Re: what relation do mathematical models have with reality?
Hal Finney wrote: No doubt this is true. But there are still two somewhat-related problems. One is, you can go back in time to the first replicator on earth, and think of its evolution over the ages as a learning process. During this time it learned this intuitive physics, i.e. mathematics and logic. But how did it learn it? Was it a Bayesian-style process? And if so, what were the priors? Can a string of RNA have priors? I'd say that biological evolution bears little resemblance to Bayesian learning, because Bayesian learning assumes logical omniscience, whereas evolution cannot be viewed as having much ability to make logical deductions. And more abstractly, if you wanted to design a perfect learning machine, one that makes observations and optimally produces theories based on them, do you have to give it prior beliefs and expectations, including math and logic? Or could you somehow expect it to learn those? But to learn them, what would be the minimum you would have to give it? I'm trying to ask the same question in both of these formulations. On the one hand, we know that life did it, it created a very good (if perhaps not optimal) learning machine. On the other hand, it seems like it ought to be impossible to do that, because there is no foundation. Suppose we create large numbers of robots with much computational power, but random programs, and set them to compete against each other for limited resources in a computable environment. If the initial number is sufficiently large, we can expect that the ones that survive in the end will approximate Bayesian reasoners with priors where actual reality has a significant probabilty. We can further expect that the priors will mostly be UDist because that is the simplest prior where the actual environment has a significant probabilty. Thus we've created foundation out of none. Actual evolution can be seen as a more efficient version of this. Now suppose one of these suriviving robots has an interest in philosophy. We might expect that it would notice that its learning process resembles that of a Bayesian reasoner with UDist as prior, and therefore invent a Schmidhuberian-style philosophy to provide self justification. I wonder if this is what has happened in our own case as well.
Re: what relation do mathematical models have with reality?
Hi Lee, Thanks for answering all my mails, but I see you send on the list only the one where you disagree. Have you done this purposefully? Can I quote some piece of the mail you did not send on the list? I will answer asap. Also, for this one, I did not intend to insult you. Sorry if it looks like that, Bruno Le 26-juil.-05, à 23:31, Lee Corbin a écrit : Bruno writes Look, it's VERY simple: take as a first baby-step the notion that the 19th century idea of a cosmos is basically true, and then add just the Big Bang. What we then have is a universe that operates under physical laws. So far---you'll readily agree---this is *very* simple conceptually. Next, look at this picture after 14.7 billion years. Guess what has evolved? Finally, there is intelligence and there are entities who can *perceive* all this grandeur. So, don't forget which came first. Not people. Not perceptions. Not ideas. Not dich an sich. Not 1st person. Not 3rd person. NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps* will have a chance to understand what is going on. But both the quantum facts, and then just the comp hyp are incompatible with that type of naive realism. At this level of discourse, dear Bruno, I don't give a ___ for your *hypothesis*. Moreover, please google for naive realism. You'll find that this is the world view of children who have *no* idea of the processes by which their brains are embedded in physical reality. Since no one claims to be a naive realist, this rises to the level of insult. But then, I'm not too surprised that the most *basic* understanding of our world has been forgotten by some who deal everyday with only the most high level abstractions. Lee http://iridia.ulb.ac.be/~marchal/
Re: what relation do mathematical models have with reality?
Le 27-juil.-05, à 00:12, Aditya Varun Chadha a écrit : I think a reconciliation between Bruno and Lee's arguments can be the following: Thanks for trying to reconciliate us :) Our perception of reality is limited by the structure and composition of brains. (we can 'enhance' these to be able to perceive and understand 'more', but at ANY point of time the above limitation holds). I think this is closer to what Lee wants to say, and I totally agree with it. This is what I have tried to elaborate on in my earlier (my first here) email. But the very fact that this limitation is absolutely inescapable (observation and understanding is ALWAYS limited to the observer's capabilities) gives us the following insight: That which cannot be modelled (understood) cannot figure in ANY of our models of reality. Why ? (I have explicit counterexamples, like the notion of knowledge for machine). Logic has evolved up to the point we are able to build formal theory bearing on non formalizable notions (like truth or knowledge). Amazing and counterintuitive I agree. Therefore although our models of reality keep changing, at any given time instance there is no way for us to perceive anything beyond the model, because as soon as something outside our current model is perceived, we have moved to a future instance, and can create a model that includes it. Thus it is kind of senseless to talk of a reality beyond our perception. Why? We can bet on some theories and derive consequences bearing indirectly on some non perceivable structure. In other words, we can call something reality only once we perceive it. In this sense models may be more real than reality to us. This is an argument of the Shroedinger's Cat kind. In fact if I am correct about what both Bruno and Lee want to say, then Lee's arguments are a prerequisite to understanding to what Bruno is hinting at. Actually I agree with it. I do think Lee is close to what I want to say, at the level of our assumptions. But Lee is quite honest and cannot not be sure that my conclusion must be non sense (which means that he grasped them at least). Quantum Physics says that an observer and his observation are impossible to untangle. OK. But I don't use this. Actually I don't use physics at all. Physics is emergent, not fundamental (once we assume seriously enough digital mechanism (or computationalism). From the above fact, A Realist (Lee) would conclude that absolute reality is unknowable. (follows from heisenburg's uncertainty also btw:-) ). But for this the realist assumes that this absolute reality exists. A Nihilist (Bruno) would conclude that since this tanglement of observer and observation is inescapable, it is meaningless to talk about any absolute reality outside the perceived and understood reality (models). Actually I am a platonist, that is, a mathematical realist. I do also believe in physical reality. My point is just that if you make some hypothesis in the cognitive science (mechanism, computationalism) then physics is 100% derivable from mathematics. The physical laws are mathematical (even statistical) laws emerging from what any machine can correctly bet concerning invariant feature of their most probable computational history. Nihilism is what happens when you believe in both computationalism and materialism. This has been illustrated by La Mettrie and mainly Sade (but also Heidegger and Nietsche in a less direct way, and then perhaps Hitler or Bin Laden in in very more indirect way). I am not at all a nihilist. I just show that the computationalist hypothesis makes the physical world emerge from the truth on numbers. I take those truth as being independent of me. I am not a physical realist perhaps, although I do believe in an independent physical world. I just don't physical reality is primitive. Like Plato I take what we see and measure as some shadows of something quite bigger, and non material ... None of the views is naive. In fact neither view can ever disprove the other, because both belong to different belief (axiomatic) systems. apples and oranges, both tasty. P.S.: If what I have said above sounds ok and does help put things in perspective, then I would like to think that in this WHOLE discussion there is NO NEED of invoking terms like comp hyp, ASSA, RSSA, OMs, etc. I, being clearly a lesser being in this new domain of intellectual giants at eskimo.com, would highly appreciate if atleast the full forms are given so that I can google them and put them in context. OK, but I think those you mention are used in so many posts that I suggest you to remember them: ASSA = A SSA = Absolute Self-Sampling Assumption, RSSA = R SSA = Relative Self-Sampling Assumption, comp hyp = Computationalist Hypothesis (or digital mechanism, ...) OM = Observer-moment Bruno http://iridia.ulb.ac.be/~marchal/
RE: what relation do mathematical models have with reality?
Hal wrote Brent Meeker wrote: In practice we use coherence with other theories to guide out choice. With that kind of constraint we may have trouble finding even one candidate theory. Well, in principle there still should be an infinite number of theories, starting with the data is completely random and just happens to look lawful by sheer coincidence. I think the difficulty we have in finding new ones is that we are implicitly looking for small ones, which means that we implicitly believe in Occam's Razor, which means that we implicitly adopt something like the Universal Distribution, a priori. An intriguing way of putting it; yes, the amount of data compression possible is necessarily related to both Occam's Razor and the UDist. We begin with an intuitive physics that is hardwired into us by evolution. And that includes mathematics and logic. There's an excellent little book on this, The Evolution of Reason by Cooper. No doubt this is true. But there are still two somewhat-related problems. One is, you can go back in time to the first replicator on earth, and think of its evolution over the ages as a learning process. During this time it learned this intuitive physics, i.e. mathematics and logic. But how did it learn it? Was it a Bayesian-style process? And if so, what were the priors? Can a string of RNA have priors? I would say that the current state of the RNA string at any given time can be regarded as its prior. After all, it survived up to now, eh? The idea that evolution has to be pretty conservative, ---that is, the mechanisms must not allow too many new guesses--- also follows at once. And more abstractly, if you wanted to design a perfect learning machine, one that makes observations and optimally produces theories based on them, do you have to give it prior beliefs and expectations, including math and logic? Or could you somehow expect it to learn those? But to learn them, what would be the minimum you would have to give it? I'm trying to ask the same question in both of these formulations. On the one hand, we know that life did it, it created a very good (if perhaps not optimal) learning machine. On the other hand, it seems like it ought to be impossible to do that, because there is no foundation. I strongly urge you to read the new book What is Thought, by Eric Baum. He very insightfully and carefully attends to these questions. Lee
RE: what relation do mathematical models have with reality?
Lee Corbin writes: It's just amazing on this list. Does no one speak up for realism? The *default* belief among *all* people up until they take their first fatal dive into a philosophy book is that there is an ordinary three-dimensional world that we are all running around in. (Yes---one *may* look at it as a model, but is this *really* necessary? It prevents accurate understanding as well as fosters terrible misunderstandings.) When 99% of the human race use the word reality, they mean the world outside their skins. If you sacrifice our common understanding of reality, then you'll find yourself in a hole out of which you'll never climb. Yes, but what *is* this 3D world we can all stub our toe on? If we go back to the start of last century, Rutherford's quaintly pre-QM atom, amazingly, turned out to be mostly empty space. Did this mean that, suddenly, it doesn't hurt when you walk into a brick wall, because it isn't nearly as solid as you initially thought it was? Of course not; our experience of the world is one thing, and the reality behind the experience is a completely different thing. If it is discovered tomorrow beyond any doubt that the entire universe is just a game running in the down time on God's pocket calculator, how is this fundamentally different to discovering that, contrary to appearances, atoms are mostly empty space, or subatomic particles have no definite position, or any other weird theory of modern physics? And how could, say, the fact that brick walls feel solid enough possibly count as evidence against such an anti-realist theory? --Stathis Papaioannou _ Low rate ANZ MasterCard. Apply now! http://clk.atdmt.com/MAU/go/msnnkanz003006mau/direct/01/ Must be over 18 years.
Re: what relation do mathematical models have with reality?
Hi Stephen, I merely wish to comprehend the ideas of those that take a Pythagorean approach to mathematics; e.g. that Mathematics is more real than the physical world - All is number. One thing that I have learned in my study of philosophy is that no single finite model of reality can be complete. Perhaps that asymptotic optimum involves the comprehension of how such a disparate set of models can obtain in the first place. I agree with you that no single finite theory of reality can be complete. Actually Godel's incompleteness theorem just proves that in the case of arithmetical truth. And that was an argument for realism in math (platonism). You should not confuse a theory (like Peano Arithmetic, or Zermelo Set theory) and its intended reality (called model by logician), which by incompleteness, are not fully describable by finite theory (or by any machine). About the idea that math (or just arithmetic) is more real than the physical worlds is a logical consequence of comp. And comp is testable, it entails quite strong constraints on the observable propositions (like being necessarily not boolean for example). Regards, Bruno http://iridia.ulb.ac.be/~marchal/
Re: what relation do mathematical models have with reality?
Le 23-juil.-05, à 08:14, Hal Finney a écrit : My current view is a little different, which is that all of the equations fly. Each one does come to life but each is in its own universe, so we can't see the result. But they are all just as real as our own. In fact one of the equations might even be our own universe but we can't easily tell just by looking at it. This is so true that we cannot even localize ourself in *one* universe/history. What we call a universe emerges from the interference of an infinity of (similar) histories. (Are you not dismissing the first and third person distinction?). Bruno http://iridia.ulb.ac.be/~marchal/
Re: what relation do mathematical models have with reality?
Le 26-juil.-05, à 02:17, Lee Corbin a écrit : Look, it's VERY simple: take as a first baby-step the notion that the 19th century idea of a cosmos is basically true, and then add just the Big Bang. What we then have is a universe that operates under physical laws. So far---you'll readily agree---this is *very* simple conceptually. Next, look at this picture after 14.7 billion years. Guess what has evolved? Finally, there is intelligence and there are entities who can *perceive* all this grandeur. So, don't forget which came first. Not people. Not perceptions. Not ideas. Not dich an sich. Not 1st person. Not 3rd person. NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps* will have a chance to understand what is going on. But both the quantum facts, and then just the comp hyp are incompatible with that type of naive realism. You are reifying Nature, like those who confuses Aristotle's methodology and its metaphysical questions. It seems to me you are confusing the map and the territory, like you ask us not to do in your other recent posts. I'm confuse about what you really think (about fundamental matters). Bruno http://iridia.ulb.ac.be/~marchal/
Re: what relation do mathematical models have with reality?
Le 26-juil.-05, à 04:06, Lee Corbin a écrit : Well, all that I ask is that the *basics* be kept firmly in mind while we gingerly probe forward. The basics (basic epistemology, that is) include 1. the map is not the territory, and perception is not reality This is ambiguous. A trivial example is that for someone who studies *maps*, maps are the territory. Also: perception of x is not reality of x. But perception itself is more probably real (unless we are all zombies), so perception is a reality (independently of the gap between perceiving and the things at the origin of perception). 2. the words we have for things are not the things themselves, but only labels NOT ALWAYS. I agree that *in general* we must not confuse the word and what they are intended for. But here too we can study the words themselves, and, with comp, we can even make some non trivial identification. 3. we must *not* use basic language and terminology that conflicts with that used by twelve-year olds I agree. It is an important point. Actually I am willing to believe that we can go much further in that direction. We should NOT use basic language and terminology that we are unable to translate in a language interpretable by any Lobian Machine. Russell: For most of us in this list, the 3+1 dimensional spacetime we inhabit, with its stars and galaxies etc is an appearance, phenomena emerging out of constraints imposed by the process of observation. Right there is the problem. Let's focus on what you are *referring* to in your first sentence: the 3+1 spacetime with its stars and galaxies. We must keep clear the difference between what you are *referring* to and our observations of it, or our perceptions of it. They're not at all the same thing. So when you use the dread is and write For most of us... the spacetime *is* an appearance, we've already gone over the edge. No. The spacetime that you probably meant is *not* an appearance, and we should not talk about it as if it is an appearance. *It* is whatever is out there. Yes, our understanding of it may be poor. Yes, it may not be at all as we *think*. In fact, it cannot in in any literal sense *be* what we *think*. Come on. What Russell said was the fact that many in this list could imagine that the very idea of out there could be part of the perception, like in a simulation (real, virtual or even just arithmetical but I will not insist too much here). Besides, please take comp seriously (if only just for one week), but it makes almost literally the sky out there be what we think! Only *we* denotes something much larger than usual. We, the (hopefully) consistent Machine. Please correct me, but I have the feeling you take physicalism (the doctrine that physics is necessarily the fundamental science, or that physics cannot be reduced to another body of knowledge) as so obviously true that we should not even *doubt* about it. Thanks to your conversation with Stathis, and our last posts, I know you are ready to tackle the fourth step of the Universal Dovetailer Argument (UDA) ... My point is that if we take comp seriously enough then it is not a matter of choice: physics has to be reducible to computer science, and this in a verifiable way (already partially verified). I think it is up to you to find an error in the argument (of course you can wait someone else find it if you have not the time ;). The UDA is not technical, and *is* the proof. Only the translation of UDA in the language of a (Lobian) Machine is obviously technical (like assembly language can be). The goal of that translation does not consist in making the UDA more rigorous, but only more constructive (and indeed it gives the shortest path to derive physics from computer science). Bruno PS And all what I say here is compatible with both the ASSA Schmidhuberian view (a-la Hal Finney) and the RSSA view (Levy, Standish, me, ...). Our discussion is internal on how we structure the OMs. I think (well, some like Schmidhuber explicitly invokes some physicalist predicate at some points, and I could argue the very notion of prior is basically physicalist, but we have already discussed this ...). http://iridia.ulb.ac.be/~marchal/
RE: what relation do mathematical models have with reality?
Bruno writes Look, it's VERY simple: take as a first baby-step the notion that the 19th century idea of a cosmos is basically true, and then add just the Big Bang. What we then have is a universe that operates under physical laws. So far---you'll readily agree---this is *very* simple conceptually. Next, look at this picture after 14.7 billion years. Guess what has evolved? Finally, there is intelligence and there are entities who can *perceive* all this grandeur. So, don't forget which came first. Not people. Not perceptions. Not ideas. Not dich an sich. Not 1st person. Not 3rd person. NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps* will have a chance to understand what is going on. But both the quantum facts, and then just the comp hyp are incompatible with that type of naive realism. At this level of discourse, dear Bruno, I don't give a ___ for your *hypothesis*. Moreover, please google for naive realism. You'll find that this is the world view of children who have *no* idea of the processes by which their brains are embedded in physical reality. Since no one claims to be a naive realist, this rises to the level of insult. But then, I'm not too surprised that the most *basic* understanding of our world has been forgotten by some who deal everyday with only the most high level abstractions. Lee
Re: what relation do mathematical models have with reality?
I think a reconciliation between Bruno and Lee's arguments can be the following: Our perception of reality is limited by the structure and composition of brains. (we can 'enhance' these to be able to perceive and understand 'more', but at ANY point of time the above limitation holds). I think this is closer to what Lee wants to say, and I totally agree with it. This is what I have tried to elaborate on in my earlier (my first here) email. But the very fact that this limitation is absolutely inescapable (observation and understanding is ALWAYS limited to the observer's capabilities) gives us the following insight: That which cannot be modelled (understood) cannot figure in ANY of our models of reality. Therefore although our models of reality keep changing, at any given time instance there is no way for us to perceive anything beyond the model, because as soon as something outside our current model is perceived, we have moved to a future instance, and can create a model that includes it. Thus it is kind of senseless to talk of a reality beyond our perception. In other words, we can call something reality only once we perceive it. In this sense models may be more real than reality to us. This is an argument of the Shroedinger's Cat kind. In fact if I am correct about what both Bruno and Lee want to say, then Lee's arguments are a prerequisite to understanding to what Bruno is hinting at. Quantum Physics says that an observer and his observation are impossible to untangle. From the above fact, A Realist (Lee) would conclude that absolute reality is unknowable. (follows from heisenburg's uncertainty also btw:-) ). But for this the realist assumes that this absolute reality exists. A Nihilist (Bruno) would conclude that since this tanglement of observer and observation is inescapable, it is meaningless to talk about any absolute reality outside the perceived and understood reality (models). None of the views is naive. In fact neither view can ever disprove the other, because both belong to different belief (axiomatic) systems. apples and oranges, both tasty. P.S.: If what I have said above sounds ok and does help put things in perspective, then I would like to think that in this WHOLE discussion there is NO NEED of invoking terms like comp hyp, ASSA, RSSA, OMs, etc. I, being clearly a lesser being in this new domain of intellectual giants at eskimo.com, would highly appreciate if atleast the full forms are given so that I can google them and put them in context. On 7/27/05, Lee Corbin [EMAIL PROTECTED] wrote: Bruno writes Look, it's VERY simple: take as a first baby-step the notion that the 19th century idea of a cosmos is basically true, and then add just the Big Bang. What we then have is a universe that operates under physical laws. So far---you'll readily agree---this is *very* simple conceptually. Next, look at this picture after 14.7 billion years. Guess what has evolved? Finally, there is intelligence and there are entities who can *perceive* all this grandeur. So, don't forget which came first. Not people. Not perceptions. Not ideas. Not dich an sich. Not 1st person. Not 3rd person. NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps* will have a chance to understand what is going on. But both the quantum facts, and then just the comp hyp are incompatible with that type of naive realism. At this level of discourse, dear Bruno, I don't give a ___ for your *hypothesis*. Moreover, please google for naive realism. You'll find that this is the world view of children who have *no* idea of the processes by which their brains are embedded in physical reality. Since no one claims to be a naive realist, this rises to the level of insult. But then, I'm not too surprised that the most *basic* understanding of our world has been forgotten by some who deal everyday with only the most high level abstractions. Lee -- Aditya Varun Chadha [EMAIL PROTECTED] Mobile: +91 98 400 76411 Home: +91 11 2431 4486 Room #1034, Cauvery Hostel Indian Institute of Technology, Madras Chennai - 600 036 India
Re: what relation do mathematical models have with reality?
Dear Aditya, I find your attempt to reconcile the arguments to be very good! I most appresiate that you point out that our notion of Realism must include both the invariants with respect to point of view and an allowance for novelity. I do agree that we could use a FAQ defining the strange terms that we use. ;-) Kindest regards, Stephen - Original Message - From: Aditya Varun Chadha [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Tuesday, July 26, 2005 6:12 PM Subject: Re: what relation do mathematical models have with reality? I think a reconciliation between Bruno and Lee's arguments can be the following: Our perception of reality is limited by the structure and composition of brains. (we can 'enhance' these to be able to perceive and understand 'more', but at ANY point of time the above limitation holds). I think this is closer to what Lee wants to say, and I totally agree with it. This is what I have tried to elaborate on in my earlier (my first here) email. But the very fact that this limitation is absolutely inescapable (observation and understanding is ALWAYS limited to the observer's capabilities) gives us the following insight: That which cannot be modelled (understood) cannot figure in ANY of our models of reality. Therefore although our models of reality keep changing, at any given time instance there is no way for us to perceive anything beyond the model, because as soon as something outside our current model is perceived, we have moved to a future instance, and can create a model that includes it. Thus it is kind of senseless to talk of a reality beyond our perception. In other words, we can call something reality only once we perceive it. In this sense models may be more real than reality to us. This is an argument of the Shroedinger's Cat kind. In fact if I am correct about what both Bruno and Lee want to say, then Lee's arguments are a prerequisite to understanding to what Bruno is hinting at. Quantum Physics says that an observer and his observation are impossible to untangle. From the above fact, A Realist (Lee) would conclude that absolute reality is unknowable. (follows from heisenburg's uncertainty also btw:-) ). But for this the realist assumes that this absolute reality exists. A Nihilist (Bruno) would conclude that since this tanglement of observer and observation is inescapable, it is meaningless to talk about any absolute reality outside the perceived and understood reality (models). None of the views is naive. In fact neither view can ever disprove the other, because both belong to different belief (axiomatic) systems. apples and oranges, both tasty. P.S.: If what I have said above sounds ok and does help put things in perspective, then I would like to think that in this WHOLE discussion there is NO NEED of invoking terms like comp hyp, ASSA, RSSA, OMs, etc. I, being clearly a lesser being in this new domain of intellectual giants at eskimo.com, would highly appreciate if atleast the full forms are given so that I can google them and put them in context.
Re: what relation do mathematical models have with reality?
Stephen Paul King wrote: BTW, Scott Aaronson has a nice paper on the P=NP problem that is found here: http://www.scottaaronson.com/papers/npcomplete.pdf That describes different proposals for physical mechanisms for efficiently solving NP-complete problems: things like quantum computing variants, relativity, analog computing, and so on. He actually looked at a claim that soap bubble films effectively solve NP complete problems and tested it himself, to find that they don't work. He also discusses time travel and even what we call quantum suicide, where you kill yourself if the machine doesn't guess right. I am skeptical though about something he says in conclusion: Even many computer scientists do not seem to appreciate how different the world would be if we could solve NP-complete problems efficiently If such a procedure existed, then we could quickly find the smallest Boolean circuits that output (say) a table of historical stock market data, or the human genome, or the complete works of Shakespeare. It seems entirely conceivable that, by analyzing these circuits, we could make an easy fortune on Wall Street, or retrace evolution, or even generate Shakespeare's 38th play. For broadly speaking, that which we can compress we can understand, and that which we can understand we can predict if we could solve the general case - if knowing something was tantamount to knowing the shortest efficient description of it - then we would be almost like gods. This doesn't seem right to me, the notion that an NP solving oracle would be able to find the shortest efficient description of any data. That would require a more complex oracle, one that would be able to solve the halting problem. I think Aaronson is blurring the lines between finding the smallest Boolean circuit and finding the smallest efficient description. Maybe finding the smallest Boolean circuit is in NP; it's not obvious to me but it's been a while since I've studied this stuff. But even if we could find such a circuit I'm doubtful that all the rest of Aaronson's scenario follows. Hal Finney
Re: what relation do mathematical models have with reality?
Brent Meeker wrote: [Hal Finney wrote:] When you observe evidence and construct your models, you need some basis for choosing one model over another. In general, you can create an infinite number of possible models to match any finite amount of evidence. It's even worse when you consider that the evidence is noisy and ambiguous. This choice requires prior assumptions, independent of the evidence, about which models are inherently more likely to be true or not. In practice we use coherence with other theories to guide out choice. With that kind of constraint we may have trouble finding even one candidate theory. Well, in principle there still should be an infinite number of theories, starting with the data is completely random and just happens to look lawful by sheer coincidence. I think the difficulty we have in finding new ones is that we are implicitly looking for small ones, which means that we implicitly believe in Occam's Razor, which means that we implicitly adopt something like the Universal Distribution, a priori. We begin with an intuitive physics that is hardwired into us by evolution. And that includes mathematics and logic. Ther's an excellent little book on this, The Evolution of Reason by Cooper. No doubt this is true. But there are still two somewhat-related problems. One is, you can go back in time to the first replicator on earth, and think of its evolution over the ages as a learning process. During this time it learned this intuitive physics, i.e. mathematics and logic. But how did it learn it? Was it a Bayesian-style process? And if so, what were the priors? Can a string of RNA have priors? And more abstractly, if you wanted to design a perfect learning machine, one that makes observations and optimally produces theories based on them, do you have to give it prior beliefs and expectations, including math and logic? Or could you somehow expect it to learn those? But to learn them, what would be the minimum you would have to give it? I'm trying to ask the same question in both of these formulations. On the one hand, we know that life did it, it created a very good (if perhaps not optimal) learning machine. On the other hand, it seems like it ought to be impossible to do that, because there is no foundation. Mathematics and logic are more than models of reality. They are pre-existent and guide us in evaluating the many possible models of reality which exist. I'd say they are *less* than models of reality. They are just consistency conditions on our models of reality. They are attempts to avoid talking nonsense. But note that not too long ago all the weirdness of quantum mechanics and relativity would have been regarded as contrary to logic. I guess we could agree that they are other than models of reality? It still strikes me as paradoxical: ultimately we have learned our intuitions about mathematics and logic from reality, via the mechanisms of evolution and also our own individual learning experiences. And yet it seems that at some level a degree of logic, and certain mathematical assumptions, are necessary to get learning off the ground in the first place, and that they should not depend on reality. I'm pretty confused about this right now. Hal Finney
Re: what relation do mathematical models have with reality?
Hal Finney wrote: Brent Meeker wrote: [Hal Finney wrote:] When you observe evidence and construct your models, you need some basis for choosing one model over another. In general, you can create an infinite number of possible models to match any finite amount of evidence. It's even worse when you consider that the evidence is noisy and ambiguous. This choice requires prior assumptions, independent of the evidence, about which models are inherently more likely to be true or not. In practice we use coherence with other theories to guide out choice. With that kind of constraint we may have trouble finding even one candidate theory. Well, in principle there still should be an infinite number of theories, starting with the data is completely random and just happens to look lawful by sheer coincidence. I think the difficulty we have in finding new ones is that we are implicitly looking for small ones, which means that we implicitly believe in Occam's Razor, which means that we implicitly adopt something like the Universal Distribution, a priori. We begin with an intuitive physics that is hardwired into us by evolution. And that includes mathematics and logic. Ther's an excellent little book on this, The Evolution of Reason by Cooper. No doubt this is true. But there are still two somewhat-related problems. One is, you can go back in time to the first replicator on earth, and think of its evolution over the ages as a learning process. During this time it learned this intuitive physics, i.e. mathematics and logic. But how did it learn it? Was it a Bayesian-style process? And if so, what were the priors? Can a string of RNA have priors? An RNA string, arising naturally in a particular envirionment, can be modelled as expressing a prior about the probability of such RNA strings. And more abstractly, if you wanted to design a perfect learning machine, one that makes observations and optimally produces theories based on them, do you have to give it prior beliefs and expectations, including math and logic? Or could you somehow expect it to learn those? But to learn them, what would be the minimum you would have to give it? You'd have to give it the ability to reproduce and an environment in which it competed with other reproducing learners. I'm trying to ask the same question in both of these formulations. On the one hand, we know that life did it, it created a very good (if perhaps not optimal) learning machine. On the other hand, it seems like it ought to be impossible to do that, because there is no foundation. Why aren't elementary particles and entropy gradients enough foundation? Mathematics and logic are more than models of reality. They are pre-existent and guide us in evaluating the many possible models of reality which exist. I'd say they are *less* than models of reality. They are just consistency conditions on our models of reality. They are attempts to avoid talking nonsense. But note that not too long ago all the weirdness of quantum mechanics and relativity would have been regarded as contrary to logic. I guess we could agree that they are other than models of reality? It still strikes me as paradoxical: ultimately we have learned our intuitions about mathematics and logic from reality, via the mechanisms of evolution and also our own individual learning experiences. And yet it seems that at some level a degree of logic, and certain mathematical assumptions, are necessary to get learning off the ground in the first place, and that they should not depend on reality. Why should they be any more independent of reality than say evolution or folk-physics? I highly recommend Cooper's book. Brent Meeker
RE: what relation do mathematical models have with reality?
Aditya writes Although it is of course debatable, I hold that what we call reality is our minds' understanding of our sensory perceptions. It's just amazing on this list. Does no one speak up for realism? The *default* belief among *all* people up until they take their first fatal dive into a philosophy book is that there is an ordinary three-dimensional world that we are all running around in. (Yes---one *may* look at it as a model, but is this *really* necessary? It prevents accurate understanding as well as fosters terrible misunderstandings.) When 99% of the human race use the word reality, they mean the world outside their skins. If you sacrifice our common understanding of reality, then you'll find yourself in a hole out of which you'll never climb. Janos wrote later How do you (all) imagine experience/knowledge WITHOUT experience and knowledge to absorb/create it? It is a (vicious?) circle. Do we start with a blank form to fill in? What empty lines? what relations? where from? You all use the word reality - who's and who knows what is 'behind' it? We interpret some figment by our own (1st mostly, but applying 3rd pers. info as well - to the extent how we absorbed it as our own 1st pers compliance) We are part of the reality-word See? This is what happens. Look, it's VERY simple: take as a first baby-step the notion that the 19th century idea of a cosmos is basically true, and then add just the Big Bang. What we then have is a universe that operates under physical laws. So far---you'll readily agree---this is *very* simple conceptually. Next, look at this picture after 14.7 billion years. Guess what has evolved? Finally, there is intelligence and there are entities who can *perceive* all this grandeur. So, don't forget which came first. Not people. Not perceptions. Not ideas. Not dich an sich. Not 1st person. Not 3rd person. NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps* will have a chance to understand what is going on. And have a common language with which to describe it. Lee
RE: what relation do mathematical models have with reality?
Hal writes I'd say they are *less* than models of reality. They are just consistency conditions on our models of reality. They are attempts to avoid talking nonsense. But note that not too long ago all the weirdness of quantum mechanics and relativity would have been regarded as contrary to logic. I guess we could agree that they are other than models of reality? What do you mean by reality, by the way, since it's seems to be confounding so many here? It still strikes me as paradoxical: ultimately we have learned our intuitions about mathematics and logic from reality, via the mechanisms of evolution and also our own individual learning experiences. That's exactly right! And yet it seems that at some level a degree of logic, and certain mathematical assumptions, are necessary to get learning off the ground in the first place, and that they should not depend on reality. In the first place? What does that mean? It sounds like you're using English tenses and even English time-ordering adjectives. If so, then that takes us, by the hand, back before the big bang, and I'm not so sure that our English temporal vocabulary and grammar are really of much use there. Yes, there indeed are mysteries about the relationship between physics and mathematics. But a lot of the math is now in our genes, because it turns out that it really is a feature of the real physical universe. And it had to be learned if we wanted to survive. On a much more abstruse level are our philosophical meanderings about Tegmark and Tipler universes. I'm just writing this so that we keep the basics firmly in mind as we explore. Lee
Re: what relation do mathematical models have with reality?
Hi Lee, I am trying to speak up for Realism! I feel your exasperation! The problem is that our language is demonstrably NOT any good at giving us a basic set of tools to make sense of our common world outside their skins! The closer we look at this world of ours, including what is inside our skins, we find that our naive ideas simply are wrong. If we are to have any hope of finding models and methods to make sense of our universe we absolutely must take into consideration all of the empirical data that we have so far found. I would really like to see a version of realism that can handle the implication of the delayed choice experiments! http://www.bottomlayer.com/bottom/basic_delayed_choice.htm Stephen - Original Message - From: Lee Corbin [EMAIL PROTECTED] To: EverythingList everything-list@eskimo.com Sent: Monday, July 25, 2005 8:17 PM Subject: RE: what relation do mathematical models have with reality? Aditya writes Although it is of course debatable, I hold that what we call reality is our minds' understanding of our sensory perceptions. It's just amazing on this list. Does no one speak up for realism? The *default* belief among *all* people up until they take their first fatal dive into a philosophy book is that there is an ordinary three-dimensional world that we are all running around in. (Yes---one *may* look at it as a model, but is this *really* necessary? It prevents accurate understanding as well as fosters terrible misunderstandings.) When 99% of the human race use the word reality, they mean the world outside their skins. If you sacrifice our common understanding of reality, then you'll find yourself in a hole out of which you'll never climb. Janos wrote later How do you (all) imagine experience/knowledge WITHOUT experience and knowledge to absorb/create it? It is a (vicious?) circle. Do we start with a blank form to fill in? What empty lines? what relations? where from? You all use the word reality - who's and who knows what is 'behind' it? We interpret some figment by our own (1st mostly, but applying 3rd pers. info as well - to the extent how we absorbed it as our own 1st pers compliance) We are part of the reality-word See? This is what happens. Look, it's VERY simple: take as a first baby-step the notion that the 19th century idea of a cosmos is basically true, and then add just the Big Bang. What we then have is a universe that operates under physical laws. So far---you'll readily agree---this is *very* simple conceptually. Next, look at this picture after 14.7 billion years. Guess what has evolved? Finally, there is intelligence and there are entities who can *perceive* all this grandeur. So, don't forget which came first. Not people. Not perceptions. Not ideas. Not dich an sich. Not 1st person. Not 3rd person. NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps* will have a chance to understand what is going on. And have a common language with which to describe it. Lee
Re: what relation do mathematical models have with reality?
On Mon, Jul 25, 2005 at 05:17:37PM -0700, Lee Corbin wrote: Aditya writes Although it is of course debatable, I hold that what we call reality is our minds' understanding of our sensory perceptions. It's just amazing on this list. Does no one speak up for realism? The *default* belief among *all* people up until they take their first fatal dive into a philosophy book is that there is an ordinary three-dimensional world that we are all running around in. (Yes---one *may* look at it as a model, but is this *really* necessary? It prevents accurate understanding as well as fosters terrible misunderstandings.) When 99% of the human race use the word reality, they mean the world outside their skins. If you sacrifice our common understanding of reality, then you'll find yourself in a hole out of which you'll never climb. Sadly, your wish for the common sense understanding of reality to hold will be thwarted - the more one thinks about such things, the less coherent a concept it becomes. For most of us in this list, the 3+1 dimensional spacetime we inhabit, with its stars an galaxies etc is an appearance, phenomena emerging out of constraints imposed by the process of observation. For Kant, the noumenon, or Ding an Sich is reality, and it could be completely unlike what we observe, or phenomenon. For most on this list, reality might refer to the laws of quantum mechanics, or the Multiverse, or even the various Plenitudes proposed. My particular Plenitude is the simplest possible object, it should really be called Nothing. If I were to use reality, I'm more likely to be referring to the Multiverse, or an individual (observer relative) universe of phenomena. Consequently, I will mostly dispense with the term reality altogether, its too confusing. I may sometimes use the term realism to refer to the proposition that there exists an unexplainable noumenon to which phenomena can be causally related. Idealism contrasts this by asserting no such thing exists. This is largely how these terms are used in philosophy. I would usually say my ontology of bitstrings is idealistic, but then again, one could argue that the Plenitude _is_ the noumenon. This often manifests itself with Platonism being described as realist. So you could say these terms are incoherent too - perhaps I shall have to stop using them, oh bother! Cheers. -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpTjtw77rule.pgp Description: PGP signature
RE: what relation do mathematical models have with reality?
Russell writes Sadly, your wish for the common sense understanding of reality to hold will be thwarted - the more one thinks about such things, the less coherent a concept it becomes. Well, all that I ask is that the *basics* be kept firmly in mind while we gingerly probe forward. The basics (basic epistemology, that is) include 1. the map is not the territory, and perception is not reality 2. the words we have for things are not the things themselves, but only labels 3. we must *not* use basic language and terminology that conflicts with that used by twelve-year olds For most of us in this list, the 3+1 dimensional spacetime we inhabit, with its stars and galaxies etc is an appearance, phenomena emerging out of constraints imposed by the process of observation. Right there is the problem. Let's focus on what you are *referring* to in your first sentence: the 3+1 spacetime with its stars and galaxies. We must keep clear the difference between what you are *referring* to and our observations of it, or our perceptions of it. They're not at all the same thing. So when you use the dread is and write For most of us... the spacetime *is* an appearance, we've already gone over the edge. No. The spacetime that you probably meant is *not* an appearance, and we should not talk about it as if it is an appearance. *It* is whatever is out there. Yes, our understanding of it may be poor. Yes, it may not be at all as we *think*. In fact, it cannot in in any literal sense *be* what we *think*. I'm just urging everyone to keep in mind this key difference, that's all. If we lose the language of realism, we lose our real ability to communicate. There is no longer any constraint at all that keeps one's words having meaning to others. I understand and appreciate your remaining remarks. Lee For Kant, the noumenon, or Ding an Sich is reality, and it could be completely unlike what we observe, or phenomenon. For most on this list, reality might refer to the laws of quantum mechanics, or the Multiverse, or even the various Plenitudes proposed. My particular Plenitude is the simplest possible object, it should really be called Nothing. If I were to use reality, I'm more likely to be referring to the Multiverse, or an individual (observer relative) universe of phenomena. Consequently, I will mostly dispense with the term reality altogether, its too confusing. I may sometimes use the term realism to refer to the proposition that there exists an unexplainable noumenon to which phenomena can be causally related. Idealism contrasts this by asserting no such thing exists. This is largely how these terms are used in philosophy. I would usually say my ontology of bitstrings is idealistic, but then again, one could argue that the Plenitude _is_ the noumenon. This often manifests itself with Platonism being described as realist. So you could say these terms are incoherent too - perhaps I shall have to stop using them, oh bother! Cheers. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
Re: what relation do mathematical models have with reality?
Dear Lee, Are you the continuer of Niels Bohr? Seriously! The argument that your making is very similar to the argument that lead to the Copenhagen Interpretation. ;-) This is not a crtitisism, you are making some very good points. My problem is that I agree with both you and Russell and am having a hardtime finding the middle ground. ;-) Onward! Stephen - Original Message - From: Lee Corbin [EMAIL PROTECTED] To: everything-list@eskimo.com Cc: EverythingList everything-list@eskimo.com Sent: Monday, July 25, 2005 10:06 PM Subject: RE: what relation do mathematical models have with reality? Russell writes Sadly, your wish for the common sense understanding of reality to hold will be thwarted - the more one thinks about such things, the less coherent a concept it becomes. Well, all that I ask is that the *basics* be kept firmly in mind while we gingerly probe forward. The basics (basic epistemology, that is) include 1. the map is not the territory, and perception is not reality 2. the words we have for things are not the things themselves, but only labels 3. we must *not* use basic language and terminology that conflicts with that used by twelve-year olds For most of us in this list, the 3+1 dimensional spacetime we inhabit, with its stars and galaxies etc is an appearance, phenomena emerging out of constraints imposed by the process of observation. Right there is the problem. Let's focus on what you are *referring* to in your first sentence: the 3+1 spacetime with its stars and galaxies. We must keep clear the difference between what you are *referring* to and our observations of it, or our perceptions of it. They're not at all the same thing. So when you use the dread is and write For most of us... the spacetime *is* an appearance, we've already gone over the edge. No. The spacetime that you probably meant is *not* an appearance, and we should not talk about it as if it is an appearance. *It* is whatever is out there. Yes, our understanding of it may be poor. Yes, it may not be at all as we *think*. In fact, it cannot in in any literal sense *be* what we *think*. I'm just urging everyone to keep in mind this key difference, that's all. If we lose the language of realism, we lose our real ability to communicate. There is no longer any constraint at all that keeps one's words having meaning to others. I understand and appreciate your remaining remarks. Lee
Re: what relation do mathematical models have with reality?
On Mon, Jul 25, 2005 at 07:06:50PM -0700, Lee Corbin wrote: For most of us in this list, the 3+1 dimensional spacetime we inhabit, with its stars and galaxies etc is an appearance, phenomena emerging out of constraints imposed by the process of observation. Right there is the problem. Let's focus on what you are *referring* to in your first sentence: the 3+1 spacetime with its stars and galaxies. We must keep clear the difference between what you are *referring* to and our observations of it, or our perceptions of it. They're not at all the same thing. So when you use the dread is and write For most of us... the spacetime *is* an appearance, we've already gone over the edge. No. The spacetime that you probably meant is *not* an appearance, and we should not talk about it as if it is an appearance. *It* is whatever is out there. Yes, our understanding of it may be poor. Yes, it may not be at all as we *think*. In fact, it cannot in in any literal sense *be* what we *think*. The trouble is, _is_ is exactly what I do mean. 3+1 spacetime is an appearance, an emergent thing, an illusion perhaps (although I detest that term). Whatever the territory may be, what most people think of as reality is the map, not the territory. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpMwMWATraJr.pgp Description: PGP signature
Re: what relation do mathematical models have with reality?
Greetings, Here's my Rupee 1 on the connection between abstract models and reality; Although it is ofcourse debatable, I hold that what we call reality is our minds' understanding of our sensory perceptions. Thus the notion of (our) reality depends on: 1. The nature of mind Let's assume that the mind is simply the brain + the processes the brain is capable of + the information it stores/processes. Then the nature of the mind is the (sub)set of data-structures and computations that the brain is capable of. 2. The process of understanding Using the above informal definition of the mind, understanding is simply the following process: a. organize incoming data into data-structures that the brain is capable of storing and processing (itself a brain-process), b. process these data structures (computation) to make predictions (just more data), c. compare these predictions with more incoming feeds from our senses (experiment/testing), d. and finally re-adjust the organization of data in our brain (data-structures) to accommodate the differences in prediction data and sensory data. The above process continues iteratively, thus the iterative refinements in our theories of reality, aka physics. 3. Our sensory perceptions The data that comes in to the brain. This clearly depends on the instruments of perception (senses) themselves. For example a person born with a microscope attached to his eyes will transfer very different data to the brain than most of us, and thus may have a very different understanding of reality. In other words, our understanding of reality depends on brains and our senses. It can never be any more real or imaginary. [SPK] we have to come up with an explanation of how it is that our individual experiences of a world seem to be confined to sharp valuations and the appearance of property definiteness. response: This is simply because of the similar constitution of our sensory organs and brains (closeness in genotype and therefore phenotype if you may). A fly's understanding of reality is probably very very different (may or may not be sharp) [SPK] What does this have to do with mathematics and models? If we are going to create/discover models of what we can all agree is sharp and definite- our physical world, we must be sure that our models agree with each other. This, of course, assumes that there is some connection between abstract and concrete aspect of *reality*. response: If we presume to take my above description of the nature of mental models (mathematical/physical/etc.) as physical reality, then physical reality itself guarantees that our models will always depend on not only objective reality but also the nature of our mind and our sensory perceptions, which themselves form a subset of reality. It is much easier to make other humans understand (have their brains recalibrated to) a new model or theory than to attempt the same with a fly (unless the fly is given a human brain and human sensory organs). Thus this agreement is NOT a certificate of validity for our models. But this does NOT imply that there is no connection between abstract and physical reality. Abstract reality is a parallel universe created by extrapolation on a very limited (finite?) subset of concrete reality, namely our brain, sensory perceptions and the computations therein. The purpose of creating and refining this abstract reality (aka mathematical/physical models) is to recalibrate the brain and senses so that the abstract models it can hold predict incoming data (concrete reality) with increasing accuracy. Yet this accuracy itself is limited by laws like those given by QM (that limits the power of our senses). This suggests that we are close to the best we can do, although we may continue coming monotonically closer to the asymptotic optimum that we are limited to. [SPK] Ok, I would agree completely with you if we are using Kant's definition of *reality*- Dasein: existence in itself, but I was trying to be point out that we must have some kind of connection between the abstract and the concrete. One thing that I hope we all can agree upon about *reality* is that what ever it is, its properties are invariant with respect to transformations from one point of view to any other. It is this trait that makes it independent, but the problems with realism seem to arise when we consider whether or not this *reality* has some set of properties to the exclusion of any others independent of some observational context. QM demands that we not treat objects as having some sharp set of properties independent of context and thus the main source of counterintuitive aspects that make QM so difficult to deal with when we approach the subject of Realism. OTOH, we have to come up with an explanation of how it is that our individual experiences of a world seem to be confined to sharp valuations and the appearance of property definiteness.
Re: what relation do mathematical models have with reality?
Brent Meeker writes: Here's my $0.02. We can only base our knowledge on our experience and we don't experience *reality*, we just have certain experiences and we create a model that describes them and predicts them. Using this model to predict or describe usually involves some calculations and interpretation of the calculation in terms of the model. The relation of the model to reality, if it's a good one, is it gives us the right answer, i.e. it predicts accurately. Their are other criteria for a good model too, such as fitting in with other models we have; but prediction is the main standard. This makes sense but you need another element as well. This shows up most explicitly in Bayesian reasoning models, but it is implicit in others as well. That is the assumption of priors. When you observe evidence and construct your models, you need some basis for choosing one model over another. In general, you can create an infinite number of possible models to match any finite amount of evidence. It's even worse when you consider that the evidence is noisy and ambiguous. This choice requires prior assumptions, independent of the evidence, about which models are inherently more likely to be true or not. This implies that at some level, mathematics and logic has to come before reality. That is the only way we can have prior beliefs about the models. Whether it is the specific Universal Priori (1/2^n) that I have been describing or some other one, you can't get away without having one. So in my view, mathematics and theorems about computer science are just models too, albeit more abstract ones. Persis Diaconsis says, Statistics is just the physics of numbers. I have a similar view of all mathematics, e.g. arithmetic is just the physics of counting. I don't think this works, for the reasons I have just explained. Mathematics and logic are more than models of reality. They are pre-existent and guide us in evaluating the many possible models of reality which exist. Hal Finney
Re: what relation do mathematical models have with reality?
On Sat, Jul 23, 2005 at 06:09:39PM +1000, [EMAIL PROTECTED] wrote: On that note I'm not sure Wheeler's description is the same. In my idea of the calculus all there is is the sheets of paper. There are no symbols (no intrinsic representation). There are intrinsic rules of formation and transformation that relate and associate the bits of paper. If the bits of paper were jigsaw pieces with implicit connective rules then it is more like my idea. If you try an build a universe as a monism from an enormous quantity of only one thing (a primitive sign - piles of little bits of paper :) ) then you can construct space and the leftovers become the stuff we call matter. Deep down it's all the one thing, however. It's been a fascinating mental exercise for me. The problem is to let go of all the maths in a symbolic sense. We have this huge and very historically justified tendency to think the linear maths is the 'real stuff' of the natural world. I have been able to think of ways in which that is not the case, but that look 'as if' it was. It doesn't invalidate our maths, it just makes it look like it's not justified to ascribe anything more to the existence of our maths than that of a useful limited description. The main thing is to get used to the idea of ridding your preconceptions of symbolic 'aboutness'. There is no intrinsically meaningful sign. However an intrinsic event: the expression of the sign (any sign), can literally be a truth in itself. The fact of the utterance of the sign itself is a truth. From that all other truths can be expressed through meaningless signs combining through intrinsic properties (affinities) for other signs. It's more like a reified mega-dimensional cellular automata, actually. Not a traditional computational one. It took me a long time to be able to let go of my symbolic mathematical tendencies when I needed to. You can make our universe out of hierarchically structured noise starting from nothing. The 'sign' in the calculus is basically the elemental noise event of the entropy calculus I have played with. Stuff that looks like the rules of quantum mechanics appears well up the hirearchy. Waay up the hierarchy it looks ontological but with structure all the way down to the elemental signs. The one that makes us is somewhere between 15? and 40? organisational layers deep. Very busy, these Leibniz's !! Lots of fun! Don't know what to make of it but at least it has enabled me to post to this thread with a little bit of novelty! cheers colin Hi Colin, Have you written up your entropy calculus in a paper, so we could have a more detailed look at it? I know you sent me a paper of yours recently (and apologies - I haven't read your latest draft yet either :( ), but it doesn't seem to connect with what you are saying here. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpm4RSSpm7Rx.pgp Description: PGP signature
Re: what relation do mathematical models have with reality?
Hi Aditya, I do not see anything in your reasoning that I would disagree with. ;-) It seems that you subscribe to a concrete interpretation of mathematics, which is one that I take on occasion. I merely wish to comprehend the ideas of those that take a Pythagorean approach to mathematics; e.g. that Mathematics is more real than the physical world - All is number. One thing that I have learned in my study of philosophy is that no single finite model of reality can be complete. Perhaps that asymptotic optimum involves the comprehension of how such a disparate set of models can obtain in the first place. Kindest regards, Stephen - Original Message - From: Aditya Varun Chadha [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Sunday, July 24, 2005 2:20 AM Subject: Re: what relation do mathematical models have with reality? Greetings, Here's my Rupee 1 on the connection between abstract models and reality; Although it is ofcourse debatable, I hold that what we call reality is our minds' understanding of our sensory perceptions. Thus the notion of (our) reality depends on: 1. The nature of mind Let's assume that the mind is simply the brain + the processes the brain is capable of + the information it stores/processes. Then the nature of the mind is the (sub)set of data-structures and computations that the brain is capable of. 2. The process of understanding Using the above informal definition of the mind, understanding is simply the following process: a. organize incoming data into data-structures that the brain is capable of storing and processing (itself a brain-process), b. process these data structures (computation) to make predictions (just more data), c. compare these predictions with more incoming feeds from our senses (experiment/testing), d. and finally re-adjust the organization of data in our brain (data-structures) to accommodate the differences in prediction data and sensory data. The above process continues iteratively, thus the iterative refinements in our theories of reality, aka physics. 3. Our sensory perceptions The data that comes in to the brain. This clearly depends on the instruments of perception (senses) themselves. For example a person born with a microscope attached to his eyes will transfer very different data to the brain than most of us, and thus may have a very different understanding of reality. In other words, our understanding of reality depends on brains and our senses. It can never be any more real or imaginary. [SPK] we have to come up with an explanation of how it is that our individual experiences of a world seem to be confined to sharp valuations and the appearance of property definiteness. response: This is simply because of the similar constitution of our sensory organs and brains (closeness in genotype and therefore phenotype if you may). A fly's understanding of reality is probably very very different (may or may not be sharp) [SPK] What does this have to do with mathematics and models? If we are going to create/discover models of what we can all agree is sharp and definite- our physical world, we must be sure that our models agree with each other. This, of course, assumes that there is some connection between abstract and concrete aspect of *reality*. response: If we presume to take my above description of the nature of mental models (mathematical/physical/etc.) as physical reality, then physical reality itself guarantees that our models will always depend on not only objective reality but also the nature of our mind and our sensory perceptions, which themselves form a subset of reality. It is much easier to make other humans understand (have their brains recalibrated to) a new model or theory than to attempt the same with a fly (unless the fly is given a human brain and human sensory organs). Thus this agreement is NOT a certificate of validity for our models. But this does NOT imply that there is no connection between abstract and physical reality. Abstract reality is a parallel universe created by extrapolation on a very limited (finite?) subset of concrete reality, namely our brain, sensory perceptions and the computations therein. The purpose of creating and refining this abstract reality (aka mathematical/physical models) is to recalibrate the brain and senses so that the abstract models it can hold predict incoming data (concrete reality) with increasing accuracy. Yet this accuracy itself is limited by laws like those given by QM (that limits the power of our senses). This suggests that we are close to the best we can do, although we may continue coming monotonically closer to the asymptotic optimum that we are limited to. snip
Re: what relation do mathematical models have with reality?
Forwarded on behalf of Brent Meeker: On 24-Jul-05, you wrote: Brent Meeker writes: Here's my $0.02. We can only base our knowledge on our experience and we don't experience *reality*, we just have certain experiences and we create a model that describes them and predicts them. Using this model to predict or describe usually involves some calculations and interpretation of the calculation in terms of the model. The relation of the model to reality, if it's a good one, is it gives us the right answer, i.e. it predicts accurately. Their are other criteria for a good model too, such as fitting in with other models we have; but prediction is the main standard. This makes sense but you need another element as well. This shows up most explicitly in Bayesian reasoning models, but it is implicit in others as well. That is the assumption of priors. When you observe evidence and construct your models, you need some basis for choosing one model over another. In general, you can create an infinite number of possible models to match any finite amount of evidence. It's even worse when you consider that the evidence is noisy and ambiguous. This choice requires prior assumptions, independent of the evidence, about which models are inherently more likely to be true or not. In practice we use coherence with other theories to guide out choice. With that kind of constraint we may have trouble finding even one candidate theory. We begin with an intuitive physics that is hardwired into us by evolution. And that includes mathematics and logic. Ther's an excellent little book on this, The Evolution of Reason by Cooper. This implies that at some level, mathematics and logic has to come before reality. That is the only way we can have prior beliefs about the models. Whether it is the specific Universal Priori (1/2^n) that I have been describing or some other one, you can't get away without having one. So in my view, mathematics and theorems about computer science are just models too, albeit more abstract ones. Persis Diaconsis says, Statistics is just the physics of numbers. I have a similar view of all mathematics, e.g. arithmetic is just the physics of counting. I don't think this works, for the reasons I have just explained. Mathematics and logic are more than models of reality. They are pre-existent and guide us in evaluating the many possible models of reality which exist. I'd say they are *less* than models of reality. They are just consistency conditions on our models of reality. They are attempts to avoid talking nonsense. But note that not too long ago all the weirdness of quantum mechanics and relativity would have been regarded as contrary to logic. Brent Meeker
Re: what relation do mathematical models have with reality?
Colin Hales writes: The idea brings with it one unique aspect: none of the calculii we hold so dear, that are so wonderful to play with, so poweful in their predictive nature in certain contexts, are ever reified. None of them actually truly capture reality in any way. They only appear to in certain contexts. The only actual mathematics that captures the true nature of the universe is the universe itself as a calculus. It doesn't invalidate the maths we love. It just makes it merely a depiction in a certain context. Very useful but thats all. You might like this quote from John Wheeler, in his textbook Gravitation written with Charles Misner and Kip Thorne, which perhaps expresses a similar idea: : Paper in white the floor of the room, and rule it off in one-foot : squares. Down on one's hands and knees, write in the first square : a set of equations conceived as able to govern the physics of the : universe. Think more overnight. Next day put a better set of equations : into square two. Invite one's most respected colleagues to contribute : to other squares. At the end of these labors, one has worked oneself : out into the door way. Stand up, look back on all those equations, : some perhaps more hopeful than others, raise one's finger commandingly, : and give the order `Fly!' Not one of those equations will put on wings, : take off, or fly. Yet the universe 'flies'. My current view is a little different, which is that all of the equations fly. Each one does come to life but each is in its own universe, so we can't see the result. But they are all just as real as our own. In fact one of the equations might even be our own universe but we can't easily tell just by looking at it. Hal Finney
Re: what relation do mathematical models have with reality?
Hal Finney writes: : Paper in white the floor of the room, and rule it off in one-foot : squares. Down on one's hands and knees, write in the first square : a set of equations conceived as able to govern the physics of the : universe. Think more overnight. Next day put a better set of equations : into square two. Invite one's most respected colleagues to contribute : to other squares. At the end of these labors, one has worked oneself : out into the door way. Stand up, look back on all those equations, : some perhaps more hopeful than others, raise one's finger commandingly, : and give the order `Fly!' Not one of those equations will put on wings, : take off, or fly. Yet the universe 'flies'. My current view is a little different, which is that all of the equations fly. Each one does come to life but each is in its own universe, so we can't see the result. But they are all just as real as our own. In fact one of the equations might even be our own universe but we can't easily tell just by looking at it. Hal Finney Hi Hal, Your 'flying equations' sound a bit like the idealist 'a-priori'... interesting but different topic for another day. :-) Thanks for the wheeler link On that note I'm not sure Wheeler's description is the same. In my idea of the calculus all there is is the sheets of paper. There are no symbols (no intrinsic representation). There are intrinsic rules of formation and transformation that relate and associate the bits of paper. If the bits of paper were jigsaw pieces with implicit connective rules then it is more like my idea. If you try an build a universe as a monism from an enormous quantity of only one thing (a primitive sign - piles of little bits of paper :) ) then you can construct space and the leftovers become the stuff we call matter. Deep down it's all the one thing, however. It's been a fascinating mental exercise for me. The problem is to let go of all the maths in a symbolic sense. We have this huge and very historically justified tendency to think the linear maths is the 'real stuff' of the natural world. I have been able to think of ways in which that is not the case, but that look 'as if' it was. It doesn't invalidate our maths, it just makes it look like it's not justified to ascribe anything more to the existence of our maths than that of a useful limited description. The main thing is to get used to the idea of ridding your preconceptions of symbolic 'aboutness'. There is no intrinsically meaningful sign. However an intrinsic event: the expression of the sign (any sign), can literally be a truth in itself. The fact of the utterance of the sign itself is a truth. From that all other truths can be expressed through meaningless signs combining through intrinsic properties (affinities) for other signs. It's more like a reified mega-dimensional cellular automata, actually. Not a traditional computational one. It took me a long time to be able to let go of my symbolic mathematical tendencies when I needed to. You can make our universe out of hierarchically structured noise starting from nothing. The 'sign' in the calculus is basically the elemental noise event of the entropy calculus I have played with. Stuff that looks like the rules of quantum mechanics appears well up the hirearchy. Waay up the hierarchy it looks ontological but with structure all the way down to the elemental signs. The one that makes us is somewhere between 15? and 40? organisational layers deep. Very busy, these Leibniz's !! Lots of fun! Don't know what to make of it but at least it has enabled me to post to this thread with a little bit of novelty! cheers colin
Re: what relation do mathematical models have with reality?
Hi Brent, - Original Message - From: Brent Meeker [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Friday, July 22, 2005 8:31 PM Subject: Re: what relation do mathematical models have with reality? On 22-Jul-05,Stephen P. King wrote: Hi Brent, Ok, I am rapidly loosing the connection that abstract models have with the physical world, at least in the case of computations. If there is no constraint on what we can conjecture, other than what is required by one's choice of logic and set theory, what relation do mathematical models have with reality? Is this not as obvious as it appears? [BM] Here's my $0.02. We can only base our knowledge on our experience and we don't experience *reality*, we just have certain experiences and we create a model that describes them and predicts them. Using this model to predict or describe usually involves some calculations and interpretation of the calculation in terms of the model. The relation of the model to reality, if it's a good one, is it gives us the right answer, i.e. it predicts accurately. Their are other criteria for a good model too, such as fitting in with other models we have; but prediction is the main standard. So in my view, mathematics and theorems about computer science are just models too, albeit more abstract ones. Persis Diaconsis says, Statistics is just the physics of numbers. I have a similar view of all mathematics, e.g. arithmetic is just the physics of counting. [SPK] Ok, I would agree completely with you if we are using Kant's definition of *reality*- Dasein: existence in itself, but I was trying to be point out that we must have some kind of connection between the abstract and the concrete. One thing that I hope we all can agree upon about *reality* is that what ever it is, its properties are invariant with respect to transformations from one point of view to any other. It is this trait that makes it independent, but the problems with realism seem to arise when we consider whether or not this *reality* has some set of properties to the exclusion of any others independent of some observational context. QM demands that we not treat objects as having some sharp set of properties independent of context and thus the main source of counterintuitive aspects that make QM so difficult to deal with when we approach the subject of Realism. OTOH, we have to come up with an explanation of how it is that our individual experiences of a world seem to be confined to sharp valuations and the appearance of property definiteness. Everett and others gave us the solution to this conundrum with the MWI. Any given object has eigenstates (?) that have eigenvalues (?) that are sharp and definite relative to some other set of eigenstates, but as a whole a state/wave function is a superposition of all possible. So, what does this mean? We are to take the a priori and context independent aspect of *reality* as not having any one set of sharp and definite properties, it has a superposition of all possible. The trick is to figure out a reason why we have one basis and not some other, one partitioning of the eigenstates and not some other. What does this have to do with mathematics and models? If we are going to create/discover models of what we can all agree is sharp and definite- our physical world, we must be sure that our models agree with each other. This, of course, assumes that there is some connection between abstract and concrete aspect of *reality*. Stephen
Re: what relation do mathematical models have with reality?
On 23-Jul-05, you wrote: Hi Brent, - Original Message - From: Brent Meeker [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Friday, July 22, 2005 8:31 PMMichael Godfrey [EMAIL PROTECTED] Date Subject: Re: what relation do mathematical models have with reality? On 22-Jul-05,Stephen P. King wrote: Hi Brent, Ok, I am rapidly loosing the connection that abstract models have with the physical world, at least in the case of computations. If there is no constraint on what we can conjecture, other than what is required by one's choice of logic and set theory, what relation do mathematical models have with reality? Is this not as obvious as it appears? [BM] Here's my $0.02. We can only base our knowledge on our experience and we don't experience *reality*, we just have certain experiences and we create a model that describes them and predicts them. Using this model to predict or describe usually involves some calculations and interpretation of the calculation in terms of the model. The relation of the model to reality, if it's a good one, is it gives us the right answer, i.e. it predicts accurately. Their are other criteria for a good model too, such as fitting in with other models we have; but prediction is the main standard. So in my view, mathematics and theorems about computer science are just models too, albeit more abstract ones. Persis Diaconsis says, Statistics is just the physics of numbers. I have a similar view of all mathematics, e.g. arithmetic is just the physics of counting. [SPK] Ok, I would agree completely with you if we are using Kant's definition of *reality*- Dasein: existence in itself, but I was trying to be point out that we must have some kind of connection between the abstract and the concrete. One thing that I hope we all can agree upon about *reality* is that what ever it is, its properties are invariant with respect to transformations from one point of view to any other. It is this trait that makes it independent, but the problems with realism seem to arise when we consider whether or not this *reality* has some set of properties to the exclusion of any others independent of some observational context. QM demands that we not treat objects as having some sharp set of properties independent of context and thus the main source of counterintuitive aspects that make QM so difficult to deal with when we approach the subject of Realism. OTOH, we have to come up with an explanation of how it is that our individual experiences of a world seem to be confined to sharp valuations and the appearance of property definiteness. Everett and others gave us the solution to this conundrum with the MWI. MWI is *a* solution. But it is also possible to regard QM as a theory of what we know or can say about a system. Have you read Bohm's interpretation of QM? MWI seemed very promising when it seemed to solve the Born problem. But since it has been shown that the Born postulate is independent, then one might as well postulate that only one thing happens - as in consistent histories, or Bohm's intepretation. Any given object has eigenstates (?) that have eigenvalues (?) that are sharp and definite relative to some other set of eigenstates, but as a whole a state/wave function is a superposition of all possible.I I'm not sure what you mean by object. In general an object, such as an electron, has different eigenvalues depending on how it is prepared/measured. So they are not necessarily properties of the object alone. So, what does this mean? We are to take the a priori and context independent aspect of *reality* as not having any one set of sharp and definite properties, it has a superposition of all possible. That's not how I'd take it. The trick is to figure out a reason why we have one basis and not some other, one partitioning of the eigenstates and not some other. That's the decoherence program of Zeh, Zurek, Joos, Schlosshauer, et al. What does this have to do with mathematics and models? If we are going to create/discover models of what we can all agree is sharp and definite- our physical world, we must be sure that our models agree with each other. This, of course, assumes that there is some connection between abstract and concrete aspect of *reality*. Or that we pick out those parts of our experience which we can describe by models indpendent of viewpoint. The rest we call subjective experience. Brent Meeker
Re: what relation do mathematical models have with reality?
Hi Brent, Ok, I am rapidly loosing the connection that abstract models have with the physical world, at least in the case of computations. If there is no constraint on what we can conjecture, other than what is required by one's choice of logic and set theory, what relation do mathematical models have with reality? Is this not as obvious as it appears? BTW, Scott Aaronson has a nice paper on the P=NP problem that is found here: http://www.scottaaronson.com/papers/npcomplete.pdf I recommend this paper as well: http://www.scottaaronson.com/papers/are.ps Kindest regards, Stephen - Original Message - From: Brent Meeker [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Friday, July 22, 2005 3:40 PM Subject: Re: is induction unformalizable? But I'm not sure what it would mean for an instance of P=NP computation to exist in nature. What it would mean in computer science is that there was an algorithm for translating any NP algorithm into a P algorithm for the same problem. This refers to classes of algorithms for classes of problems. If you observe a certain instance of protein folding - that's not an algorithm. If you study many instances of protein folding you may develop an algorithm that will predict how a class of proteins will fold and that may scale as NP. Someone else might find another algorithm that scales as P. But that's not the same as finding a way of translating any NP algorithm into a P one. And neither one shows that nature is using an algorithm. Nature isn't predicting how a class of proteins is going to fold - it's just folding a few specific examples. Brent Meeker On 22-Jul-05, you wrote: Hi Brent, You make a very good point and I agree with you completely! But I am arguing that it is the distinction between physical and abstract systems that seems to require some closer examination, and a slightly different point. If we are going to use arguments that are only in principlebased to make decisions about situations in the physical world, does it not follow that we might be making serious errors? My claim stands! ... if there did occurs an instance of a P=NP computation within our physical universe then it follows that Nature would have found a way to implement it widely. If P=NP Oracles are allowed at all in our physical universe, then it follows that some evidence could be found of their occurance. If they can only exist in the very special case of an abstract universe, what connection do they have with physics or anything other than metaphysics? Stephen PS. Please cc your reply to the Everything List, I am sure that others are interested in this thread. - Original Message - From: Brent Meeker [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Sent: Friday, July 22, 2005 3:07 PM Subject: Re: is induction unformalizable? On 22-Jul-05, you wrote: Dear Brent, Could you name some examples? In the real world, computations obey the laws of thermodynamics, among other things, thus for problems with the same number of independent degrees of freedom, the P problems can be computed faster than the NP. Of course this is just an average, but baring some counter-examples I fail to understand your point. Stephen The laws of thermodynamics apply to physical processes, not abstractions like algorithms. Of course computations are physical processes - but P and NP are classes of algorithms, not computations. I'll see if I can find some specific examples, but the general point is that a polynomial algorithm may have a large fixed cost and then scale, say, linearly with the size of the problem; while another algorithm for the same class of problem may have a small fixed cost yet scale exponentially. Then up to some size (which may be very large) the latter will be faster than the former. It is only in the limit of infinite size that a P algorithm is necessarily faster than an NP one. Since all examples from Nature are finite, you can't infer that Nature must have found P algorithms for problems we think are NP. Brent Meeker Regards -- Brent Meeker
