On Sunday, June 7, 2020 at 6:43:28 AM UTC-5, Bruno Marchal wrote:
>
>
> On 6 Jun 2020, at 12:44, Lawrence Crowell <[email protected]
> <javascript:>> wrote:
>
> On Friday, June 5, 2020 at 4:57:06 AM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 5 Jun 2020, at 00:39, Lawrence Crowell <[email protected]>
>> wrote:
>>
>> On Thursday, June 4, 2020 at 6:07:45 AM UTC-5, Bruno Marchal wrote:
>>>
>>>
>>> > On 2 Jun 2020, at 19:34, 'Brent Meeker' via Everything List <
>>> [email protected]> wrote:
>>> >
>>> >
>>> >
>>> > On 6/2/2020 2:49 AM, Bruno Marchal wrote:
>>> >>> On 1 Jun 2020, at 22:43, 'Brent Meeker' via Everything List <
>>> [email protected]> wrote:
>>> >>>
>>> >>>
>>> >>>
>>> >>> On 6/1/2020 2:08 AM, Bruno Marchal wrote:
>>> >>>> Brent suggest that we might recover completeness by restricting N
>>> to a finite domain. That is correct, because all finite function are
>>> computable, but then, we have incompleteness directly with respect to the
>>> computable functions, even limited on finite but arbitrary domain. In fact,
>>> that moves makes the computer simply vanishing, and it makes Mechanism not
>>> even definable or expressible.
>>> >>> That's going to come as a big shock to IBM stockholders.
>>> >>
>>> >> Why? On the contrary. IBM bets on universal machine
>>> >
>>> > No, they bet only on finite machines, and they will be very surprised
>>> to hear that they have vanished.
>>>
>>> They bet on finite machines … including the universal machine, which I
>>> insist is a finite machine. That is even the reason why I called it from
>>> times to times universal number.
>>>
>>> I recall that once we get the phi_i, which can be defined in elementary
>>> arithmetic, we get all the universal numbers, that is all u such that there
>>> phi_u(x, y) = phi_x(y), and such u can be used to define all the recursive
>>> enumeration of all digital machines.
>>>
>>> The implementation of this fine but universal machines are called
>>> (physical) computer, and is the domain of expertise of IBM.
>>>
>>> Bruno
>>>
>>>
>> Of course any computation is going to be finite or involve a finite
>> number of bits.
>>
>>
>> Any halting computation.
>>
>> Some non halting computation requires infinite time and space, virtual,
>> arithmetical or physical.
>>
>>
>>
> It is easy to make a nonhalting computation that is finite. A few lines of
> code with a line
>
> 4 GOTO 3
>
>
> The one line "4 goto 4” would be enough.
>
> Or just the combinators MM (SII(SII), or S(SKK)(SKK). Mx = xx, and MM does
> not stop.
>
> But my point was that not only to get all total computable functions, we
> need to have all partial one too, and that no effective theories at all can
> distinguish all total function codes from codes of the strictly partial
> functions.
>
>
>
>
> will be nonhalting. When your desk or lap computer freezes up it has
> entered into a state where something like this is happening. With codes
> that have a bounded length
>
>
> All codes are fine words on a finite alphabet. Of course some have
> generalised this, using non standard models, where some finite object are
> actually infinite, but not seen as such from the pow of some machines.
>
>
>
>
> it is in principle possible for a UTM that can catch all nonhalting codes.
>
>
> ?
>
> No. That is impossible. If such machine exists, you can use it to build a
> recursive enumeration of all codes of all total computable functions, and
> Kleene’s diagonal will bring again 0 = 1.
>
>
>
I mis-wrote that. I should have set a finite set of algorithms.
>
>
>
> Though for programs with thousands of lines the number of possibilities is
> ~ n^{1000}, which is a tad large. The finite UTM is very difficult. Just
> ponder Microsoft the next time your machine freezes up.
>
>
> All UTM are finite (unless working in a non standard model, but that has
> to be made precise, and it is something entirely different).
>
> Ana dall finite UTM leads to undecidability. For all UTM M and U, there is
> some x for which no UTM M cannot say if Ux stops or not.
>
>
>
>
I meant a finite list.
>
>
>
>>
>> This happens as well with quantum computers, but there is one difference.
>> Two states can be prepared and entangled so they have a continuum of
>> probabilities depending upon measurement angle. This is what separates QM
>> from classical mechanics. This separates entanglement of spins from the
>> Bergman's socks, where knowing the left sock is in one box the right must
>> be in the other. So while there is a finitude to the entanglement entropy
>> or the quantity of quantum information, the possible ways an entanglement
>> can register outcomes is infinite. This is what gives a violation of Bell's
>> theorem in QM. With the measurement of a quantum system the pair of a state
>> and measurement forms a type of Godel numbering. This connects QM
>> foundations with the phi_u(x, y) = phi_x(y),you state above.
>>
>>
>> OK. But you assume some quantum universe, where the UDA explains why you
>> have to derive the quantum from arithmetic or (Turing) equivalent.
>>
>>
>>
> As John Wheeler asked, "Why the quantum?”
>
>
>
> And Wheeler gave the correct answer: It for bit. Although a more precise
> one is: qubits from the theology of bits.
>
>
>
It from bits that are in self-referential loops.
> The quantum horizon and a general undecidability of all possible
> propositions are related and maybe ultimately equivalent. Quantum mechanics
> may entirely be due to this limitation.
>
>
> It has to. This is what I have proven. (Assuming the digital mechanist
> theory, to be sure).
>
>
>
> I wrote a paper, under adjudication right now, that entanglement types are
> topologically distinct removed from any unitary equivalence by topological
> obstruction due to mathematical undecidability.
>
>
>
> If you can give a link toward your text, I would be pleased.
>
>
>
I entered this into the FQXi essay contest. I read the announcement on this
topic of undecidability and uncertainty, and was inspired to work like
crazy on this. I had been kicking this idea around for a while. I furiously
worked this theory and hammered out this paper.
https://fqxi.org/data/essay-contest-files/Crowell_fqxi_2020.pdf
My essay did fair to decent in the voting. If you click on community rating
in the page linked below you can see my paper made nearly 90 percentile
rating.
https://fqxi.org/community/forum/category/31427?sort=community
This essay contest is not the highest ranked place to host a paper. but on
the other hand this is such a "way out there" sort of idea that it is hard
to get this sort of thing published in more standard peer review. The FQXi
poobahs tend to give the prizes to their own members and members of the
Perimeter Institute, so my prospects are not entirely great.
I will try to get to the rest later
LC
>
>
>
>>
>>
>> A classical computer will always be finite, and you can't have an
>> infinite Cantor diagonalization.
>>
>>
>> The Kleene diagonalisation is constructive. It shows the inexistence of
>> some finite machine having some “arithmetical omniscience”. It requires
>> potential infinities, not the cantorian infinities.
>>
>>
>>
> Yes, I have heard of this. It is similar to my approach to Hilbert space
> as finite and unbounded. By making it unbounded it just means that even if
> the HIlbert space is infinite the most extreme UV states are unoccupied or
> inaccessible.
>
>
> OK. But here, you are presupposing the quantum, which cannot be done if we
> want to derive it from the theology of universal numbers.
>
>
>
>
> With quantum gravitation this is where the Planck scale comes in. Quantum
> states with a wavelength smaller than the Planck length ℓ_p = √(Għ/c^3) are
> unentangled with states in the rest of the universe. The accelerated
> expansion of the universe increases their wavelength and in effect pulls
> them out of this tiny scale. These then become entangled with the rest of
> the observable universe. Quantum states that have very low energy are
> similarly stretched out these eventually exceed the cosmological horizon
> length √(3/Λ) for the cosmological constant Λ = 8πGρ/c^2 and are then no
> longer entangled with any local region bounded by the cosmological horizon.
> This keeps the number of quantum states finite.
>
>
> This might help, or not. Today, even the role of PI in physics is still an
> open problem, … (it is important to understand than mechanism is not
> supposed to replace physics, that would be like using superstring theory to
> make a cup of coffee). The goal of mechanism is to give a context where the
> mind-body becomes a problem in pure mathematics, yet with testable
> experimental consequences.
>
>
>
>
>
>>
>> The computers that are manufactured are done so to solve certain
>> problems, RSA encyrption, user interfaces for service personnel from travel
>> agents to sales, word processors, games, cell phone signal shifters, data
>> processors of medical measurements and on it goes.
>>
>>
>>
>> All computers exists in arithmetic, and all computations exist in an
>> internal limit of arithmetic (by step 2, actually!).
>>
>> With mechanism, the physical reality is not the fundamental reality. The
>> physical reality emerges from the computation executed in virtue of the
>> number relations, like the prime number distribution, for example.
>>
>>
>>
> I guess I have not seen any reason to be concerned with the distinction
> between mechanism and physicalism. This strikes me as sort of philosophical
> hair splitting that is of no utility to doing physics.
>
>
> Sure it does, if the goal is doing physics. But the goal is o solve the
> mind body problem, and if we assume digital mechanism (YD + CT), we have no
> choice: we have to derive QM and GR from Kxy = x and Sxyz = xz(yz), without
> assuming anything else (beyond some equality rules). Precisely: the theory
> of everything is given by:
>
> RULES:
>
> 1) If A = B and A = C, then B = C
> 2) If A = B then AC = BC
> 3) If A = B then CA = CB
>
> AXIOMS:
>
> 4) KAB = A
> 5) SABC = AC(BC)
>
>
>
> Again, the ultimate relationship between the physical world and that of
> mathematics is not something that may be knowable.
>
>
> It is knowable modulo the mechanist hypothesis. The physical world is a
> collective universal number hallucination.
>
>
>
> At some point here we are in an existential nullity, where our
> understanding of what it means to exist is not longer definite.
>
>
> It depends on your assumption in the theory of mind (aka cognitive
> science).
>
>
>
> With QM we have less certitude over what is meant by an event or objective
> meaning to an object and with mathematics there is no clear definition of
> what is meant by mathematical truth.
>
>
> Mechanism allows to limit ourselves to the arithmetical truth, which is
> well defined. I mean that it is as well defined than real numbers, Hilbert
> space, etc.
>
>
>
> Hardy tries to raise this point below, but it appears we have today a lack
> of clarity with respect to what is meant by a proof
>
>
> We have a total clarity fro first order logic proof, like in PA or ZF,
> etc. This is enough to make the derivation of physics from arithmetic, as
> asked by the mechanist hypothesis, so that we can test Mechanism. If
> confirmed, we learn nothing. If refuted, we learn that either mechanism is
> false, or we are in some second order type of simulation, by malevolent
> descendent amor ancestors. That is a bit conspiratorial, and most people
> would conclude simply that mechanism is false. Form a logic point of view,
> some conspiracy theories are hard to evacuate.
>
>
>
>
>
> and clearly Gödel showed that within an axiomatic system
>
>
>
> Or any mind of any machine (finite by definition of (standard) machine).
>
>
>
> there are holes of undecidability and these things have a dualism of being
> objective and almost Platonic, but also on the other hand little more than
> model systems.
>
>
>
> There are just theories or machines. Logician, like painters, use “models”
> for “realities”. A group is a model of the theory of group. A set universe
> is a model of “set theory” (which should be called set-universe theory, if
> we use “of” in the same set as in “theory of groups”.
>
> Bruno
>
>
>
>
>
> LC
>
>
>>
>> Even with quantum computers this will take off, and in fact I have
>> thought quantum computing would be a way of managing a dynamics network
>> defined by millions of drones over a city. Even if as I think the
>> Godel-Turing result underlies obstructions between entanglement types
>> quantum computers will in time become the province of engineering and
>> business applications.
>>
>>
>> No doubt on this. It is just that with mechanism, the physical universe
>> is not ontological, but more like a collective hallucination made by the
>> relative universal number relations which are as true, and independent of
>> the physical laws, than 117 is composite and 317 is prime.
>>
>> Bruno
>>
>>
>>
>>
>> *<<Of this reality, as I explained […], I take a 'realistic" view. At any
>> rate (and this is my main point) this realistic view is much more plausible
>> of mathematical than of physical reality, because mathematical objects are
>> so much more what they seem. A chair or a star is not in the least like
>> what it seems to be ; the more we think of it, the fuzzier its outlines
>> become in the haze of sensations which surrounds it; but '2' and '317' has
>> nothing to do with sensations, and its properties stand out the more
>> clearly the more closely we scrutinize it. It may be that modern physics
>> fits best in the framework of idealistic philosophy---I do not believe it,
>> but there are eminent physicist who say so. Pure Mathematics, on the other
>> hand, seems to me a rock on which all idealism founders: 317 is prime, not
>> because we think so, or because our minds are shaped in one way rather than
>> another, but because it is so, because mathematical is built that way.>>G.
>> H. Hardy, "A Mathematician's Apology", Cambridge University Press, 1940
>> (1998).*
>>
>>
>>
>>
>>
>> LC
>>
>>
>>>
>>>
>>> >
>>> > Brent
>>> >
>>> >> and know well what is a computer: a finite arithmetical being in
>>> touch with the infinite, and indeed, always asking for more memory, which
>>> is the typical symptom of liberty/universality. IBM might be finitist, like
>>> Mechanism, but is not ultrafinist at all. Anyway, mathematically, Mechanism
>>> is consistent with ulrafinitsim, even if to prove this, you need to go
>>> beyond finitism, (but then that’s the case for all consistent theory: none
>>> can prove its own consistency once “rich enough” (= just Turing universal,
>>> not “Löbian”).
>>> >>
>>> >> Bruno
>>> >
>>> >
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>>>
>>>
>>>
>>>
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>>
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