Re: Coherent states of a superposition

2019-01-29 Thread agrayson2000


On Tuesday, January 29, 2019 at 4:37:34 AM UTC-7, Bruno Marchal wrote:
>
>
> On 28 Jan 2019, at 22:50, agrays...@gmail.com  wrote:
>
>
>
> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 24 Jan 2019, at 09:29, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:


 On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:



 On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>
>
>
> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:



 On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:

 This means, to me, that the arbitrary phase angles have absolutely 
 no effect on the resultant interference pattern which is observed. But 
 isn't this what the phase angles are supposed to effect? AG


 The screen pattern is determined by *relative phase angles for the 
 different paths that reach the same point on the screen*.  The 
 relative angles only depend on different path lengths, so the overall 
 phase 
 angle is irrelevant.

 Brent

>>>
>>>
>>> *Sure, except there areTWO forms of phase interference in Wave 
>>> Mechanics; the one you refer to above, and another discussed in the 
>>> Stackexchange links I previously posted. In the latter case, the wf is 
>>> expressed as a superposition, say of two states, where we consider two 
>>> cases; a multiplicative complex phase shift is included prior to the 
>>> sum, 
>>> and different complex phase shifts multiplying each component, all of 
>>> the 
>>> form e^i (theta). Easy to show that interference exists in the latter 
>>> case, 
>>> but not the former. Now suppose we take the inner product of the wf 
>>> with 
>>> the ith eigenstate of the superposition, in order to calculate the 
>>> probability of measuring the eigenvalue of the ith eigenstate, applying 
>>> one 
>>> of the postulates of QM, keeping in mind that each eigenstate is 
>>> multiplied 
>>> by a DIFFERENT complex phase shift.  If we further assume the 
>>> eigenstates 
>>> are mutually orthogonal, the probability of measuring each eigenvalue 
>>> does 
>>> NOT depend on the different phase shifts. What happened to the 
>>> interference 
>>> demonstrated by the Stackexchange links? TIA, AG *
>>>
>>> Your measurement projected it out. It's like measuring which slit 
>>> the photon goes through...it eliminates the interference.
>>>
>>> Brent
>>>
>>
>> *That's what I suspected; that going to an orthogonal basis, I 
>> departed from the examples in Stackexchange where an arbitrary 
>> superposition is used in the analysis of interference. Nevertheless, 
>> isn't 
>> it possible to transform from an arbitrary superposition to one using an 
>> orthogonal basis? And aren't all bases equivalent from a linear algebra 
>> pov? If all bases are equivalent, why would transforming to an 
>> orthogonal 
>> basis lose interference, whereas a general superposition does not? TIA, 
>> AG*
>>
>>
>> I don’t understand this. All the bases we have used all the time are 
>> supposed to be orthonormal bases. We suppose that the scalar product 
>> (e_i 
>> e_j) = delta_i_j, when presenting the Born rule, and the quantum 
>> formalism.
>>
>> Bruno
>>
>
> *Generally, bases in a vector space are NOT orthonormal. *
>
>
> Right. But we can always build an orthonormal base with a decent 
> scalar product, like in Hilbert space, 
>
>
>
> *For example, in the vector space of vectors in the plane, any pair of 
> non-parallel vectors form a basis. Same for any general superposition of 
> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
> orthogonal.*
>
>
> Absolutely. And when choosing a non degenerate 
> observable/measuring-device, we work in the base of its eigenvectors. A 
> superposition is better seen as a sum of some eigenvectors of some 
> observable. That is the crazy thing in QM. The same particle can be 
> superposed in the state of being here and there. Two different positions 
> of 
> one particle can be 

Re: Histories Of Phenomenally Everything (HOPE)

2019-01-29 Thread Philip Thrift


On Tuesday, January 29, 2019 at 7:29:43 AM UTC-6, Bruno Marchal wrote:
>
>
> On 29 Jan 2019, at 12:03, Philip Thrift > 
> wrote:
>
>
> This replaces space, time, particles, fields with histories.
>
> I think this is compatible with universal machines.
>
>
> https://codicalist.wordpress.com/2019/01/28/histories-of-phenomenally-everything-hope/
>
>
>
>
> That space and time, and energy, emerges from histories is compatible with 
> mechanism; even necessary; with mechanism.
>
> With mechanism you need to convince the universal machine, and the only 
> way too do that, is to let doing the work and discovering this by itself. 
> That has been partially done, and the logic of the observable is a quantum 
> logic, and should be the one that von Neumann and Birkhoff were 
> searching,and which is the one defining all the relative probabilities, 
> imposing a unique measure, like with Gleason theorem.
>
> A history is not a curve in some space though. A history is defined by a 
> universal number U, its number local data X, and the sequence of steps 
> which follows from U and X (like the phi_U,s(X), s = 0, 1, 2, …).
>
> Continua and analog situations officers from the first person 
> indeterminacy on all relative computations + the structure imposed by the 
> modal theology of the machine (the intensional variants of auto reference 
> imposed by incompleteness).
>
> Bruno
>




By  "historical paths (curves or walks)", "Histories have a path 
representation as a sequence" I mean sequences as having a linearly ordered 
index I  [ https://en.wikipedia.org/wiki/Total_order ], so each element of 
the history is indexed: 

 (στ,φ)ᵢ   i ∈ I

(So can mean sequence as you defined it.)

- pt


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Re: Planck Length

2019-01-29 Thread Philip Thrift


On Tuesday, January 29, 2019 at 5:30:18 AM UTC-6, Bruno Marchal wrote:
>
>
> On 28 Jan 2019, at 15:07, Philip Thrift > 
> wrote:
>
>
>
> On Monday, January 28, 2019 at 6:27:37 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 25 Jan 2019, at 14:53, Philip Thrift  wrote:
>>
>>
>>
>> On Friday, January 25, 2019 at 6:27:44 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 24 Jan 2019, at 15:19, Philip Thrift  wrote:
>>>
>>>
>>>
>>> On Thursday, January 24, 2019 at 7:14:15 AM UTC-6, Bruno Marchal wrote:


 On 23 Jan 2019, at 19:01, Philip Thrift  wrote:



 On Wednesday, January 23, 2019 at 5:52:01 AM UTC-6, Bruno Marchal wrote:
>
>
> On 22 Jan 2019, at 01:49, Philip Thrift  wrote:
>
> One of the oddest of things is when physicists use the language of 
> (various) theories of physics to express what can or cannot be the case. 
> It's just a language, which is probably wrong.
>
> There is a sense in which the Church/Turing thesis is true: All out 
> languages are Turing in their syntax and grammar. What they refer to is 
> another matter (pun intended).
>
>
> They refer to the set of computable functions, or to the universal 
> machine which understand that language. But not all language are Turing 
> universal. Only the context sensitive automata (in Chomski hierarchy) are 
> Turing universal. Simple languages, like the “regular” one are typically 
> not Turing universal. Bounded loops formalism cannot be either.
>
> But the notion of language is ambiguous with respect to computability, 
> and that is why I prefer to avoid that expression and always talk about 
> theories (set of beliefs) or machine (recursively enumerable set of 
> beliefs), which avoids ambiguity. 
> For example, is “predicate calculus” Turing universal? We can say yes, 
> given that the programming language PROLOG (obviously Turing universal) 
> is 
> a tiny subset of predicate logic. But we can say know, if we look at 
> predicate logic as a theory. A prolog program is then an extension of 
> that 
> theory, not something proved in predicate calculus.
> Thus, I can make sense of your remark. Even the language with only one 
> symbol {I}, and the rules that “I” is a wff, and if x is wwf, then Ix is 
> too, can be said Turing universal, as each program can be coded by a 
> number, which can be coded by a finite sequence of I. But of course, that 
> makes the notion of “universality” empty, as far as language are 
> concerned. 
> Seen as a theory, predicate calculus is notoriously not universal. 
> Even predicate calculus + the natural numbers, and the law of addition, 
> (Pressburger arithmetic) is not universal. Or take RA with its seven 
> axioms. Taking any axiom out of it, and you get a complete-able theory, 
> and 
> thus it cannot be Turing complete.
>
> Bruno
>
>
>
 Here's an example of a kind of "non-digital" language:

 *More Analog Computing Is on the Way*
 https://dzone.com/articles/more-analog-computing-is-on-the-way



 *The door on this new generation of analog computer programming is 
 definitely open. Last month, at the Association for Computing Machinery’s 
 (ACM) conference on Programming Language Design and Implementation, 
 a paper  was 
 presented that described a compiler that uses a text based, high-level, 
 abstraction language to generate the necessary low-level circuit wiring 
 that defines the physical analog computing implementation. This research 
 was done at MIT’s Computer Science and Artificial Intelligence Laboratory 
 (CSAIL) and Dartmouth College. The main focus of their investigation was 
 to 
 improve the simulation of biological systems. *


 *Configuration Synthesis for ProgrammableAnalog Devices with Arco*
 https://people.csail.mit.edu/sachour/res/pldi16_arco.pdf

 *Programmable analog devices have emerged as a powerful*
 *computing substrate for performing complex neuromorphic*
 *and cytomorphic computations. We present Arco, a new*
 *solver that, given a dynamical system specification in the*
 *form of a set of differential equations, generates physically*
 *realizable configurations for programmable analog devices*
 *that are algebraically equivalent to the specified system.*
 *On a set of benchmarks from the biological domain, Arco*
 *generates configurations with 35 to 534 connections and 28*
 *to 326 components in 1 to 54 minutes.*


 - pt


 Intersting.

 Yet, that does not violate the Church-Thesis, even if very useful FAPP. 
 But such computations arise in arithmetic, either directly, or through a 
 infinite sequence of approximations. If all decimals of the 

Re: Strict finitism

2019-01-29 Thread Philip Thrift


On Tuesday, January 29, 2019 at 5:23:36 AM UTC-6, Bruno Marchal wrote:
>
>
> On 28 Jan 2019, at 14:55, Philip Thrift > 
> wrote:
>
>
>
> On Monday, January 28, 2019 at 5:46:12 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 26 Jan 2019, at 08:36, Philip Thrift  wrote:
>>
>>
>>
>> *Varieties of finitism*
>> http://www.mbph.de/Logic/Finitism.pdf
>> Manuel Bremer
>> http://www.mbph.de
>>
>> *Annotated bibliography of strict finitism*
>> http://jeanpaulvanbendegem.be/home/papers/strict-finitism/
>> Jean Paul Van Bendegem
>> http://jeanpaulvanbendegem.be
>>
>> Apparently, strict finitism requires a (likely) paraconsistent modality 
>> (implying there may be inconsistencies). If one takes strict finitism 
>> seriously (Tegmark would have to be a strict finitist, if he isn't kidding 
>> people about what he said) then of course physics (and mathematics, of 
>> course) would be radically different.
>>
>>
>>
>> Computationalism (digital mechanism) is consistent with strict finitisme, 
>> but rather unsound.
>>
>> Mechanism is a finitisme, but it keeps the potentially infinite of the 
>> classical and intuitionist thinkers. 
>>
>> But with mechanism, we cannot put the induction axioms in the ontology, 
>> so we cannot prove that there is no biggest natural numbers in the 
>> ontology. From outside, we know that this is consistent only because we 
>> believe in some infinite objects, making strict finitisme consistent, but 
>> rather arithmetically unsound.
>>
>> Nothing in Tegmark suggests that he would espouse anything like “strict” 
>> finitisme, but when he moved to computationalism, he might become a 
>> finitist.
>>
>> The best book (beside my work :) ) on the subject of mechanism and 
>> finitism is the book by Judson Webb, 1980. 
>>
>> WEBB J. C., 1980, Mechanism, Mentalism and Metamathematics : An essay on 
>> Finitism, D. Reidel Pub. Company, Dordrecht, Holland.
>>
>> Bruno
>>
>
>
>
>
> Max Tegmark writes that the mathematics of physics in the future needs to 
> be "infinity-free".
>
>   
> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/
>
> (Almost like it's a sin to have infinities around.) That sounds like 
> strict finitism to me.
>
>
> Not it is not. It is finitism, not strict finitism. Actually you need 
> sting actual infinities to make sense of strict finitism. Finitism need 
> only potential infinite to be define, but strict finitism needs actual 
> infinities at the metalevel. To define what is a machine, or what is 
> “finite", you need potential infinite. Strict finitisme makes sense … 
> thanks to big infinities at the meta-level. Absolute strict finitism cannot 
> be Turing universal.
>
>
>
>
>
>
>
>
> As Manuel Bremer's paper above shows, a strictly-finite arithmetic is 
> (likely) inconsistent,
>
>
> It is not valid. RA can be strictly finitist, but again, at the semantical 
> level this is made possible by the existence of a non standard natural 
> number which are bigger than all standard numbers.
>
>
>
>
> which is OK, since "inconsistent mathematics can have a branch which is 
> applied mathematics”.
>
>
> Inconsistency treatment I useful for natural language, and human 
> psychology, but in most applied math, we need consistent theories. In 
> metaphysics, paraconsitency is a red herring. It hides the problems instead 
> of solving them. But now, self-reference makes inconsistency consistent, 
> and G/G* has a small quasi-para-consistent part, useful indeed for the 
> embedded machine (in sheaves of arithmetical computations).
>
> Bruno
>
>
>
>
>
> https://plato.stanford.edu/entries/mathematics-inconsistent/
>
> - pt
>
>



I am familiar with the theory of potential infinity (currently being 
pursued by Hamkins).


I am skeptical that it is coherent. *You can't be a little bit pregnant.*




[image: Joel David Hamkins]

Joel David Hamkins
@JDHamkins

·
Jan 26

I'll be giving the Jowett Society lecture here in Oxford on 8 February: 
"Potentialism and implicit actualism in the foundations of mathematics".

*Abstract.* Potentialism is the view, originating in the classical dispute 
between actual and potential infinity, that one’s mathematical universe is 
never fully completed, but rather unfolds gradually as new parts of it 
increasingly come into existence or become accessible or known to us. 
Recent work emphasizes the modal aspect of potentialism, while decoupling 
it from arithmetic and from infinity: the essence of potentialism is about 
approximating a larger universe by means of universe fragments, an idea 
that applies to set-theoretic as well as arithmetic foundations. The modal 
language and perspective allows one precisely to distinguish various 
natural potentialist conceptions in the foundations of mathematics, whose 
exact modal validities are now known. Ultimately, this analysis suggests a 
refocusing of potentialism on 

Re: Histories Of Phenomenally Everything (HOPE)

2019-01-29 Thread Bruno Marchal

> On 29 Jan 2019, at 12:03, Philip Thrift  wrote:
> 
> 
> This replaces space, time, particles, fields with histories.
> 
> I think this is compatible with universal machines.
> 
> https://codicalist.wordpress.com/2019/01/28/histories-of-phenomenally-everything-hope/



That space and time, and energy, emerges from histories is compatible with 
mechanism; even necessary; with mechanism.

With mechanism you need to convince the universal machine, and the only way too 
do that, is to let doing the work and discovering this by itself. That has been 
partially done, and the logic of the observable is a quantum logic, and should 
be the one that von Neumann and Birkhoff were searching,and which is the one 
defining all the relative probabilities, imposing a unique measure, like with 
Gleason theorem.

A history is not a curve in some space though. A history is defined by a 
universal number U, its number local data X, and the sequence of steps which 
follows from U and X (like the phi_U,s(X), s = 0, 1, 2, …).

Continua and analog situations officers from the first person indeterminacy on 
all relative computations + the structure imposed by the modal theology of the 
machine (the intensional variants of auto reference imposed by incompleteness).

Bruno



> 
> 
> - pt
> 
> 
> Histories Of Phenomenally Everything (HOPE)
> 
>  
> or Everything Histories (EH)
> 
>  
>  
> 
>  
> Perhaps… we must also give up, by principle, the space-time continuum,” he 
> wrote. “It is not unimaginable that human ingenuity will some day find 
> methods which will make it possible to proceed along such a path. At the 
> present time, however, such a program looks like an attempt to breathe in 
> empty space.
> — Albert Einstein
> 
>  
> In a HOPE-ful ontology, histories  are the 
> fundamental constituents of the universe. They replace spacetime 
> —by
>  embedding(bits of) spacetime within themselves.
> 
> Spacetime is derived from histories. (Some like the word emergeshere.) The 
> spacetime continuum is replaced with historical paths (curves or walks).
>  
> There are possible histories and actual histories. Possible histories 
> reenforce or interfere with each other (via the path integral).
>  
> Histories replace not only spacetime, but particles and fields as well, which 
> are defined in terms of ensembles of histories. Histories have physical 
> properties, so a particular history can be an ‘electron’ history, for example.
>  
> Histories have a path representation as a sequence going backwards in time. 
> An element of the path sequence could be (στ,φ), where στ is some sort of 
> spacetime-like parameter and φ is a physical parameter.* The reverse paths 
> (going forward in time) are called futures. In a biverse (reflective path 
> integral  
> universe), retrocausality could be a feature.
>  
> Underspecified above: The type of path (sequence) and στ; how histories 
> interact.
> * In a panpsychist theory 
> , it would 
> be (στ,φ,ψ), where ψ is the psychical parameter.
> 
> HOPE can also be Histories Of Practically Everything
> 
>  
> Philip Thrif 
> 
> 
> -- 
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Re: Coherent states of a superposition

2019-01-29 Thread Bruno Marchal

> On 28 Jan 2019, at 22:50, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Friday, January 25, 2019 at 7:33:05 AM UTC-7, Bruno Marchal wrote:
> 
>> On 24 Jan 2019, at 09:29, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com 
>>  wrote:
>> 
>> 
>> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>> 
>>> On 18 Jan 2019, at 18:50, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>> 
 On 17 Jan 2019, at 14:48, agrays...@gmail.com <> wrote:
 
 
 
 On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:
 
> On 17 Jan 2019, at 09:33, agrays...@gmail.com <> wrote:
> 
> 
> 
> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
> 
> 
> On 1/16/2019 7:25 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>> 
>> 
>> On 1/13/2019 9:51 PM, agrays...@gmail.com <> wrote:
>>> This means, to me, that the arbitrary phase angles have absolutely no 
>>> effect on the resultant interference pattern which is observed. But 
>>> isn't this what the phase angles are supposed to effect? AG
>> 
>> The screen pattern is determined by relative phase angles for the 
>> different paths that reach the same point on the screen.  The relative 
>> angles only depend on different path lengths, so the overall phase angle 
>> is irrelevant.
>> 
>> Brent
>> 
>> Sure, except there areTWO forms of phase interference in Wave Mechanics; 
>> the one you refer to above, and another discussed in the Stackexchange 
>> links I previously posted. In the latter case, the wf is expressed as a 
>> superposition, say of two states, where we consider two cases; a 
>> multiplicative complex phase shift is included prior to the sum, and 
>> different complex phase shifts multiplying each component, all of the 
>> form e^i (theta). Easy to show that interference exists in the latter 
>> case, but not the former. Now suppose we take the inner product of the 
>> wf with the ith eigenstate of the superposition, in order to calculate 
>> the probability of measuring the eigenvalue of the ith eigenstate, 
>> applying one of the postulates of QM, keeping in mind that each 
>> eigenstate is multiplied by a DIFFERENT complex phase shift.  If we 
>> further assume the eigenstates are mutually orthogonal, the probability 
>> of measuring each eigenvalue does NOT depend on the different phase 
>> shifts. What happened to the interference demonstrated by the 
>> Stackexchange links? TIA, AG 
>> 
> Your measurement projected it out. It's like measuring which slit the 
> photon goes through...it eliminates the interference.
> 
> Brent
> 
> That's what I suspected; that going to an orthogonal basis, I departed 
> from the examples in Stackexchange where an arbitrary superposition is 
> used in the analysis of interference. Nevertheless, isn't it possible to 
> transform from an arbitrary superposition to one using an orthogonal 
> basis? And aren't all bases equivalent from a linear algebra pov? If all 
> bases are equivalent, why would transforming to an orthogonal basis lose 
> interference, whereas a general superposition does not? TIA, AG
 
 I don’t understand this. All the bases we have used all the time are 
 supposed to be orthonormal bases. We suppose that the scalar product (e_i 
 e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.
 
 Bruno
 
 Generally, bases in a vector space are NOT orthonormal. 
>>> 
>>> Right. But we can always build an orthonormal base with a decent scalar 
>>> product, like in Hilbert space, 
>>> 
>>> 
>>> 
 For example, in the vector space of vectors in the plane, any pair of 
 non-parallel vectors form a basis. Same for any general superposition of 
 states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
 orthogonal.
>>> 
>>> Absolutely. And when choosing a non degenerate observable/measuring-device, 
>>> we work in the base of its eigenvectors. A superposition is better seen as 
>>> a sum of some eigenvectors of some observable. That is the crazy thing in 
>>> QM. The same particle can be superposed in the state of being here and 
>>> there. Two different positions of one particle can be superposed.
>>> 
>>> This is a common misinterpretation. Just because a wf can be expressed in 
>>> different ways (as a vector in the plane can be expressed in uncountably 
>>> many different bases), doesn't mean a particle can exist in different 
>>> positions in space at the same time. AG
>> 
>> It has a non null amplitude of probability of being here and there at the 
>> same time, like having 

Re: Planck Length

2019-01-29 Thread Bruno Marchal

> On 28 Jan 2019, at 15:07, Philip Thrift  wrote:
> 
> 
> 
> On Monday, January 28, 2019 at 6:27:37 AM UTC-6, Bruno Marchal wrote:
> 
>> On 25 Jan 2019, at 14:53, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Friday, January 25, 2019 at 6:27:44 AM UTC-6, Bruno Marchal wrote:
>> 
>>> On 24 Jan 2019, at 15:19, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Thursday, January 24, 2019 at 7:14:15 AM UTC-6, Bruno Marchal wrote:
>>> 
 On 23 Jan 2019, at 19:01, Philip Thrift > wrote:
 
 
 
 On Wednesday, January 23, 2019 at 5:52:01 AM UTC-6, Bruno Marchal wrote:
 
> On 22 Jan 2019, at 01:49, Philip Thrift > wrote:
> 
> One of the oddest of things is when physicists use the language of 
> (various) theories of physics to express what can or cannot be the case. 
> It's just a language, which is probably wrong.
> 
> There is a sense in which the Church/Turing thesis is true: All out 
> languages are Turing in their syntax and grammar. What they refer to is 
> another matter (pun intended).
 
 They refer to the set of computable functions, or to the universal machine 
 which understand that language. But not all language are Turing universal. 
 Only the context sensitive automata (in Chomski hierarchy) are Turing 
 universal. Simple languages, like the “regular” one are typically not 
 Turing universal. Bounded loops formalism cannot be either.
 
 But the notion of language is ambiguous with respect to computability, and 
 that is why I prefer to avoid that expression and always talk about 
 theories (set of beliefs) or machine (recursively enumerable set of 
 beliefs), which avoids ambiguity. 
 For example, is “predicate calculus” Turing universal? We can say yes, 
 given that the programming language PROLOG (obviously Turing universal) is 
 a tiny subset of predicate logic. But we can say know, if we look at 
 predicate logic as a theory. A prolog program is then an extension of that 
 theory, not something proved in predicate calculus.
 Thus, I can make sense of your remark. Even the language with only one 
 symbol {I}, and the rules that “I” is a wff, and if x is wwf, then Ix is 
 too, can be said Turing universal, as each program can be coded by a 
 number, which can be coded by a finite sequence of I. But of course, that 
 makes the notion of “universality” empty, as far as language are 
 concerned. 
 Seen as a theory, predicate calculus is notoriously not universal. Even 
 predicate calculus + the natural numbers, and the law of addition, 
 (Pressburger arithmetic) is not universal. Or take RA with its seven 
 axioms. Taking any axiom out of it, and you get a complete-able theory, 
 and thus it cannot be Turing complete.
 
 Bruno
 
 
 
 Here's an example of a kind of "non-digital" language:
 
 More Analog Computing Is on the Way
 https://dzone.com/articles/more-analog-computing-is-on-the-way 
 
 
 
 The door on this new generation of analog computer programming is 
 definitely open. Last month, at the Association for Computing Machinery’s 
 (ACM) conference on Programming Language Design and Implementation, a 
 paper  was 
 presented that described a compiler that uses a text based, high-level, 
 abstraction language to generate the necessary low-level circuit wiring 
 that defines the physical analog computing implementation. This research 
 was done at MIT’s Computer Science and Artificial Intelligence Laboratory 
 (CSAIL) and Dartmouth College. The main focus of their investigation was 
 to improve the simulation of biological systems. 
 
 
 Configuration Synthesis for ProgrammableAnalog Devices with Arco
 https://people.csail.mit.edu/sachour/res/pldi16_arco.pdf 
 
 
 Programmable analog devices have emerged as a powerful
 computing substrate for performing complex neuromorphic
 and cytomorphic computations. We present Arco, a new
 solver that, given a dynamical system specification in the
 form of a set of differential equations, generates physically
 realizable configurations for programmable analog devices
 that are algebraically equivalent to the specified system.
 On a set of benchmarks from the biological domain, Arco
 generates configurations with 35 to 534 connections and 28
 to 326 components in 1 to 54 minutes.
 
 
 - pt
>>> 
>>> Intersting.
>>> 
>>> Yet, that does not violate the Church-Thesis, even if very useful FAPP. But 
>>> such computations arise in arithmetic, either directly, or through a 
>>> infinite sequence of approximations. If all decimals of the analog 
>>> phenomenon needs to be 

Re: Strict finitism

2019-01-29 Thread Bruno Marchal

> On 28 Jan 2019, at 14:55, Philip Thrift  wrote:
> 
> 
> 
> On Monday, January 28, 2019 at 5:46:12 AM UTC-6, Bruno Marchal wrote:
> 
>> On 26 Jan 2019, at 08:36, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> Varieties of finitism
>> http://www.mbph.de/Logic/Finitism.pdf 
>> Manuel Bremer
>> http://www.mbph.de 
>> 
>> Annotated bibliography of strict finitism
>> http://jeanpaulvanbendegem.be/home/papers/strict-finitism/ 
>> 
>> Jean Paul Van Bendegem
>> http://jeanpaulvanbendegem.be 
>> 
>> Apparently, strict finitism requires a (likely) paraconsistent modality 
>> (implying there may be inconsistencies). If one takes strict finitism 
>> seriously (Tegmark would have to be a strict finitist, if he isn't kidding 
>> people about what he said) then of course physics (and mathematics, of 
>> course) would be radically different.
> 
> 
> Computationalism (digital mechanism) is consistent with strict finitisme, but 
> rather unsound.
> 
> Mechanism is a finitisme, but it keeps the potentially infinite of the 
> classical and intuitionist thinkers. 
> 
> But with mechanism, we cannot put the induction axioms in the ontology, so we 
> cannot prove that there is no biggest natural numbers in the ontology. From 
> outside, we know that this is consistent only because we believe in some 
> infinite objects, making strict finitisme consistent, but rather 
> arithmetically unsound.
> 
> Nothing in Tegmark suggests that he would espouse anything like “strict” 
> finitisme, but when he moved to computationalism, he might become a finitist.
> 
> The best book (beside my work :) ) on the subject of mechanism and finitism 
> is the book by Judson Webb, 1980. 
> 
> WEBB J. C., 1980, Mechanism, Mentalism and Metamathematics : An essay on 
> Finitism, D. Reidel Pub. Company, Dordrecht, Holland.
> 
> Bruno
> 
> 
> 
> 
> Max Tegmark writes that the mathematics of physics in the future needs to be 
> "infinity-free".
> 
>   
> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/
> 
> (Almost like it's a sin to have infinities around.) That sounds like strict 
> finitism to me.

Not it is not. It is finitism, not strict finitism. Actually you need sting 
actual infinities to make sense of strict finitism. Finitism need only 
potential infinite to be define, but strict finitism needs actual infinities at 
the metalevel. To define what is a machine, or what is “finite", you need 
potential infinite. Strict finitisme makes sense … thanks to big infinities at 
the meta-level. Absolute strict finitism cannot be Turing universal.







> 
> As Manuel Bremer's paper above shows, a strictly-finite arithmetic is 
> (likely) inconsistent,

It is not valid. RA can be strictly finitist, but again, at the semantical 
level this is made possible by the existence of a non standard natural number 
which are bigger than all standard numbers.




> which is OK, since "inconsistent mathematics can have a branch which is 
> applied mathematics”.

Inconsistency treatment I useful for natural language, and human psychology, 
but in most applied math, we need consistent theories. In metaphysics, 
paraconsitency is a red herring. It hides the problems instead of solving them. 
But now, self-reference makes inconsistency consistent, and G/G* has a small 
quasi-para-consistent part, useful indeed for the embedded machine (in sheaves 
of arithmetical computations).

Bruno




> 
> https://plato.stanford.edu/entries/mathematics-inconsistent/
> 
> - pt
> 
> 
> 
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Histories Of Phenomenally Everything (HOPE)

2019-01-29 Thread Philip Thrift

This replaces space, time, particles, fields with histories.

I think this is compatible with universal machines.

https://codicalist.wordpress.com/2019/01/28/histories-of-phenomenally-everything-hope/


- pt


Histories Of Phenomenally Everything (HOPE)
 

*or* Everything Histories (EH)
 


 

*Perhaps… we must also give up, by principle, the space-time continuum,” he 
wrote. “It is not unimaginable that human ingenuity will some day find 
methods which will make it possible to proceed along such a path. At the 
present time, however, such a program looks like an attempt to breathe in 
empty space.*
— Albert Einstein
 

In a HOPE-ful ontology, histories  are the 
fundamental constituents of the universe. They replace spacetime 

—by *embedding*(bits of) spacetime within themselves.

   - Spacetime is derived from histories. (Some like the word *emerges*here.) 
   The spacetime continuum is replaced with historical paths (curves or walks).

   - There are possible histories and actual histories. Possible histories 
   reenforce or interfere with each other (via the path integral).

   - Histories replace not only spacetime, but particles and fields as 
   well, which are defined in terms of *ensembles* of histories. Histories 
   have *physical* properties, so a particular history can be an ‘electron’ 
   history, for example.

   - Histories have a path representation as a *sequence* going backwards 
   in time. An element of the path sequence could be (στ,φ), where στ is some 
   sort of spacetime-like parameter and φ is a physical parameter.* The 
   reverse paths (going forward in time) are called *futures*. In a biverse 
   (*reflective path integral* 
    universe), 
   retrocausality could be a feature.

   - Underspecified above: The type of path (*sequence*) and στ; how 
   histories interact.

* In a panpsychist theory 
, it 
would be (στ,φ,ψ), where ψ is the psychical parameter.

HOPE can also be Histories Of Practically Everything
 

Philip Thrif 


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