least one who might subscribe to Tegmark's 4-level hierarchy of parallel universes, a structure with this property might be of interest under the hypothesis that reality is a mathematical structure. If we suppose that reality is something which is all encompassing, then the structure with the aforementioned property /could/ be said to be all encompassing. Now that I have this structure in hand, I can try to go further by looking at the structure from a model-theoretic point of view. This task to further the investigation will be undertaken soon. Here is a link http://www.alphaomegadimension.info/media/A_Mathematical_Structure_Isomorphic_to_Reality_ver_5-12_anon.pdf Any feedback is encouraged, critical or otherwise. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Another paper for your Comments
My apologies, I didn't mean to insert this into your thread! Sorry! On Oct 6, 8:43 am, Brian Tenneson tenn...@gmail.com wrote: I figure this is especially of interest because of the references to Tegmark's works. From a logician's standpoint, it may be of interest that I show that there is a structure U such that all structures, regardless of symbol set, can be elementarily embedded within it. From a physicist's point of view, at least one who might subscribe to Tegmark's 4-level hierarchy of parallel universes, a structure with this property might be of interest under the hypothesis that reality is a mathematical structure. If we suppose that reality is something which is all encompassing, then the structure with the aforementioned property /could/ be said to be all encompassing. Now that I have this structure in hand, I can try to go further by looking at the structure from a model-theoretic point of view. This task to further the investigation will be undertaken soon. Here is a linkhttp://www.alphaomegadimension.info/media/A_Mathematical_Structure_Is... Any feedback is encouraged, critical or otherwise. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: numbers?
John Mikes wrote: ...Rectangles are not found in nature and not are numbers; both are abstractions of things we see in nature... Pray: what things? and how are they 'abstracted into numbers? (Rectangles etc. - IMO - are artifacts made (upon/within) a system of human application). Yet numbers and rectangles (and many other abstractions) have a suspiciously good use for modeling in nature --- - u s e - . (?) - Number systems like the one asserted by the Peano axioms are abstractions of the process of counting. The box has no apples, the box has one apple, etc.. The numbers 0, 1, etc., are abstracted so that 0 can universally mean none of anything, 1 can universally mean 1 of anything, etc.. When we say 3+4=7, it is an abstraction because it universally means 3 of anything added to 4 of that anything is 7 of that anything. A rectangle traditionally is a set of points with special additional requirements. You will never find a rectangle in nature because points are smaller than particles and the edge of a rectangle is more dense than any physical arrangement. Dense meaning that between any two points there is another point in between the two. This is not true of naturally occurring arrangement of things: it is not the case that you can always find a third object between two other objects. Physical arrangements are not infinitely fine, they are coarse even if only discernibly coarse on a very small scale. Numbers are good models and have a use in a variety of applications such as finance and rectangles are good models for architecture and a whole lot more. Equivalence of III + IV as VII? Or in other numbering systems (letters, etc.) used in various languages? In Bruno's example some time ago the II + I = III definitely referred to the quantity of the I lines. He even went up to some I or similar. Now in my feeble mind to construct 'symbols' for expressing /_how many Is there are_/ is not the other way around. 3 stands for III, the COUNTED amount of the lines and not vice versa. So: what are those _naturally occurring_ things that serve for being abstracted into numbers? * Seems like the concept of number system is getting mixed up with the concept of numeral system. It does not matter if you use III, 3, three, @@@, etc. It does not matter that III can be written 7 or seven. The numeral system is the notation and the number system are what the symbols in the numeral system point to. So while we may write III or 3 or three, what those symbols point to is a number. If you will, imagine two domains: one domain is of symbols and the other domain is what those symbols point to. Numeral systems are of the first domain and number systems are of the second domain. Counting inspired number systems. Numeral systems are used to describe counting. Axioms are statements - not controversial to what I stated. And please, do not divert into quite different topics, where you may have a point in some other aspect. We are talking about numbers, not the masculinity of the US president. Fine, not controversial. My examples, admittedly not all drawn from mathematics, were just illustrations of my point that statements exist independently of humans. What you said was this: /_Axioms_/ however sounds to my vocabulary like inventions helping to justify our theories. Sometimes quite weird. Yet axioms exist independently of humans. What a human does is select axioms to his or her liking to momentarily assume for some purpose or another. Basically, because axioms exist independently of humans (as do all statements), they are not inventions of humans. Not inventions but a human will choose which axioms to assume momentarily for some purpose. Choose, not invent. Exist is something to be identified. IMO physical existence is a figment pertinent to the figment of a physical world - quite outside of my position. I don't permit physical existence. Well then perhaps numbers exist for you. I do not put the physical condition on existence; for me numbers do indeed exist. If I may repeat: so WHAT ARE NUMBERS? (symbols for what? how do they apply them to quantitative considerations? what if another 'logic' uses them in a different math (e.g. where 17 is not identifiable as a prime number? Is it likely that more will be found - as was the zero, or are we in a mathematical omniscience already? Is our restriction to the 'naturals' - natural, or just a consequence of our insufficient knowledge (caabilities)? May I quote a smart person: there are no stupid questions, only stupid answers. I ask them. John Mikes When considering number systems such as naturals, rationals, and (finite or infinite) cardinal numbers, it seems to me to not be a question with a quick answer. Division is not possible in all number systems, so I would have to say that in order to count (no pun intended) as
Re: numbers?
Bruno Marchal wrote: Tegmark argues that reality is a mathematical structure and states that an open problem is finding a mathematical structure which is isomorphic to reality. This might or might not be clear: the mathematical structure with the property that all mathematical structures can be embedded within it is precisely the mathematical structure we are looking for. The problem is in defining embedded. I am not sure it makes set theoretical sense, unless you believe in Quine's New foundation (NF). I am neutral on the consistency of NF. With a large sense of embedded I may argue that the mathematical structure you are looking for is just the (mathematical) universal machine. In which case Robinson arithmetic (a tiny fragment of arithmetical truth, on which both platonist and non platonist (intuitionist) is enough. Indeed, I argue with comp that Robinson arithmetic, or any first order specification of a (Turing) universal theory is enough to derive the appearance of quanta and qualia. Actually, I'm using what's called NF with urelements (NFU) which according to what I've read is consistent. http://plato.stanford.edu/archives/sum2009/entries/quine-nf/ (section 7. Coda). Where would I go about finding out a survey of concepts including universal machine? Are they known to exist? How are they defined? It would be much easier if I didn't have to reinvent the wheel. The last sentence in the quote excites me: The leap from mathematics to things such as quanta and qualia is something I haven't really understood. Digital mechanism (the tiny arithmetic TOE) entails already a large part of Quantum Mechanics, and then group or category theoretic considerations (and knot theory) might explain the 'illusions' of time, space, particle, and (symmetrical) hamiltonians, and why indeed physical reality should appear as an indeterminate state of a physical vacuum. But the logic-math problems remaining are not easy to solve. That is normal in a such top down, mind-body problem driven, approach to physics (and psychology/theology/biology). Interesting! -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: numbers?
John Mikes wrote: Brian, nothing could be more remote for me than to argue 'math' (number's application and theories) with you. I thinkyou mix up* 'counting'* for the stuff that serves it. As I usually do, I looked up Google for the Peano axioms and found nothing in them that pertains to the origination of numbers. They USE them and EXPLAIN sich usage. Use what Indeed, counting and what I'm referring to as numbers are different. Counting is a mental process while numbers have nothing to do with mind though the mind may apprehend and understand numbers to some extent. Counting is not the origin of numbers. Counting inspired the discovery of numbers as elucidated by people like Peano. Numbers are idealized models for the process of counting much like how a rectangle is an idealized model for the blueprint of an architectural structure's foundation. Rectangles are not found in nature and neither are numbers; both are abstractions of things we see in nature. Yet numbers and rectangles (and many other abstractions) have a suspiciously good use for modeling things in nature. I wonder if you have an example where application of numbers is extractable from ANY quantity the numbers refer to? Three plus four is not different from blue plus loud, sound plus speed, /_whatever_/, meaningless words bound together. UNless - of course - you as a human, with human logic and complexity, UNDERSTAND the amount *three* added to a _comparable_ amount of *four *and RESULT in /_*seven* pertaining to the same kind of amount._/ I only mean to reference the difference between numbers and the quantity they point to. In an important way, 3+4 is different from your other examples in that 3+4 can be translated into a language devoid of human baggage and symbolically manipulated so as to show an equivalence between the symbols 3+4 and 7. /_ _/ // /_Axioms_/ however sounds to my vocabulary like inventions helping to justify our theories. Sometimes quite weird. And *Brent* was so right: /...I don't think the existence of some number of distinct things is the same as the existence of numbers/ - Tegmark's quoted accounted for... is not consists of. /_To 'explain' _/something by a conceptualization does not substitute for the existence and justification of such conceptualization. Axioms are statements. Do humans need to exist in order for the statement the galaxy is approximately a spiral shape to exist? How about 3+4=7, does that require humans to exist in order for the statement to exist? What about the existence of the statement the president of the US is male; if all the humans were to die out, that statement would still exist. Statements are uttered by humans but do not depend on humans for their existence. This is how axioms exist independent of humans, because they are statements. The notation differs and are invented but what is being referred to by the symbols is independent of humans. Moreover, I'm not talking about the truth of statements; I'm talking about the statements themselves not requiring anyone to utter them in order to exist. Numbers do not physically exist; so if physical existence is the only form of existence you permit, then numbers do not exist... in the same sense that math might as well be about Luke Skywalker, who does not exist physically. However, math has a suspiciously good use in nature like I said, unlike a novel about Luke Skywalker. Does it make sense that 'numbers existed' when nobody was around to */_K N O W or U S E??_/* Especially when they did not/_ *C O U N T*_/ anything? BTW: what are those abstract symbols you refer to as numbers? (and this question is understood for times way before humans and human thinking). Sorry I asked John M Does it make sense? Let me ask you a question. Way back when, in the earliest stages of counting, let's assume there was a point at which a hundred thousand was the furthest anyone had counted to. Now.. Did the number 1,000,000 exist at this stage of counting? I think it did. A million and all of its successors. Bruno, - Hmm... Lawvere has tried to build an all encompassing universal mathematical structure, but he failed. It was an interesting failure as he discovered the notion of topos, (discovered also independently by Groethendieck) which is more a mathematical mathematician than a mathematical universe. Also Tegmark is not aware that Digital Mechanism entails the non locality, the indeterminacy and the non cloning of matter, and that DM makes the physical into a person-modality due to the presence of the mathematician in the arithmetical reality. Quanta are special case of first person plural sharable qualia. - I'm not looking for a truly all-encompassing mathematical structure. What I'm looking for is a mathematical structure in which all mathematical structures can be embedded. By mathematical structure, I mean
Re: numbers?
I quite agree that counting and the existence of numbers are different. The Peano axioms for numbers makes it seem like numbers are not dependent on us humans to exist which entails that there are infinite sets by assuming an induction property held by (sets of) numbers. So while counting may not have been around forever, numbers have, independent of us humans. The Peano axioms are totally free of human baggage and did not need Peano to utter them in order for numbers to exist. Consequently, I believe most if not all of math is discovered. The formalism for counting as describing a one-to-one correspondence to a (formally defined) finite set of numbers also exists independent of humans in the same way that the unit circle exists. The formalism for counting is of course not how biological machines such as we count; the formalism is just meant to intuitively express what we actually do when we count. Brent Meeker wrote: On 7/29/2010 3:28 PM, Mark Buda wrote: Quantum mechanics suggests maybe not. If there were no conscious observers to collapse the wave function of the universe after the big bang, then what, pray tell, would constitute an atom that might be counted? This assumes that conscious observers are necessary to collapse the wave function, of course. -- Mark Buda her...@acm.org mailto:her...@acm.org I get my monkeys for nothing and my chimps for free. On Jul 29, 2010 2:01 PM, Brian Tenneson tenn...@gmail.com wrote: Numbers existed before people on this rock began to understand them. If not number of atoms in the universe, then the number of cells in organisms one day prior to 10,000 years ago. or anything really, that had the potential to be counted, one day prior to 10,000 years ago. I don't think the existence of some number of distinct things is the same as the existence of numbers. Numbers are defined by order and successor - neither of which are present or implicit in a mere collection of atoms or anything else. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: numbers?
As a corollary to some of Tegmark's theory I believe it will be possible to prove that the level 4 multiverse is accounted for by a mathematical structure.. It's a project I've been working on which assumes that the reality hypothesis implies the mathematical universe hypothesis. Bruno Marchal wrote: ... and if you believe that the universe can be accounted for by a some consistent mathematical structure. Which is an open problem. Assuming mechanism, physical universes have no real existence at all, except as first person sharable experience by machines (mathematical digital machines). -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
