Re: Seeing numbers.

> On 23 Jun 2020, at 01:55, 'Brent Meeker' via Everything List > wrote: > > https://medicalxpress.com/news/2020-06-insight-awareness.html > > So much for the arithmetical theory of awareness. :-) Indeed. Typically, like truth, machine’s awareness/consciousness is not arithmetical, like

Re: Seeing numbers.

Could be an elaborate lie to avoid math homework. Telmo. Am Mo, 22. Jun 2020, um 23:55, schrieb 'Brent Meeker' via Everything List: > https://medicalxpress.com/news/2020-06-insight-awareness.html > > So much for the arithmetical theory of awareness.  :-) > > Brent > > > > -- > You received

Seeing numbers.

https://medicalxpress.com/news/2020-06-insight-awareness.html So much for the arithmetical theory of awareness.  :-) Brent -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it,

Re: The real numbers are not interpretable in the complex numbers as a field

On Wednesday, February 26, 2020 at 5:40:41 AM UTC-6, Bruno Marchal wrote: > > > On 24 Feb 2020, at 13:19, Philip Thrift > > wrote: > > > https://twitter.com/JDHamkins/status/1231910305439064064 > > Theorem. The real numbers are not interpretable in the

Re: The real numbers are not interpretable in the complex numbers as a field

> On 24 Feb 2020, at 13:19, Philip Thrift wrote: > > > https://twitter.com/JDHamkins/status/1231910305439064064 > > Theorem. The real numbers are not interpretable in the complex numbers as a > field. > > The result, well-known in model theory, often su

Re: The real numbers are not interpretable in the complex numbers as a field

On Monday, February 24, 2020 at 1:48:52 PM UTC-6, Philip Thrift wrote: > > > What is proved: > > > RR is not a definable subset of C: There is no purely field-theoretic > property > φ(x)φ(x), expressible in the language of fields, that holds in CC of all > and only th

Re: The real numbers are not interpretable in the complex numbers as a field

What is proved: RR is not a definable subset of C: There is no purely field-theoretic property φ(x)φ(x), expressible in the language of fields, that holds in CC of all and only the real numbers xx. But more: not only is RR not definable in CC as a subfield, we cannot even define a copy

Re: The real numbers are not interpretable in the complex numbers as a field

om/JDHamkins/status/1231910305439064064 > > Theorem. The real numbers are not interpretable in the complex numbers as > a field. > > The result, well-known in model theory, often surprises mathematicians, > who sometimes expect to easily define R in C. Yet, this isn't possible

The real numbers are not interpretable in the complex numbers as a field

https://twitter.com/JDHamkins/status/1231910305439064064 Theorem. The real numbers are not interpretable in the complex numbers as a field. The result, well-known in model theory, often surprises mathematicians, who sometimes expect to easily define R in C. Yet, this isn't possible

Re: Are Real Numbers Really Real?

Overcomplete coherent states, such as laser states of light have a symplectic and Riemannian structure. This makes these states "classical-like " These are states in a huge quantum correlation, or a form of entanglement. This is the classical spacetime that has no quantum fluctuations. Quantum

Re: Are Real Numbers Really Real?

The sp -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit

Re: Are Real Numbers Really Real?

on about them. > > > >> So if the Gamma Ray Burst results hold up and spacetime really is smooth > >> and continuous then, would it be correct to say there are a infinite (not > >> just astronomically large) number of quantum symmetries and the Planck

Re: Are Real Numbers Really Real?

No that is not the point. Quantum states on the entropy surface deviate from horizon states by the measure to which they are separable. There are no quantum metric fluctuations of a virtual nature. LC -- You received this message because you are subscribed to the Google Groups "Everything

Re: Are Real Numbers Really Real?

nct quantum gravitational states. Am I wrong? >>>>>> >>>>> >>>>> No it is not possible to know. If you localize a quantum bit to a >>>>> Planck length it is in a black hole. If you try to localize two qubits >>>>&g

Re: Are Real Numbers Really Real?

t;>>> arbitrarily closely they caon only be within 2 Planck areas, if on a >>>> horizon,or in two Planck volumes if in the bulk. A Planck volume is V_p = >>>> (4π/3)ℓ_p^3.So if you try to localize a field is less than two Planck >>>> volumes,

Re: Are Real Numbers Really Real?

hin 2 Planck areas, if on a horizon,or in two >>> Planck volumes if in the bulk. A Planck volume is V_p = (4π/3)ℓ_p^3.So >>> if you try to localize a field is less than two Planck volumes, or within a >>> length 1.26ℓ_p there is a loss of any information ab

Re: Are Real Numbers Really Real?

a loss of any information about them. >> >> >>> >>> >> So if the Gamma Ray Burst results hold up and spacetime really is >>>>> smooth and continuous then, would it be correct to say there are a >>>>> infinite >>>>> (not just

Re: Are Real Numbers Really Real?

ocalize a field is less than two Planck volumes, or within a > length 1.26ℓ_p there is a loss of any information about them. > > >> >> >> So if the Gamma Ray Burst results hold up and spacetime really is >>>> smooth and continuous then, would it be correct to say there are a >

Re: Are Real Numbers Really Real?

here are a infinite >>> (not just astronomically large) number of quantum symmetries and the Planck >>> Length and the Planck Time have no physical significance, they are just >>> numbers in units of time and space that for no particular reason happen >&g

Re: Are Real Numbers Really Real?

On Wednesday, December 4, 2019 at 12:08:01 PM UTC-6, Brent wrote: > > > > On 12/4/2019 2:50 AM, Lawrence Crowell wrote: > > On Tuesday, December 3, 2019 at 8:32:43 AM UTC-6, Philip Thrift wrote: >> >> >> >> On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote: >>> >>> For

Re: Are Real Numbers Really Real?

o say there are a infinite (not >> just astronomically large) number of quantum symmetries and the Planck >> Length and the Planck Time have no physical significance, they are just >> numbers in units of time and space that for no particular reason happen >> to pop out when yo

Re: Are Real Numbers Really Real?

On 12/4/2019 8:14 AM, Lawrence Crowell wrote: But this can be nonlocally correlated in both space and time as an observer finds quantum modes on the BH and outside as Hawking radiation. What can "nonlocal" in time mean?...at two different times, but the same place?  That's what "local"

Re: Are Real Numbers Really Real?

On 12/4/2019 2:50 AM, Lawrence Crowell wrote: On Tuesday, December 3, 2019 at 8:32:43 AM UTC-6, Philip Thrift wrote: On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote: For symmetry protected quantum states, which are local entanglements, they

Re: Are Real Numbers Really Real?

they are quantum gravitational. >> > > So if the Gamma Ray Burst results hold up and spacetime really is smooth > and continuous then, would it be correct to say there are a infinite (not > just astronomically large) number of quantum symmetries and the Planck > Length and the P

Re: Are Real Numbers Really Real?

mmetries and the Planck Length and the Planck Time have no physical significance, they are just numbers in units of time and space that for no particular reason happen to pop out when you mathematically play around with the constants of nature in certain ways? *> As Arkani Hamed puts it, "Spa

Re: Are Real Numbers Really Real?

On Tuesday, December 3, 2019 at 8:32:43 AM UTC-6, Philip Thrift wrote: > > > > On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote: >> >> For symmetry protected quantum states, which are local entanglements, >> they are local because the symmetry or group action is generally

Re: Are Real Numbers Really Real?

On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote: > > For symmetry protected quantum states, which are local entanglements, they > are local because the symmetry or group action is generally covariant. This > covariant property enforces what we think of as space and

Re: Are Real Numbers Really Real?

For symmetry protected quantum states, which are local entanglements, they are local because the symmetry or group action is generally covariant. This covariant property enforces what we think of as space and time. LC On Tuesday, December 3, 2019 at 7:29:13 AM UTC-6, John Clark wrote: > > > On

Re: Are Real Numbers Really Real?

On Mon, Dec 2, 2019 at 8:30 PM Lawrence Crowell < goldenfieldquaterni...@gmail.com> wrote: > *Spacetime is an epiphenomenology of entanglement. There are several ways > entanglement can happen. There is topological order that has no scaling, or > where the entanglement occurs without any

Re: Are Real Numbers Really Real?

On Tuesday, December 3, 2019 at 4:38:56 AM UTC-6, Lawrence Crowell wrote: > > >> > I am not thinking of this. In fact this idea seems completely wrong > headed. It might have been that people would have tried to capture QM by > imposing stochastic Wiener processes and the like. > > LC > >

Re: Are Real Numbers Really Real?

On Tuesday, December 3, 2019 at 2:40:27 AM UTC-6, Philip Thrift wrote: > > > > On Monday, December 2, 2019 at 7:30:13 PM UTC-6, Lawrence Crowell wrote: >> >> On Monday, December 2, 2019 at 2:52:05 PM UTC-6, John Clark wrote: >>> >>> On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell < >>>

Re: Are Real Numbers Really Real?

> On 2 Dec 2019, at 19:10, 'Brent Meeker' via Everything List > wrote: > > > > On 12/2/2019 12:41 AM, Bruno Marchal wrote: >> In First Order Logic, Real Numbers are the one which simplifies. The first >> order theory of the real is decidable,

Re: Are Real Numbers Really Real?

On Monday, December 2, 2019 at 7:30:13 PM UTC-6, Lawrence Crowell wrote: > > On Monday, December 2, 2019 at 2:52:05 PM UTC-6, John Clark wrote: >> >> On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell < >> goldenfield...@gmail.com> wrote: >> >> > Spacetime does not really fundamentally exist. It

Re: Are Real Numbers Really Real?

On Monday, December 2, 2019 at 2:52:05 PM UTC-6, John Clark wrote: > > On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell > wrote: > > > Spacetime does not really fundamentally exist. It is just a geometric >> representation for how qubits interact and are entangled with each other. >> > > I agree

Re: Are Real Numbers Really Real?

On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell < goldenfieldquaterni...@gmail.com> wrote: > Spacetime does not really fundamentally exist. It is just a geometric > representation for how qubits interact and are entangled with each other. > I agree it's possible Spacetime is not fundamental, it

Re: Are Real Numbers Really Real?

On Monday, December 2, 2019 at 11:58:13 AM UTC-6, Lawrence Crowell wrote: > > > > Spacetime does not really fundamentally exist. It is just a geometric > representation for how qubits interact and are entangled with each other. > > LC > Or it could be the other way around: qubits come out

Re: Are Real Numbers Really Real?

On 12/2/2019 12:41 AM, Bruno Marchal wrote: In First Order Logic, Real Numbers are the one which simplifies. The first order theory of the real is decidable, unlike the first order theory of the natural numbers. The digital, or discrete, reality is more complex than the reals, which fits

Re: Are Real Numbers Really Real?

On Monday, December 2, 2019 at 10:48:48 AM UTC-6, John Clark wrote: > > On Mon, Dec 2, 2019 at 6:10 AM Lawrence Crowell > wrote: > > >> what does "discrete spacetime" mean? >>> >> >> > It is a form of quotient geometry. >> > > Hawking said the Entropy of a Black Hole is one quarter of it's Event

Re: Are Real Numbers Really Real?

On Mon, Dec 2, 2019 at 6:10 AM Lawrence Crowell < goldenfieldquaterni...@gmail.com> wrote: >> what does "discrete spacetime" mean? >> > > > It is a form of quotient geometry. > Hawking said the Entropy of a Black Hole is one quarter of it's Event Horizon in areas of Planck Length squared, so

Re: Are Real Numbers Really Real?

On Monday, December 2, 2019 at 5:10:54 AM UTC-6, Lawrence Crowell wrote: > > > > Quantum physics has complementaries that are both deterministic and > nondeterministic. As a system of wave mechanics it is completely > deterministic. However, the Fourier components are amplitudes that in polar

Re: Are Real Numbers Really Real?

On Sunday, December 1, 2019 at 2:19:44 AM UTC-6, Philip Thrift wrote: > > > > On Saturday, November 30, 2019 at 6:11:37 PM UTC-6, Lawrence Crowell wrote: >> >> On Saturday, November 30, 2019 at 4:30:28 PM UTC-6, John Clark wrote: >>> >>> >>> >>> On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell <

Re: Are Real Numbers Really Real?

In First Order Logic, Real Numbers are the one which simplifies. The first order theory of the real is decidable, unlike the first order theory of the natural numbers. The digital, or discrete, reality is more complex than the reals, which fits all holes, and provides (in the complex

Re: Are Real Numbers Really Real?

On Saturday, November 30, 2019 at 6:11:37 PM UTC-6, Lawrence Crowell wrote: > > On Saturday, November 30, 2019 at 4:30:28 PM UTC-6, John Clark wrote: >> >> >> >> On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell < >> goldenfield...@gmail.com> wrote: >> >> *> The Planck unit of length and time

Re: Are Real Numbers Really Real?

On Saturday, November 30, 2019 at 4:30:28 PM UTC-6, John Clark wrote: > > > > On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell > wrote: > > *> The Planck unit of length and time does not mean space or spacetime is >> discrete. All it means is this is the smallest scale one can localize a >>

Re: Are Real Numbers Really Real?

On 11/30/2019 2:29 PM, John Clark wrote: On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell > wrote: /> The Planck unit of length and time does not mean space or spacetime is discrete. All it means is this is the smallest scale one can

Re: Are Real Numbers Really Real?

On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell < goldenfieldquaterni...@gmail.com> wrote: *> The Planck unit of length and time does not mean space or spacetime is > discrete. All it means is this is the smallest scale one can localize a > quantum bit of information. It does not mean that

Re: Are Real Numbers Really Real?

On Saturday, November 30, 2019 at 3:08:42 PM UTC-6, John Clark wrote: > > I think it depends on if the Planck Length and Planck Time have physical > significance, it they do then spacetime is not continuous and Real Numbers > are not real; but if spacetime is smooth and continuous

Re: Are Real Numbers Really Real?

I think it depends on if the Planck Length and Planck Time have physical significance, it they do then spacetime is not continuous and Real Numbers are not real; but if spacetime is smooth and continuous as the data from Gamma Ray Bursters seems to indicate then Real Numbers are real

Are Real Numbers Really Real?

https://arxiv.org/abs/1803.06824 (V2: several *mineurs* changes ) ! Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real? Nicolas Gisin <https://arxiv.org/search/quant-ph?searchtype=author=Gisin%2C+N> (Submitted on 19 Mar 2018 (v1 <https://

Re: Long-Standing Problem of 'Golden Ratio' and Other Irrational Numbers Solved with 'Magical Simplicity' | Space

On Saturday, September 21, 2019 at 4:15:17 AM UTC-5, Samiya wrote: > > > > https://www.scientificamerican.com/article/new-proof-solves-80-year-old-irrational-number-problem/ > > This is curious. The golden mean or φ = ½(1 + √5) is connected to a range of mathematics with exceptional and

Re: Long-Standing Problem of 'Golden Ratio' and Other Irrational Numbers Solved with 'Magical Simplicity' | Space

> On 21 Sep 2019, at 11:15, Samiya Illias wrote: > > > https://www.scientificamerican.com/article/new-proof-solves-80-year-old-irrational-number-problem/ That is actually very interesting, but not directly related to our discussion, except such conjecture illustrates the non fiction and

Long-Standing Problem of 'Golden Ratio' and Other Irrational Numbers Solved with 'Magical Simplicity' | Space

https://www.scientificamerican.com/article/new-proof-solves-80-year-old-irrational-number-problem/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to

Re: Universal numbers and Game of Thrones

hat the original question of the greek was about the reality of the > nature: is reality what we see/observe/measure, or is that observable reality > only the border, the projection of a deeper and simpler reality. > Mathematics/music was conceived as the concurrent reality of physics, in p

Re: Universal numbers and Game of Thrones

nough >> theory and means of testing them. >> >> Science does not really exist. What exists is human having a scientific >> attitude, and this does not depend on any domain investigated, be it >> gardening or metaphysics, or theology. >> >> The las

Re: Universal numbers and Game of Thrones

t like a trick to make us > forget that the original question of the greek was about the reality of the > nature: is reality what we see/observe/measure, or is that observable > reality only the border, the projection of a deeper and simpler reality. > Mathematics/music was conceived

Re: Universal numbers and Game of Thrones

hematics/music was conceived as the concurrent reality of physics, in part to the refutation of the earlier Pythagorean conception of numbers (the arithmetical reality kicks back). Science is a fuzzy terms. In the theology of the universal machine, theology itself extends science, but it does it in a j

Re: Universal numbers and Game of Thrones

>> >>> https://www.sciencealert.com/this-is-what-the-standard-model-of-physics-actually-looks-like >>> >>> How does one "derive" this Lagrangian_{SM} from the logic of elementary >>> arithmetic (Logic_{EA}) -- even given the translation of the language of &

Re: Universal numbers and Game of Thrones

what-the-standard-model-of-physics-actually-looks-like> >>> >>> How does one "derive" this Lagrangian_{SM} from the logic of elementary >>> arithmetic (Logic_{EA}) -- even given the translation of the language of >>> Lagrangians into the language of

Re: Universal numbers and Game of Thrones

> On 18 Apr 2019, at 19:51, 'Brent Meeker' via Everything List > wrote: > > > > On 4/18/2019 2:53 AM, Bruno Marchal wrote: >> >> That would be the mistake of Dgital Physics/Physicalism. >> >> It is like saying that some program u generate the physical universe. That >> is not entirely

Re: Universal numbers and Game of Thrones

> Yet, the main ideas are rather well explained in the more readable book by > Vic. Stenger. > > > Unfortunately, even if the correct universal quantum field theory is > successfully extracted from the elementary arithmetic of the prime number, > or other sort of number

Re: Universal numbers and Game of Thrones

On Thu, Apr 18, 2019 at 05:31:06AM -0700, PGC wrote: > > > On Thursday, April 18, 2019 at 11:53:36 AM UTC+2, Bruno Marchal wrote: > > > > On 16 Apr 2019, at 15:06, Philip Thrift wrote: > > > > On Tuesday, April 16, 2019 at 6:39:28 AM UTC-5, Bruno Marchal wrote: > > > >

Re: Universal numbers and Game of Thrones

quot; this Lagrangian_{SM} from the logic of elementary >> arithmetic (Logic_{EA}) -- even given the translation of the language of >> Lagrangians into the language of Logic_{EA}. >> >> >> Yes, formalising a theory is not the same as deriving it. >> &g

Re: Universal numbers and Game of Thrones

On 4/18/2019 2:53 AM, Bruno Marchal wrote: That would be the mistake of Dgital Physics/Physicalism. It is like saying that some program u generate the physical universe. That is not entirely excluded from the mechanist hypothesis, but even if that is the case, such an u (and of course all

Re: Universal numbers and Game of Thrones

gic of elementary >> arithmetic (Logic_{EA}) -- even given the translation of the language of >> Lagrangians into the language of Logic_{EA}. > > Yes, formalising a theory is not the same as deriving it. > > How, to derive it? By studying the “material modes of self

Re: Universal numbers and Game of Thrones

On Thursday, April 18, 2019 at 11:53:36 AM UTC+2, Bruno Marchal wrote: > > > On 16 Apr 2019, at 15:06, Philip Thrift > > wrote: > > > > On Tuesday, April 16, 2019 at 6:39:28 AM UTC-5, Bruno Marchal wrote: >> >> >> On 15 Apr 2019, at 11:04, Philip Thrift wrote: >> >> >> If our physics is in a

Re: Universal numbers and Game of Thrones

nguage of > Lagrangians into the language of Logic_{EA}. > > > Yes, formalising a theory is not the same as deriving it. > > How, to derive it? By studying the “material modes of self-reference, that > the mode of the first person self, or the first person plural self. How, >

Re: Universal numbers and Game of Thrones

agrangians into the language of Logic_{EA}. Yes, formalising a theory is not the same as deriving it. How, to derive it? By studying the “material modes of self-reference, that the mode of the first person self, or the first person plural self. How, and why is explained in most of my papers.

Re: Universal numbers and Game of Thrones

On Tuesday, April 16, 2019 at 6:39:28 AM UTC-5, Bruno Marchal wrote: > > > On 15 Apr 2019, at 11:04, Philip Thrift > > wrote: > > > If our physics is in a number, is Game of Thrones physics > > *The physics of Game of Thrones* > >

Re: Universal numbers and Game of Thrones

> On 15 Apr 2019, at 11:04, Philip Thrift wrote: > > > If our physics is in a number, is Game of Thrones physics > > The physics of Game of Thrones > https://winteriscoming.net/2017/09/29/neil-degrasse-tyson-cant-stop-talking-physics-game-thrones/ > >

Universal numbers and Game of Thrones

If our physics is in a number, is Game of Thrones physics *The physics of Game of Thrones* https://winteriscoming.net/2017/09/29/neil-degrasse-tyson-cant-stop-talking-physics-game-thrones/ in another number? Or: Is there a a GoT reality? - pt -- You received this message because you are

Re: Are there real numbers that cannot be defined?

Note: Strawson uses "physicalism" to mean “materialism" > > That is not problem. Physicalism is a slight nuance on “materialism”. It is > the same thing if you define matter to be the object of study of physics. > > > >> since he thinks physics - what co

Re: Are there real numbers that cannot be defined?

> On 8 Mar 2019, at 11:16, Philip Thrift wrote: > > > > On Friday, March 8, 2019 at 3:18:39 AM UTC-6, Bruno Marchal wrote: > >> On 7 Mar 2019, at 12:26, Philip Thrift > >> wrote: >> >> >> >> On Thursday, March 7, 2019 at 5:11:57 AM UTC-6, Bruno Marchal wrote: >> >>> On 6 Mar 2019, at

Re: Are there real numbers that cannot be defined?

On Friday, March 8, 2019 at 3:18:39 AM UTC-6, Bruno Marchal wrote: > > > On 7 Mar 2019, at 12:26, Philip Thrift > > wrote: > > > > On Thursday, March 7, 2019 at 5:11:57 AM UTC-6, Bruno Marchal wrote: >> >> >> On 6 Mar 2019, at 14:43, John Clark wrote: >> >> On Wed, Mar 6, 2019 at 8:30 AM Bruno

Re: Are there real numbers that cannot be defined?

> On 7 Mar 2019, at 12:26, Philip Thrift wrote: > > > > On Thursday, March 7, 2019 at 5:11:57 AM UTC-6, Bruno Marchal wrote: > >> On 6 Mar 2019, at 14:43, John Clark > wrote: >> >> On Wed, Mar 6, 2019 at 8:30 AM Bruno Marchal > > wrote: >> >> > You confirm my theory that strong (non

Re: Are there real numbers that cannot be defined?

> On 6 Mar 2019, at 14:43, John Clark wrote: > > On Wed, Mar 6, 2019 at 8:30 AM Bruno Marchal > wrote: > > > You confirm my theory that strong (non agnostic) atheism is radical > > religious fundamentalism > > I've never heard you or anybody else criticize me that

Re: Are there real numbers that cannot be defined?

On Wed, Mar 6, 2019 at 8:30 AM Bruno Marchal wrote: *> You confirm my theory that strong (non agnostic) atheism is radical > religious fundamentalism* I've never heard you or anybody else criticize me that brilliantly before, you sure put me in my place. I am devastated! > By theology, you

Re: Are there real numbers that cannot be defined?

> On 5 Mar 2019, at 19:13, John Clark wrote: > > > > On Tue, Mar 5, 2019 at 9:57 AM Bruno Marchal > wrote: > > > But in the “theology of the machine” [...] > > Given the fact that I don't have an infinite amount of time to read things my > rule of thumb is to

Re: Are there real numbers that cannot be defined?

> On 5 Mar 2019, at 15:53, John Clark wrote: > > > On Tue, Mar 5, 2019 at 8:03 AM Bruno Marchal <mailto:marc...@ulb.ac.be>> wrote: > > > The expression "Non computable numbers” appears only in intuitionist logic, > > If so then just by reading the

Re: Are there real numbers that cannot be defined?

On Monday, March 4, 2019 at 3:35:55 AM UTC-7, Lawrence Crowell wrote: > > On Saturday, March 2, 2019 at 8:28:01 PM UTC-6, John Clark wrote: >> >> >> On Fri, Mar 1, 2019 at 4:23 PM Lawrence Crowell >> wrote: >> >> > There are numbers

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 9:57 AM Bruno Marchal wrote: *> But in the “theology of the machine”* [...] Given the fact that I don't have an infinite amount of time to read things my rule of thumb is to stop reading whenever I encounter the T word. John K Clark > -- You received this

Re: Are there real numbers that cannot be defined?

me semantics. No problem for arithmetic, as there is an acceptable notion of “standard model”. But soundness is always defined with respect to some informal reality, be it the standard model of numbers, or a physical reality, etc. > then the proof will tell you something about the nature of reality, About realit

Re: Are there real numbers that cannot be defined?

classical theory of computability to study the more advanced notion of computability on the real numbers. There are many, and there is no Church-Turing corresponding thesis. A function (from N to N, that is what I always mean by a function) is computable if there is a code which compute it. What you

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 8:03 AM Bruno Marchal wrote: > *The expression "Non computable numbers” appears only in intuitionist > logic,* If so then just by reading the title of Turing's famous 1936 paper where he first described a device that we now call a Turing Machine you'd have

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 7:40 AM Bruno Marchal wrote: > *(And what is proof anyway?)* > A proof is a construction made from a finite set of axioms using a finite set of rules. If the axioms and the rules are sound then the proof will tell you something about the nature of reality, if they are not

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 12:55 AM Russell Standish wrote: > *The usual meaning of computable integer is that there exists a program > that outputs it.* There is no point in arguing over the meaning of a word, but if that is what you mean then there is a particular form of "computation" that is

Re: Are there real numbers that cannot be defined?

> On 5 Mar 2019, at 00:42, Bruce Kellett wrote: > > On Tue, Mar 5, 2019 at 10:25 AM Russell Standish > wrote: > On Mon, Mar 04, 2019 at 05:31:00PM -0500, John Clark wrote: > > On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal > > wrote: > >

Re: Are there real numbers that cannot be defined?

R to R, for which there is no standard definition on which everyone would agree, and no corresponding Church-Turing notion, with the notion of computable function from N to N (or any set of finitely describable objects, always trivially computable). Mechanism use the Church-Turing notion. A digita

Re: Are there real numbers that cannot be defined?

> On 4 Mar 2019, at 21:34, Philip Thrift wrote: > > > > On Monday, March 4, 2019 at 12:00:05 PM UTC-6, John Clark wrote: > > > And proof is not truth. > ... > > John K Clark > > > > > Of course truth == proof in the land of radical intuitionists-constructivists. And John does not

Re: Are there real numbers that cannot be defined?

t; algorithm f(x): (r-1)+1 works for all reals r as well as for finite >> strings n. >> > >> > Bruce >> >> I don't think it's 'my definition'. The usual meaning of computable >> integer is that there exists a program that outputs it. For real >> number

Re: Are there real numbers that cannot be defined?

I don't think it's 'my definition'. The usual meaning of computable > integer is that there exists a program that outputs it. For real > numbers, this is changed to a program exists that outputs a sequence > of numbers that converges to the real number in question. One could > also consider &q

Re: Are there real numbers that cannot be defined?

is a valid > computational > > algorithm for n is that it makes all real numbers also computable, but > the > > notion of Turing computability applies only to the integers. We do not > want a > > definition of 'computable', that makes all reals comp

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 2:03 PM Russell Standish wrote: > On Tue, Mar 05, 2019 at 12:06:00PM +1100, Bruce Kellett wrote: > > > > My problem with your idea that the function: "(n-1)+1" is a valid > computational > > algorithm for n is that it make

Re: Are there real numbers that cannot be defined?

On Tue, Mar 05, 2019 at 12:06:00PM +1100, Bruce Kellett wrote: > > My problem with your idea that the function: "(n-1)+1" is a valid > computational > algorithm for n is that it makes all real numbers also computable, but the > notion of Turing computability applies on

Re: Are there real numbers that cannot be defined?

a program to compute the number 'n', 'n' being > given in > > advance. But that is no help in computing a number that can be defined, > but is > > not known in advance. > > > > So what people are really looking for here is a constructive notion of > > computability -- anything

Re: Are there real numbers that cannot be defined?

t is > fine, if you just want a program to compute the number 'n', 'n' being given in > advance. But that is no help in computing a number that can be defined, but is > not known in advance. > > So what people are really looking for here is a constructive notion of > computability -- any

Re: Are there real numbers that cannot be defined?

On Mon, Mar 04, 2019 at 06:48:19PM -0500, John Clark wrote: > > On Mon, Mar 4, 2019 at 6:25 PM Russell Standish wrote: >   > > > OK, so what about the program "print X+1", where X is the expansion of > the number BB(8000)-1? > > > Well what about it? If you don't know what BB(8000)

Re: Are there real numbers that cannot be defined?

On Mon, Mar 4, 2019 at 6:25 PM Russell Standish wrote: > > > *OK, so what about the program "print X+1", where X is the expansion of > the number BB(8000)-1?* > Well what about it? If you don't know what BB(8000) is, and you don't and neither does God, then neither of you will ever know what

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 10:25 AM Russell Standish wrote: > On Mon, Mar 04, 2019 at 05:31:00PM -0500, John Clark wrote: > > On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal wrote: > > > > > > >> I don't follow you. If the 8000th BB number is unknowable > then it is > > certainly

Re: Are there real numbers that cannot be defined?

On Mon, Mar 04, 2019 at 05:31:00PM -0500, John Clark wrote: > On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal wrote: > > > >> I don't follow you. If the 8000th BB number is unknowable then it > is > certainly uncomputable > > > > That is not true. All natural number n are

Re: Are there real numbers that cannot be defined?

On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal wrote: >> I don't follow you. If the 8000th BB number is unknowable then it is >> certainly uncomputable > > > *> That is not true. All natural number n are computable. The program is > “output n”.* > I think you're being silly. You're saying if you

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