Re: Coherent states of a superposition

2019-01-31 Thread Philip Thrift


On Thursday, January 31, 2019 at 2:10:06 PM UTC-6, agrays...@gmail.com 
wrote:

... the phase angles are responsible for interference. I doubt that result. 
Am I mistaken? AG



Whatever approach you take, it's still like each possibility has a little 
spin wheel marking its phase:

  https://www.online-stopwatch.com/images/wheel-dice.png 

When combined, phases in the same general direction reinforce. Phases that 
don't, interfere.

- pt

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Re: Coherent states of a superposition

2019-01-31 Thread agrayson2000


On Thursday, January 31, 2019 at 6:47:12 AM UTC-7, Bruno Marchal wrote:
>
>
> On 31 Jan 2019, at 01:28, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
>>>
>>>
>>> On 30 Jan 2019, at 02:59, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> 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 

Re: Histories Of Phenomenally Everything (HOPE)

2019-01-31 Thread Philip Thrift


On Thursday, January 31, 2019 at 7:52:08 AM UTC-6, Lawrence Crowell wrote:
>
>
>
> On Tuesday, January 29, 2019 at 5:03:11 AM UTC-6, 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/
>>
>>
>> - pt
>>
>
> This illustrates a problem with the epistemology of physics. It stems from 
> Newton's laws, in particular the second law of motion F = ma. On the left 
> hand side we have the dynamics in a force. We have on the right a physical 
> quantity in the mass of a body as a scalar quantity. We then have the 
> acceleration 
>
> a = lim_{Δt → 0}Δ^2x/Δt^2 = d^2x/dt^2.
>
> This then multiplies the physical scalar mass to give a dynamical, which 
> means measurable, force that has a direction. We can then think of this as 
> a strange equation that multiplies a physical quantity by a geometric 
> quantity that then gives a dynamical force that is physical. Issac Newton 
> wrote this according to a construction called fluxions, which in time gave 
> was to the calculus based more on Leibniz and ultimately Weierstrass. Yet 
> the early period was full of roiling controversy over what we meant by 
> these infinitesimals and so forth. The geometric aspect of Newton's second 
> law appeared to have a different meaning from what would be expected of 
> something physical.
>
> This confusion continues into general relativity. We might write the 
> Einstein field equation as 
>
> Geometric curvature = physical dynamics,
>
> where Einstein was most enamored with the left hand side, calling it 
> marble, while the right hand side he cited as wood. There is the mixing of 
> categories in general relativity that is remarkably similar to Newtonian 
> mechanics. The general theory of relativity is based on the equivalence 
> principle, and this tells us that for a sufficiently local frame there is 
> no experiment that can determine if the frame is global in free space or in 
> a gravitational field. This gives the sort of calculus rule, small frames 
> removes geometric information and thus dynamics, and the geometrodynamical 
> theory is built from atlas-chart constructions on such infinitesimal frames.
>
> General relativity gives geometry more of an active role. There may be 
> gravitational waves, undulations of space that evolve in time, that we 
> observe by the physical displacement of interferometer elements. We have in 
> our minds these mental models of space and spacetime, but ultimately we 
> have a category problem; space and spacetime while defined by clocks and 
> rulers, is not in of itself something that has direct physics. 
>
> We might then consider quantum gravitation. I think that spacetime is an 
> emergent property of quantum entanglement. Given a group G for the 
> symmetries of a quantum system or field, then in the Cartan decomposition G 
> = H×K the subgroup H is G modulo the action of K so H = G/K, and for a 
> quantum system this means the wave function is invariant with respect to 
> some description. Such as for entangled spins, the entangled wave function 
> has no description according to the spins. 
>
> In general relativity dynamics can be thought of as what extremizes the 
> action S = ∫d^4x sqrt(g)R, for R the Ricci curvature. Action and entropy 
> share an equivalency under the euclideanized map t/ħ = 1/kT for t time and 
> T temperature. We can also work this within complexity, and with quantum 
> gravitation the importance is with entanglement entropy or complexity. This 
> means that quantum gravitation is built from quantum states, which as we 
> all should be aware are not ontological entities in a standard sense. We 
> still have physics, in particular the aspect of physics that conveys 
> geometric or spatial relationship content, that is not ontologically solid. 
> This appears to be a fundamental aspect of physics, or at least physics as 
> we can understand.
>
> For this reason I think ideas that have spacetime composed of little 
> elements that are physical are not likely correct. This has been a long 
> standing critique I have of quantum gravitation theories outside of string 
> theory. This is not to say I think string theory has everything sewed up. 
> However, these various ideas such as LQG, DT and SD etc seem to have 
> category conflicts.
>
> LC
>
>
I should note that in my histories framework (which is all it is right now) 
I added

*29 Jan 2019*

By “historical paths (curves or walks)”, “Histories have a path 
representation as a sequence”, I mean sequence in terms of having a 
linearly ordered index I, so each element of the history is indexed:

(στ,φ)ᵢ i ∈ I



The type of "linearly ordered index" I is not specified, so it could be 
discrete or continuous, in principle.


- pt

 

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Re: Planck Length

2019-01-31 Thread Philip Thrift


On Thursday, January 31, 2019 at 6:28:14 AM UTC-6, Bruno Marchal wrote:
>
>
> On 30 Jan 2019, at 23:14, Philip Thrift > 
> wrote:
>
>
>
> On Wednesday, January 30, 2019 at 5:45:34 AM UTC-6, Bruno Marchal wrote:
>>
>>
>>> As I try to solve the mind-body problem in the Mechanist frame, I cannot 
>>> use any ontological commitment other than the term of some arbitrary but 
>>> fixed universal system. 
>>>
>>> You assume some God, but that makes everything more complex, without 
>>> evidences why to do so, except naive physical realism, but that does not 
>>> work with Mechanism.
>>>
>>> Bruno
>>>
>>>
>>>
>>>
>> There is no mind|body problem.
>> Only a language|body problem.
>>
>>
>>
>> With mechanism, we can identify body, words, numbers, and it is a pure 
>> third person notion, but mind has a first person part (indeed called the 
>> soul or the personal consciousness) which is pure 1p. The mind body problem 
>> consists in linking, without magic or ontological commitment those two 
>> things. The solution suggested by Theaetetus in Plato, has been refuted by 
>> Socrates (in Plato) but incompleteness refutes Socrates argument, and 
>> rehabilitates Theatetus’idea (the soul or the first person knower is the 
>> true-believer).
>> You can compare this with the semantic problem for language/body. To 
>> associate a semantic to a program or machine is related to the problem of 
>> associating a mind or a meaning to a body or to a code. The problem is 
>> virtually the same: once a theory/body is “rich enough”, its semantics 
>> escapes it and get multiple. Rich theories have many non isomorphic 
>> models/semantics, a bit like any computational state is supported by 
>> infinitely many computational situation, and some indeterminacy has to be 
>> taken into account.
>>
>> Bruno
>>
>
> https://codicalist.wordpress.com/2019/01/22/matter-gets-psyched/
>>
>> - pt
>>
>>
>
> Epicurus was born about the time Plato died. His "atomism" had atoms for 
> consciousness (mind) that were mixed with the bodily atoms. Modern science 
> rejected that concept, until the recent revival of (material) panpsychism 
> has a updated version of it.
>
>
>
> Unfortunately this does not explain neither what the atoms and where they 
> comes from, nor what is consciousness and where it comes from. Mechanism 
> explains this entirely, up to the testability of all its consequences, 
> which, like every where in fundamental science, needs a perpetual doubt and 
> constant verification and re-verification. 
>
> If the theory S4Grz1, Z1*, X1* violate nature, then we will have some 
> evidence for no-mechanism, and thus for primitive matter. But assuming 
> primitive matter a priori seems like wanting to not understand the problem, 
> or hiding it under ontological commitment, like materialists do since 1500 
> years, if not right since Aristotle.
>
> Bruno
>
>
>
>
On "where do atoms come from" I guess *any physicist*  you meet today has 
as good (or bad) an answer as any, in their way of thinking, anyway.

On consciousness: 

In a micropsychist* approach, the lowest-level psychical properties could 
appear in the form of their own material subatomic entities, like quarks —  
quirks? :) —  in current physical theories. Thus human-level consciousness 
is "constituted" from lower-level material entities possessing lower-level 
psychical features.


*According to constitutive micropsychism, the smallest parts of my brain 
have very basic forms of consciousness, and the consciousness of my brain 
as a whole is in some sense made up from the consciousness of its parts. 
This is the form of panpsychism that suffers most acutely from the 
combination problem, which we will explore below. However, if it can be 
made sense of, constitutive micropsychism promises an elegant and 
parsimonious view of nature, with all the richness of nature accounted for 
in terms of facts at the micro-level.*

* [ https://plato.stanford.edu/entries/panpsychism/ ]  

- pt 

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Re: Histories Of Phenomenally Everything (HOPE)

2019-01-31 Thread Lawrence Crowell


On Tuesday, January 29, 2019 at 5:03:11 AM UTC-6, 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/
>
>
> - pt
>

This illustrates a problem with the epistemology of physics. It stems from 
Newton's laws, in particular the second law of motion F = ma. On the left 
hand side we have the dynamics in a force. We have on the right a physical 
quantity in the mass of a body as a scalar quantity. We then have the 
acceleration 

a = lim_{Δt → 0}Δ^2x/Δt^2 = d^2x/dt^2.

This then multiplies the physical scalar mass to give a dynamical, which 
means measurable, force that has a direction. We can then think of this as 
a strange equation that multiplies a physical quantity by a geometric 
quantity that then gives a dynamical force that is physical. Issac Newton 
wrote this according to a construction called fluxions, which in time gave 
was to the calculus based more on Leibniz and ultimately Weierstrass. Yet 
the early period was full of roiling controversy over what we meant by 
these infinitesimals and so forth. The geometric aspect of Newton's second 
law appeared to have a different meaning from what would be expected of 
something physical.

This confusion continues into general relativity. We might write the 
Einstein field equation as 

Geometric curvature = physical dynamics,

where Einstein was most enamored with the left hand side, calling it 
marble, while the right hand side he cited as wood. There is the mixing of 
categories in general relativity that is remarkably similar to Newtonian 
mechanics. The general theory of relativity is based on the equivalence 
principle, and this tells us that for a sufficiently local frame there is 
no experiment that can determine if the frame is global in free space or in 
a gravitational field. This gives the sort of calculus rule, small frames 
removes geometric information and thus dynamics, and the geometrodynamical 
theory is built from atlas-chart constructions on such infinitesimal frames.

General relativity gives geometry more of an active role. There may be 
gravitational waves, undulations of space that evolve in time, that we 
observe by the physical displacement of interferometer elements. We have in 
our minds these mental models of space and spacetime, but ultimately we 
have a category problem; space and spacetime while defined by clocks and 
rulers, is not in of itself something that has direct physics. 

We might then consider quantum gravitation. I think that spacetime is an 
emergent property of quantum entanglement. Given a group G for the 
symmetries of a quantum system or field, then in the Cartan decomposition G 
= H×K the subgroup H is G modulo the action of K so H = G/K, and for a 
quantum system this means the wave function is invariant with respect to 
some description. Such as for entangled spins, the entangled wave function 
has no description according to the spins. 

In general relativity dynamics can be thought of as what extremizes the 
action S = ∫d^4x sqrt(g)R, for R the Ricci curvature. Action and entropy 
share an equivalency under the euclideanized map t/ħ = 1/kT for t time and 
T temperature. We can also work this within complexity, and with quantum 
gravitation the importance is with entanglement entropy or complexity. This 
means that quantum gravitation is built from quantum states, which as we 
all should be aware are not ontological entities in a standard sense. We 
still have physics, in particular the aspect of physics that conveys 
geometric or spatial relationship content, that is not ontologically solid. 
This appears to be a fundamental aspect of physics, or at least physics as 
we can understand.

For this reason I think ideas that have spacetime composed of little 
elements that are physical are not likely correct. This has been a long 
standing critique I have of quantum gravitation theories outside of string 
theory. This is not to say I think string theory has everything sewed up. 
However, these various ideas such as LQG, DT and SD etc seem to have 
category conflicts.

LC
 

>
>
> 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 
> 

Re: Coherent states of a superposition

2019-01-31 Thread Bruno Marchal

> On 31 Jan 2019, at 01:28, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Wednesday, January 30, 2019 at 2:38:58 PM UTC-7, agrays...@gmail.com wrote:
> 
> 
> On Wednesday, January 30, 2019 at 5:16:05 AM UTC-7, Bruno Marchal wrote:
> 
>> On 30 Jan 2019, at 02:59, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> 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 

Re: Planck Length

2019-01-31 Thread Bruno Marchal

> On 30 Jan 2019, at 23:14, Philip Thrift  wrote:
> 
> 
> 
> On Wednesday, January 30, 2019 at 5:45:34 AM UTC-6, Bruno Marchal wrote:
> 
>> On 29 Jan 2019, at 15:03, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> 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