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coffeetable · 2368 days ago · link ·
My training's in theoretical computer science, not physics, but this seems a very suspect paper. Crackpots do unfortunately make it onto the arXiv sometimes.
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- My training's in theoretical computer science
10 points, then, per #10 of your cite. . That said, you are in a position to make substantial contributions to this conversation. (And no, we will not add additional points for the necessity of mentioning the prior contributions of Feynman in context of computation. ..) IMO, the paper would benefit from a strict but sympathetic editor. There is a serious mind product at its core that can be (fairly trivially) extracted and dressed up in accordance to the required academic norm.a very suspect paper
The convergence in appearance of planetary nebulae, electron probability clouds, black hole jets, etc., basically results from the fact that the electromagnetic and gravitational forces both follow inverse square laws. Is his generalized thesis that the inverse square law itself, that is so common in physics, is a result of the low pass Kolmogorov filter? And that these laws can be somehow backed out of the generalized Kolmogorov complexity that he is proposing? Admittedly, I don't have any expertise on information theory, so I'm not at all qualified to critique it, but seems like a pretty awesome idea.
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Alright, so Dara says:
I found that interesting, and it 'fits' into his framework, but it is not clear to me why that specific relationship predominates. Intuitively, I would seek a group theoretic explanation. Back to numbers and our favorite formula. Regardless, that made me do a quick search and fished this out: [that law] has a very low kolmogorov complexity i.e.
few ALU operations of add and shift and multiply
(taylor series).
So LOW kolmo complexity = 1/r^2 or any other
simple law
source I would like to interrupt here to make a remark. The fact that
electrodynamics can be written in so many ways - the differential
equations of Maxwell, various minimum principles with fields, minimum
principles without fields, all different kinds of ways, was something
I knew, but I have never understood. It always seems odd to me that
the fundamental laws of physics, when discovered, can appear in so
many different forms that are not apparently identical at first, but,
with a little mathematical fiddling you can show the relationship. An
example of that is the Schrödinger equation and the Heisenberg
formulation of quantum mechanics. I don't know why this is - it
remains a mystery, but it was something I learned from experience.
There is always another way to say the same thing that doesn't look at
all like the way you said it before. I don't know what the reason for
this is. I think it is somehow a representation of the simplicity of
nature. A thing like the inverse square law is just right to be
represented by the solution of Poisson's equation, which, therefore,
is a very different way to say the same thing that doesn't look at all
like the way you said it before. I don't know what it means, that
nature chooses these curious forms, but maybe that is a way of
defining simplicity. Perhaps a thing is simple if you can describe it
fully in several different ways without immediately knowing that you
are describing the same thing.
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Ah, I think I am beginning to see more clearly his point. So can we say that a function can be said to have low Kolmogorov complexity if an infinite series expansion (Taylor series, as your example, but I suppose any infinite series could substitute) is relatively simple and repetitive? If I am making a correct assumption here, then I can better understand his point, at least qualitatively. Most physical systems are built on sets of equations that have relatively simple infinite expansions. Take for example the steady state solutions to an arbitrary separable partial diff eq, as is common in systems whose force weakens with distance. The solutions are oscillators; sines waves, bessel functions, etc. Even in QM, we see recursion formulae that determine the stable states of the wave function, single formulae that can describe the entire set of possible states for particles in a given boundary condition. I suppose this is what is meant by low Kolmogorov complexity (or I am missing the point, which is equally--or perhaps more--likely).
There is another extension of this that comes to mind, and that is the convergence of the form of equations that describe vastly different systems (beyond inverse square laws, I mean). For example, Newtonian oscillators, in some circumstances, form solutions to population models in certain ecological systems. It seems that every time that Equation X satisfies problem 1 and (unrelated) problem 2, the complexity of the system (in a descriptive sense, anyway) has decreased. If there is some generalized string out of which these common forms of equations can be backed, I would be speechless, stunned, but not really surprised. Maybe there is hope for a unified field theory in information theory, instead of quantum (or the wretched string theory).
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I think you have it. My question remains as to why 1/r^2 'emerges' over say '1/r' which is of even lower complexity. Clearly there is a sort of structural substrate that pushes up (so to speak) while the 'low pass filter' pushes down.
It has to be Number. It must be N - simple act of partitioning and counting. I'm convinced of it, but how to prove it! :(If there is some generalized string out of which these common forms of equations can be backed, I would be speechless, stunned, but not really surprised. Maybe there is hope for a unified field theory in information theory, instead of quantum (or the wretched string theory).
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I think 1/r^2 emerges because of the geometry that has emerged. If a pulse of particles is emitted uniformly in n-dimensional space, and each travels at the same speed, then their density will fall off as 1/r^(n-1), since in 3D they cover a spherical surface (2D object of size r^2), and in 2D its a line (1D circular surface of size r). Its the geometry that's important. We should search for why our world is 3D, and not some other space, if we want to know why we have inverse square laws.
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- Its the geometry that's important
Agreed. But is geometry more foundational than number? (I feel like we're back in ancient Greece.) There is a very interesting tension between number and geometric form. And addressing this will drag in Cantor as well. This question has been giving headaches to the pointy head set for thousands of years. Great insight and question. I wonder if answering that is beyond our ken. I am open to the future possibility, given the root words earth-measure, of a demonstration that provides a number theoretic basis for geometry. But indeed, why would it cap at 3-D. Per ancient lore, scripture, and even recent musings of string theory, there are additional dimensions that are 'unseen'. So I would read your "We should search for why our world is 3D" as "why our perception of the world is 3D".We should search for why our world is 3D, and not some other space, if we want to know why we have inverse square laws.
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- I would read your "We should search for why our world is 3D" as "why our perception of the world is 3D".
I actually considered writing the reply that way, but I shy away from speculation; we know the universe has at least three large dimensions (four if we count time). I would love to hear a number theoretical reason for three. I can't accept that it is arbitrary. I can generally see why we can't exist in 1 or 2D, as movement around other objects would be impossible for anything solid. But I have never been able to imagine a reason why more didn't occur. I suppose that's because we can't dream in 4D. We can imagine--and therefore reasonably reject--lower dimensions, but only math can tell us about higher ones.
- Is his generalized thesis that the inverse square law itself, that is so common in physics, is a result of the low pass Kolmogorov filter?
I'll pass the question along, but yes, that is the general thrust of the paper. The def. of causality was imo brilliant. Also note the remark regarding the threshold of broken symmetries is the most tantalizingly clue informing the pervasive phenomena of phi/fibonacci in natural systems I have found to date.
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The whole idea of convergence is an interesting one. We can see it in physics, and by extension, in biology. E.g. there are marsupial "wolves" in the fossil record that require expertise to differentiate from placental wolves, because the two creatures converged to such a high degree. These convergences are a result of creatures "solving" physical problems in their environment. So physics dictates biologic form in many cases.
Have you come across D'Arcy Thompson? He spent great effort in his career trying to generalize convergent trends in evolution based on simple mathematical models (well, as simple as he could make them). He was writing before information theory was discovered. I suspect that if physical laws are generalize-able from information theory that evolutionary trends must be, as well, given that species are forged as one possibility among seemingly infinite states. (Interestingly, I first came across Kolmogorov when studying mathematical biology; there's a strange convergence!)
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I promised myself I'll work today so this (and you too mk) will have to wait until the p.m. as this is a very deep and interesting discussion that deserves attention.
(Yes. I love On Growth and Form. [arch school days and my obsession to create a morphological system for generating buildings. Remember that drawing?])
- Consequently, the physical laws are nothing but a low-pass filter for small values of Kolmogorov Complexity.
Gotta love arxiv. Still getting my head around the meaning of this. It seems so language dependent, and not just computer language. IsDefinition: The Kolmogorov complexity of a string , denoted is the length of the shortest program which outputs given no input.
a name for 01010101010101010101010101010101010101010101010101? (Not asserting it is, just not sure that it isn't.) print "01" * 25
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- Gotta love arxiv.
I take that paper quite seriously. That initial def is relative to the language (of course). But reducible to universal turing machine L (as he goes on to prove a bit further down.) Note the the "+ O(1)" / "+ c". That's the language relative bit and it is O(1). http://bit.ly/IooFpk The above is quite elegant and to the point. K_sub_L is the irreducible universal construct. K_sub_L_prime the interpreter. If it helps, consider that number has no (representational) "base" but numeric form does. So, as an analogy, one can say Na > Nb. Naturally the inequality will hold in Na_base_x > Nb_base_x. Various bases will result in distinct length of the form. If further helps, consider the notion of image and its distinction from essence.It seems so language dependent
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- I take that paper quite seriously.
Don't get me wrong. I don't have a deep enough understanding to judge the paper. I just love arxiv because it is a sounding board for ideas that otherwise would have a much smaller audience. Only on arxiv can you find conclusions like that. I read this through once, and I need to again. There are certain parts that I am attracted to: This is something sensible to me. I've been long thinking on the inextricable link between matter and space, and I like the fact that this brings irreversibility into the relationship. But, I am only beginning to absorb this. Some immediate questions: What defines the collection of Maxwellian Robots, and what is being filtered? Does this describe the nature of physicality, or is it a useful analogy? To the descriptive end, the causality seems the most compelling part, but can something fall out of it that maps onto the physical laws? I'd love to have a beer over this. I need someone to sit down and walk me through it. I don't think the nebulae/Shrodinger’s equation solutions is strongly supportive. It feels like cherry-picking.The output of the Maxwellian Robot is collection of points (subset) in some space. They self-replicate or self-print the space. Their motion is the generation of the space, or the printing of the space.
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| I like the fact that this brings irreversibility into the relationship.|
I personally found that brilliant. Very intriguing. We share the same questions. You are the biologist: how many neurons must we rub together to get a basic Turing Machine? No, no, I would say that that conversation clearly calls for GanJah.I'd love to have a beer over this. I need someone to sit down and walk me through it.
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- You are the biologist: how many neurons must we rub together to get a basic Turing Machine?
Seems 11 might do the trick. (PDF) Oh no, I get far too silly. All sorts of confusion and even a bit of paranoia. It took me a while before I decided it just wasn't going to work out between the two of us. :) Working through this discussion...No, no, I would say that that conversation clearly calls for GanJah.
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- Seems 11 might do the trick. (PDF)
Thanks! It will have to wait for this evening. That's fine, but just remember to don't criticize it ;-)Oh no, I get far too silly. All sorts of confusion and even a bit of paranoia. It took me a while before I decided it just wasn't going to work out between the two of us. :)
- how many neurons must we rub together to get a basic Turing Machine?
I think the more neurons you put together, the less like a Turing Machine your system will look. The firing of each has a stochastic component that combines in some way (I don't exactly know how, but probably something less than purely additive) with its neighbors. The uncertainly is too high to be a Turing machine; its the reason you can't throw a dart the same way each time.
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Fine, but then as mk pointed out, where do we find this reality constructing machines? (I have my own views, but they are entirely of a meta-physical nature ;-) Dara's view (as he states in reference to Maxwell's cogs and wheels) per my reading is that that is irrelevant, so long as the conceptual model is effective. But clearly, if there ever was a viable avenue of pursuing the relationship between consciousness and materiality, this is it. Don't you agree?
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- ...if there ever was a viable avenue of pursuing the relationship between consciousness and materiality, this is it. Don't you agree?
I'll give a qualified "yes" to this question. Here's the qualification: I think it is wise to look for a connection between consciousness and materiality in some conceptual, perhaps mathematical (perhaps purely philosophical, although I find that much less appealing), framework. Whether its this particular one, I can't say, because I don't understand his logic entirely yet. But I certainly grant that I like his approach. I think the manner in which consciousness is broached in neuroscience is one of the great scientific farces of the day (and its also one of the most romanticized, unfortunately). The attempts to atomize consciousness to statements like "your occipital cortex merges image for you", or "your amygdala gives you 'fight-or-flight' instructions" make me sick to my stomach. There is not one sensible statement that grants faculties to the brain itself, yet that is the norm in neuroscience. We, as individulas, are conscious beings, whether purely material or material-metaphysical. I hope one day we can discover a conceptual framework in which this idea can be interpreted, but I know beyond doubt that it will never be discovered by a traditional neuroscientist.
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- I think the manner in which consciousness is broached in neuroscience is one of the great scientific farces of the day ..
The 'just so' science. I share your revulsion regarding this matter. An entirely chance phenomena? Consider the socio-political dimensions ..... (and its also one of the most romanticized, unfortunately).
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I think the brain is the new space exploration, which was the new sea exploration. In each of the former cases we had dramatic and fantastical tales, canelli on Mars, serpents past Gibraltar, etc. The unknown leads to rampant speculation, often wild and romantic speculation. The brain is so unknown that we ascribe to it all of our unknowns. We can find love, loss, smart, stupid, creative, dull, etc. in the brain. Its mysteriousness and complexity is what drives these speculations. (Well, that and a non-existent emphasis on philosophy in secondary and university education).