Computability in the Theory of Theories by Philip Gibbs

"You can process and compute the universe in any order."

The essence of mathematics is its freedom (Cantor). This makes it just a tool that even allows, to some extent, reasonable backpropagation.

Philip,

philosophy has always been discussed along contemporary hot topics and of course by using contemporary vocabulary. The only constant I can find in it right from its start is:

- Time versus Time-lessness (not eternity!)

- a posteriori versus a priori

- empiricism versus rationalism

which all mean the same.

The other point I want to address is that REAL progress has been made when a scientist cannot decide whether he has discovered or invented something. Then what he discovered/invented is Absolutely free from contradiction. The formal description of this state of 'universal validity' exceeds the capacity of logic, but not the capacity of the scientific metaphor.

Heinz

Phil,

Thanks for clarifying the difference between yours and MUH. And thanks for pointing out that your approach is "indistinguishable from the'multiverse' of wavefunctions in QM which is really just one field." I'm actually glad to hear that as I like your ideas, but felt they were the extreme opposite of mine. I do believe that good ideas should generally converge to a "correct" idea.

Best,

Edwin Eugene Klingman

For the FLRW metric with k = 0 the spatial surface of the Hubble frame is R^3. A similar situation occurs with how one defines coordinates in de Sitter spacetime. There is no serious problem I see with that sort of infinitude. The limit to observing an infinite amount of stuff, first pointed out by Olber in his paradox, is the expansion of the universe and cosmological horizon. The expansion factor e^{Ht} in the FLRW, or cosh(Ht) in de Sitter, defines a limit for the expansion of a Planck length at the earliest quantum gravitation stage to the scale of the CMB or cosmological horizon. This is an enormous factor e{Ht} = 8Г--10^{60}, but Ht = 140. This gives r = 140Г--в€љ{3/О›} ≈ 1800 light years.

The hunt for B-modes in the CMB is a form of this. Graviton production or gravitational waves produced in inflation should leave a polarization signature on the CMB. In this way the most distant and earliest quantum information we may receive or observe is on the CMB as a sort of cosmic quantum gravitation detector. Anything beyond this scale is sealed off from view. As a result, any observer can access only a finite amount of information.

There is a curious sort of renormalization of scale with information. As we observe further outwards the number of qubits available decreases, until at some final scale of the Planck wall there may only be one qubit. Of course, observers, or we, find themselves in a local world filled with information. The cosmological horizon at the time of inflation has an area of around 10^{15} Planck units of area. This is the amount of information potentially available from this epoch. Pushing further back to the Planck era this approaches one unit.

Cheers LC

erratum, r = 140Г--в€љ{3/О›} ≈ 1800 light years is meant to read r = 140Г--в€љ{3/О›} ≈ 1800 billion light years.

LC

"The real amount of information out there is no more than the amount in our head." If it is only "out" there, then it is not "in" our head. Where did your "information about physics" come from, if it was not in papers, books and the minds of your professors, before it got copied into your head, and probably had to overwrite older information stored there, in order to make room for it?

"Our brains can only hold a hundred terabytes of information which is tiny compared to what is required to determine the physical position of all the particles around us" - Or in us. The information content of either a computer or a brain, is not just that stored in its "memory". It requires much more information, to specify how to construct the computer, or brain, in the first place.

"This computer is not a real thing." That is your illusion. The universe merely "computes" itself, by simply being itself, just like every other computer, brain or being; things can only be whatever they are, and can only do whatever it is that they do. Humans do not have enough information storage capacity, to ever store all the information contained within all these other beings. That is no cause to believe that such other things, do not exist.

Information has nothing to do with consciousness, thought or life. As Shannon stated on the first page of his A Mathematical Theory of Communication: "semantic aspects of communication are irrelevant to the engineering problem." In other words, his conception of "information" has nothing to do with "meaning", it is simply a "quantifiable", observable pattern, encoded into an observable, physical "substance", waiting to be correctly recognized, by some other entity in the future. The fact that such an entity may not have appeared yet, and correctly copied and "decoded" that information into its circuitry, or brain, has no bearing on the existence of the information "out there"; if I write a note on a piece of paper, and cast it into the wind, the fact that some other being does not yet know that it exists, much less know what I wrote on it, is irrelevant to the fact that the paper, with its writing, does exist, and may be eventually discovered and "correctly decoded", by something.

You seem to be totally ignoring the fact that the key word in the title of Shannon's paper, is the word communication - thus, Shannon's "information" is entirely concerned with a possibility, the potential, to transfer (AKA communicate) "information", from one inanimate entity to another, without any "thought" or "meaning" entering into the process - such as the process embodied in an inanimate radio receiver. Some other entity, like a human being, may subsequently come along and attempt to attach some "meaning" onto this acquired "information", but as Shannon stated, that is "irrelevant to the engineering problem", involving the "information transmission" itself.

Rob McEachern

"Some people claim that the wave-function does not collapse and it is just decoherence. This is nonsense."

If I recall correctly, someone else called even the wave-function collapse itself a nonsense. Don't get me wrong. I don't support the two "nonsensical" opinions. I just dislike the word nonsense in a scientific discussion.

Eckard Blumschein

Your mini-prolegomena has ideas I too have pondered. I am not quite as disposed to this idea of idealism. However, locality and realism are dual constructs and Frauchiger and Renner showed how the observer of observers can have disparate reports to the observed outcomes. This illustrates how this duality can have a non-realism wing. Thus, nonlocality can give way to some element of locality if realism is weakened or dropped.

The thrust of my paper is there is no computable or dynamical reason for how outcomes of measurements obtain. What are quantum interpretations are then auxiliary postulates that share properties similar to what happens in geometry when Euclid's fifth axiom is negated. Nagel and Newman illustrate how this is an undecidable axiom, and if one includes this as an unprovable statement you get a consistent system, whereas the negation leads to a bouquet of geometries that are not consistent with each other. In QM, as I see it, there is a similar situation, where one can do the Mermin "shut up and calculate," or one can decide between whether QM is ψ-epistemic, Bohr CI or Qubism, or ψ-ontological, such as MWI. There is then a branching of various interpretations, which if they are not inconsistent with QM are workable.

I am not certain what role to give mind. I am not sure about "all idealism," but on the other hand QM has this idealism prospect. Trying to eliminate idealism might be a sort of "whack-a-mole" exercise. Penrose has in his Road to Reality a suggested triality between physical reality or materialism, mathematics and consciousness. Of course, Penrose is at an age with the stature that he can propose something like this. I am not entirely certain about these ideas. It is evident the universe existed long before biology, at least on Earth, and certainly long before intelligent life or consciousness. There are many reasons and evidences that force me to not completely throw my lot towards idealism. This is even if the door for idealism is slightly open.

Cheers LC

Nature in a sense computes itself. QCD has roots that tell us how color charge is flipped between quarks and gluons in three-vertex diagrams. A QCD gluon is then a complicated statistical computer of sorts where color charge, a form of quantum information, is exchanged. Along with that of course spin is flipped. The idea the universe is a computer is a sort of human imposed model. There is an old and long tradition of considering the world according to technology of the day, from pumps as models in the renaissance, clocks then steam engines and so forth.

We really do not know what consciousness is. I am not an exponent of panpsychism that is growing in popularity. Consciousness does have some connection to information, for if the underlying neural system closes down consciousness either lapses or ends. At least our outward measure of what it is to be conscious goes to zero. We do not have a lot of information about this and Monty Python did a sketch on interviewing dead people that made light of this. We all will subjectively get to experience this at some time.

LC

"... Fredkin .. deterministic vision of reality ..." Do you have an opinion concerning the following?

Viewpoint 1. Electrons travel through spacetime. Electrons are wave-like when they are not measured. Electrons are particle-like when they are measured.

Viewpoint 2. Electrons and spacetime are approximations generated by Wolfram's cosmological automaton. Electrons do not travel through spacetime. Measurement is a natural process that separates the boundary of the multiverse from the interior of the multiverse. The multiverse is mathematically isomorphic to a 72-dimensional holographic, digital computer. An electron is an approximate pattern of Fredkin-Wolfram information, and the electron's pattern is computationally and holographically propagated through the interior of the multiverse. The electron approximately consists of discontinuous displays of Fredkin-Wolfram information that are psychologically merged together in the minds of those electromagnetic fields called the "minds of physicists". How might Viewpoint 2 be tested?

Prediction 1: dark-matter-compensation-constant = (3.9±.5) * 10^-5 .

Prediction 2: The Riofrio-Sanejouand cosmological model is empirically valid, i.e., the radius of our universe is a constant, and the speed of light in a perfect vacuum steadily decreases as our universe ages.

"As Shannon stated on the first page of his A Mathematical Theory of Communication: "semantic aspects of communication are irrelevant to the engineering problem.""

This is not correct. Shannon's theory is about a transmitter and a receiver which have agreed upon a certain symbol alphabet. So there is lots of meaning (semantics) in it. Only past this meaning stage the above quote holds (only then it does't matter what meaning is communicated). Hence it does not make any sense to say that the universe computes itself, if no one is able to pick up that information.

The philosophical problem behind this discussion is Kant's famous thing-in-itself, the thing as it is independent of what we think about it. Does it exist? Kant does NOT claim that it exists in some certain form, which humans are just too limited to ever grasp. What he says is that the question after the thing in itself is non-sensical. For any answer to what the thing in itself is, would make it into a thing for us.

"This is not correct. Shannon's theory is about a transmitter and a receiver which have agreed upon a certain symbol alphabet."

As Shannon states on page 44, each "symbol" will be little more than "samples of white noise", for a system operating at the maximum capacity. So any meaning that might be attached to such noise samples, cannot be deduced from any observation of them; any meaning, if such exists, must be extrinsic to any such message/observable. Upon detecting the existence of any such "noise sample", the receiver merely decodes it, by replacing it with some agreed upon binary number, which remains as meaningless to the receiver, as it was to the transmitter.

There never even has to be any meaning - the original message to be transmitted, may itself be nothing more than a meaningless noise sequence.

"Hence it does not make any sense to say that the universe computes itself, if no one is able to pick up that information"

"picking up information" involves nothing more than picking up an oak leaf (and regarding it as an alphabetic symbol). That is the point. Because this makes the recipient of the information, free to associate (by accident, chance, or any other mechanism) any possible meaning, or behavior, with that "picking up" - thereby enabling the "emergence" of a previously non-existent, cause-and-effect relationship. If you decide to slap your face with your right hand, every time you pick-up an oak leaf, but pat your head, every time you pick-up a maple leaf, an observer watching you, might reasonably suppose that an oak leaf means "slap your face" and a maple leaf means "pat your head" and the same observer, seeing every person doing the same thing, might even suppose that there is some "law of nature" necessitating the behavior. The fact that the oak tree, did not intend its leaf to serve that function, is of no consequence. Any repeatable behavior, that becomes associated with "picking up information", becomes the "meaning" of that information, and may take on the appearance of a "law of nature", to any observer witnessing such repeatable behaviors. The law did not cause the behavior, rather, the behavior caused the observer to suppose the existence of a law.

Rob McEachern

Robert,

""picking up information" involves nothing more than picking up an oak leaf (and regarding it as an alphabetic symbol). That is the point."

How can you know that what Shannon wrote (for example on page 44) isn't also merely meaningless noise?

What you really are exemplifying is (when one logically deciphers your lines of reasoning) either that you

1. do not know that you don't know what you are talking about

or

2. you know that you don't know what you are talking about

In any case I think you wildly mix up various categories like meaning, information, laws of nature and human conditional learning.