On Sun, Jun 5, 2011 at 11:58 AM, Rex Allen <rexallen31...@gmail.com> wrote:

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> On Sat, Jun 4, 2011 at 4:14 PM, Jason Resch <jasonre...@gmail.com> wrote: > > On Jun 4, 2011, at 1:03 PM, Rex Allen <rexallen31...@gmail.com> wrote: > >> On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <jasonre...@gmail.com> > wrote: > >>> > >>> Godel showed no single axiomatic system captures all mathematical > truth, > >>> any > >>> fixed set of axioms can at best approximate mathematical truth. If > >>> mathematical truth cannot be fully captured by a set of axioms, it must > >>> exist outside sets of axioms altogether. > >> > >> Then perhaps the correct conclusion to draw is that there is no such > >> thing as "mathematical truth"? > >> > >> Perhaps there is just human belief. > >> > > > > Perhaps so, perhaps there is only Rex's beliefs. Perhaps only rex's > beliefs > > at this exact moment. > > Not obviously impossible. Thought not obviously necessitated either. > > Does the possibility that there are only Jason’s beliefs at this exact > moment scare you? > > Would you prefer it to be otherwise? > > It makes the universe much smaller, less varied, less fascinating, etc. to believe my current thought is all there is. It also makes answering any questions futile (why does this thought exist?, can I change it? Am I a static thought or an evolving thought? What determines or controls the content of this thought?) How can any of those questions be approached if only thought exists? > > > What model for decision making can there be with such a > > world view? > > But we don’t need metaphysics for decision making. > > We must act. And there’s nothing guide those actions except that > which can be “distilled” from past experience. > > But what to make of the distillate? Is it just a compact description > of past observations? Or is it a “true” description of reality? > > Classical mechanics turned out to be a compact description of past > observations. No one looks to Newton’s equations for metaphysical > guidance, do they? > > But computationalism is, you think, a true description of reality? > Physics explains physical interactions within this universe but it alone can only take our understanding so far. Physics won't explain why there is the apparent randomness seen in quantum mechanics, it won't explain why there is a physical universe, nor why it has the laws that it does. Expanding our definition of reality from "things we can see" to "things we can interact with" leads to arithmetical realism. And arithmetical realism can help explain all the previous questions I listed, while physics alone can not. I agree with Leibniz when he said "Everything that is possible demands to exist." Follow the trend science has made over the past few thousand years, the concept of what is real has been exploding: 1. This world and the sky above it are all that exist 2. This world is one of many worlds, orbiting the Sun (Copernicus in 1543) 3. Our sun is one of many stars in this galaxy (First demonstrated in 1838 by Friedrich Bessel) 4. This galaxy is one of many galaxies (Hubble in 1920) 5. This universe is just one possible history all possible histories (Everett in 1957) 6. The observable universe is only a very small piece of the whole of the universe (Alan Guth in 1980) 7. The standard model is just one possible solution of the 10^500 or so possible solutions to string theory (Weinberg in 1987, and Susskind) 8. Physical systems are not limited to the equations of string theory, all structures in math exist (Tegmark in 1998) Starting from 5 and onward, there is some ongoing debate, but the trend is clear, reality is far grander than we initially conceived. Mathematical Realism is only a small step from 7. One can look at Everett simply as all solutions to the Schroedinger equation are real. And the landscape of string theory: All solutions to the mathematics of string theory are real. But why should we stop there? What makes the equations of string theory any more privledged with the blessing of reality compared to others? We have gathered no evidence suggesting that solutions to other types of equations cannot exist, so why believe it? The only argument I see is Ockham's razor, why believe in additional entitites if it makes the theory more complex? But this is incorrect, the theory that "all solutions to all equations exists" is far simpler than the theory that "only certain very complex equations of string theory exist, and the others are impossible because ...". > > > But what explanatory power does that offer? > > It seems plausible to me that physics (or computationalists) may be > able to generate a complete, compact framework that describes the > world that I observe. > > And since I observe behavior of the people around me, and the > framework is a compact description of my observations, then I should > be able to “explain” people’s behavior in terms of the framework. > > And if I can explain my neighbor’s behavior in terms of the framework, > maybe I can explain my own behavior in those terms as well. > > However... > > Explanation is something that occurs *within* a descriptive framework. > Those explanations don’t reach beyond the framework. > > Going “metaphysical” (instead of instrumental) with an explanatory > framework could only be justified if we had some reason to believe > that our observations plus our reason gave us reliable access to what > is real. > > But notice that “reason” shows up twice in that sentence...which is a > problem. > > > >>> The fractal is just an example of a simple formula leading to very > >>> complex > >>> output. The same is true for the UDA: > >>> for i = 0 to inf: > >>> for each j in set of programs: > >>> execute single instruction of program j > >>> add i to set of programs > >>> That simple formula executes all programs. > >> > >> Following those instructions will let someone "execute" all "programs". > > > > What is the engine providing the computations which drive the universe? > > That assumes that computations do drive the universe. > > Which is the assumption that I’m questioning. > The physical universe may be computational or it may be a mathematical structure, but what enforces its consistency and constancy of its laws? If it were a mathematical structure, or a computation then the consistency comes for free. > > > >> Or, alternatively, configuring a physical system in a way that > >> represents those instructions will allow someone to interpret the > >> system's subsequent states as being analogous to the "execution" of > >> all "programs". > >> > > > > Do you think pi has an objective (not human invented or approximated) > value, > > whether or not any person computed it? > > I think that everyone who starts from the same assumptions and makes > the same inferences will always reach the same conclusions regarding > the value of pi. > > So that would make pi an objectively studiable object, would it not? What makes the study of such objects less valid than the study of other objects in science, for example in biology? To define a bacterium as a life form Earth scientists and alien scientists both have to start from similar assumptions and make similar inferences. Based on different starting assumptions some might say a virus is alive others may not, this doesn't mean that viruses don't exist. In your postings you seem to suggest that given there could be disagreement on what starting assumptions to use the reality of mathematical objects should be called into question, but this would be like questioning whether viruses exist because biologists can't agree on whether or not they are alive. The numbers, their properties and relations are objectively studiable, as much as planets and viruses are. If math is invented, then you should invent a prime number with a billion digits and claim the $250,000 prize ( http://www.eff.org/awards/coop ). If you cannot invent such a number, then perhaps mathematics truly is a space to be explored, much like the vacuum that surrounds our planet. > > > Is there an answer to the question what is the googleplexth decimal digit > of > > pi given no one in this universe could ever computed it? > > Is there an answer to the question of whether this penny would have > melted had I taken an oxyacetylene torch to it yesterday - given that > this didn’t actually happen? > > If there is an answer to the inner question, and that answer is “yes” > (or “no” for that matter), what makes it “yes” (or “no”)? > > So I can answer the question today relative to some explanatory > framework. But given that the framework is just the distillation of > past experience, and is only intended as a guide to action...the > answer I give today about what would have happened yesterday isn’t > meaningful except in relation to the framework. It’s “for > entertainment purposes only”. > > In the “real world” (whatever that is), I’d guess that there is no > fact of the matter about what would have happened yesterday with the > penny and the torch. > > SO...applying the same reasoning to your question: > > I’ll say that relative to some framework that includes my experience > with the assumptions and inferences and rules needed to calculate pi - > the answer is yes. Because in that framework, given enough time and > enough “universe”, it seems likely that someone *could* calculate the > googleplexth digit of pi. > So the value is there, waiting to be found (even though no one has bothered to go through the motions to compute it)? Does it have a value if it is computed but no person reads the result? What if it is computed and then all traces of the result are destroyed, does the value determined disappear? > > But that answer is for entertainment purposes only...since it is an > answer based on a framework distilled from past experience for the > purposes of guiding action which is instead being applied to a purely > hypothetical situation that has no chance of being enacted. > > The answer is only relevant relative to the framework that generated > it and there’s no grounds for ascribing metaphysical significance to > the framework, and so there’s no grounds for ascribing metaphysical > significance to the answer. > > There is no fact of the matter except relative to the framework. > > It’s like asking “who would win an arm wrestling match between the > Incredible Hulk and Spiderman”. I can confidently say the Incredible > Hulk. But that answer doesn’t really mean anything outside of the > “Marvel Universe”. The Marvel Universe has no metaphysical > significance, and so my answer to this hypothetical question involving > it has no metaphysical significance either. > > See? > > Unlike the marvel universe, if mathematical objects exist it is of huge metaphysical significance, as it makes so called physical universes redundant and completely unnecessary for explaining observations. > > > If there is, then there are also objective values to the omega constant, > or > > the state of the uda after X steps. These values exist without the need > for > > someone to execute them, anymore than we need to compute the billionth > digit > > of pi for it to have it's value. > > Relative to some detailed fictional framework, sure. Such an > imagination you have! > > You and I happen to inhabit the "detailed fictional framework" we call the physical universe, which only seems real relative to us because we inhabit it. Information and computations are built upon relations between objects. They could be pulses of charged solutions between nerve cells, electrical fields travelling through wires in a chip, gears turning in Babbage's analytical engine, etc. What X and Y are in the computer is not the important factor, it is the relation between X and Y. Regardless of whether the objects X and Y are atoms in a physical universe or objects in mathematics, their power to represent information (and correspondingly consciousness) is not any different. No program can make any determination as to the ultimate hardware it is being executed on, by Turing universality. Therefore if consciousness is regarded as a computation, you cannot with full confidence conclude you are Rex whose mind runs on the physics of this universe confidently and not Rex whose mind is executed in a mathematical object. > > >>>> Is extraordinary complexity required for the manifestation of "mind"? > >>>> If so, why? > >>> > >>> I don't know what lower bound of information or complexity is required > >>> for minds. > >> > >> Then why do you believe that information of complexity is required for > >> minds? > >> > > > > I think information is a critical component of consciousness. The very > > definition of consciousness: "having awareness of ones own thoughts and > > sensations.". Awareness is defined as having knowledge or information. > > Therefore consciousness is the possession of information (about ones > > thoughts ir sensations). > > We can say that we have information about what we are aware of...but > that is not the same as saying that awareness *is* information. > I think there is an important difference between saying "consciousness = awareness of information" vs. "consciousness = awareness = information". > > Information is a difference that makes a difference. But it has to > make a difference *to* someone. > > This is why the consciousness requires a process accepting or operating on information. If a process is not defined there can be no interpretation. > A randomly generated string of bits can be identical to a string of > bits representing an image...but the randomly generated string of bits > contain no real information whereas the image file does. > > The difference being that I know how to correctly interpret an image > file, but there is no “correct” interpretation of a random string of > bits. > > But with the right “interpretation” any information can be found > anywhere. The magic is all in the interpreter, not in what’s being > interpreted. > > Information is observer-relative. Observers aren’t information-relative. > > Are you a computationalist? This line of thought sounds like you are.. > > > There are also reasons to believe in the informational basis if > > consciousness due to multiple realizeability. Minds can take different > > physical forms because information cab take many physical forms. > > I can take anything to represent anything else. So “representation” > is multiply realizable. > > But again, that has to do with me, not with information. If I > remember what my encoding scheme was, I can “re-present” things to > myself. If I forget what my encoding scheme was, or that I even > encoded anything - then all I have are a bunch of bits...which for all > I know might be random. > > If they really were random bits, but for some reason I was convinced > they weren’t - I might find all sorts of “meaningful” interpretations > of them using all sorts of decoding schemes - but none of these would > be correct. > > In this case, I’m doing all of the work...the bits aren’t doing > anything. Which, as it turns out, is also true of non-random bit > strings. I do all of the work. The bits are just reminders...hints. > > I think you’re getting it all backwards. Representation depends on > me. I don’t depend on representation. > What I mean by multiple realizability is parts of your brain can be replaced with any part which is functionally equivalent without impacting your consciousness. While true, different programs can interpret different encodings differently, those programs can be realized with different representations. > > You’re saying: “Hey, look at all the great things I can do with > representation! What if I represented myself in some way??? Would > that be me?” > > Well...no. That would be a representation of you. How are you defining the person in this case? Different functionally equivalent representations of you would be as conscious as you are now, would they not? > Representation is > something you do, not something that you are. > If by representation you mean the representation of consciousness, then this is the functionalist/computationalist philosophy in a nutshell. > > > > Lastly there is an argument realted to zombies. A zombie cannot feel any > > different or be less conscious than a conscious person who is physically > > identical. This is because the informational content of both the person > and > > the zombie is necessarily the same (given the identical physical states). > > Therefore the conscious person does not and cannot know anything more > about > > what they are feeling or experiencing than the zombie does. Both must be > > equally conscious. > > That’s one way of looking at it. That might be true relative to some > explanatory framework. But it’s true for entertainment purposes only. > Like the Hulk-Spiderman matchup above. > > > > >>>> Is it that these recursive relations cause our experience, or are just > >>>> a way of thinking about our experience? > >>>> > >>>> Is it: > >>>> > >>>> Recursive relations cause thought. > >>>> > >>>> OR: > >>>> > >>>> Recursion is just a label that we apply to some of our implicational > >>>> beliefs. > >>>> > >>>> The latter seems more plausible to me. > >>>> > >>> > >>> Through recursion one can implement any form of computation. > >> > >> But, ultimately, what is computation? > >> > > > > A process. More specifically one that connects a succession of states > via > > some well-defined relation(s). > > So why would a process that connects a succession of states via > well-defined relations - in addition to being that - *also* be my > conscious experience of sitting in this chair drinking coffee, writing > this email? > Because as you said, you need something to impart meaning to the bits, and that requires well defined relations which indicate meaning of the bits to the overall process. While you can look at any bit string and say it means this, you cannot look at a program which is calculating Pi and say it is calculating e. > > Why would that be? Why would this process be *two* things instead of > just one? Not interpretable as two things (by me) - but really, > intrinsically two entirely different things? > > I am not sure what you are asking here. There are third and first person perspectives of course, does that mean there are two things? 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