Feynman and the Everything

[Jason Resch]

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

Does computationalism provide the answer to this question, in the sense that even the tiniest region of space is the result of an infinity of computations going through an observer's mind state as it observes the tiniest region of space?

Jason

[John Clark]

On Sun, Nov 26, 2017 at 10:04 PM, Jason Resch <jason...@gmail.com> wrote:

​> ​

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

​

Obviously infinite logic is not required unless infinite precision is also required, but sometimes (and protein folding

​ 

would be a good example of this) an astronomically huge number of calculations are required for even a

​ 

very

​ 

modest approximation

​ 

of what is happening in a tiny piece of spacetime, and yet nature can do it with great precision in a fraction of a second. How come? Feynman himself took the first first tentative steps toward answering that question just before he died, as far as I know he was the first person to introduce the idea of a quantum computer.
 

​> ​

Does computationalism provide the answer to this question,

 

No natural phenomenon has ever been found where nature has solved a  NP-hard problem in polynomial time.

​Quantum Computer expert​

 Scott Aaronson actually

​tested this​

 and this is what he

​found​

: 

" taking two glass plates with pegs between them, and dipping the resulting contraption into a tub of soapy water. The idea is that the soap bubbles that form between the pegs should trace out the minimum Steiner tree — that is, the minimum total length of line segments connecting the pegs, where the segments can meet at points other than the pegs themselves. Now, this is known to be an NP-hard optimization problem. So, it looks like Nature is solving NP-hard problems in polynomial time!

Long story short, I went to the hardware store, bought some glass plates, liquid soap, etc., and found that, while Nature does often find a minimum Steiner tree with 4 or 5 pegs, it tends to get stuck at local optima with larger numbers of pegs. Indeed, often the soap bubbles settle down to a configuration which is not even a tree (i.e. contains “cycles of soap”), and thus provably can’t be optimal.

The situation is similar for protein folding. Again, people have said that Nature seems to be solving an NP-hard optimization problem in every cell of your body, by letting the proteins fold into their minimum-energy configurations. But there are two problems with this claim. The first problem is that proteins, just like soap bubbles, sometimes get stuck in suboptimal configurations — indeed, it’s believed that’s exactly what happens with Mad Cow Disease. The second problem is that, to the extent that proteins do usually fold into their optimal configurations, there’s an obvious reason why they would: natural selection! If there were a protein that could only be folded by proving the Riemann Hypothesis, the gene that coded for it would quickly get weeded out of the gene pool." 

For

​ more I highly ​recommend 

 Aaronson's book "Quantum Computing since Democritus".

 ​John K Clark​

 

 

[Bruno Marchal]

On 27 Nov 2017, at 04:04, Jason Resch wrote:

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

Does computationalism provide the answer to this question,

Yes.    :)

in the sense that even the tiniest region of space is the result of an infinity of computations going through an observer's mind state as it observes the tiniest region of space?

That might be OK, if space was something entirely physical, which is suggested by the physics of the vacuum, or general relativity, but with Mechanism, spece and time might be less physical than here suggested. The reason is that it is not clear how "empty space" could make a computation different from another, and so space could be only a marker differentiating some computations, like time seems to be in the indexical approach. All this would need big advance in the mathematics of the intelligible and sensible arithmetical matter. I expect space to be explained by quantum knot invariant algebra due to subtil relation between BDB and DBD logical operators (I mean []<>[] and <>[]<>). Kant might be right on this, apparently space and time are really in the "categorie de l'entendement", I don't know Kant in English sorry, but this means mainly that they belong to the mind).

Bruno

Jason

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[Jason Resch]

On Tue, Nov 28, 2017 at 6:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 27 Nov 2017, at 04:04, Jason Resch wrote:

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

Does computationalism provide the answer to this question,

Yes.    :)

Very nice. It seems then Feynman's intuition was in the right place. The second half of the above quote was:

"So I have often made the hypothesis ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this is just speculation."

So it looks like that simple machinery is the machinery of the universal machine and the simple laws  are those of Peano (or Robinson?) Arithmetic.

 

in the sense that even the tiniest region of space is the result of an infinity of computations going through an observer's mind state as it observes the tiniest region of space?

That might be OK, if space was something entirely physical, which is suggested by the physics of the vacuum, or general relativity, but with Mechanism, spece and time might be less physical than here suggested. The reason is that it is not clear how "empty space" could make a computation different from another,

I think what I was thinking here were "closed loop feyman diagrams", where any possible diagram might be drawn in the tiniest area of space, so long as it is closed, e.g. fluctuations/particle creations are permitted so long as they all cancel out. So if space is physical, and enables any of these fluctuations to happen, then this noise can take any possible value from the observer's point of view (like the polarization of a photon).

 

and so space could be only a marker differentiating some computations, like time seems to be in the indexical approach. All this would need big advance in the mathematics of the intelligible and sensible arithmetical matter. I expect space to be explained by quantum knot invariant algebra due to subtil relation between BDB and DBD logical operators (I mean []<>[] and <>[]<>). Kant might be right on this, apparently space and time are really in the "categorie de l'entendement", I don't know Kant in English sorry, but this means mainly that they belong to the mind).

Thanks I very much appreciate these additional insights. I do subscribe to the belief that time is an illusion created by the mind. I have a little more trouble seeing that when extended to spacetime as a whole.  Though perhaps what's come closest to helping me see this picture is Amanda Gefter's excellent book "Trespassing on Einstein's Lawn"--I would recommend it to everyone on the Everything list. It takes the approach that only things that are invariant are real, and from there proceeds to deconstruct almost all of physics.

Jason

[Jason Resch]

I wanted to add, it also shows that the function (if you can call it that) of practically every physical law is to ensure consistency between observers. I think you would like it.

Jason

[Bruno Marchal]

On 27 Nov 2017, at 23:08, John Clark wrote:

On Sun, Nov 26, 2017 at 10:04 PM, Jason Resch <jason...@gmail.com> wrote:

​> ​

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

​

Obviously infinite logic is not required unless infinite precision is also required, but sometimes (and protein folding

​ 

would be a good example of this) an astronomically huge number of calculations are required for even a

​ 

very

​ 

modest approximation

​ 

of what is happening in a tiny piece of spacetime, and yet nature can do it with great precision in a fraction of a second. How come? Feynman himself took the first first tentative steps toward answering that question just before he died, as far as I know he was the first person to introduce the idea of a quantum computer.

I think Feynman did much more than that. He made lecture on computation(*), and get some contributions on quantum circuit and the non emulability of quantum machine by probabilistic Turing machine, + some idea on the thermodynamic of computation, not well mentioned by some followers, according to Hey(**).  He might just have ignored, as far as I can search, the mathematical notion of universal machine. Deutsch got it and was able to define a quantum universal machine, and gives a clear-cut problem where a quantum machine is very plausibly much more efficient (Of course Shor will do even much more in that respect). 

Feynman disliked philosophy, but seems to get the point that the quantum reality was not Turing emulable in polynomial or real time. 

Deustch shows also that the quantum digital universal machine does *not* violate the Church-Turing thesis, making (trivially) very elementary arithmetic emulating all quantum computers (obviously not in "real time" if that needs to be said, not even in "real space", but the "first person" can't know that ...). 

... so that the question, needed to be solved to progress in the mind-body problem, consist in showing why the quantum computer seems to win "below the substitution level". 

The answer is that the modal translation of the "certain bet" which is in arithmetic Bp & ~Bf, on p semi-computable (sigma_1) gives a quantum logic.  This put a highly non trivial structure accessible on the consistent extensions (in some sense slightly different from the one use in the provability logics, to be sure).

(And thanks to the G/G* separation, which splits also the quantum logic, we get the quanta (first person sharable (by a linear tensor product)) and the qualia, which extend them with non communicable personal data).

Bruno

(*) Feynman Lectures on Computation

https://www.amazon.com/Feynman-Lectures-Computation-Richard-P/dp/0738202967

(**) The book of Anthony J.G. Hey

https://www.amazon.com/Feynman-Computation-Anthony-Hey/dp/081334039X

 

​> ​

Does computationalism provide the answer to this question,

 

No natural phenomenon has ever been found where nature has solved a  NP-hard problem in polynomial time.

​Quantum Computer expert​

 Scott Aaronson actually

​tested this​

 and this is what he

​found​

: 

" taking two glass plates with pegs between them, and dipping the resulting contraption into a tub of soapy water. The idea is that the soap bubbles that form between the pegs should trace out the minimum Steiner tree — that is, the minimum total length of line segments connecting the pegs, where the segments can meet at points other than the pegs themselves. Now, this is known to be an NP-hard optimization problem. So, it looks like Nature is solving NP-hard problems in polynomial time!

Long story short, I went to the hardware store, bought some glass plates, liquid soap, etc., and found that, while Nature does often find a minimum Steiner tree with 4 or 5 pegs, it tends to get stuck at local optima with larger numbers of pegs. Indeed, often the soap bubbles settle down to a configuration which is not even a tree (i.e. contains “cycles of soap”), and thus provably can’t be optimal.

The situation is similar for protein folding. Again, people have said that Nature seems to be solving an NP-hard optimization problem in every cell of your body, by letting the proteins fold into their minimum-energy configurations. But there are two problems with this claim. The first problem is that proteins, just like soap bubbles, sometimes get stuck in suboptimal configurations — indeed, it’s believed that’s exactly what happens with Mad Cow Disease. The second problem is that, to the extent that proteins do usually fold into their optimal configurations, there’s an obvious reason why they would: natural selection! If there were a protein that could only be folded by proving the Riemann Hypothesis, the gene that coded for it would quickly get weeded out of the gene pool." 

For

​ more I highly ​recommend 

 Aaronson's book "Quantum Computing since Democritus".

 ​John K Clark​

 

 

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[David Nyman]

On 28 November 2017 at 13:50, Jason Resch <jason...@gmail.com> wrote:

On Tue, Nov 28, 2017 at 6:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 27 Nov 2017, at 04:04, Jason Resch wrote:

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

Does computationalism provide the answer to this question,

Yes.    :)

Very nice. It seems then Feynman's intuition was in the right place. The second half of the above quote was:

"So I have often made the hypothesis ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this is just speculation."

So it looks like that simple machinery is the machinery of the universal machine and the simple laws  are those of Peano (or Robinson?) Arithmetic.

​Note also that what we call the 'laws' of physics are in fact inferences from observation postulated to explain and predict the behaviour​ of physical phenomena. They are not themselves in principle observable and physics doesn't concern itself with how the postulated entities 'know' how to behave with such precision, or indeed behave at all. Wheeler, and in turn his student Feynman, were so impressed with this precision in the case of the electron that Wheeler was moved to suggest to Feynman (though not entirely seriously) the idea that they might in fact all be the same one.

Computation by contrast is explicitly 'all of a piece' in this respect, in that its entities and relations are (in principle at least) exposable and cut from the same arithmetical cloth, as it were. Further, if entities such as the electron were indeed to be associated with a class of identical computations it would perhaps be less surprising that they are observed to behave identically. In that sense Wheeler would have been right.

David

 

in the sense that even the tiniest region of space is the result of an infinity of computations going through an observer's mind state as it observes the tiniest region of space?

That might be OK, if space was something entirely physical, which is suggested by the physics of the vacuum, or general relativity, but with Mechanism, spece and time might be less physical than here suggested. The reason is that it is not clear how "empty space" could make a computation different from another,

I think what I was thinking here were "closed loop feyman diagrams", where any possible diagram might be drawn in the tiniest area of space, so long as it is closed, e.g. fluctuations/particle creations are permitted so long as they all cancel out. So if space is physical, and enables any of these fluctuations to happen, then this noise can take any possible value from the observer's point of view (like the polarization of a photon).

 

and so space could be only a marker differentiating some computations, like time seems to be in the indexical approach. All this would need big advance in the mathematics of the intelligible and sensible arithmetical matter. I expect space to be explained by quantum knot invariant algebra due to subtil relation between BDB and DBD logical operators (I mean []<>[] and <>[]<>). Kant might be right on this, apparently space and time are really in the "categorie de l'entendement", I don't know Kant in English sorry, but this means mainly that they belong to the mind).

Thanks I very much appreciate these additional insights. I do subscribe to the belief that time is an illusion created by the mind. I have a little more trouble seeing that when extended to spacetime as a whole.  Though perhaps what's come closest to helping me see this picture is Amanda Gefter's excellent book "Trespassing on Einstein's Lawn"--I would recommend it to everyone on the Everything list. It takes the approach that only things that are invariant are real, and from there proceeds to deconstruct almost all of physics.

Jason

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[Bruno Marchal]

On 28 Nov 2017, at 14:50, Jason Resch wrote:

On Tue, Nov 28, 2017 at 6:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 27 Nov 2017, at 04:04, Jason Resch wrote:

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

Does computationalism provide the answer to this question,

Yes.    :)

Very nice. It seems then Feynman's intuition was in the right place. The second half of the above quote was:

"So I have often made the hypothesis ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this is just speculation."

So it looks like that simple machinery is the machinery of the universal machine and the simple laws  are those of Peano (or Robinson?) Arithmetic.

Any first order specification of a universal (Church-Turing)  machinery will do. But it seems to me that we should avoid using induction axioms for the ontology (as I could explain someday, I discovered this more recently). So it is Robinson Arithmetic, and it is better to avoid Peano (for the ontology). Then, the "observer" (which is also a believer, knower, ...) we can use PA (whose existence is a theorem in RA).

But we could use combinators, of Lamdda Expressions. In fact any inductive structure who terms admits laws making it into a universal machinery will do. Iuse the numbers only because we are all familiar with them. 

I have recent reason to suspect that if we put the induction axioms in the ontology, we can no more hunt away the white rabbit. Unfortunately, to prove this is not easy.

 

in the sense that even the tiniest region of space is the result of an infinity of computations going through an observer's mind state as it observes the tiniest region of space?

That might be OK, if space was something entirely physical, which is suggested by the physics of the vacuum, or general relativity, but with Mechanism, spece and time might be less physical than here suggested. The reason is that it is not clear how "empty space" could make a computation different from another,

I think what I was thinking here were "closed loop feyman diagrams", where any possible diagram might be drawn in the tiniest area of space, so long as it is closed, e.g. fluctuations/particle creations are permitted so long as they all cancel out. So if space is physical, and enables any of these fluctuations to happen, then this noise can take any possible value from the observer's point of view (like the polarization of a photon).

That could make sense. But I am still not at ease with quantum field theory enough, notably on how to interpret the "virtual particles". I would treat them as superposition, but some remark by Brent sometimes ago made me doubt this. I am not enough competent on this to get my hand to it.

 

and so space could be only a marker differentiating some computations, like time seems to be in the indexical approach. All this would need big advance in the mathematics of the intelligible and sensible arithmetical matter. I expect space to be explained by quantum knot invariant algebra due to subtil relation between BDB and DBD logical operators (I mean []<>[] and <>[]<>). Kant might be right on this, apparently space and time are really in the "categorie de l'entendement", I don't know Kant in English sorry, but this means mainly that they belong to the mind).

Thanks I very much appreciate these additional insights. I do subscribe to the belief that time is an illusion created by the mind. I have a little more trouble seeing that when extended to spacetime as a whole.  Though perhaps what's come closest to helping me see this picture is Amanda Gefter's excellent book "Trespassing on Einstein's Lawn"--I would recommend it to everyone on the Everything list. It takes the approach that only things that are invariant are real, and from there proceeds to deconstruct almost all of physics.

Thank you, it seems interesting, I might try to take a look (when time permits),

Bruno

Jason

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[Bruno Marchal]

That is needed to have first person plural realities, but truth is also very useful. "just consistency" is good for multi-user video game, but the truth requires sound proposition, and consistency is too cheap (PA + []f is consistent), that is why we need both nuances: []p & <>t and []p & <>t & p. 

So yes, I like what you say, and it is the main motivation for the Z1* logic ("intelligible matter", []p & <>t), but the X1* logic (sensible matter, []p & <>t & p) requires some notion of Truth/God/One.

Bruno

Jason

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[Brent Meeker]

On 11/29/2017 2:21 AM, Bruno Marchal wrote:

I think what I was thinking here were "closed loop feyman diagrams", where any possible diagram might be drawn in the tiniest area of space, so long as it is closed, e.g. fluctuations/particle creations are permitted so long as they all cancel out. So if space is physical, and enables any of these fluctuations to happen, then this noise can take any possible value from the observer's point of view (like the polarization of a photon).

That could make sense. But I am still not at ease with quantum field theory enough, notably on how to interpret the "virtual particles". I would treat them as superposition, but some remark by Brent sometimes ago made me doubt this. I am not enough competent on this to get my hand to it.

Virtual particles should only be thought of in terms of measurements, i.e. calculations of what happens in an interaction with something we treat as classical.  There's no reason to postulate they are "out there" independent of interactions, and good reasons not to (like blowing up the CC).

Brent

[Brent Meeker]

On 11/29/2017 2:27 AM, Bruno Marchal wrote:

On 28 Nov 2017, at 14:52, Jason Resch wrote:

On Tue, Nov 28, 2017 at 7:50 AM, Jason Resch <jason...@gmail.com> wrote:

On Tue, Nov 28, 2017 at 6:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 27 Nov 2017, at 04:04, Jason Resch wrote:

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

Does computationalism provide the answer to this question,

Yes.    :)

Very nice. It seems then Feynman's intuition was in the right place. The second half of the above quote was:

"So I have often made the hypothesis ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this is just speculation."

So it looks like that simple machinery is the machinery of the universal machine and the simple laws  are those of Peano (or Robinson?) Arithmetic.

 

in the sense that even the tiniest region of space is the result of an infinity of computations going through an observer's mind state as it observes the tiniest region of space?

That might be OK, if space was something entirely physical, which is suggested by the physics of the vacuum, or general relativity, but with Mechanism, spece and time might be less physical than here suggested. The reason is that it is not clear how "empty space" could make a computation different from another,

I think what I was thinking here were "closed loop feyman diagrams", where any possible diagram might be drawn in the tiniest area of space, so long as it is closed, e.g. fluctuations/particle creations are permitted so long as they all cancel out. So if space is physical, and enables any of these fluctuations to happen, then this noise can take any possible value from the observer's point of view (like the polarization of a photon).

 

and so space could be only a marker differentiating some computations, like time seems to be in the indexical approach. All this would need big advance in the mathematics of the intelligible and sensible arithmetical matter. I expect space to be explained by quantum knot invariant algebra due to subtil relation between BDB and DBD logical operators (I mean []<>[] and <>[]<>). Kant might be right on this, apparently space and time are really in the "categorie de l'entendement", I don't know Kant in English sorry, but this means mainly that they belong to the mind).

Thanks I very much appreciate these additional insights. I do subscribe to the belief that time is an illusion created by the mind. I have a little more trouble seeing that when extended to spacetime as a whole.  Though perhaps what's come closest to helping me see this picture is Amanda Gefter's excellent book "Trespassing on Einstein's Lawn"--I would recommend it to everyone on the Everything list. It takes the approach that only things that are invariant are real, and from there proceeds to deconstruct almost all of physics.

Jason

I wanted to add, it also shows that the function (if you can call it that) of practically every physical law is to ensure consistency between observers. I think you would like it.

That is needed to have first person plural realities, but truth is also very useful. "just consistency" is good for multi-user video game, but the truth requires sound proposition,

What does "sound" mean?  "True" is not definable in logic.  ISTM it's just a marker "t" for the rules of inference, i.e. those transformations that preserve "t".  Without empiricism or something like it "t" has no interpretation.

Brent

[Bruno Marchal]

What precisely means "out there" in the Everett theory? Is not "blowing up the CC" like saying that Everett theory does not conserve the mass? 

I really don't know. I should revise QED, in the Everett approach. Not simple. if you know some references which can help?

Thanks,

Bruno

Brent

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[Bruno Marchal]

On 29 Nov 2017, at 20:45, Brent Meeker wrote:

On 11/29/2017 2:27 AM, Bruno Marchal wrote:

On 28 Nov 2017, at 14:52, Jason Resch wrote:

On Tue, Nov 28, 2017 at 7:50 AM, Jason Resch <jason...@gmail.com> wrote:

On Tue, Nov 28, 2017 at 6:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 27 Nov 2017, at 04:04, Jason Resch wrote:

Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:

"It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?" 

Does computationalism provide the answer to this question,

Yes.    :)

Very nice. It seems then Feynman's intuition was in the right place. The second half of the above quote was:

"So I have often made the hypothesis ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this is just speculation."

So it looks like that simple machinery is the machinery of the universal machine and the simple laws  are those of Peano (or Robinson?) Arithmetic.

 

in the sense that even the tiniest region of space is the result of an infinity of computations going through an observer's mind state as it observes the tiniest region of space?

That might be OK, if space was something entirely physical, which is suggested by the physics of the vacuum, or general relativity, but with Mechanism, spece and time might be less physical than here suggested. The reason is that it is not clear how "empty space" could make a computation different from another,

I think what I was thinking here were "closed loop feyman diagrams", where any possible diagram might be drawn in the tiniest area of space, so long as it is closed, e.g. fluctuations/particle creations are permitted so long as they all cancel out. So if space is physical, and enables any of these fluctuations to happen, then this noise can take any possible value from the observer's point of view (like the polarization of a photon).

 

and so space could be only a marker differentiating some computations, like time seems to be in the indexical approach. All this would need big advance in the mathematics of the intelligible and sensible arithmetical matter. I expect space to be explained by quantum knot invariant algebra due to subtil relation between BDB and DBD logical operators (I mean []<>[] and <>[]<>). Kant might be right on this, apparently space and time are really in the "categorie de l'entendement", I don't know Kant in English sorry, but this means mainly that they belong to the mind).

Thanks I very much appreciate these additional insights. I do subscribe to the belief that time is an illusion created by the mind. I have a little more trouble seeing that when extended to spacetime as a whole.  Though perhaps what's come closest to helping me see this picture is Amanda Gefter's excellent book "Trespassing on Einstein's Lawn"--I would recommend it to everyone on the Everything list. It takes the approach that only things that are invariant are real, and from there proceeds to deconstruct almost all of physics.

Jason

I wanted to add, it also shows that the function (if you can call it that) of practically every physical law is to ensure consistency between observers. I think you would like it.

That is needed to have first person plural realities, but truth is also very useful. "just consistency" is good for multi-user video game, but the truth requires sound proposition,

What does "sound" mean? 

In our context, a  theory T is sound if its theorems are true in the standard model of arithmetic.  i.e. when (T proves A) -> [ (N, 0, +, *) satisfies A].

"True" is not definable in logic.

Truth about a first order logic theory is definable in second-order logic, or in set theory. Set theoretical truth is not definable in ZF, but is definable in ZF + kappa. Truth theory is a vast sub-branch of mathematical logic.

ISTM it's just a marker "t" for the rules of inference, i.e. those transformations that preserve "t".  Without empiricism or something like it "t" has no interpretation.

Don't confuse the constant boolean t, which in our context can be interpreted by 1 = 1, and the predicate "true", which by incompleteness (à-la Tarski) needs a richer theory to be defined.  We use such richer theory all the times in many part of science, no need to do "bad philosophy". truth is not a problem when handled with some caution.

Bruno

http://iridia.ulb.ac.be/~marchal/

[Lawrence Crowell]

The matter might not directly involve this sort of logic. If spacetime is an emergent property of quantum states and entanglements we might instead think this way. I would offer the prospect that very tiny regions of space have instead of divergent complexity they instead approach nullity.

I think a more physical idea is to consider the graviton as an entanglement of a gluon-like gauge boson. An entanglement two gluons into a colorless pair for the triplet state is quantum mechanically identical to a graviton. The extension of QCD into SU(4) gives a prospect for this with an STU duality SU(4) ↔ SU(2,2). The split form defines AdS_5 and twistor gravitation. Under the STU duality the very strong QCD force is dual to this very weak force that interacts on the boson level with virtually no gauge force interaction. 

There is this article involving QCD as a source of dark matter

https://phys.org/news/2015-09-theory-stealth-dark-universe-mass.html#jCp

This is similar to my proposal for a SU(4) QCD dual to SU(2,2) of twistor space. With SU(3) there are 2 weights for gluon eigenstates and 7 roots for color changing gluons. The connection to QCD or gauge theory is that SU(3) \subset SU(4). We can think of SU(4) as a system of 15 colors, 8 corresponds to QCD as we know it with gluons

(c_i bar-c_j + c_j bar-c_)/sqrt{2}

i(c_j bar-c_i - c_i bar-c_j)/sqrt{2}

(r bar-r - b bar-b)/sqrt{2}

(r bar-r + b bar-b - 2y bar-y)/sqrt{6},

for c_ i = (r, b, y). These gluons are 3 plus 3 as the root space vectors plus 1 plus 1 as the weights, or the diagonal Gel-Mann matrices. This defines the 8 of SU(3). The first two correspond to the 6 roots and the remaining 2 are the eigenvalues of the SU(3). The additional 7 elements of SU(4) would be an additional weight or eigenvalue plus 6 additional roots. We may then include an additional color charge, say green g, and have the system

(c_i bar-c_j + c_j bar-c_)/sqrt{2}

i(c_j bar-c_i - c_i bar-c_j)/sqrt{2}

(r bar-r - b bar-b)/sqrt{2}

(r bar-r + b bar-b - 2y bar-y)/sqrt{6}

(r bar-r + b bar-b + y bar-y - 3g bar-g)/sqrt{10},

for c_ i = (r, b, y, g). 

The STU dual of this is then the SU(2,2) ~ SO(4,2) ~ AdS_4×SO(4,1) in twistor space supergravity. The standard nuclear interaction as the dual of this quantum gravity is strong, while the dual is very weak. Gravitation is extremely weak --- 40 orders magnitude weaker than electromagnetism. 

This would then mean that a tiny region of spacetime corresponds to the UV limit in QCD where the interaction is very small. This means that instead of a small region having lots of information or complexity, instead these regions asymptote to zero complexity.

LC