Re: An invisible fuzzy amoral mindless blob, aka God
On 2016-12-28 23:56, John Mikes wrote: I do not intend to participate in the discussion of this topic fpr more than one reason: 1. I am agnostic, so I just DO NOT KNOW what (who?) that "GOD" may be. *You just have to ask God what she is. Then she will answer. But it may take two years to get the full answer.* 1,A: is God a PERSON? (Or: many persons?) *Yes, God is a person. In the same way as your own personality is build up by trillions of brain cells, then Gods personality is build up by billions of human beeings.* 1,C Did He/She/It originate the World? (what draws the question: How was God originated?) *No, she did not originate the world. She is a result of the natural selection.* 3. A am also ignorant about my (or anyone else's) Subconscious. Have you ever M E T yours? I figure it must be something limitless of which we fathom only a bit. Or is all t his rather fitting the Superconscious? we have some idea about our 'conscious'? *I have talked with my subconscious. I do it every time I pray. And sometimes my subconscious answer me. And sometimes my subconscious talks directly to me, she reminds me when I have forgotten something.* 4. An immortal person? Cf. Wagner's Gotterdammerung. *No, God is not immortal. But God will live much longer than a human being. God will *live *as long as the mankind exists.* 5. "Supernatural powers"? did you ever define the "natural ones" (beyond our ever changing concept of a system of our "physical" explanations? *No, God have no supernatural powers. God can only do what a human being can do.* John M -- Torgny -- 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.
Re: An invisible fuzzy amoral mindless blob, aka God
On 2016-12-26 10:52, Stathis Papaioannou wrote: On 25 December 2016 at 19:40, Torgny Tholerus <mailto:tor...@dsv.su.se>> wrote: I have found that God is exactly the same as my subconscious. And my subconscious is connected to other peoples subconsciouses. When I pray, I talk to my own subconscious. Then my subconscious talks to other peoples subconsciouses. Then one persons subconscious is affecting this persons behavior, so that I get answer to my prayer. How do you know that your subconscious talks to and affects other people? -- Stathis Papaioannou = I have had several experiences of it. Not so often, only when needed. These experiences can be explained away as coincidence and chance. But it happens too often to be mere coincidence. -- Torgny -- 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.
Re: An invisible fuzzy amoral mindless blob, aka God
On 2016-12-26 00:09, Brent Meeker wrote: On 12/25/2016 12:40 AM, Torgny Tholerus wrote: I have found that God is exactly the same as my subconscious. And my subconscious is connected to other peoples subconsciouses. When I pray, I talk to my own subconscious. Then my subconscious talks to other peoples subconsciouses. Then one persons subconscious is affecting this persons behavior, so that I get answer to my prayer. Psychiatrist: "Look--how do you know you're God?" Lord Gurney: "Well, every time I pray, I find that I'm talking to myself." --- Peter Barnes, "The Ruling Class" Yes, this is true. I have a part of God inside me. So I can say that I am (a part of) God. The whole of God consists of the sum of all the subconsciouses of all human beeings. Nothing more and nothing less than that. -- Torgny -- 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.
Re: An invisible fuzzy amoral mindless blob, aka God
2016-12-25 03:07 skrev John Clark: On Wed, Dec 14, 2016 at 9:56 AM, Bruno Marchal wrote: >> usage says that "God" means an immortal person with supernatural power who wants, and deserves, to be worshipped. > That's the Christian use . Why do atheists insist so much we use the christian notion, Well... at least atheists have some notation in mind when they use the word . It may not exist but at least "an immortal person with supernatural power who wants and deserves to be worshiped" means something. Theists, at least most of those on this list, quite literally don't know what they're talking about when they talk about "God". As near as I can tell to them the word "God" means an invisible fuzzy amoral blob that does nothing and knows nothing and thinks about nothing that we can not effect and that does not effect our lives. Why even invent a word for a concept as useless as that? I have found that God is exactly the same as my subconscious. And my subconscious is connected to other peoples subconsciouses. When I pray, I talk to my own subconscious. Then my subconscious talks to other peoples subconsciouses. Then one persons subconscious is affecting this persons behavior, so that I get answer to my prayer. -- Torgny -- 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.
Re: MGA revisited paper + supervenience
LizR skrev 2014-10-01 01:44: On 1 October 2014 04:23, Platonist Guitar Cowboy mailto:multiplecit...@gmail.com>> wrote: Ultrafinitism then: "set of all numbers is finite" and whatever weird logic they need to have numbers obey some weirder upper limit, and I heard they issue fines and tickets for anybody who states a bigger number. Like "the biggest number used by ultra finitists + 1" ... oops. The biggest number + 1 is a number that does not belong to the set of all numbers... -- 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: Everything List Survey
Stathis Papaioannou skrev: 2010/1/14 Stathis Papaioannou : Interesting so far: - people are about evenly divided on the question of whether computers can be conscious - no-one really knows what to make of OM's - more people believe cats are conscious than dogs Oh, and one person does not believe that they are conscious! Come on, who's the zombie? It's me. (The question on whether computers can be conscious, should have three alternatives: 1) Both computers and humans can be conscious. 2) Humans, but not computers can be conscious. 3) Neither humans nor computers can be conscious. (The alternative: Computers, but not humans can be conscious, is not needed...)) -- Torgny Tholerus -- 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: Dreaming On
Bruno Marchal skrev: > > Then it is not "RITSIAR" in the sense of the discussion with David. > Real in the sense that "I" am real. is ambiguous. > Either the "I" refers to my first person, and then I have ontological > certainty. > As I said on FOR, I can conceive that I wake up and realize that > quark, planet, galaxies and even my body were not real. I cannot > conceive that I wake up and realize that my consciousness is not real. > When I woke up this morning, I realized that my consciousness was not real... -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: Dreams and Machines
Bruno Marchal skrev: > > On 22 Jul 2009, at 14:12, Torgny Tholerus wrote: >> What do you think about the GoL-universes? You can look at some of >> those at http://www.bitstorm.org/gameoflife/ . If you have an initial >> condition and you have an unlimited board, then you can compute what >> will happen in the future in that universe. > > What is an unlimited board for an ultrafinitist. (Ok, that was perhaps > easy). An unlimited board is a board that is "enough" big. How far away you look, you will see no border of the board. > > >> These universes are >> universes with a two-dimensional space and a one-dimensional time. >> These GoL-universes are mathematial universes. They have an initial >> condition and a mathematical rule that defines how that universe will >> look like in the next moment, and the next next moment, and so on. >> >> Does this make sense for you? > > Those are not universes, but computational histories. What is wrong with computational histories? If you can explain everything in our universe with a computational history, why do you need anything more? > Assuming comp there is a first person indeterminacy, which makes > "physical appearances" or "physical universe" emerging from the > infinity of such computational and universal computation. I suggest > you read the UDA papers. I guess you were not yet on the list when I > explained why "Wolfram" sort of computational physics, based on > cellular automata, does not work. Yes, I was not on the list then. And all the time when I have been on the list, I have wondered what COMP is? > And quantum mechanics confirms this by giving indirect but strong > evidences on the existence of many statistically interfering computations. I do not believe in that quantum mechanics implies statistically interfering computations. I believe that quantum mechanics is deterministic. Microcosmos looks indeterministic just because we do not know yet what is happening at the Planck scale. You must think of that a quark is 100.000.000.000.000.000.000 times bigger than the Planch length, so many things can happen in that interval. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: Dreams and Machines
Bruno Marchal skrev: > Le 22-juil.-09, à 10:27, Torgny Tholerus a écrit : > > > Rex Allen skrev: > > Brent: > > Do these mathematical objects "really" exist? I'd say they > have > logico-mathematical existence, not the same existence as > tables and > chairs, or quarks and electrons. > > > So which kind of existence do you believe is more fundamental? > Which > is primary? Logico-mathematical existence, or quark existence? Or > are they separate but equal kinds of existence? > > > > The most general form of existence is: All mathematical possible > universes exist. Our universe is one of those mathematical possible > existing universes. > > > This is non sense. Proof: see UDA. Or interrupt me when you have an > objection in the current explanation. I have explained this many > times, but the notion of universe or mathematical universe just makes > no sense. The notion of "our universe" is too far ambiguous for just > making even non sense. What do you think about the GoL-universes? You can look at some of those at http://www.bitstorm.org/gameoflife/ . If you have an initial condition and you have an unlimited board, then you can compute what will happen in the future in that universe. These universes are universes with a two-dimensional space and a one-dimensional time. These GoL-universes are mathematial universes. They have an initial condition and a mathematical rule that defines how that universe will look like in the next moment, and the next next moment, and so on. Does this make sense for you? Now look at a mathematical universe that have somewhat more complicated rules, and that mathematical universe looks exactly the same as our universe. The same things happens as in our universe, and there is an object there that is calling himself Bruno, and there is another object calling himself Torgny... (By the way, I think it is better to use the notion "010110" for strings. Then B_1 will be {"0", "1"}, and B_0 will be {""}. Then it is more clear that B_0 contains one element.) -- Torgny --~--~-~--~~~---~--~~ 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: Dreams and Machines
Rex Allen skrev: > Brent, > > So my first draft addressed many of the points you made, but it that > email got too big and sprawling I thought. > > So I've focused on what seems to me like the key passage from your > post. If you think there was some other point that I should have > addressed, let me know. > > So, key passage: > > >> Do these mathematical objects "really" exist? I'd say they have >> logico-mathematical existence, not the same existence as tables and >> chairs, or quarks and electrons. >> > > So which kind of existence do you believe is more fundamental? Which > is primary? Logico-mathematical existence, or quark existence? Or > are they separate but equal kinds of existence? > > The most general form of existence is: All mathematical possible universes exist. Our universe is one of those mathematical possible existing universes. The inside of a specific universe constitutes an other form of existence. In a specific universe there are objects inside that universe. In the Game of Life universe, you have the Glider object, the Glider gun object, the Exploder object, the Tumbler object, etc. In a specific instance of the GoL-universe, there exist some objects and some objects does not exist there. In our own universe, there exist tables and chairs and quarks and electrons. This is the specific form of existence. But the mathematical objects does not exist in our universe, in this form of existence. You can not find the "17" object anywhere inside our universe. Then we have the general form of existence saying that our universe exists because it is a mathematical possibility. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Bruno Marchal skrev: > Torgny, > > I agree with Quentin. > You are just showing that the naive notion of set is inconsistent. > Cantor already knew that, and this is exactly what forced people to > develop axiomatic theories. So depending on which theory of set you > will use, you can or cannot have an universal set (a set of all sets). > In typical theories, like ZF and VBG (von Neuman Bernay Gödel) the > collection of all sets is not a set. It is not the naive notion of set that is inconsistent. It is the naive *handling* of sets that is inconsistent. This problem has two possible solutions. One possible solution is to deny that it is possible to create the set of all sets. This solution is chosen by ZF and VBG. The second possible solution is to be very careful of the domain of the All quantificator. You are not allowed to substitute an object that is not included in the domain of the quantificator. It is this second solution that I have chosen. What is illegal in the two deductions below, is the substitutions. Because the sets A and B do not belong to the domain of the All quantificator. You can define "existence" by saying that only that which is incuded in the domain of the All quantificator exists. In that case it is correct to say that the sets A and B do not exist, because they are not included in the domain. But I think this is a too restrictive definition of existence. It is fully possible to talk about the set of all sets. But you must then be *very* careful with what you do with that set. That set is a set, but it does not belong to the set of all sets, it does not belong to itself. It is also a matter of definition; if you define "set" as the same as "belonging to the set of all sets", then the set of all sets is not a set. This is a matter of taste. You can choose whatever you like, but you must be aware of your choice. But if you restrict yourself too much, then your life will be poorer... > In NF, some have developed > structure with universal sets, and thus universe containing > themselves. Abram is interested in such universal sets. And, you can > interpret the UD, or the Mandelbrot set as (simple) model for such > type of structure. > > Your argument did not show at all that the set of natural numbers > leads to any trouble. Indeed, finitism can be seen as a move toward > that set, viewed as an everything, potentially infinite frame (for > math, or beyond math, like it happens with comp). > > The problem of naming (or given a mathematical status) to "all sets" > is akin to the problem of giving a name to God. As Cantor was > completely aware of. We are confused on this since we exist. But the > natural numbers, have never leads to any confusion, despite we cannot > define them. > The "proof" that there is no biggest natural number is illegal, because you are there doing an illegal deduction, you are there doing an illegal substitution, just the same as in the deductions below with the sets A and B. You are there substituting an object that is not part of the domain of the All quatificator. -- Torgny Tholerus > You argument against the infinity of natural numbers is not valid. You > cannot throw out this "little infinite" by pointing on the problem > that some "terribly big infinite", like the "set" of all sets, leads > to trouble. That would be like saying that we have to abandon all > drugs because the heroin is very dangerous. > It is just non valid. > > Normally, later I will show a series of argument very close to > Russell paradoxes, and which will yield, in the comp frame, > interesting constraints on what computations are and are not. > > Bruno > > > On 13 Jun 2009, at 13:26, Torgny Tholerus wrote: > > >> Quentin Anciaux skrev: >> >>> 2009/6/13 Torgny Tholerus : >>> >>> >>>> What do you think about the following deduction? Is it legal or >>>> illegal? >>>> --- >>>> Define the set A of all sets as: >>>> >>>> For all x holds that x belongs to A if and only if x is a set. >>>> >>>> This is an general rule saying that for some particular symbol- >>>> string x >>>> you can always tell if x belongs to A or not. Most humans who think >>>> about mathematics can understand this rule-based definition. This >>>> rule >>>> holds for all and every object, without exceptions. >>>> >>>> So this rule also holds for A itself. We can always substitute A >>>> for >>>> x. Then we will get: >>>> >>
Re: The seven step-Mathematical preliminaries
Quentin Anciaux skrev: > Well it is illegal regarding the rules meaning with these rules set B > does not exist as defined. > What is it that makes set A to exist, and set B not to exist? What is the (important) differences between the definition of set A and the definition of set B? In both cases you are defining a set by giving a property that all members of the set must fulfill. Why is the deduction legal for set A, but illegal for set B? There is the same type of deduction in both places, you are just making a substitution for the all quantificator in both cases. -- Torgny Tholerus > > 2009/6/13 Torgny Tholerus : > >> Quentin Anciaux skrev: >> >>> 2009/6/13 Torgny Tholerus : >>> >>> >>>> What do you think about the following deduction? Is it legal or illegal? >>>> --- >>>> Define the set A of all sets as: >>>> >>>> For all x holds that x belongs to A if and only if x is a set. >>>> >>>> This is an general rule saying that for some particular symbol-string x >>>> you can always tell if x belongs to A or not. Most humans who think >>>> about mathematics can understand this rule-based definition. This rule >>>> holds for all and every object, without exceptions. >>>> >>>> So this rule also holds for A itself. We can always substitute A for >>>> x. Then we will get: >>>> >>>> A belongs to A if and only if A is a set. >>>> >>>> And we know that A is a set. So from this we can deduce: >>>> >>>> A beongs to A. >>>> --- >>>> Quentin, what do you think? Is this deduction legal or illegal? >>>> >>>> >>> It depends if you allow a set to be part of itselft or not. >>> >>> If you accept, that a set can be part of itself, it makes your >>> deduction legal regarding the rules. >>> >> OK, if we accept that a set can be part of itself, what do you think >> about the following deduction? Is it legal or illegal? >> >> --- >> Define the set B of all sets that do not belong to itself as: >> >> For all x holds that x belongs to B if and only if x does not belong to x. >> >> This is an general rule saying that for some particular symbol-string x >> you can always tell if x belongs to B or not. Most humans who think >> about mathematics can understand this rule-based definition. This rule >> holds for all and every object, without exceptions. >> >> So this rule also holds for B itself. We can always substitute B for >> x. Then we will get: >> >> B belongs to B if and only if B does not belong to B. >> --- >> Quentin, what do you think? Is this deduction legal or illegal? >> >> >> -- >> Torgny Tholerus >> >> > > > > --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Quentin Anciaux skrev: > 2009/6/13 Torgny Tholerus : > >> What do you think about the following deduction? Is it legal or illegal? >> --- >> Define the set A of all sets as: >> >> For all x holds that x belongs to A if and only if x is a set. >> >> This is an general rule saying that for some particular symbol-string x >> you can always tell if x belongs to A or not. Most humans who think >> about mathematics can understand this rule-based definition. This rule >> holds for all and every object, without exceptions. >> >> So this rule also holds for A itself. We can always substitute A for >> x. Then we will get: >> >> A belongs to A if and only if A is a set. >> >> And we know that A is a set. So from this we can deduce: >> >> A beongs to A. >> --- >> Quentin, what do you think? Is this deduction legal or illegal? >> > > It depends if you allow a set to be part of itselft or not. > > If you accept, that a set can be part of itself, it makes your > deduction legal regarding the rules. OK, if we accept that a set can be part of itself, what do you think about the following deduction? Is it legal or illegal? --- Define the set B of all sets that do not belong to itself as: For all x holds that x belongs to B if and only if x does not belong to x. This is an general rule saying that for some particular symbol-string x you can always tell if x belongs to B or not. Most humans who think about mathematics can understand this rule-based definition. This rule holds for all and every object, without exceptions. So this rule also holds for B itself. We can always substitute B for x. Then we will get: B belongs to B if and only if B does not belong to B. --- Quentin, what do you think? Is this deduction legal or illegal? -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Jesse Mazer skrev: > > > Date: Fri, 12 Jun 2009 18:40:14 +0200 > > From: tor...@dsv.su.se > > To: everything-list@googlegroups.com > > Subject: Re: The seven step-Mathematical preliminaries > > > > It is, as I said above, for me and all other humans to understand what > > you are talking about. It is also for to be able to decide what > > deductions or conclusions or proofs that are legal or illegal. > > Well, most humans who think about mathematics can understand > rule-based definitions like "0 is a whole number, and N is a whole > number if it's equal to some other whole number plus one"--you seem to > be the lone exception. > > As for being "able to decide what deductions or conclusions or proofs > that are legal or illegal", how exactly would writing out all the > members of the "universe" solve that? For example, I actually write > out all the numbers from 0 to 1,038,712 and say that they are members > of the "universe" I want to talk about. But if I write out some axioms > used to prove various propositions about these numbers, they are still > going to be in the form of general *rules* with abstract variables > like x and y (where these variables stand for arbitrary numbers in the > set), no? Or do you also insist that instead of writing axioms and > making deductions, we also spell out in advance every proposition that > shall be deemed true? In that case there is no room at all for > mathematicians to make "deductions" or write "proofs", all of math > would just consist of looking at the pre-established list of true > propositions and checking if the proposition in question is on there. What do you think about the following deduction? Is it legal or illegal? --- Define the set A of all sets as: For all x holds that x belongs to A if and only if x is a set. This is an general rule saying that for some particular symbol-string x you can always tell if x belongs to A or not. Most humans who think about mathematics can understand this rule-based definition. This rule holds for all and every object, without exceptions. So this rule also holds for A itself. We can always substitute A for x. Then we will get: A belongs to A if and only if A is a set. And we know that A is a set. So from this we can deduce: A beongs to A. --- Quentin, what do you think? Is this deduction legal or illegal? -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Jesse Mazer skrev: > > > Date: Wed, 10 Jun 2009 09:18:10 +0200 > > From: tor...@dsv.su.se > > To: everything-list@googlegroups.com > > Subject: Re: The seven step-Mathematical preliminaries > > > > Jesse Mazer skrev: > >> > >>> Date: Tue, 9 Jun 2009 18:38:23 +0200 > >>> From: tor...@dsv.su.se > >>> To: everything-list@googlegroups.com > >>> Subject: Re: The seven step-Mathematical preliminaries > >>> > >>> For you to be able to use the word "all", you must define the "domain" > >>> of that word. If you do not define the domain, then it will be > >>> impossible for me and all other humans to understand what you are > >>> talking about. > >> > >> OK, so how do you say I should define this type of "universe"? Unless > >> you are demanding that I actually give you a list which spells out > >> every symbol-string that qualifies as a member, can't I simply provide > >> an abstract *rule* that would allow someone to determine in principle > >> if a particular symbol-string they are given qualifies? Or do you have > >> a third alternative besides spelling out every member or giving an > >> abstract rule? > > > > You have to spell out every member. > > Where does this "have to" come from? Again, is it something you have a > philosophical or logical definition for, or is it just your aesthetic > preference? It is, as I said above, for me and all other humans to understand what you are talking about. It is also for to be able to decide what deductions or conclusions or proofs that are legal or illegal. It has nothing to do with my aesthetic preference. > > > Because in a *rule* you are > > (implicitely) using this type of "universe", and you will then get a > > circular definition. > > A good rule (as opposed to a 'bad' rule like 'the set of all sets that > do not contain themselves') gives a perfectly well-defined criteria > for what is contained in the universe, such that no one will ever have > cause to be unsure about whether some particular symbol-string they're > given at belongs in this universe. It's only "circular" if you say in > advance that there is something problematic about rules which define > infinite universes, but again this just seems like your aesthetic > preference and not something you have given any philosophical/logical > justification for. What do you mean by "some particular symbol-string"? I suppose that you mean by this is: If you take any particular symbol-string from this universe, then no one will ever have cause to be unsure about whether this symbol-string belongs in this universe. So you are defining "this universe" by supposing that you have "this universe" to start with. Is that not a typical circular definition? -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Jesse Mazer skrev: > > > > Date: Tue, 9 Jun 2009 18:38:23 +0200 > > From: tor...@dsv.su.se > > To: everything-list@googlegroups.com > > Subject: Re: The seven step-Mathematical preliminaries > > > > For you to be able to use the word "all", you must define the "domain" > > of that word. If you do not define the domain, then it will be > > impossible for me and all other humans to understand what you are > > talking about. > > OK, so how do you say I should define this type of "universe"? Unless > you are demanding that I actually give you a list which spells out > every symbol-string that qualifies as a member, can't I simply provide > an abstract *rule* that would allow someone to determine in principle > if a particular symbol-string they are given qualifies? Or do you have > a third alternative besides spelling out every member or giving an > abstract rule? You have to spell out every member. Because in a *rule* you are (implicitely) using this type of "universe", and you will then get a circular definition. When you say that *every* number have a successor, you are presupposing that you already know what *every* means. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Jesse Mazer skrev: > > > > Date: Sat, 6 Jun 2009 21:17:03 +0200 > > From: tor...@dsv.su.se > > To: everything-list@googlegroups.com > > Subject: Re: The seven step-Mathematical preliminaries > > > > My philosophical argument is about the mening of the word "all". To be > > able to use that word, you must associate it with a value set. > > What's a "value set"? And why do you say we "must" associate it in > this way? Do you have a philosophical argument for this "must", or is > it just an edict that reflects your personal aesthetic preferences? > > > Mostly that set is "all objects in the universe", and if you stay > inside the > > universe, there is no problems. > > *I* certainly don't define numbers in terms of any specific mapping > between numbers and objects in the universe, it seems like a rather > strange notion--shall we have arguments over whether the number 113485 > should be associated with this specific shoelace or this specific > kangaroo? When I talk about "universe" here, I do not mean our physical universe. What I mean is something that can be called "everything". It includes all objects in our physical universe, as well as all symbols and all words and all numbers and all sets and all other universes. It includes everything you can use the word "all" about. For you to be able to use the word "all", you must define the "domain" of that word. If you do not define the domain, then it will be impossible for me and all other humans to understand what you are talking about. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Jesse Mazer skrev: > > > > Date: Sat, 6 Jun 2009 16:48:21 +0200 > > From: tor...@dsv.su.se > > To: everything-list@googlegroups.com > > Subject: Re: The seven step-Mathematical preliminaries > > > > Jesse Mazer skrev: > >> > >> Here you're just contradicting yourself. If you say BIGGEST+1 "is then > >> a natural number", that just proves that the set N was not in fact the > >> set "of all natural numbers". The alternative would be to say > >> BIGGEST+1 is *not* a natural number, but then you need to provide a > >> definition of "natural number" that would explain why this is the case. > > > > It depends upon how you define "natural number". If you define it by: n > > is a natural number if and only if n belongs to N, the set of all > > natural numbers, then of course BIGGEST+1 is *not* a natural number. In > > that case you have to call BIGGEST+1 something else, maybe "unnatural > > number". > > OK, but then you need to define what you mean by "N, the set of all > natural numbers". Specifically you need to say what number is > "BIGGEST". Is it arbitrary? Can I set BIGGEST = 3, for example? Or do > you have some philosophical ideas related to what BIGGEST is, like the > number of particles in the universe or the largest number any human > can conceptualize? It is rather the last, the largest number any human can conceptualize. More natural numbers are not needed. > > Also, any comment on my point about there being an infinite number of > possible propositions about even a finite set, There is not an infinite number of possible proposition. You can only create a finite number of proposition with finite length during your lifetime. Just like the number of natural numbers are unlimited but finite, so are the possible propositions unlimited but finte. > or about my question about whether you have any philosophical/logical > argument for saying all sets must be finite, My philosophical argument is about the mening of the word "all". To be able to use that word, you must associate it with a value set. Mostly that set is "all objects in the universe", and if you stay inside the universe, there is no problems. But as soon you go outside universe, you must be carefull with what substitutions you do. If you have "all" quantified with all object inside the universe, you can not substitute it with an object outside the universe, because that object was not included in the original statement. > as opposed to it just being a sort of aesthetic preference on your > part? Do you think there is anything illogical or incoherent about > defining a set in terms of a rule that takes any input and decides > whether it's a member of the set or not, such that there may be no > upper limit on the number of possible inputs that the rule would > define as being members? (such as would be the case for the rule 'n is > a natural number if n=1 or if n is equal to some other natural number+1') In the last sentence you have an implicite "all": The full sentence would be: For all n in the universe hold that n is a natural number if n=1 or if n is equal to some other natural number+1. And you may now be able to understand, that if the number of objects in the universe is finite, then this sentence will just define a finite set. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Jesse Mazer skrev: > > > > Date: Fri, 5 Jun 2009 08:33:47 +0200 > > From: tor...@dsv.su.se > > To: everything-list@googlegroups.com > > Subject: Re: The seven step-Mathematical preliminaries > > > > > > Brian Tenneson skrev: > >> > >> How can BIGGEST+1 be a natural number but not belong to the set of all > >> natural numbers? > > > > One way to represent natural number as sets is: > > > > 0 = {} > > 1 = {0} = {{}} > > 2 = {0, 1} = 1 union {1} = {{}, {{}}} > > 3 = {0, 1, 2} = 2 union {2} = ... > > . . . > > n+1 = {0, 1, 2, ..., n} = n union {n} > > . . . > > > > Here you can then define that a is less then b if and only if a belongs > > to b. > > > > With this notation you get the set N of all natural numbers as {0, > 1, 2, > > ...}. But the remarkable thing is that N is exactly the same as > > BIGGEST+1. BIGGEST+1 is a set with the same structure as all the other > > natural numbers, so it is then a natural number. But BIGGEST+1 is not a > > member of N, the set of all natural numbers. > > Here you're just contradicting yourself. If you say BIGGEST+1 "is then > a natural number", that just proves that the set N was not in fact the > set "of all natural numbers". The alternative would be to say > BIGGEST+1 is *not* a natural number, but then you need to provide a > definition of "natural number" that would explain why this is the case. It depends upon how you define "natural number". If you define it by: n is a natural number if and only if n belongs to N, the set of all natural numbers, then of course BIGGEST+1 is *not* a natural number. In that case you have to call BIGGEST+1 something else, maybe "unnatural number". -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Kory Heath skrev: > On Jun 4, 2009, at 8:27 AM, Torgny Tholerus wrote: > >> How do you handle the Russell paradox with the set of all sets that >> does >> not contain itself? Does that set contain itself or not? >> >> My answer is that that set does not contain itself, because no set can >> contain itself. So the set of all sets that does not contain >> itself, is >> the same as the set of all sets. And that set does not contain >> itself. >> This set is a set, but it does not contain itself. It is exactly the >> same with the natural numbers, BIGGEST+1 is a natural number, but it >> does not belong to the set of all natural numbers. The set of all >> sets >> is a set, but it does not belong to the set of all sets. >> > > So you're saying that the set of all sets doesn't contain all sets. > How is that any less paradoxical than the Russell paradox you're > trying to avoid? > The secret is the little word "all". To be able to use that word, you have to define it. You can define it by saying: "By 'all sets' I mean that set and that set and that set and ...". When you have made that definition, you are then able to create a new set, the set of all sets. But you must be carefull with what you do with that set. That set does not contain itself, because it was not included in your definition of "all sets". If you call the set of all sets for A, then you have: For all x such that x is a set, then x belongs to A. A is a set. But it is illegal to substitute A for x, so you can not deduce: A is a set, then A belongs to A. This deductuion is illegal, because A is not included in the definition of "all x". -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Brian Tenneson skrev: > > > On Thu, Jun 4, 2009 at 8:27 AM, Torgny Tholerus <mailto:tor...@dsv.su.se>> wrote: > > > Brian Tenneson skrev: > > > > > > Torgny Tholerus wrote: > >> It is impossible to create a set where the successor of every > element is > >> inside the set, there must always be an element where the > successor of > >> that element is outside the set. > >> > > I disagree. Can you prove this? > > Once again, I think the debate ultimately is about whether or not to > > adopt the axiom of infinity. > > I think everyone can agree without that axiom, you cannot "build" or > > "construct" an infinite set. > > There's nothing right or wrong with adopting any axioms. What > results > > is either interesting or not, relevant or not. > > How do you handle the Russell paradox with the set of all sets > that does > not contain itself? Does that set contain itself or not? > > > If we're talking about ZFC set theory, then the axiom of foundation > prohibits sets from being elements of themselves. > I think we agree that in ZFC, there is no set of all sets. But there is a set of all sets. You can construct it by taking all sets, and from them doing a new set, the set of all sets. But note, this set will not contain itself, because that set did not exist before. > > > > > My answer is that that set does not contain itself, because no set can > contain itself. So the set of all sets that does not contain > itself, is > the same as the set of all sets. And that set does not contain > itself. > This set is a set, but it does not contain itself. It is exactly the > same with the natural numbers, *BIGGEST+1 is a natural number, but it > does not belong to the set of all natural numbers. *The set of > all sets > is a set, but it does not belong to the set of all sets. > > How can BIGGEST+1 be a natural number but not belong to the set of all > natural numbers? One way to represent natural number as sets is: 0 = {} 1 = {0} = {{}} 2 = {0, 1} = 1 union {1} = {{}, {{}}} 3 = {0, 1, 2} = 2 union {2} = ... . . . n+1 = {0, 1, 2, ..., n} = n union {n} . . . Here you can then define that a is less then b if and only if a belongs to b. With this notation you get the set N of all natural numbers as {0, 1, 2, ...}. But the remarkable thing is that N is exactly the same as BIGGEST+1. BIGGEST+1 is a set with the same structure as all the other natural numbers, so it is then a natural number. But BIGGEST+1 is not a member of N, the set of all natural numbers. BIGGEST+1 is bigger than all natural numbers, because all natural numbers belongs to BIGGEST+1. > > > > > > >> What the largest number is depends on how you define "natural > number". > >> One possible definition is that N contains all explicit numbers > >> expressed by a human being, or will be expressed by a human > being in the > >> future. Amongst all those explicit numbers there will be one > that is > >> the largest. But this "largest number" is not an explicit number. > >> > >> > > This raises a deeper question which is this: is mathematics > dependent > > on humanity or is mathematics independent of humanity? > > I wonder what would happen to that human being who finally expresses > > the largest number in the future. What happens to him when he wakes > > up the next day and considers adding one to yesterday's number? > > This is no problem. If he adds one to the explicit number he > expressed > yesterday, then this new number is an explicit number, and the number > expressed yesterday was not the largest number. Both 17 and 17+1 are > explicit numbers. > > This goes back to my earlier comment that it's hard for me to believe > that the following statement is false: > every natural number has a natural number successor > We -must- be talking about different things, then, when we use the > phrase natural number. > I can't say your definition of natural numbers is right and mine is > wrong, or vice versa. I do wonder what advantages there are to the > ultrafinitist approach compared to the math I'm familiar with. The biggest advantage is that everything is finite, and you can then really know that the mathematical theory you get is consistent, it does not contain any contradictions. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Brian Tenneson skrev: > > > Torgny Tholerus wrote: >> It is impossible to create a set where the successor of every element is >> inside the set, there must always be an element where the successor of >> that element is outside the set. >> > I disagree. Can you prove this? > Once again, I think the debate ultimately is about whether or not to > adopt the axiom of infinity. > I think everyone can agree without that axiom, you cannot "build" or > "construct" an infinite set. > There's nothing right or wrong with adopting any axioms. What results > is either interesting or not, relevant or not. How do you handle the Russell paradox with the set of all sets that does not contain itself? Does that set contain itself or not? My answer is that that set does not contain itself, because no set can contain itself. So the set of all sets that does not contain itself, is the same as the set of all sets. And that set does not contain itself. This set is a set, but it does not contain itself. It is exactly the same with the natural numbers, BIGGEST+1 is a natural number, but it does not belong to the set of all natural numbers. The set of all sets is a set, but it does not belong to the set of all sets. > >> What the largest number is depends on how you define "natural number". >> One possible definition is that N contains all explicit numbers >> expressed by a human being, or will be expressed by a human being in the >> future. Amongst all those explicit numbers there will be one that is >> the largest. But this "largest number" is not an explicit number. >> >> > This raises a deeper question which is this: is mathematics dependent > on humanity or is mathematics independent of humanity? > I wonder what would happen to that human being who finally expresses > the largest number in the future. What happens to him when he wakes > up the next day and considers adding one to yesterday's number? This is no problem. If he adds one to the explicit number he expressed yesterday, then this new number is an explicit number, and the number expressed yesterday was not the largest number. Both 17 and 17+1 are explicit numbers. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Brian Tenneson skrev: > This is a denial of the axiom of infinity. I think a foundational set > theorist might agree that it is impossible to -construct- an infinite > set from scratch which is why they use the axiom of infinity. > People are free to deny axioms, of course, though the result will not > be like ZFC set theory. The denial of axiom of foundation is one I've > come across; I've never met anyone who denies the axiom of infinity. > > For me it is strange that the following statement is false: every > natural number has a natural number successor. To me it seems quite > arbitrary for the ultrafinitist's statement: every natural number has > a natural number successor UNTIL we reach some natural number which > does not have a natural number successor. I'm left wondering what the > largest ultrafinist's number is. It is impossible to lock a box, and quickly throw the key inside the box before you lock it. It is impossible to create a set and put the set itself inside the set, i.e. no set can contain itself. It is impossible to create a set where the successor of every element is inside the set, there must always be an element where the successor of that element is outside the set. What the largest number is depends on how you define "natural number". One possible definition is that N contains all explicit numbers expressed by a human being, or will be expressed by a human being in the future. Amongst all those explicit numbers there will be one that is the largest. But this "largest number" is not an explicit number. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Quentin Anciaux skrev: > If you are ultrafinitist then by definition the set N does not > exist... (nor any infinite set countably or not). > All sets are finite. It it (logically) impossible to construct an infinite set. You can construct the set N of all natural numbers. But that set must be finite. What the set N contains depends on how you have defined "natural number". > If you pose the assumption of a biggest number for N, you come to a > contradiction because you use the successor operation which cannot > admit a biggest number.(because N is well ordered any successor is > strictly bigger and the successor operation is always valid *by > definition of the operation*) > You have to define the successor operation. And to do that you have to define the definition set for that operation. So first you have to define the set N of natural numbers. And from that you can define the successor operator. The value set of the successor operator will be a new set, that contains one more element than the set N of natural numbers. This new element is BIGGEST+1, that is strictly bigger than all natural numbers. -- Torgny Tholerus > So either the set N does not exists in which case it makes no sense to > talk about the biggest number in N, or the set N does indeed exists > and it makes no sense to talk about the biggest number in N (while it > makes sense to talk about a number which is strictly bigger than any > natural number). > > To come back to the proof by contradiction you gave, the assumption > (2) which is that BIGGEST+1 is in N, is completely defined by the mere > existence of BIGGEST. If BIGGEST exists and well defined it entails > that BIGGEST+1 is not in N (but this invalidate the successor > operation and hence the mere existence of N). If BIGGEST in contrary > does not exist (as such, means it is not the biggest) then BIGGEST+1 > is in N by definition of N. > > Regards, > Quentin > > --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Brian Tenneson skrev: > >> How do you know that there is no biggest number? Have you examined all >> the natural numbers? How do you prove that there is no biggest number? >> >> >> > In my opinion those are excellent questions. I will attempt to answer > them. The intended audience of my answer is everyone, so please forgive > me if I say something you already know. > > Firstly, no one has or can examine all the natural numbers. By that I > mean no human. Maybe there is an omniscient machine (or a "maximally > knowledgeable" in some paraconsistent way) who can examine all numbers > but that is definitely putting the cart before the horse. > > Secondly, the question boils down to a difference in philosophy: > mathematicians would say that it is not necessary to examine all natural > numbers. The mathematician would argue that it suffices to examine all > essential properties of natural numbers, rather than all natural numbers. > > There are a variety of equivalent ways to define a natural number but > the essential features of natural numbers are that > (a) there is an ordering on the set of natural numbers, a well > ordering. To say a set is well ordered entails that every =nonempty= > subset of it has a least element. > (b) the set of natural numbers has a least element (note that it is > customary to either say 0 is this least element or say 1 is this least > element--in some sense it does not matter what the starting point is) > (c) every natural number has a natural number successor. By successor > of a natural number, I mean anything for which the well ordering always > places the successor as larger than the predecessor. > > Then the set of natural numbers, N, is the set containing the least > element (0 or 1) and every successor of the least element, and only > successors of the least element. > > There is nothing wrong with a proof by contradiction but I think a > "forward" proof might just be more convincing. > > Consider the following statement: > Whenever S is a subset of N, S has a largest element if, and only if, > the complement of S has a least element. > > By complement of S, I mean the set of all elements of N that are not > elements of S. > > Before I give a longer argument, would you agree that statement is > true? One can actually be arbitrarily explicit: M is the largest > element of S if, and only if, the successor of M is the least element of > the compliment of S. > I do not agree that statement is true. Because if you call the Biggest natural number B, then you can describe N as = {1, 2, 3, ..., B}. If you take the complement of N you will get the empty set. This set have no least element, but still N has a biggest element. In your statement you are presupposing that N has no biggest element, and from that axiom you can trivially deduce that there is no biggest element. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Quentin Anciaux skrev: > 2009/6/3 Torgny Tholerus : > >> Bruno Marchal skrev: >> >>> On 02 Jun 2009, at 19:43, Torgny Tholerus wrote: >>> >>> >>> >>>> Bruno Marchal skrev: >>>> >>>> >>>>> 4) The set of all natural numbers. This set is hard to define, yet I >>>>> hope you agree we can describe it by the infinite quasi exhaustion by >>>>> {0, 1, 2, 3, ...}. >>>>> >>>>> >>>>> >>>> Let N be the biggest number in the set {0, 1, 2, 3, ...}. >>>> >>>> Exercise: does the number N+1 belongs to the set of natural numbers, >>>> that is does N+1 belongs to {0, 1, 2, 3, ...}? >>>> >>>> >>> Yes. N+1 belongs to {0, 1, 2, 3, ...}. >>> This follows from classical logic and the fact that the proposition "N >>> be the biggest number in the set {0, 1, 2, 3, ...}" is always false. >>> And false implies all propositions. >>> >>> >> No, you are wrong. The answer is No. >> >> Proof: >> >> Define "biggest number" as: >> >> a is the biggest number in the set S if and only if for every element e >> in S you have e < a or e = a. >> >> Now assume that N+1 belongs to the set of natural numbers. >> >> Then you have N+1 < N or N+1 = N. >> >> But this is a contradiction. So the assumption must be false. So we >> have proved that N+1 does not belongs to the set of natural numbers. >> > > Hi, > > No, what you've demonstrated is that there is no biggest number (you > falsified the hypothesis which is there exists a biggest number). You > did a "demonstration par l'absurde" (in french, don't know how it is > called in english). And you have shown a contradiction, which implies > that your assumption is wrong (there exists a biggest number), not > that this number is not in the set. > How do you know that there is no biggest number? Have you examined all the natural numbers? How do you prove that there is no biggest number? --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Bruno Marchal skrev: > On 02 Jun 2009, at 19:43, Torgny Tholerus wrote: > > >> Bruno Marchal skrev: >> >>> 4) The set of all natural numbers. This set is hard to define, yet I >>> hope you agree we can describe it by the infinite quasi exhaustion by >>> {0, 1, 2, 3, ...}. >>> >>> >> Let N be the biggest number in the set {0, 1, 2, 3, ...}. >> >> Exercise: does the number N+1 belongs to the set of natural numbers, >> that is does N+1 belongs to {0, 1, 2, 3, ...}? >> > > > Yes. N+1 belongs to {0, 1, 2, 3, ...}. > This follows from classical logic and the fact that the proposition "N > be the biggest number in the set {0, 1, 2, 3, ...}" is always false. > And false implies all propositions. > No, you are wrong. The answer is No. Proof: Define "biggest number" as: a is the biggest number in the set S if and only if for every element e in S you have e < a or e = a. Now assume that N+1 belongs to the set of natural numbers. Then you have N+1 < N or N+1 = N. But this is a contradiction. So the assumption must be false. So we have proved that N+1 does not belongs to the set of natural numbers. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: The seven step-Mathematical preliminaries
Bruno Marchal skrev: > 4) The set of all natural numbers. This set is hard to define, yet I > hope you agree we can describe it by the infinite quasi exhaustion by > {0, 1, 2, 3, ...}. > Let N be the biggest number in the set {0, 1, 2, 3, ...}. Exercise: does the number N+1 belongs to the set of natural numbers, that is does N+1 belongs to {0, 1, 2, 3, ...}? -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: Consciousness is information?
Bruno Marchal skrev: > On 08 May 2009, at 19:15, Torgny Tholerus wrote: > >> Bruno Marchal skrev: >> >>> On 07 May 2009, at 18:29, Torgny Tholerus wrote: >>> >>>> Yes it is right. There is no infinity of natural numbers. But the >>>> natural numbers are UNLIMITED, you can construct as many natural >>>> numbers as you want. But how many numbers you construct, the >>>> number of >>>> numbers will always be finite. You can never construct an >>>> infinite number of >>>> natural numbers. >>>> >>> This is no more ultrafinitism. Just the usal finitism or >>> intuitionism. >>> It seems I recall you have had a stronger view on this point. >>> Ontologically I am neutral on this question. With comp I don't need >>> any actual infinity in the third person ontology. Infinities are not >>> avoidable from inside, at least when the inside view begins some >>> self-reflexion studies. >>> >> I was an ultrafinitist before, but I have changed my mind. >> > Excellent. The ability of changing its mind is a wonderful gift. > It was the Mathematical Universe that made me change my mind: Earlier I was convinced that the number of time steps in the universe was explicitely finite, that time goes in a circle. But the Mathematical Universe says that all mathematically possible universes exists. And it is possible to construct an EXPANDING universe, where you have a simple rule stating that the status of a space-time point is a combination of the statuses of the neighboring space-time points in the previous time point. In this universe there will never happen that the same space will be repeated at a later time, because the space consists of more space points at the later time. So in that case the universe is UNLIMITED, it will never stop, but continue for ever... -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: Consciousness is information?
Quentin Anciaux skrev: > Hi, > > 2009/5/8 Torgny Tholerus : > >> I was an ultrafinitist before, but I have changed my mind. Now I accept >> that you can say that the natural numbers are unlimited. I only deny >> actual infinities. The set of all natural numbers are always finite, >> but you can always increase the set of all natural number by adding more >> natural numbers to it. >> > Then it's not the set of *all* natural numbers. You do nothing by > adding a number... you don't create numbers by writing them down, you > don't invent properties about them, it's absurd... especially for a > zombie. > What do you mean by *all*? How do you define *all*? Can you give a definition that is not a circular definition? -- Torgny --~--~-~--~~~---~--~~ 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: Consciousness is information?
Bruno Marchal skrev: > On 07 May 2009, at 18:29, Torgny Tholerus wrote: > > >> Bruno Marchal skrev: >> >> >>> you are human, all right? >>> >> I look exactly as a human. When you look at me, you will not be >> able to know if I am a human or a zombie, because I behave exacly like a >> human. >> > So you believe that human are not zombie, and you agree that you are > not human. > Where do you come from? Vega? Centaur? > I come from Stockholm, Sweden. I was constructed by my parents. In reality I think that all humans are zombies, but because I am a polite person, I do not tell the other zombies that they are zombies. I do not want to hurt the other zombies by telling them the truth. >> Yes it is right. There is no infinity of natural numbers. But the >> natural numbers are UNLIMITED, you can construct as many natural >> numbers as you want. But how many numbers you construct, the number of >> numbers will always be finite. You can never construct an infinite number of >> natural numbers. >> > This is no more ultrafinitism. Just the usal finitism or intuitionism. > It seems I recall you have had a stronger view on this point. > Ontologically I am neutral on this question. With comp I don't need > any actual infinity in the third person ontology. Infinities are not > avoidable from inside, at least when the inside view begins some self- > reflexion studies. > I was an ultrafinitist before, but I have changed my mind. Now I accept that you can say that the natural numbers are unlimited. I only deny actual infinities. The set of all natural numbers are always finite, but you can always increase the set of all natural number by adding more natural numbers to it. >> An ordinary computer can never be arithmetically unsound. >> > ? (this seems to me plainly false, unless you mean "perfect" for > "ordinary". But computers can be as unsound as you and me. > There is no vaccine against soundness: all computers can be unsound > soo or later. there is no perfect computer. Most gods are no immune, > you have to postulate the big unnameable One and be very near to It, > to have some guaranty ... if any ... > OK, I misunderstood what you meant by "unsound", I thougth you meant something like "unlogical". But now I see that you mean something like "irrational". And I sure am irrational. > >> I do not want to be tortured, I behave as if I try to avoid that as >> strongly as I can. Because I behave in this way, I answer "no" to >> your question, because that answer will decrease the probability of you >> torturing me. >> > Do you realize that to defend your point you are always in the > obligation, when talking about any first person notion, like > consciousness, fear, desire, to add "I behave like ". But if you > can do that successfully you will make me doubt that you are a zombie. > Or ... do you think a zombie could eventually find a correct theory of > consciousness, so that he can correctly fake consciousness, and delude > the humans? > An intelligent zombie can correctly fake consciousness, and I am an intelligent zombie. >>> 3) Do you have any "sort-of" feeling, insight, dreams, impression, >>> sensations, subjective or mental life, ... ? >>> >> I behave as if I have "sort-of" feelings, I behave as if I have >> insights, I behave as if I have dreams, I behave as if I have >> impressions, I behave as if I have sensations, I behave as if I have a >> subjective or mental life, ... >> > As I said. But if you know that, I mean if you can behave like if you > were knowing that, it would mean that such words do have some meaning > for you. > > How can you know that you are not conscious? Why do you behave like if > you are conscious, and then "confess" to us that you are not. Why > don't you behave like if you were not conscious. Should not a zombie > defend the idea that he is conscious, if he behaves like if he was > conscious. If you ask me if I am conscious, I will reply "yes". But I am so intelligent that I can look at myself from the outside, and then I understand why I behave like I do. I can see that all my behaviour is explained by chemical reactions in my brain, and there is no more than that. So when I talk about myself on the meta level, then I can say that I have no consciousness. But most people are not intelligent enough to realize that. -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: Consciousness is information?
Bruno Marchal skrev: > On 06 May 2009, at 11:35, Torgny Tholerus wrote: > > >> Bruno Marchal skrev: >> >>> Someone unconscious cannot doubt either ... (A zombie can only fake >>> doubts) >>> >> Yes, you are right. I can only fake doubts... >> > > > > I suspect you are faking faking doubts, but of course I cannot provide > any argument. > I mean it is hard for me to believe that you are a zombie, still less > a zombie conscious to be a zombie! > I am a zombie that behaves AS IF it knows that it is a zombie. > > > > > > >> >>> When you say "yes" to the doctor, we >>> assume the "yes" is related to the belief that you will survive. This >>> means you believe that you will not loose consciousness, not become a >>> zombie, nor will you loose (by assumption) your own consciousness, by >>> becoming someone else you can't identify with. >>> >> I can say "yes" to the doctor, because it will not be any difference >> for me, I will still be a zombie afterwards... >> > > > > > I don't know if you do this to please me, but you illustrate quite > well the Löbian "consciousness" theory. > Indeed the theory says that "consciousness" can be very well > approximated logically by "consistency". > So a human (you are human, all right? I look exactly as a human. When you look at me, you will not be able to know if I am a human or a zombie, because I behave exacly like a human. > ) who says "I am a zombie", means > "I am not conscious", which can mean "I am not consistent". > By Gödel's second theorem, you remain consistent(*), but you loose > arithmetical soundness, which is quite coherent with your > ultrafinitism. If I remember well, you don't believe that there is an > infinity of natural numbers, right? > Yes it is right. There is no infinity of natural numbers. But the natural numbers are UNLIMITED, you can construct as many natural numbers as you want. But how many numbers you construct, the number of numbers will always be finite. You can never construct an infinite number of natural numbers. > We knew already you are not arithmetically sound. Nevertheless it is > amazing that you pretend that you are a zombie. This confirms, in the > lobian frame, that you are a zombie. I doubt all ultrafinitists are > zombie, though. > > It is coherent with what I tell you before: I don't think a real > ultrafinitist can know he/she is an ultrafinitist. No more than a > zombie can know he is a zombie, nor even give any meaning to a word > like "zombie". > > My diagnostic: you are a consistent, but arithmetically unsound, > Löbian machine. No problem. > An ordinary computer can never be arithmetically unsound. So I am not arithmetically unsound. I am build by a finite number of atoms, and the atoms are build by a finite number of elementary parts. (And these elementary parts are just finite mathematics...) > There are not many zombies around me, still fewer argue that they are > zombie, so I have some questions for you, if I may. > > 1) Do you still answer yes to the doctor if he proposes to substitute > your brain by a sponge? > If the sponge behaves exactly in the same way as my current brain, then it will be OK. > 2) Do humans have the right to torture zombie? > Does an ordinary computer have the "right" to do anything? I do not want to be tortured, I behave as if I try to avoid that as strongly as I can. Because I behave in this way, I answer "no" to your question, because that answer will decrease the probability of you torturing me. > 3) Do you have any "sort-of" feeling, insight, dreams, impression, > sensations, subjective or mental life, ... ? > I behave as if I have "sort-of" feelings, I behave as if I have insights, I behave as if I have dreams, I behave as if I have impressions, I behave as if I have sensations, I behave as if I have a subjective or mental life, ... > 4) Does the word "pain" have a meaning for you? In particular, what if > the doctor, who does not know that you are a zombie, proposes to you a > cheaper artificial brain, but warning you that it produces often > unpleasant hard migraine? Still saying yes? > No, I will say "no" in this case, because I avoid things that causes "pain". I have an "avoiding center" in my brain, and when this center in my brain is stimulated, then my behavior will be to avoid those things that causes this center to be stimulated. Stimulating this center will cause me to say: "I feel pain". -- Torgny Tholerus --~--~-~--~~~---~--~~ 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: Consciousness is information?
Bruno Marchal skrev: > > Something conscious cannot doubt about the existence of its > consciousness, I think, although it can doubt everything else it can > be conscious *about*. > It is the unprovable (but coverable) fixed point of Descartes > systematic doubting procedure (this fit well with the self-reference > logics, taking consciousness as consistency). > > Someone unconscious cannot doubt either ... (A zombie can only fake > doubts) Yes, you are right. I can only fake doubts... > > We live on the overlap of a subjective un-sharable certainty (the > basic first person knowledge) and an objective doubtful but sharable > possible reality (the third person belief). > > To keep 3-comp, and to abandon consciousness *is* the correct > materialist step, indeed. But you cannot keep 1-comp(*) then, because > it is defined > by reference to consciousness. When you say "yes" to the doctor, we > assume the "yes" is related to the belief that you will survive. This > means you believe that you will not loose consciousness, not become a > zombie, nor will you loose (by assumption) your own consciousness, by > becoming someone else you can't identify with. I can say "yes" to the doctor, because it will not be any difference for me, I will still be a zombie afterwards... -- Torgny Tholerus --~--~-~--~~~---~--~~ 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 methods for the discrete space-time.
Jason Resch skrev: > I am not sure how related this is to what you ask in your original > post, but as for a model (and candidate TOE) of physics which is > discrete, there is a theory known as Hiem Theory > ( http://en.wikipedia.org/wiki/Heim_Theory ) which posits there are > six discrete dimensions. Interestingly, the theory is able to predict > the masses of many subatomic particles entirely from some force > constants, something which even the standard model is unable to explain. I have now looked at Heim Theory, but it does not look enough serious to me. Every theory that compute the masses of the elementary particles from nothing, must be wrong. Because in different possible universa the masses of the elementary particles are different. Besides, the Heim Theory could not explain the quarks. But from the Heim Theory article I followed a link to "Difference operator" ( http://en.wikipedia.org/wiki/Difference_operator ), and that article was much more interesting, because there you could find the extended Leibniz rule. And from that article I found a link to "Umbral calculus" ( http://en.wikipedia.org/wiki/Umbral_calculus ), that look like exactly what I am looking for. The Umbral calculus seems to be a good candidate for a tool for handling discrete space-time! -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Mathematical methods for the discrete space-time.
Torgny Tholerus skrev: > > What I want to know is what result you will get if you start from the > axiom that *everything in universe is finite*. > One important function in Quantum Theory is the harmonic oscillator. So I want to know: What is the corresponding function in discrete mathematics? In continuous mathematics you have the harmonic oscillator defined by the differential equation D^2(f) + k^2*f = 0, which will have one of its solutions as: f(t) = exp(i*k*t) = cos(k*t) + i*sin(k*t), where i is sqrt(-1). In discrete mathematics you have the corresponding oscillator defined by the difference equation D^2(f) + k^2*f = 0, which will have one of its solutions as: f(t) = (1 + i*k)^t = dcos(k*t) + i*dsin(k*t), where dcos() och dsin() are the corresponding discrete functions of the continuous functions cos() and sin(). So what is dcos() and dsin()? If you do Taylor expansion of the continuos function you get: exp(i*k*t) = Sum((i*k*t)^n/n!) = Sum((-1)^m*k^(2*m)*t^(2*m)/(2*m)!) + i*Sum((-1)^m*k^(2*m+1)*t^(2*m+1)/(2*m+1)!) And if you do binominal expansion of the discrete function you get: (1 + i*k)^t = Sum(t!/((t-n)!*n!)*(i*k)^n) = Sum((-1)^m*k^(2*m)*(t!/(t-2*m)!)/(2*m)!) + i*Sum((-1)^m*k^(2*m+1)*(t!/(t-2*m-1)!)/(2*m+1)!) When you compare these two expession, you see a remarkable resemblance! If you replace t^n in the upper expression with t!/(t-n)! you will then get exactly the lower expression! This suggest the general rule: If the Taylor expansion of a continuous function f(x) is: f(x) = Sum(a(n)*x^n) = Sum(a(n)*Prod(n;x)), then the corresponding discrete funtion f(x) is: f(x) = Sum(a(n)*x!/(x-n)!) = Sum(a(n)*Prod(n;x-m)), where Prod(n;x-m) = x*(x-1)*(x-2)* ... *(x-n+2)*(x-n+1) is a finite product. I have no strict proof of this general rule. But this rule is such a beautifil result, that it simply *must* be true! -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: QTI & euthanasia (brouillon)
Bruno Marchal skrev: > For example, a zombie is just some entity which looks like you and me, > i.e. has all the appearance of a human, and who has no consciousness. > There is no *need* to make them a priori fundamentally material. Now a > materialist can and even should interpret this as a zombie in the > sense of Dennett, but the definition continues to make sense for a non > materialist, who for example just consider itself that physics is > implemented or emerge from something else. It shows that the notion of > zombie does not depend on the materialist or non materialist belief. A > zombie is just something NON conscious despite it has all the > appearance of a human like you and me (and thus is material for a > materialist, and immaterial for an immaterialist). > If you want a concrete example of a zombie, you can just think of me. I am an entity that have all the appearance of a human, but I have no consciousness... -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Mathematical methods for the discrete space-time.
Torgny Tholerus skrev: > > Exercise: Show that the extended Leibniz rule in the discrete > mathematics: D(f*g) = f*D(g) + D(f)*g + D(f)*D(g), is correct! > Another way to see both form of the Leibniz rule is in the graphical set theory, where you represent the sets by circles on a paper. Here I will represent the union of the sets A and B with "A + B", and the intersection as "A*B". Then you can represent the D operator as the border of the circle. Then you will have: D(A*B) = A*D(B) + D(A)*B, ie the Leibniz rule, ie the border of the area of the intersection is the union of the border of B inside A, and the border of A inside B. I can not show this figure in this message, but you can draw two circles on a paper before you, and you will then see what I mean. Now the interesting thing is what will happen if the circles have *thick* borders: Then the set A is represented by two circles inside each other, and the border will then be the area between the two circles. The set A will then be the interior of the inner circle, and the outside of A will be the outside of the outer circle. What will you then get if you look at the border of the intersection of A and B? This time you will get: D(A*B) = A*D(B) + D(A)*B + D(A)*D(B), ie the extended Leibniz rule. The extra term then comes from the two small squares you get where the two borders cross each other. (Do draw this figure om the paper before you, and you will understand.) This picture with the circles with thick borders is a way to represent intiutionistic logic. The interior of the inner circle is the objects that represent A (such as "red"), and the outside of the outer circle represent not-A (such as "not red"). Inside the border you will have all that is neither A nor not-A (such as red-orange, where you don't know if it is red or not...) -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Mathematical methods for the discrete space-time.
Bruno Marchal skrev: > I have to think. I think that to retrieve a Leibniz rule in discrete > mathematics, you have to introduce an operator and some non > commutativity rule. This can be already found in the book by Knuth on > numerical mathematics. This has been exploited by Kauffman and one of > its collaborator, and they have published a book which I have ordered > already two times ... without success. It is a very interesting matter. > Dirac quantum relativistic wave equation can almost be retrieved form > discrete analysis on complex or quaternion. It is worth investigating > more. Look at Kauffman page (accessible from my url), and download his > paper on discrete mathematics. I will look closer at the Kauffman paper on Non-commutative Calculus and Discrete Physics. It seems interesting, but not quite what I am looking for. Kauffman only gets the ordinary Leibniz rule, not the extended rule I have found. What I want to know is what result you will get if you start from the axiom that *everything in universe is finite*. For this you will need a function calculus. A function is then a mapping from a (finite) set of values to this set of values. Because this value set is finite, you can then map the values on the numbers 0,1,2,3, ... , N-1. So a function calculus can be made starting from a set of values consisting of the numbers 0,1,2,3, ... , N-1, where N is a very large number, but not too large. N should be a number of the order of a googol, ie 10^100. Because the size of our universe is 10^60 Planck units, and our universe has existed for 10^60 Planck times. As the arithmetic, we can count modulo N, ie (N-1) + 1 = 0. This makes it possible for the calculus to describe our reality. A function can then be represented as an ordered set of N numbers, namely: f = [f(0), f(1), f(2), f(3), ... , f(N-1)]. This means that S(f) becomes: S(f) = [f(1), f(2), f(3), ... , f(N-1), f(0)]. The sum or the product of two functions is obtained by adding or multiplying each element, namely: f*g = [f(0)*g(0), f(1)*g(1), f(2)*g(2), ... , f(N-1)*g(N-1)]. and to apply a function f on a function g then becomes: f(g) = [f(g(0)), f(g(1)), f(g(2)), ... , f(g(N-1))]. Exercise: Show that the extended Leibniz rule in the discrete mathematics: D(f*g) = f*D(g) + D(f)*g + D(f)*D(g), is correct! -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Mathematical methods for the discrete space-time.
When you are going to do exact mathematical computations for the discrete space-time, then the continuous mathematics is not enough, because then you will only get an approximation of the reality. So there is a need for developing a special calculus for a discrete mathematics. One difference between continuous and discrete mathematics is the rule for how to derívate the product of two functions. In continuous mathematics the rule says: D(f*g) = f*D(g) + D(f)*g. But in the discrete mathematics the corresponding rule says: D(f*g) = f*D(g) + D(f)*g + D(f)*D(g). In discrete mathematics you have difference equations of type: x(n+2) = x(n+1) + x(1), x(0) = 0, x(1) = 1, which then will give the number sequence 0,1,1,2,3,5,8,13,21,34,55,... etc. For a general difference equation you have: Sum(a(i)*x(n+i)) = 0, plus a number of starting conditions. If you then introduce the step operator S with the effect: S(x(n)) = x(n+1), then you can express the difference equation as: Sum((a(i)*S^i)(x(n)) = 0. You will then get a polynom in S. If the roots (the eigenvalues) to this polynom are e(i), you will then get: Sum(a(i)*S^i) = Prod(S - e(i)) = 0. This will give you the equations S - e(i) = 0, or more complete: (S - e(i))(x(n)) = S(x(n)) - e(i)*x(n) = x(n+1) - e(i)*x(n) = 0, which have the solutions x(n) = x(0)*e(i)^n. The general solution to this difference equation will then be a linear combination of these solutions, such as: x(n) = Sum(k(i)*e(i)^n), where k(i) are arbitrary constants. To get the integer solutions you can then build the eigenfunctions: x(j,n) = Sum(k(i,j)*e(i)^n) = delta(j,n), for n < the grade of the difference equation. With the S-operator it is then very easy to define the difference- or derivation-operator D as: D = S-1, so D(x(n)) = x(n+1) - x(n). What do you think, is this a good starting point for handling the mathematics of the discrete space-time? -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: QTI & euthanasia
Bruno Marchal skrev: > On 09 Nov 2008, at 20:29, Brent Meeker wrote: > > >> Many physicists think that an ultimate theory would be >> discrete, >> > This is highly implausible, assuming comp. I know that if we want > quantize gravitation, then space and time should be quantized, but > then I hope other things will remain continuous, like the statistics > (hoping it is enough). > But for the reason above, the first persons cannot escape the > "feeling" or the "appearances" of continua (assuming mech.). > You do not need anything continuous. When you look at a movie, you are shown 24 pictures every second, but you feel like it is a continuous movie. But in reality it is just 24 discrete events every second. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Which mathematical structure -is- the universe in Physics?
Brian Tenneson skrev: > Now on to the subject of time. > > If Tegmark is correct and an ultimate structure literally is all of > physical reality, what strikes me is that this ultimate structure > appears quite static. What then is the source of our perceptions of > transition, ie, time? This ultimate structure I presume (safely, I > believe) is constant yet we perceive things to change. Why and how? IOW, > what is the mechanism that converts the static ultimate structure into a > fluid appearance of transition? These questions are still valid even if > the ultimate structure I have in mind is wrong; Tegmark still > hypothesizes that some math structure is all of physical reality. > If you look at our universe as a 4-dimensional space-time structure, then that structure will be completely static. It is nothing peculiar with that. The time is just a direction in that static structure. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: UDA paper
Bruno Marchal skrev: > Hi Torgny, > > Le 29-févr.-08, à 15:25, Torgny Tholerus a écrit : > > >> >> I have just tested to upload a file to the group (PofSTorgny1.doc). >> You >> can try to see if you can see that file. (You have to log in to Google >> groups first.) >> > > I see (and did print) your file. I have put the movie there, in two > version but I cannot retrieve it. With the first I get the code, and > with the other (the one with ".mpeg") I get the QuickTime logo with an > interrogation mark. If you or someone can see the movie from there, > just tell me. > > I have not succeeded to view your movie. I have downloaded your files to my computer. But it seems as if your files are corrupted in some way. I have tried three different movie players (Windows Media Player, RealPlayer, and QuickTime), but no one was able to recognize your files. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: UDA paper
Bruno Marchal skrev: > Hi Wei, > > I have not succeeded to upload the movie, nor do I have seen files > which I heard should have been already uploaded by people on the list. > The system complains that I am not a member of the list. > I will try again Monday, because it looks like the discussion are not > currently available too, so the problem is perhaps with the > Googlegroups. > > But if that works it is of course the good idea, thanks, > > I have just tested to upload a file to the group (PofSTorgny1.doc). You can try to see if you can see that file. (You have to log in to Google groups first.) -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
[EMAIL PROTECTED] skrev: > On Nov 28, 9:56 pm, Torgny Tholerus <[EMAIL PROTECTED]> wrote: > > >> You only need models of cellular automata. If you have a model and >> rules for that model, then one event will follow after another event, >> according to the rules. And after that event will follow another more >> event, and so on unlimited. The events will follow after eachother even >> if you will not have any implementation of this model. Any physics is >> not needed. You don't need any geometric properties. >> >> In this model you may have a person called Torgny writing a message on a >> google group, and that event may be followed by a person called Marc >> writing a reply to this message. And you don't need any implementation >> of that model. >> >> > A whole lot of unproven assumptions in there. For starters, we don't > even know that the physical world can be modelled solely in terms of > cellular automata at all. Why can't our universe be modelled by a cellular automata? Our universe is very complicated, but why can't it be modelled by a very complicated automata? An automata where you have models for protons and electrons and photons and all other elementary particles, that obey the same laws as the particles in our universe? > Digital physics just seems to be the latest > 'trendy' thing, but actual evidence is thin on the ground. > Mathematics is much richer than just discrete math. Discrete math > deals only with finite collections, and as such is just a special case > of algebra. Isn't it enough with this special case? You can do a lot with finite collections. There is not any need for anything more. > Algebraic relations extend beyond computational models. > Finally, the introduction of complex analysis, infinite sets and > category theory extends mathematics even further, beyond even > algebraic relations. So you see that cellular automata are only a > small part of mathematics as a whole. There is no reason for thinking > for that space is discrete and in fact physics as it stands deals in > continuous differential equations, not cellular automata. > The reason why physics deals in continuous differential equations is that they are a very good approximation to a world where the distance between the space points and the time points are very, very small. And if you read a book in Quantum Field Theory, they often start from a discrete model, and then take the limit when the distances go to zero. > Further, the essential point I was making is that an informational > model of something is not neccesserily the same as the thing itself. > An informational model of a person called Marc would capture only my > mind, not my body. The information has to be super-imposed upon the > physical, or embodied in the physical world. > If the model models every atom in your body, then that model will describe your body. That model will describe how the atoms in your body react with eachother, and they will describe all your actions. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Bruno Marchal skrev: > > > Le 29-nov.-07, à 17:22, Torgny Tholerus a écrit : > > There is a difference between "unlimited" and "infinite". "Unlimited" > just says that it has no limit, but everything is still finite. If > you > add something to a finite set, then the new set will always be > finite. > It is not possible to create an infinite set. > > Come on! Now you talk like a finitist, who accepts the idea of > "potential infinity" (like Kronecker, Brouwer and the intuitionnist) > and who rejects only the so called actual infinities, like ordinal and > cardinal "numbers" (or sets). Yes, I am more like a finitist than an ultrafinitist in this respect. I accept that something can be without limit. But I don't want to use the word "potential infinity", because "infinity" is a meaningless word for me. > > At the ontic level, (or ontological, I mean the minimum we have to bet > on at the third person pov), comp is mainly finitist. Judson Webb put > comp (he calls it mechanism) in Finitism. But that is no more > ultrafinitism. With finitism: every object of the "universe" is > finite, but the universe itself is infinite (potentially or actually). > With ultrafinitism, every object is finite AND the universe itself is > finite too. Here I am an ultrafinitist. I believe that the universe is strictly finite. The space and time are discrete. And the space today have a limit. But the time might be without limit, that I don't know. > > Jesse wrote: > > My instinct would be to say that a "well-defined" criterion is one > that, given any mathematical object, will give you a clear answer > as to whether the object fits the criterion or not. And obviously > this one doesn't, because it's impossible to decide where R fits > it or not! But I'm not sure if this is the right answer, since my > notion of "well-defined criteria" is just supposed to be an > alternate way of conceptualizing the notion of a set, and I don't > actually know why "the set of all sets that are not members of > themselves" is not considered to be a valid set in ZFC set theory. > > Frege and Cantor did indeed define or identify sets with their > defining properties. This leads to the Russell's contradiction. (I > think Frege has abandoned his work in despair after that). > One solution (among many other one) to save Cantor's work from that > paradox consists in formalizing set theory, which means using > "belongness" as an undefined symbol obeying some axioms. Just two > examples of an axiom of ZF (or its brother ZFC = ZF + axiom of > choice): is the extensionality axiom: > AxAyAz ((x b z <-> y b z) -> x = y) "b" is for "belongs". It says that > two sets are equal if they have the same elements. > AxEy(z included-in x -> z b y) with "z included-in x" is a macro for > Ar(r b z -> r b x). This is the power set axiom, saying that the set > of all subsets of some set is also a set). For me "belongness" is not a problem, because everything is finite. For me the axiom of choice always is true, because you can always do a chioce in a finite world. > > Paradoxes a-la Russell are evacuated by restricting Jesse's > "well-defined criteria" by > 1) first order formula (in the set language, that is with "b" as > unique relational symbols (+ equality) ... like the axioms just above. > 2) but such first order formula have to be applied only to an already > defined set. This 2) rule is a very important restriction, and it is just this that my "type theory" is about. When you construct new things, those things can only be constructed from things that are already defined. So when you construct the set of all sets, then that new set will not be included in the new set. > For example, you can defined the set of x such that x is in y and has > such property P(x). With P defined by a set formula, and y an already > defined set. > > Also, ZFC has the foundation axiom which forbids a set to belong to > itself. This is a natural consequence of my type theory. When you construct a set, that set can never belong to itself, because that set is not defined before it is constructed. > In particular the informal collection of all sets which does not > belongs to themselves is the universe itself, which cannot be a set > (its power set would be bigger than the universe!). Yes, the set of all sets which does not belongs to themselves is the universe itself. But this is not a problem for me, because you can always extend the
Re: Theory of Everything based on E8 by Garrett Lisi
Jesse Mazer skrev: > > > >> Date: Thu, 29 Nov 2007 19:55:20 +0100 >> From: [EMAIL PROTECTED] >> >> >> As soon as you say "the set of ALL numbers", then you are forced to >> define the word ALL here. And for every definition, you are forced to >> introduce a "limit". It is not possible to define the word ALL without >> introducing a limit. (Or making an illegal circular definition...) >> > > Why can't you say "If it can be generated by the production rule/fits the > criterion, then it's a member of the set"? I haven't used the word "all" > there, and I don't see any circularity either. What do you mean by a "well-defined criterion"? Is this a well-defined criterion? : The set R is defined by: (x belongs to R) if and only if (x does not belong to x). If it fits the criterion (x does not belong to x), then it's a member of the set R. Then we ask the question: "Is R a member of the set R?". How shall we use the criterion to answer that question? If we substitute R for x in the criterion, we will get: (R belongs to R) if and only if (R does not belong to R)... What is wrong with this? -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Jesse Mazer skrev: > > >> From: [EMAIL PROTECTED] >> >> >> As soon as you talk about "the set N", then you are making a "closure" >> and making that set finite. >> > > > Why is that? How do you define the word "set"? > > > The only possible way to talk about > >> something without limit, such as natural numbers, is to give a >> "production rule", so that you can produce as many of that type of >> objects as you want. If you have a natural number n, then you can >> "produce" a new number n+1, that is the successor of n. >> > > > Why can't I say "the set of all numbers which can be generated by that > production ruler"? As soon as you say "the set of ALL numbers", then you are forced to define the word ALL here. And for every definition, you are forced to introduce a "limit". It is not possible to define the word ALL without introducing a limit. (Or making an illegal circular definition...) > It almost makes sense to say a set is *nothing more* than a criterion for > deciding whether something is a member of not, although you would need to > refine this definition to deal with problems like Russell's "set of all sets > that are not members of themselves" (which could be translated as the > criterion, 'any criterion which does not match its own criterion'--I suppose > the problem is that this criterion is not sufficiently well-defined to decide > whether it matches its own criterion or not). > A "well-defined criterion" is the same as what I call a "production rule". So you can use that, as long as the criterion is well-defined. (What does the criterion, that decides if an object n is a natural number, look like?) > >> >> It is not possible for "a set" to have no limit. As soon as you >> construct "a set", then that set will always have a limit. >> > > > Is there something intrinsic to your concept of the word "set" that makes > this true? Is your concept of a set fundamentally different than my concept > of well-defined criteria for deciding if any given object is a member or not? > Yes, the definition of the word "all" is intrinsic in the concept of the word "set". -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Quentin Anciaux skrev: > Le Thursday 29 November 2007 18:52:36 Torgny Tholerus, vous avez écrit : > >> Quentin Anciaux skrev: >> >> >>> What is the production rules of the "no"set R ? >>> >> How do you define "the set R"? >> > > http://en.wikipedia.org/wiki/Construction_of_real_numbers > > Choose your method... > The most important part of that definition is: 4. The order ? is /complete/ in the following sense: every non-empty subset of *R* bounded above <http://en.wikipedia.org/wiki/Upper_bound> has a least upper bound <http://en.wikipedia.org/wiki/Least_upper_bound>. This definition can be translated to: "If you have a production rule that produces rational numbers that are bounded above, then this production rule is producing a real number." This is the production rule for real numbers. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Quentin Anciaux skrev: > Le Thursday 29 November 2007 18:25:54 Torgny Tholerus, vous avez écrit : > >> >> As soon as you talk about "the set N", then you are making a "closure" >> and making that set finite. >> > > Ok then the set R is also finite ? > Yes. > >> The only possible way to talk about >> something without limit, such as natural numbers, is to give a >> "production rule", so that you can produce as many of that type of >> objects as you want. If you have a natural number n, then you can >> "produce" a new number n+1, that is the successor of n. >> > > What is the production rules of the "no"set R ? > How do you define "the set R"? -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Quentin Anciaux skrev: > Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit : > >> >> There is a difference between "unlimited" and "infinite". "Unlimited" >> just says that it has no limit, but everything is still finite. If you >> add something to a finite set, then the new set will always be finite. >> It is not possible to create an infinite set. >> > > I'm sorry I don't get it... The set N as an infinite numbers of elements > still > every element in the set is finite. Maybe it is an english subtility that I'm > not aware of... but in french I don't see a clear difference between "infini" > and "illimité". > As soon as you talk about "the set N", then you are making a "closure" and making that set finite. The only possible way to talk about something without limit, such as natural numbers, is to give a "production rule", so that you can produce as many of that type of objects as you want. If you have a natural number n, then you can "produce" a new number n+1, that is the successor of n. > > >> So it is OK to use the word "unlimited". But it is not OK to use the >> word "infinite". Is this clear? >> > > No, I don't see how a set which have not limit get a finite number of > elements. > It is not possible for "a set" to have no limit. As soon as you construct "a set", then that set will always have a limit. Either you have to accept that the set N is finite, or you must stop talking about "the set N". It is enough to have a production rule for natural numbers. > >> Another important word is the word "all". You can talk about "all >> events". But in that case the number of events will be finite, and you >> can then talk about "the last event". But you can't deduce any >> contradiction from that, because that is forbidden by the type theory. >> And there will be more events after "the last event", because the number >> of events is "unlimited". >> > > If there are events after the last one, how can the last one be the last ? > The last event is the last event in the set of "all" events. But because you have a production rule for the events, it is always possible to produce new events after the last event. But these events do not belong to the set of "all" events. > >> As soon as you use the word "all", you will >> introduce a limit - all up to this limit. And you must then think of >> only doing conclusions that are legal according to type theory. >> > > o_O... could you explain what is type theory ? > Type theory is one of the solutions of Russel's paradox. You have a hierarchy of "types". Type theory says that the "all quantifiers" only can span objects of the same "type" (or lower types). When you create new objects, such that "the set of all sets that do not belong to themselves", then you will get an object of a higher "type", so that you can not say anything about if this set belongs to itself or not. The same thing with "the set of all sets". You can not say anything about if it belongs to itself. > >> So the best thing is to avoid the word "all" (and all synonyms of that >> word). >> > > like everything ? > Yes... :-) -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Quentin Anciaux skrev: > Hi, > > Le Wednesday 28 November 2007 09:56:17 Torgny Tholerus, vous avez écrit : > >> >> You only need models of cellular automata. If you have a model and >> rules for that model, then one event will follow after another event, >> according to the rules. And after that event will follow another more >> event, and so on unlimited. The events will follow after eachother even >> if you will not have any implementation of this model. Any physics is >> not needed. You don't need any geometric properties. >> >> > Sure, but you can't be ultrafinitist and saying things like "And after that > event will follow another more event, and so on unlimited". > There is a difference between "unlimited" and "infinite". "Unlimited" just says that it has no limit, but everything is still finite. If you add something to a finite set, then the new set will always be finite. It is not possible to create an infinite set. So it is OK to use the word "unlimited". But it is not OK to use the word "infinite". Is this clear? Another important word is the word "all". You can talk about "all events". But in that case the number of events will be finite, and you can then talk about "the last event". But you can't deduce any contradiction from that, because that is forbidden by the type theory. And there will be more events after "the last event", because the number of events is "unlimited". As soon as you use the word "all", you will introduce a limit - all up to this limit. And you must then think of only doing conclusions that are legal according to type theory. So the best thing is to avoid the word "all" (and all synonyms of that word). -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Bruno Marchal skrev: > > > Le 28-nov.-07, à 09:56, Torgny Tholerus a écrit : > > You only need models of cellular automata. If you have a model > and rules for that model, then one event will follow after another > event, according to the rules. And after that event will follow > another more event, and so on unlimited. The events will follow > after eachother even if you will not have any implementation of > this model. Any physics is not needed. You don't need any > geometric properties. > > In this model you may have a person called Torgny writing a > message on a google group, and that event may be followed by a > person called Marc writing a reply to this message. And you don't > need any implementation of that model. > > > > OK. Do you agree now that the "real Torgny", by which I mean you from > your first person point of view, cannot known if it belongs to a state > generated by automata 345 or automata 6756, or automata 6756690003121, > or automata 65656700234676611084899 , and so one ... > Do you agree we have to take into account this first person > indeterminacy when making a first person prediction? I agree that the "real Torgny" belongs to exactly one of those automata, but I don't know which one. So I can not tell what will happen to the "real Torgny" in the future. I can not do any prediction. If we call the automata that the "real Torgny" belongs to, for automata X, then I can look at automata X from the outside, and I will then see that all that the "real Torgny" will do in the future is completely determined. There is no indeterminacy in automata X. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
[EMAIL PROTECTED] skrev: > >> When I talk about "pure mathematics" I mean that kind of mathematics you >> have in GameOfLife. There you have "gliders" that move in the >> GameOfLife-universe, and these gliders interact with eachother when they >> meet. These gliders you can see as physical objects. These physical >> objects are reducible to pure mathematics, they are the consequences of the >> rules behind GameOfLife. >> > > -- > Torgny > > That kind of mathematics - models of cellular automata - is the > domain of the theory of computation. These are just that - models. > But there is no reason for thinking that the models or mathematical > rules are identical to the physical entities themselves just because > these rules/models can precisely predict/explain the behaviour of the > physical objects. > You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
[EMAIL PROTECTED] skrev: On Nov 23, 8:49 pm, Torgny Tholerus <[EMAIL PROTECTED]> wrote: I think that everything is reducible to physical substances and properties. And I think that all of physics is reducible to pure mathematics... You can't have it both ways. If physics was reducible to pure mathematics, then physics could not be the 'ontological base level' of reality and hence everything could not be expressed solely in terms of physical substance and properties. Besides which, mathematics and physics are dealing with quite different distinctions. It is a 'type error' it try to reduce or identity one with the other. Mathematics deals with logical properties, physics deals with spatial (geometric) properties. Although geometry is thought of as math, it is actually a branch of physics, since in addition to pure logical axioms, all geometry involves 'extra' assumptions or axioms which are actually *physical* in nature (not purely mathematical) . When I talk about "pure mathematics" I mean that kind of mathematics you have in GameOfLife. There you have "gliders" that move in the GameOfLife-universe, and these gliders interact with eachother when they meet. These gliders you can see as physical objects. These physical objects are reducible to pure mathematics, they are the consequences of the rules behind GameOfLife. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
rafael jimenez buendia skrev: Sorry, but I think Lisi's paper is fatally flawed. Adding altogether fermions and bosons is plain wrong. Best What is wrong with adding fermions and bosons together? Xiao-Gang Wen is working with a condensed string-net where the waves behave just like bosons (fotons) and the end of the open strings behave just like fermions (electrons). -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
[EMAIL PROTECTED] skrev: > > As far as I tell tell, all of physics is ultimately > geometry. But as we've pointed out on this list many times, a theory > of physics is *not* a theory of everything, since it makes the > (probably false) assumption that everything is reducible to physical > substances and properties. I think that everything is reducible to physical substances and properties. And I think that all of physics is reducible to pure mathematics... I have now read Garrett Lisis paper. It was interesting, but it is still to early to say if it is important. There is a lot of symmetries in the elementary particles, and there is a lot of symmetries in the E8 Lie group. So it is not any suprise that they both can be mapped on each other. Lisi has mapped 222 elementary particles on the 242 elements of E8, and he has predicted that the rest of the 20 elements correspond to 20 yet to be discovered elementary particles. If it is true, then Lisi will have the Nobel price. If it is not, then we will have to look for another TOE. But it is possible that we will never find any TOE. Because there is 10^500 different possiblities for our universe, and all of these 10^500 universes exist in the same way. By experiments we will have to decide which of those that is our universe, but we will never reach the correct answer, the number of experiments needed will be too many. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cantor's Diagonal
Bruno Marchal skrev: Le 20-nov.-07, à 23:39, Barry Brent wrote : You're saying that, just because you can *write down* the missing sequence (at the beginning, middle or anywhere else in the list), it follows that there *is* no missing sequence. Looks pretty wrong to me. Cantor's proof disqualifies any candidate enumeration. You respond by saying, "well, here's another candidate!" But Cantor's procedure disqualified *any*, repeat *any* candidate enumeration. Barry Brent Torgny, I do agree with Barry. Any bijection leads to a contradiction, even in some effective way, and that is enough (for a classical logician). What do you think of this "proof"?: Let us have the bijection: 0 {0,0,0,0,0,0,0,...} 1 {1,0,0,0,0,0,0,...} 2 {0,1,0,0,0,0,0,...} 3 {1,1,0,0,0,0,0,...} 4 {0,0,1,0,0,0,0,...} 5 {1,0,1,0,0,0,0,...} 6 {0,1,1,0,0,0,0,...} 7 {1,1,1,0,0,0,0,...} 8 {0,0,0,1,0,0,0,...} ... omega --- {1,1,1,1,1,1,1,...} What do we get if we apply Cantor's Diagonal to this? -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cantor's Diagonal
meekerdb skrev: Torgny Tholerus wrote: An ultrafinitist comment to this: == You can add this complementary sequence to the end of the list. That will make you have a list with this complementary sequence included. But then you can make a new complementary sequence, that is not inluded. But you can then add this new sequence to the end of the extended list, and then you have a bijection with this new sequence also. And if you try to make another new sequence, I will add that sequence too, and this I will do an infinite number of times. So you will not be able to prove that there is no bijection... == What is wrong with this conclusion? You'd have to insert the new sequence in the beginning, as there is no "end of the list". Why can't you add something to the end of the list? In an earlier message Bruno wrote: "Now omega+1 is the set of all ordinal strictly lesser than omega+1, with the convention above. This gives {0, 1, 2, 3, ... omega} = {0, 1, 2, 3, 4, {0, 1, 2, 3, 4, }}." In this sentence he added omega to the end of the list of natural numbers... -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Bijections (was OM = SIGMA1)
Bruno Marchal skrev: > > But infinite ordinals can be different, and still have the same > cardinality. I have given examples: You can put an infinity of linear > well founded order on the set N = {0, 1, 2, 3, ...}. > The usual order give the ordinal omega = {0, 1, 2, 3, ...}. Now omega+1 > is the set of all ordinal strictly lesser than omega+1, with the > convention above. This gives {0, 1, 2, 3, ... omega} = {0, 1, 2, 3, 4, > {0, 1, 2, 3, 4, }}. As an order, and thus as an ordinal, it is > different than omega or N. But as a cardinal omega and omega+1 are > identical, that means (by definition of cardinal) there is a bijection > between omega and omega+1. Indeed, between {0, 1, 2, 3, ... omega} and > {0, 1, 2, 3, ...}, you can build the bijection: > > 0omega > 10 > 21 > 32 > ... > n --- n-1 > ... > > All right?"-" represents a rope. > An ultrafinitist comment: In the last line of this sequence you will have: ? - omega-1 But what will the "?" be? It can not be omega, because omega is not included in N... -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cantor's Diagonal
Bruno Marchal skrev: But then the complementary sequence (with the 0 and 1 permuted) is also well defined, in Platonia or in the mind of God(s) 0 1 1 0 1 1 ... But this infinite sequence cannot be in the list, above. The "God" in question has to ackonwledge that. The complementary sequence is clearly different -from the 0th sequence (1, 0, 0, 1, 1, 1, 0 ..., because it differs at the first (better the 0th) entry. -from the 1th sequence (0, 0, 0, 1, 1, 0, 1 ... because it differs at the second (better the 1th) entry. -from the 2th sequence (0, 0, 0, 1, 1, 0, 1 ... because it differs at the third (better the 2th) entry. and so one. So, we see that as far as we consider the bijection above well determined (by God, for example), then we can say to that God that the bijection misses one of the neighbor sheep, indeed the "sheep" constituted by the infinite binary sequence complementary to the diagonal sequence cannot be in the list, and that sequence is also well determined (given that the whole table is). But this means that this bijection fails. Now the reasoning did not depend at all on the choice of any particular bijection-candidate. Any conceivable bijection will lead to a well determined infinite table of binary numbers. And this will determine the diagonal sequence and then the complementary diagonal sequence, and this one cannot be in the list, because it contradicts all sequences in the list when they cross the diagonal (do the drawing on paper). Conclusion: 2^N, the set of infinite binary sequences, is not enumerable. All right? An ultrafinitist comment to this: == You can add this complementary sequence to the end of the list. That will make you have a list with this complementary sequence included. But then you can make a new complementary sequence, that is not inluded. But you can then add this new sequence to the end of the extended list, and then you have a bijection with this new sequence also. And if you try to make another new sequence, I will add that sequence too, and this I will do an infinite number of times. So you will not be able to prove that there is no bijection... == What is wrong with this conclusion? -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Bijections (was OM = SIGMA1)
Bruno Marchal skrev: > > To sum up; finite ordinal and finite cardinal coincide. Concerning > infinite "number" there are much ordinals than cardinals. In between > two different infinite cardinal, there will be an infinity of ordinal. > We have already seen that omega, omega+1, ... omega+omega, > omega+omega+1, 3.omega, ... 4.omega omega.omega . > omega.omega.omega, .omega^omega . are all different ordinals, > but all have the same cardinality. > Was it not an error there? 2^omega is just the number of all subsets of omega, and the number of all subsets always have bigger cardinality than the set. So omega^omega can not have the same cardinality as omega. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: The big-black-cloud-interpretation.
Torgny Tholerus skrev: Now you define a new concept INNFINITE, that is defined by: If you have a bijection from all visible numbers of a set S, to all visible numbers of a true subset of S, then you say that the set S in INNFINITE. Then you can use this concept INNFINITE, and you will get a consistent theory with no contradictions, because you have a finite visualization of this theory. This concept INNFINITY behaves in exact the same way as the concept infinity in ordinary mathematics. So you do not need the concept infinity. Every conclusion you do with the concept infinity, you can do with the concept INNFINITY. So you will not lose anything, if you discard the concept infinity. Infinity is not needed in mathematics. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Bijections (was OM = SIGMA1)
Torgny Tholerus skrev: If you define the set of all natural numbers N, then you can pull out the biggest number m from that set. But this number m has a different "type" than the ordinary numbers. (You see that I have some sort of "type theory" for the numbers.) The ordinary deduction rules do not hold for numbers of this new type. For all ordinary numbers you can draw the conclusion that the successor of the number is included in N. But for numbers of this new type, you can not draw this conclusion. You can say that all ordinary natural numbers are of type 0. And the biggest natural number m, and all numbers you construct from that number, such that m+1, 2*m, m/2, and so on, are of type 1. And you can construct a set N1 consisting of all numbers of type 1. In this set there exists a biggest number. You can call it m1. But this new number is a number of type 2. It may look like a contradiction to say that m is included in N, and to say that all numbers in N have a successor in N, and to say that m have no successor in N. But it is not a constrdiction because the rule "all numbers in N have a successor in N" can be expanded to "all numbers of type 0 in N have a successor in N". And because m is a number of type 1, then that rule is not applicable to m. You can comapre this with the Russell's paradox. This paradox says: Construct the set R of all sets that does not contain itself. For this set R there will be the rule: For all x, if x does not contain itself, then R contains x. If we here substitute R for x, then we get: If R does not contain itself, then R contains R. This is a contradiction. The contradiction is caused by an illegal conclusion, it is illegal to substitute R for x in the "For all x"-quantifier above. This paradox is solved by "type theory". If you say that all ordinary sets are of type 0, then the set R will be of type 1. And every all-quantifiers are restricted to objects of a special type. So the rule above should read: For all x of type 0, if x does not contain itself, then R contains x. In this case you will not get any contradiction, because you can not substitute R for x in that rule. == Compare this with the case of the biggest natural number: Construct the set N of all natural numbers. For this set N there will be the rule: For all x, if N contains x, then N contains x+1. Suppose that there exists a biggest natural number m in N. If we substitute m for x, then we get: If N contains m, then N contains m+1. This is a contradiction, because m+1 is bigger than m, so m can not be the biggest number then. But the contradiction is caused by an illegal conclusion, it is illegal to substitute m for x in the "For all x"-quantifier above. This paradox is solved by "type theory". If you say that all ordinary natural numbers are of type 0, then the natural number m will be of type 1. And every all-quantifiers are restricted to objects of a special type. So the rule above should read: For all x of type 0, if N contains x, then N contains x+1. In this case you will not get any contradiction, because you can not substitute m for x in that rule. === Do you see the similarities in both these cases? -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
The big-black-cloud-interpretation.
Bruno Marchal skrev: Le 15-nov.-07, à 14:45, Torgny Tholerus a écrit : Do you have the big-black-cloud interpretation of "..."? By that I mean that there is a big black cloud at the end of the visible part of universe, Concerning what I am trying to convey, this is problematic. The word "universe" is problematic. The word "visible" is also problematic. and the sequence of numbers is disappearing into the cloud, so that you can only see the numbers before the cloud, but you can not see what happens at the end of the sequence, because it is hidden by the cloud. I don't think that math is about seeing. I have never seen a number. It is a category mistake. I can interpret sometimes some symbol as refering to number, but that's all. A way to prove the consistency of a theory is to make a "visualization" of the theory. If you can visualize all that happens in the theory, then you know the theory is consistent. To visualize the natural numbers, you can think of them as a long sequence {0,1,2,3,4,5,...}, and this sequence is going far, far, away. But you can only visualize finite sequences. So you can think that you have a finite sequence of numbers, and you have a big black cloud far, far, away. You see the first part of the sequence {0,1,2,...,m} before the cloud. But inside the cloud you can imagine that you have the finite sequence {m+1,m+2,...,4*m-1,4*m}. This whole sequence {0,1,2,...,m,m+1,...4*m} is what you call the set N of all natural numbers. >From that set N you construct the true subset {0,2,4,6,...,2*m,2*m+2,...,4*m}, which you call the set E of all even numbers. The visible part of the set E is then {0,2,4,...,2*m}, and the hidden part of that sequence is {2*m+2,...,4*m}. Now you define a new concept INNFINITE, that is defined by: If you have a bijection from all visible numbers of a set S, to all visible numbers of a true subset of S, then you say that the set S in INNFINITE. Then you can use this concept INNFINITE, and you will get a consistent theory with no contradictions, because you have a finite visualization of this theory. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Bijections (was OM = SIGMA1)
Bruno Marchal skrev: Le 15-nov.-07, à 14:45, Torgny Tholerus a écrit : But m+1 is not a number. This means that you believe there is a finite sequence of "s" of the type A = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s( s(0)...) where "..." here represents a finite sequence, and which is such that s(A) is not a number. Yes, exactly. When you construct the set of ALL natural numbers N, you have to define ALL these numbers. And you can only define a finite number of numbers. See more explanations below. BTW, do you agree that 100^(100^(100^(100^(100^(100^(100^(100^100)], and 100^(100^(100^(100^(100^(100^(100^(100^100)] +1 are numbers? I am just curious, Yes, I agree. All explicitly given numbers are numbers. The biggest number is bigger than all by human beeings explicitly given numbers. If you define the set of all natural numbers N, then you can pull out the biggest number m from that set. But this number m has a different "type" than the ordinary numbers. (You see that I have some sort of "type theory" for the numbers.) The ordinary deduction rules do not hold for numbers of this new type. For all ordinary numbers you can draw the conclusion that the successor of the number is included in N. But for numbers of this new type, you can not draw this conclusion. You can say that all ordinary natural numbers are of type 0. And the biggest natural number m, and all numbers you construct from that number, such that m+1, 2*m, m/2, and so on, are of type 1. And you can construct a set N1 consisting of all numbers of type 1. In this set there exists a biggest number. You can call it m1. But this new number is a number of type 2. There is some sort of "temporal" distinction between the numbers of different type. You have to "first" have all numbers of type 0, "before" you can construct the numbers of type 1. And you must have all numbers of type 1 "before" you can construct any number of type 2, and so on. The construction of numbers of type 1 presupposes that the set of all numbers of type 0 is fixed. When the set N of all numbers of type 0 is fixed, then you can construct new numbers of type 1. It may look like a contradiction to say that m is included in N, and to say that all numbers in N have a successor in N, and to say that m have no successor in N. But it is not a constrdiction because the rule "all numbers in N have a successor in N" can be expanded to "all numbers of type 0 in N have a successor in N". And because m is a number of type 1, then that rule is not applicable to m. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Bijections (was OM = SIGMA1)
Quentin Anciaux skrev: Hi, Le Thursday 15 November 2007 14:45:24 Torgny Tholerus, vous avez écrit : What do you mean by "each" in the sentence "for each natural number"? How do you define ALL natural numbers? There is a natural number 0. Every natural number a has a natural number successor, denoted by S(a). What do you mean by "Every" here? Can you give a *non-circular* definition of this word? Such that: "By every natural number I mean {1,2,3}" or "By every naturla number I mean every number between 1 and 100". (This last definition is non-circular because here you can replace "every number" by explicit counting.) How do you prove that each x in N has a corresponding number 2*x in E? If m is the biggest number in N, By definition there exists no biggest number unless you add an axiom saying there is one but the newly defined set is not N. I can prove by induction that there exists a biggest number: A) In the set {m} with one element, there exists a biggest number, this is the number m. B) If you have a set M of numbers, and that set have a biggest number m, and you add a number m2 to this set, then this new set M2 will have a biggest number, either m if m is bigger than m2, or m2 if m2 is bigger than m. C) The induction axiom then says that every set of numbers have a biggest number. Q.E.D. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Bijections (was OM = SIGMA1)
Bruno Marchal skrev: Le 14-nov.-07, à 17:23, Torgny Tholerus a écrit : What do you mean by "..."? Are you asking this as a student who does not understand the math, or as a philospher who, like an ultrafinist, does not believe in the potential infinite (accepted by mechanist, finistist, intuitionist, etc.). I am asking as an ultrafinitist. I have already explained that the meaning of "...'" in {I, II, III, , I, II, III, , I, ...} is *the* mystery. Do you have the big-black-cloud interpretation of "..."? By that I mean that there is a big black cloud at the end of the visible part of universe, and the sequence of numbers is disappearing into the cloud, so that you can only see the numbers before the cloud, but you can not see what happens at the end of the sequence, because it is hidden by the cloud. For example, the function which sends x on 2*x, for each x in N is such a bijection. What do you mean by "each x" here? I mean "for each natural number". What do you mean by "each" in the sentence "for each natural number"? How do you define ALL natural numbers? How do you prove that each x in N has a corresponding number 2*x in E? If m is the biggest number in N, There is no biggest number in N. By definition of N we accept that if x is in N, then x+1 is also in N, and is different from x. How do you know that m+1 is also in N? You say that for ALL x then x+1 is included in N, but how do you prove that m is included in "ALL x"? If you say that m is included in "ALL x", then you are doing an illegal deduction, and when you do an illegal deduction, then you can prove anything. (This is the same illegal deduction that is made in the Russell paradox.) then there will be no corresponding number 2*m in E, because 2*m is not a number. Of course, but you are not using the usual notion of numbers. If you believe that the usual notion of numbers is wrong, I am sorry I cannot help you. I am using the usual notion of numbers. But m+1 is not a number. But you can define a new concept: "number-2", such that m+1 is included in that new concept. And you can define a new set N2, that contains all natural numbers-2. This new set N2 is bigger than the old set N, that only contains all natural numbers. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Bijections (was OM = SIGMA1)
Bruno Marchal skrev: > 0) Bijections > > Definition: A and B have same cardinality (size, number of elements) > when there is a bijection from A to B. > > Now, at first sight, we could think that all *infinite* sets have the > same cardinality, indeed the "cardinality" of the infinite set N. By N, > I mean of course the set {0, 1, 2, 3, 4, ...} > What do you mean by "..."? > By E, I mean the set of even number {0, 2, 4, 6, 8, ...} > > Galileo is the first, to my knowledge to realize that N and E have the > "same number of elements", in Cantor's sense. By this I mean that > Galileo realized that there is a bijection between N and E. For > example, the function which sends x on 2*x, for each x in N is such a > bijection. > What do you mean by "each x" here? How do you prove that each x in N has a corresponding number 2*x in E? If m is the biggest number in N, then there will be no corresponding number 2*m in E, because 2*m is not a number. > Now, instead of taking this at face value like Cantor, Galileo will > instead take this as a warning against the use of the infinite in math > or calculus. > -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Bruno Marchal skrev: Le 19-sept.-07, à 09:59, Youness Ayaita wrote (in two posts): Probably, we won't find the set of natural numbers within this universe, the number of identical particles (as far as we can talk about that) of any kind is finite. Not in all "models" (cf type 1 multi-realty of Tegmark). The type 1 multi-reality of Tegmark does not require infinity. The type 1 multi-reality is true also in a finite universe, that is *enough* big... -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Space-time is a liquid!
John Mikes skrev: > > JM: Then what makes them into a continuous 'string'? OR: do those > individual points arrange in unassigned directions they just wish? If > they only fluctuate by themselves, what reference do they > (individually) follow to be callable 'string' -'fluctuate' - or just > "vibrate on their own"? > (below you said it: "there the strings consist of discrete points.") > > JM: so THOSE (discrete) points are SPACE and also VACUUM. Now what > keeps them 'discrete' if there is NO space between them? They mold > together into an 'undivided' continuum - without any divider in > between. Two discrete points have got to be discretized by something > interstitial separational - in the geometrical view: their spatial > image (what they do not have, because they ARE space). > In this same image vacuum is also a bunch of discontinuous points that > move. Vibrate. Fluctuate. Undulate into waves. But without anything > "interstitial" they melt into a continuum? If you look at a meter, then there is a finite number of space points in that meter (it is about 10^35 space points in this meter). There is no space between two space points, because the space is the space points. The best way to imagine this discrete space and discrete time, is to look at the Game of Life. There you have discrete space points, that can have two states, on/off (or black/white or spin up/spin down). In this discrete space-time, you can see the gliders move. It is the same thing with the vibrating strings in the string-net liquid. There you have string-like structures, waving back and forth. These string-like structure is the wacuum. And the elementary particles are macroscopic vawes in this string-net liquid, just like sound waves in water. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Space-time is a liquid!
John Mikes skrev: 1.- Q: What are light and fermions? A: Light is a fluctuation of closed strings of arbitrary sizes. Fermions are ends of open strings. 2.- Q: Where do light and fermions come from? A: Light and fermions come from the collective motions of string-like objects that form nets and fill our vacuum. 3.- Q: Why do light and fermions exist? A: Light and fermions exist because our vacuum is a quantum liquid of string-nets. This is from the introduction of the URL so kindly provided by Torgny. It looks very interesting, a gteat idea indeed. I like better a 'liquid' of spacetime than a 'fabric'. Xiao-Gang Wen looks like a very open-minded wise man. I wonder if he made the circularity of his Q#1 and Q#3 deliberately? (if, of course, we include Q#2). Originally - before reading Q#3 I wanted to ask 'what is OUR vacuum? but here it is: a QUANTUM liqud and it has the substance of "string-nets". He also postulates closed strings and open ones. (What-s?) the closed ones fluctuate in waves (=photons) and the open ones have endings we consider electrically charged (also callable: particles). In my original (uneducted) question I wanted to ask what kind of a vacuum is "filled"? is it still a (full) vacuum? Do the 'strings' have a 'filling' quale? or is a 'string-filled' plenum still empty (as in vacuum)? If the strings fluctuate into waves, what fluctuates? I am afraid that ANY answer will start another string of questions. The vocabulary is not so clear, then again it is the nth consequence of the mth consequential result of an old assumption: the assumption of the physical world. Please, do not reply! I just realizes that this entire topic is way above my preparedness and just have "let it out". Some clarifications: The vacuum IS a string-net liquid. But the strings are not continous. As you can see in the picture in Figure 1.8 at page 9 (page 14 in the pdf file) in Xiao-Gang Wen: "Introduction to Quantum Many-boson Theory (-: a theory of almost everything :-)", that can be found at http://dao.mit.edu/~wen/pub/intr-frmb.pdf , and in the 10th slide of his talk "An unification of light and electron" at http://dao.mit.edu/~wen/talks/06TDLee.pdf , there the strings consist of discrete points. And it is these discrete points that ARE the space. There is no space between the points. The vacuum IS these points. This might be hard to understand. But this is the same thing that there were no time "before" the Big Bang. The time started with Big Bang. And there is the same thing with the space points in the strings in the discrete space. There is no space "between" the space points. This is hard to understand mentally, but it can be understood mathematically. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Space-time is a liquid!
(From the swedish Allting List:) The discrete space-time is a liquid. This explains why the space is isomorph in all directions. The one that discovered that the space-time is a liquid, was Xiao-Gang Wen (Home Page: http://dao.mit.edu/~wen ). He has found that elementary particles are not the fundamental building blocks of matter. Instead, they emerge as defects or "whirlpools" in the deeper organized structure of space-time. The space-time is a string-net liquid, and the photons, the light, are waves in this liquid. And the charged electrons are the the ends of open-ended strings. Xiao-Gang Wen has written a lot of articles about this, and they can all be found from his home page. But most of the articles are *very* mathematical. But there is an easy-to-read article at https://dao.mit.edu/~wen/NSart-wen.html . And there is a rather-easy-to-read article in 12 pages at https://dao.mit.edu/~wen/pub/intr-frmb.pdf , that explains more about these very interesting theories. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Why Objective Values Exist
[EMAIL PROTECTED] skrev: > > (7) From (3) mathematical concepts are objectively real. But there > exist mathematical concepts (inifinite sets) which cannot be explained > in terms of finite physical processes. How can you prove that infinite sets exists? -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Message to swedish language members.
This is a message to the swedish language members of the Everything List: Efersom jag har svårt att uttrycka det jag vill säga på engelska, så har jag nu startat en svenskspråkig sublista till Everything List, som jag har kallat Allting List. Du hittar den nya listan på: http://groups.google.com/group/allting-list?hl=sv . Gå gärna med i den listan, och hjälp mej förklara universum. Jag har redan lagt in 11 (korta) inlägg i denna lista, som en startpunkt för diskussionerna. Resultaten som vi kommer fram till i sublistan ska sedan överföras till den övergripande Everything List. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
Brent Meeker skrev: > Torgny Tholerus wrote: >> >> That is exactly what I wanted to say. You don't need to have a complete >> description of arithmetic. Our universe can be described by doing a >> number of computations from a finite set of rules. (To get to the >> current view of our universe you have to do about 10**60 computations >> for every point of space...) > > How did you arrive at that number? > It is the number of Planck times since the birth of Universe. The age of Universe is 13,7 billion years, number of seconds in a year is 31 million, and the Planck time is 5,4 * 10**-44 seconds. That gives 13,7*10**9 * 31*10**6 / (5,4*10**-44) = 8*10**60. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
Brent Meeker skrev: Bruno Marchal wrote: Le 09-juil.-07, à 17:41, Torgny Tholerus a écrit : ... Our universe is the result of some set of rules. The interesting thing is to discover the specific rules that span our universe. Assuming comp, I don't find plausible that "our universe" can be the result of some set of rules. Even without comp the "arithmetical universe" or arithmetical truth (the "ONE" attached to the little Peano Arithmetic Lobian machine) cannot be described by finite set of rules. But it can be "the result of" a finite set of rules. Arithmetic results from Peano's axioms, but a complete description of arithmetic is impossible. That is exactly what I wanted to say. You don't need to have a complete description of arithmetic. Our universe can be described by doing a number of computations from a finite set of rules. (To get to the current view of our universe you have to do about 10**60 computations for every point of space...) -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
Quentin Anciaux skrev: >> I claim that "our universe" is the result of a finite set of rules. Just >> as a GoL-universe is the result of a finite set of rules, so is our universe >> the result of a set of rules. But these rules are more complicated than the >> GoL-rules... >> > What are your "proofs" or set of evidences that our universe as it is > is 1) resulting from a finite set of rules 2) by 1) computable. > There are two "proofs": A) Everything is finite. So our universe must be the result from a finite set of rules. B) Occams razor. Because we can explain everything in our universe from this finite set of rules, we don't need anything more complicated. > If 2) is true what difference do you make between functionnaly > equivalent model of your set of rules ? is it the same universe ? > Our universe has nothing to do with different models of our universe. A model is more like a picture of our universe. You can make a model of a GoL-universe with red balls, or you can make a model with black dots, but still there will hold the same relations in both these models. It is the relations that are the important things. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
Bruno Marchal skrev: Le 09-juil.-07, à 17:41, Torgny Tholerus a écrit : Bruno Marchal skrev: I agree with you (despite a notion as "universe" is not primitive in my opinion, unless you mean it a bit like the logician's notion of model perhaps). As David said, this is arithmetical realism. Yes, you can see a universe as the same thing as a model. When you have a (finite) set of rules, you will always get a universe from that set of rules, by just applying those rules an unlimited number of times. And the result of these rules is existing, in the same way as our universe is existing. The problem here is that an effective syntactical description of a intended model ("universe") admits automatically an infinity of non isomorphic models (cf Lowenheim-Skolem theorems, Godel, ...). Yes, you are right, the word "model" is not quite appropriate here. The universe is not a model that satisfies a set of axioms. The kind of rules I am thinking of, is rather that kind of rules you have in Game of Life. When you have a situation at one moment of time and at one place in space, you can compute the situation the next moment of time at the same place by using the situations near this place. The important thing is that the rules uniquely describes the whole universe by applying the rules over and over again. (But I want something more general than GoL-like rules, because the GoL-rules presupposes that you have a space-time from the beginning. I want a set of rules that are such that the space-time is a result of the rules. But I don't know how to get there...) Our universe is the result of some set of rules. The interesting thing is to discover the specific rules that span our universe. Assuming comp, I don't find plausible that "our universe" can be the result of some set of rules. Even without comp the "arithmetical universe" or arithmetical truth (the "ONE" attached to the little Peano Arithmetic Lobian machine) cannot be described by finite set of rules. The Universal Dovetailer Argument (UDA) shows that even a cup of coffee is eventually described by the probabilistic interferences of an infinity of computations occurring in the Universal deployment (UD*), which by the way explains why we cannot really duplicate exactly any piece of apparent matter (comp-no cloning). It is an open question if those theoretical interferences correspond to the quantum one. Studying the difference between the comp interference and the quantum interferences gives a way to measure experimentally the degree of plausibility of comp. I claim that "our universe" is the result of a finite set of rules. Just as a GoL-universe is the result of a finite set of rules, so is our universe the result of a set of rules. But these rules are more complicated than the GoL-rules... -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Some thoughts from Grandma
David Nyman skrev: On 11/07/07, Brent Meeker <[EMAIL PROTECTED]> wrote: (quite contrary to the premise of the everything-list, but one that I'm glad to entertain). For what it's worth, I really don't see that this is necessarily contrary to the premise of this list. The proposition is that all POSSIBLE worlds exist, not that anything describable in words (or for that matter mathematically) 'exists'. My analysis is an attempt to place a constraint on what can be said to exist in any sense strong enough to have any discernible consequences, either for us, or for any putative denizens of such 'worlds'. So I would argue that non-reflexive worlds are not possible in any consequential sense of the term. What do you mean with a POSSIBLE world? One exemple of a possible world is that GoL-universe, of which there is a picture of on the Wikipedia page. One interesting thing about this particular GoL-universe is that it is finite, the time goes in a circle in that universe. That universe only consists of 14 situations. After the 14th situation follows the 1st situation again. This GoL-universe exists, but it is a non-reflexive world, I can not see anything reflexive in that universe. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
David Nyman skrev: On 09/07/07, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: There can be no dynamic time. In the space-time, time is always static. Then you must get very bored ;) David But I am not bored, because I don't know what will happen tomorrow. If I look at our universe from the outside, I see that I will do something tomorrow, and I see what will happen in one million years. There will never be any changes in the situations that will happen in the future. But it is impossible to know today what will happen in the future, because we can not have total knowledge about how the universe looks like just now. If we try to find the exact position and the exact speed of an electron, then that electron will be disturbed by me looking at it. So it is impossible for me to compute how our universe will look like tomorrow. But the rules of our universe decide what our universe will look like tomorrow. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
(Reposted because of some techical problems...) On Jul 7, 2:00 pm, Bruno Marchal <[EMAIL PROTECTED]> wrote: > Le 05-juil.-07, à 14:19, Torgny Tholerus wrote: > > > > > David Nyman skrev: > >> You have however drawn our attention to something very interesting and > >> important IMO. This concerns the necessary entailment of 'existence'. > > 1. The relation 1+1=2 is always true. It is true in all universes. > > Even if a universe does not contain any humans or any observers. The > > truth of 1+1=2 is independent of all observers. > > I agree with you (despite a notion as "universe" is not primitive in my > opinion, unless you mean it a bit like the logician's notion of model > perhaps). As David said, this is arithmetical realism. Yes, you can see a universe as the same thing as a model. When you have a (finite) set of rules, you will always get a universe from that set of rules, by just applying those rules an unlimited number of times. And the result of these rules is existing, in the same way as our universe is existing. Our universe is the result of some set of rules. The interesting thing is to discover the specific rules that span our universe. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
On Jul 9, 7:47 pm, "David Nyman" <[EMAIL PROTECTED]> wrote: > On 09/07/07, Torgny Tholerus <[EMAIL PROTECTED]> wrote: > > > Because > > everything that happens in A-Universe will also happen in B-Universe. > > All objects in A-Universe obey the laws of physics, and all objects in > > B-Universe obey the same laws, so the same things will happen in both > > universes. > > We're disagreeing because you just don't accept my basic point about > reflexive existence, which IMO is a pity, because ISTM to clarify what > the "stuff" might be, and makes it much more difficult to take the > 'zombie world' seriously. In fact, as I've said, I think you would > have to postulate the absence of dynamic time in the B-Universe in > order to make your claims plausible, but then the B-Universe could > hardly be claimed to be "exactly the same". There can be no dynamic time. In the space-time, time is always static. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
Bruno Marchal skrev: Le 05-juil.-07, à 14:19, Torgny Tholerus wrote: David Nyman skrev: You have however drawn our attention to something very interesting and important IMO. This concerns the necessary entailment of 'existence'. 1. The relation 1+1=2 is always true. It is true in all universes. Even if a universe does not contain any humans or any observers. The truth of 1+1=2 is independent of all observers. I agree with you (despite a notion as "universe" is not primitive in my opinion, unless you mean it a bit like the logician's notion of model perhaps). As David said, this is arithmetical realism. Yes, you can see a universe as the same thing as a model. When you have a (finite) set of rules, you will always get a universe from that set of rules, by just applying those rules an unlimited number of times. And the result of these rules is existing, in the same way as our universe is existing. Our universe is the result of some set of rules. The interesting thing is to discover the specific rules that span our universe. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
David Nyman skrev: > Consequently we can't 'interview' B-Universe objects. > It is true that we can not interview objects in B-Universe. One object in one universe can not affect any object in some other universe. But we can look at the objects in an other universe. Just in the same way that we can look at a GoL-universe. So we in the A-Universe can look at the objects in B-Universe, and see what they are doing. One way to interview the objects in B-Universe is to do interviewing in the A-Universe. If A-Torgny is interviewing A-David in the A-Universe, then B-Torgny will be interviewing B-David in the B-Universe. Because everything that happens in A-Universe will also happen in B-Universe. All objects in A-Universe obey the laws of physics, and all objects in B-Universe obey the same laws, so the same things will happen in both universes. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Some thoughts from Grandma
David Nyman skrev: > You're right, we must distinguish zombies. The kind I have in mind > are the kind that Torgny proposes, where 'everything is the same' as > for a human, except that 'there's nothing it is like' to be such a > person. My key point is that this must become incoherent in the face > of self-relativity. My reasoning is that a claim for the 'existence' > of something like Torgny's B-Universe is implicitly a claim for > self-relative existence: i.e. independent of other causality, like the > One. When Torgny proposed the Game of Life as an example of 'another > universe', I pointed out that GoL clearly doesn't possess independent > existence: it's just a part of the A-Universe. It is intresting to study the GoL-universe we can see on the Wikipedia page. What will happen if we stop the program that shows this GoL-universe? Will the GoL-universe stop to exist then? No, the GoL-universe will not stop, it will continue for ever. The rules for this GoL-universe makes it possible to compute all future situations. It is this that is important. This GoL-universe is not dependent of the A-Universe. What we see when we look at the Wikipedia page is just a picture of a part of this GoL-universe. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
David Nyman skrev: > You have however drawn our attention to something very interesting and > important IMO. This concerns the necessary entailment of 'existence'. 1. The relation 1+1=2 is always true. It is true in all universes. Even if a universe does not contain any humans or any observers. The truth of 1+1=2 is independent of all observers. 2. If you have a set of rules and an initial condition, then there exist a universe with this set of rules and this initial condition. Because it is possible to compute a new situation from a situation, and from this new situation it is possible to compute another new situation, and this can be done for ever. This unlimited set of situations will be a universe that exists independent of all humans and all observers. Noone needs to make these computations, the results of the computations will exist anyhow. 3. All mathmatically possible universes exists, and they all exist in the same way. Our universe is one of those possible universes. Our universe exists independant of any humans or any observers. 4. For us humans are the universes that contain observers more interesting. But there is no qualitaive difference between universes with observers and universes without observers. They all exist in the same way. The GoL-universes (every initial condition will span a separate universe) exist in the same way as our universe. But because we are humans, we are more intrested in universes with observers, and we are specially interested in our own universe. But otherwise there is noting special with our universe. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
David Nyman skrev: On 04/07/07, Stathis Papaioannou <[EMAIL PROTECTED]> wrote: SP: We can imagine an external observer looking at two model universes A and B side by side, interviewing their occupants. DN: Yes, and my point precisely is that this is an illegitimate sleight of imagination where the thought experiment goes amiss. When one imagines the 'external' observer 'looking' at two universes, one constructs precisely the false relationship that is the source of the confusion with respect to consciousness. Any possible observer must in fact be integral to their own universe. You can look at the Game-of-Life-Universe, where you can see how the "gliders" move. If you look at "Conway's game of Life" in Wikipedia, you can look at how the Glider Gun is working in the top right corner. This is possible although there is no observer integral to that Universe. The same is true about the B-Universe. You can look at it as an outside observer. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
Jason skrev: > Note that you did not say "thought" was non-existent in B-universe, I > think one can construct complex conscious awareness to the collection > of a large number of simultaneous thoughts. I had the intention to include "thoughts", but I was unsure about how to spell that word (where to put all those "h":s...), so I included the thoughts in "all that kind of stuff". The B-Universe should not include any thouths(!). The B-Universe should be a strictly materialistic Universe. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Asifism revisited.
Imagine that we have a second Universe, that looks exactly the same as the materialistic parts of our Universe. We may call this second Universe B-Universe. (Our Universe is A-Universe.) This B-Universe looks exactly the same as A-Universe. Where there is a hydrogen atom in A-Universe, there will also be a hydrogen atom in B-Universe, and everywhere that there is an oxygen atom in A-Universe, there will be an oxygen atom i B-universe. The only difference between A-Universe and B-Universe is that B-Universe is totally free from consciousness, feelings, minds, souls, and all that kind of stuff. The only things that exist in B-Universe are atoms reacting with eachother. All objects in B-Universe behave in exactly the same way as the objects in A-Universe. The objects in B-Universe produces the same kind of sounds as we produce in A-Universe, and the objects in B-Universe pushes the same buttons on their computers as we do in our A-Universe. Questions: Is B-Universe possible? If we interview an object in B-Universe, what will that object answer, if we ask it: "Are you conscious?"? -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Justifying the Theory of Everything
Jason skrev: > I have seen two main justifications on this list for the everything > ensemble, the first comes from information theory which says the > information content of everything is zero (or close to zero). The > other is mathematicalism/arithmatical realism which suggests > mathematical truth exists independandly of everything else and is the > basis for everything. > > My question to the everything list is: which explaination do you > prefer and why? Are these two accounts compatible, incompatible, or > complimentary? Additionally, if you subscribe to or know of other > justifications I would be interesting in hearing it. > Both justifications are true. All mathematical possible universes exist. (Game of Life is one possibility...) But this theory doesn't say anything about our universe. So the information content is zero. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Quentin Anciaux skrev: On Thursday 28 June 2007 16:52:12 Torgny Tholerus wrote: Consciouslike behaviour is good for a species to survive. Therefore human beings show that type of behaviour. I don't know what is consciouslike behaviour without consciousness in the first place. An animal can show a consciouslike behaviour. When a dog sees a rabbit, then the dog behaves as if he is conscious about that there is food in front of him. He starts running after the rabbit as quick as he can. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Bruno Marchal skrev: > > But nobody really doubts about his own consciousness > (especially going to the dentist), despite we cannot define it nor > explain it completely. That sentence is wrong. There is at least one person (me...) that really doubts about my own consciousness. I am conscious about that I am not conscious. I know that I does not know anything. When I go to the dentist I behave as if I am feeling strong pain, because my pain center is directly stimulated by the dentist, which is causing my behaviour. Consciouslike behaviour is good for a species to survive. Therefore human beings show that type of behaviour. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
> > On Tuesday 19 June 2007 11:37:09 Torgny Tholerus wrote: >> What you call "the subjective experience of first person" is just some >> sort of behaviour. When you claim that you have "the subjective >> experience >> of first person", I can see that you are just showing a special kind of >> behaviour. You behave as if you have "the subjective experience of >> first >> person". And it is possible for an enough complicated computer to show >> up >> the exact same behaviour. But in the case of the computer, you can see >> that there is no "subjective experience", there are just a lot of >> electrical fenomena interacting with each other. >> >> There is no first person experience problem, because there is no first >> person experience. > > In all your reasoning you implicitely use "consciousness" for example when > you > says "When you claim that you have the subjective experience > of first person, *I* can see that you are just showing a special kind of > behaviour." > > Who/what is "I" ? Who/what is seeing ? What does it means for you to see > if > you have no inner representation of what you (hmmm if you're not > conscious, > you is not an appropriate word) see, what does it means to see at all ? > > In all your reasonning you allude to "I", this is what 1st pov is about > not > about you (the conscious being/knower) looking at another person as if > there > was no obsever (means you) in the observation. > > Quentin Our language is very primitive. You can not decribe the reality with it. If you have a computer robot with a camera and an arm, how should that robot express itself to descibe what it observes? Could the robot say: "I see a red brick and a blue brick, och when I take the blue brick and places it on the red brick, then I see that the blue brick is over the red brick."? But if the robot says this, then you will say that this proves that the robot is conscious, because it uses the word "I". How shall the robot express itself, so it will be correct? It this possible? Or is our language incapable of expressing reality? We human beings are slaves under our language. The language restricts out thinking. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Mohsen Ravanbakhsh skrev: >The "subjective experience" is just some sort of behaviour. You can make computers show the same sort of >behavior, if the computers are enough complicated. But we're not talking about 3rd person point of view. I can not see how you reduce the subjective experience of first person to the behavior that a third person view can evaluate! All the problem is this first person experience. What you call "the subjective experience of first person" is just some sort of behaviour. When you claim that you have "the subjective experience of first person", I can see that you are just showing a special kind of behaviour. You behave as if you have "the subjective experience of first person". And it is possible for an enough complicated computer to show up the exact same behaviour. But in the case of the computer, you can see that there is no "subjective experience", there are just a lot of electrical fenomena interacting with each other. There is no first person experience problem, because there is no first person experience. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Quentin Anciaux skrev: > 2007/6/14, Torgny Tholerus <[EMAIL PROTECTED]>: > >> If a rock shows the same behavior as a human being, then you should be able >> to use the same words ("know", believe", "think") to describe this >> behaviour. >> > If the rock know something and it behaves like it knows it, then it is > conscious. > If the rock does *not* know anything, *but* the rock behaves as if it knows it, then it is reasonable to say that "the rock knows it". -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Quentin Anciaux skrev: 2007/6/14, Stathis Papaioannou <[EMAIL PROTECTED]>: On 14/06/07, Quentin Anciaux <[EMAIL PROTECTED]> wrote: Sure but I still don't understand what could mean 'to know', 'to believe' for an entity which is not conscious. Also if you're not conscious, there is no 'me', no 'I', so there exists no 'person like you' because then you're not a person. Sure, but Torgny is just displaying the person-like behaviour of claiming to be a person. Yes, in this case his writing is just garbage because it doesn't have any meaning. I can't understand what it means for an unconscious thing (for example a rock) to know something, to believe in something, to have thought (especially this one, because it could be a definition of consciousness, ie: something which has thought). If the rock behaves as if it knows something (if you say something to the rock, and the rock gives you an intelligent answer), then you can say that the rock knows something. When the rock behaves as if it believes in something, then you can say that the rock believes in something. If the rock behaves as if it has thought, then you can say that the rock has thought. If a rock shows the same behavior as a human being, then you should be able to use the same words ("know", believe", "think") to describe this behaviour. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Bruno Marchal skrev: Le 07-juin-07, à 15:47, Torgny Tholerus a écrit : What is the philosophical term for persons like me, that totally deny the existence of the consciousness? An eliminativist. "Eliminativist" is not a good term for persons like me, because that term implies that you are eliminating an important part of reality. But you can't eliminate something that does not exists. If you don't believe in ghosts, are you then an eliminativist? If you don't believe in Santa Claus, are you then an eliminativist, eliminating Santa Claus? -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Mark Peaty skrev: > MP: There is possibly a loose end or two here and perhaps > clarification is needed, yet again: > > * Or this could conceivably be construed as a 'state of grace' > in that Torgny is operating with no mental capacity being wasted > on self-talk or internal commentary: 'just doing' whatever needs > to be done and 'just being' what he needs to be; very Zen! > To discuss the nature of consciousness is waste of time, because consciousness or mind is not an entity that exists in the real world. The only thing that exists in the real world is matter. What you can talk about is consciouslike behaviour, objects that behave as if they were conscious, objects that claim that they are conscious. > * Then again it may be that I have misunderstood TT's grammar > and that what he is denying is simply the separate existence of > something called 'consciousness'. If that be the case then I > would not argue because I agree that the subjective impression > of being here now is simply what it is like to be part of the > processing the brain does, ie updating the model of self in the > world. > Yes, I simpy deny the separate existence of something called 'consciousness'. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Mohsen Ravanbakhsh skrev: What is the subjective experience then? The "subjective experience" is just some sort of behaviour. You can make computers show the same sort of behavior, if the computers are enough complicated. -- Torgny Tholerus On 6/8/07, Torgny Tholerus <[EMAIL PROTECTED]> wrote: The question, as I see it, is if there is anything "more" than just atoms reacting with each other in our brains. I claim that there is not anything "more". The atoms reacting with each other explain fully my (and your...) behaviour. Our brains are very complicated structures, but it is nothing supernatural with them. Physics explains everything. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism
Quentin Anciaux skrev: On Friday 08 June 2007 17:37:06 Torgny Tholerus wrote: What is the problem? If a computer behaves as if it knows anything, what is the problem with that? That type of behaviour increases the probability for the computer to survive, so the natural selection will favour that type of behaviour. I claim that if it behaves as if, then it means it has consciousness... Philosophical zombie (which is what it is all about) are not possible... If it is impossible to discern it with what we define as conscious (and when I say impossible, I mean there exists no test that can show between the presuposed zombie and a conscious being a difference of behavior) then there is no point whatsover you can say to prove that one is conscious and one is not. Either both are conscious or both aren't... While you say you're not conscious... I am, therefore you're conscious. The question, as I see it, is if there is anything "more" than just atoms reacting with each other in our brains. I claim that there is not anything "more". The atoms reacting with each other explain fully my (and your...) behaviour. Our brains are very complicated structures, but it is nothing supernatural with them. Physics explains everything. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---