Models of arithmetic

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Philip Thrift

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Aug 18, 2019, 7:57:54 AM8/18/19
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On Sunday, August 18, 2019 at 4:53:28 AM UTC-5, Bruno Marchal wrote:

Model theory illustrate that pure mathematics has meaning. 
 

A model is a so-called 'structure': 

But allowable structures, typically mathematical entities in the model theories of many, are only material (physical) entities in the model theory of Hartry Field.

For example, a model of arithmetic could be an actual  semiconductor logic gate chip with RAM.

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Bruno Marchal

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Aug 19, 2019, 5:08:58 AM8/19/19
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On 18 Aug 2019, at 13:57, Philip Thrift <cloud...@gmail.com> wrote:



On Sunday, August 18, 2019 at 4:53:28 AM UTC-5, Bruno Marchal wrote:

Model theory illustrate that pure mathematics has meaning. 
 

A model is a so-called 'structure': 

But allowable structures, typically mathematical entities in the model theories of many, are only material (physical) entities in the model theory of Hartry Field.

That is a bit of nonsense. Or Hartree Field notion of model has nothing to do with what logicians called a model (a mathematical structure with a notion of satisfaction). 



For example, a model of arithmetic could be an actual  semiconductor logic gate chip with RAM.


I don’t understand this. A model of arithmetic is a set of object which provides an interpretation of the terms (0, S(0), …), and an interpretation of + and * (in terms of infinite set of couples).

Bruno




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Philip Thrift

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Aug 19, 2019, 5:50:44 AM8/19/19
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On Monday, August 19, 2019 at 4:08:58 AM UTC-5, Bruno Marchal wrote:

On 18 Aug 2019, at 13:57, Philip Thrift <cloud...@gmail.com> wrote:



On Sunday, August 18, 2019 at 4:53:28 AM UTC-5, Bruno Marchal wrote:

Model theory illustrate that pure mathematics has meaning. 
 

A model is a so-called 'structure': 

But allowable structures, typically mathematical entities in the model theories of many, are only material (physical) entities in the model theory of Hartry Field.

That is a bit of nonsense. Or Hartree Field notion of model has nothing to do with what logicians called a model (a mathematical structure with a notion of satisfaction). 



For example, a model of arithmetic could be an actual  semiconductor logic gate chip with RAM.


I don’t understand this. A model of arithmetic is a set of object which provides an interpretation of the terms (0, S(0), …), and an interpretation of + and * (in terms of infinite set of couples).

Bruno





Conventional mathematical logicians only speak, write, and think in terms of a fictional world. 

And that includes their models/structures/interpretations. 

The Field type of semantics of logic and mathematics only has actual material entities (like computers at Best Buy, supercomputers at Los Alamos National Lab, natural objects found in nature) in its domains.

Conventional mathematical logicians may not like it, but that is their own psychological problem.

@philipthrift

Bruno Marchal

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Aug 19, 2019, 10:43:38 AM8/19/19
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On 19 Aug 2019, at 11:50, Philip Thrift <cloud...@gmail.com> wrote:



On Monday, August 19, 2019 at 4:08:58 AM UTC-5, Bruno Marchal wrote:

On 18 Aug 2019, at 13:57, Philip Thrift <cloud...@gmail.com> wrote:



On Sunday, August 18, 2019 at 4:53:28 AM UTC-5, Bruno Marchal wrote:

Model theory illustrate that pure mathematics has meaning. 
 

A model is a so-called 'structure': 

But allowable structures, typically mathematical entities in the model theories of many, are only material (physical) entities in the model theory of Hartry Field.

That is a bit of nonsense. Or Hartree Field notion of model has nothing to do with what logicians called a model (a mathematical structure with a notion of satisfaction). 



For example, a model of arithmetic could be an actual  semiconductor logic gate chip with RAM.


I don’t understand this. A model of arithmetic is a set of object which provides an interpretation of the terms (0, S(0), …), and an interpretation of + and * (in terms of infinite set of couples).

Bruno





Conventional mathematical logicians only speak, write, and think in terms of a fictional world. 

With mechanism, all worlds are fictional. The only real things are 0, 1, 2, …, or K, S, KK, …

Intuitively I doubt less that 4*n is even for all n, or that K is an eliminator, than F = GmM/r^2, which is an infinite extrapolation made from a finite number of fact. 

Also, when doing metaphysics, it is better to not decide in advance what is real and what is fiction.

Now, if you have a doubt that a number, when multiplied by 4, gives an even number, I am not sure I can help.




And that includes their models/structures/interpretations. 

Mechanism is OK with this. It simplifies the life to admit, even if temporarily, that a bit more exist, but at some point, that existence can be put in the phenomenology. 



The Field type of semantics of logic and mathematics only has actual material entities (like computers at Best Buy, supercomputers at Los Alamos National Lab, natural objects found in nature) in its domains.

That is the Aristotelian axiom where “real” is defined by “physically real”, or “observable”, but the dream argument rise a doubt on this, especially when we understand that all computations can be proved to exist in arithmetic (even before translating this by “all models.




Conventional mathematical logicians may not like it, but that is their own psychological problem.


If they believe in Digital Mechanism. they become inconsistent. That’s the whole point of the Universal Dovetailer argument. Unless your “matter” has a role for consciousness which is not Turing emulable,  it will be realised arithmetically.

Bruno





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Philip Thrift

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Aug 19, 2019, 3:11:08 PM8/19/19
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Given all the novel, unpredicted stuff one reads every day in the science news feeds about some new material (materials science), molecules,  phases (of matter), why is it so hard to think that matter is not some naive ("numerical-Turing-emulable") stuff that most theoretical physicists think it is and that it has no protopsychical properties.

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Bruno Marchal

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Aug 20, 2019, 7:27:51 AM8/20/19
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But matter is NOT Turing emulable, once we assume “we” are Turing emulable. Matter is only maps emerging from all relative computation going through our mind state. It sums the whole universal dovetailing at any instant. At first sight this leads to an inflation of possible histories, but if we take into account the logic of selreference, what subsist is a “nay-world”-like inflation of normal consistent histories, although the normality is only suggested right now, and the work must be pursue to compare the physics extracted from the statistics on all computations and the empirical world.

So why introduce a fundamental magic stuff, when the appearance of that “magic” is explained by Mechanism? And worst, if assumed, it requires us to find a non computationalist theory of mind, despite the lack of evidence for it.

Maybe you are right and some stuff exists. In that case Mechanism has to be wrong (by UDA or equivalent). But there are no evidences for this, and as long as there is no evidences, it is preferable, Imo, to not commit oneself in some ontology.

In the news feed in physics, we don’t find evidences for stuff, only evidence for a physical reality, and thanks to QM, it pretty well confirm Mechanism (not 19th century mechanism, but a post-Gödel antireductionist sort of Mechanism).

Mechanism predicts infinitely many surprises in “theology”, and plausibly many one are inherited in the physical realm, which realise again all computation but with a stable relative measure.

Bruno






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Philip Thrift

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Aug 20, 2019, 1:38:45 PM8/20/19
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The reason to suspect that arithmetic comes from matter (M→A) vs. matter comes from arithmetic (A→M) is that with A→M there many Ms. But we together experience only one M. When a new material phenomenon is discovered in one place, someone on the other side of the Earth can check and experience the same material phenomenon. If A→M were the case, then why would there be any stability in observations of M?

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Brent Meeker

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Aug 20, 2019, 2:04:10 PM8/20/19
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On 8/20/2019 4:27 AM, Bruno Marchal wrote:
>> Given all the novel, unpredicted stuff one reads every day in the
>> science news feeds about some new material (materials science),
>> molecules,  phases (of matter), why is it so hard to think that
>> matter is not some naive ("numerical-Turing-emulable") stuff that
>> most theoretical physicists think it is and that it has no
>> protopsychical properties.
>
> But matter is NOT Turing emulable, once we assume “we” are Turing
> emulable. Matter is only maps emerging from all relative computation
> going through our mind state. It sums the whole universal dovetailing
> at any instant

"Instant" in what time-sense...some stage of the UD computation? But
that would include a mix of different physical times, which are
many-fingered per relativity theory.

And what can it mean " relative computation going through our mind
state."  What is this "mind state" except some physical computational
thread?  Isn't that what saying yes to the doctor implied?

Brent

Bruno Marchal

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Aug 21, 2019, 4:28:42 AM8/21/19
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On the contrary: Arithmetic (A) explains why there is many geographies and history, but only one physics, the same fr all universal machine. That is due to the fact that Physics (Matter, M) emerges from the first person indeterminacy on *all* computations.
So A explains why there is only one M possible, and why the physical reality is the same for all universal machine/number.
With A, the physical laws are justified being laws, and we get some criteria (lacking in physics+physicalism) to distinguish physics and geography.




But we together experience only one M. When a new material phenomenon is discovered in one place, someone on the other side of the Earth can check and experience the same material phenomenon. If A→M were the case, then why would there be any stability in observations of M?

Because, if Mechanism is correct, physics is entirely given by the material modes imposed by incompleteness on all machines. The math confirms the presence of that physics, and already shows it to be a quantum physics, which is indeed a calculus of first person plural indeterminacy on many histories (unless we introduce the infamous collapse, of course …).

With Mechanism, the physical universe disappear, but the laws of physics are made more solid, as they become theorems in arithmetic.

Bruno






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Bruno Marchal

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Aug 21, 2019, 4:37:10 AM8/21/19
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> On 20 Aug 2019, at 20:04, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:
>
>
>
> On 8/20/2019 4:27 AM, Bruno Marchal wrote:
>>> Given all the novel, unpredicted stuff one reads every day in the science news feeds about some new material (materials science), molecules, phases (of matter), why is it so hard to think that matter is not some naive ("numerical-Turing-emulable") stuff that most theoretical physicists think it is and that it has no protopsychical properties.
>>
>> But matter is NOT Turing emulable, once we assume “we” are Turing emulable. Matter is only maps emerging from all relative computation going through our mind state. It sums the whole universal dovetailing at any instant
>
> "Instant" in what time-sense...some stage of the UD computation?

… some stage of the UD computation (UD*) seen from the first person point of view.

That explains (and predicted) the non cloning of matter, as any piece of matter requires the indeterminacy on all computations, which is not something Turing emulable a priori.




> But that would include a mix of different physical times, which are many-fingered per relativity theory.

Yes. It is “personal time”, a first person construct.



>
> And what can it mean " relative computation going through our mind state.”


It is the infinite set of all computations bringing the first person experience of the consistent extension of your current state (defined indexically). In the Helsinki WM experience, it would be the computation getting the input W and the computation getting M, in their vast majority, but of course it contains also the aberrant continuations, hopefully in a negligible set, which remains to be seen (but the material modes suggests already that this could very well be the case).

Bruno






> What is this "mind state" except some physical computational thread? Isn't that what saying yes to the doctor implied?





>
> Brent
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Philip Thrift

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Aug 21, 2019, 7:03:54 AM8/21/19
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How does Arithmetic define "only one physics"?

I know physics (fundamentally) is a disaster today (2019), but how does the hodgepodge Standard Model and haphazard unification (w/GR) attempts point to anything but an idiosyncratic Matter (which it is up to physics to "model")? 

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Bruno Marchal

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Aug 21, 2019, 8:38:49 AM8/21/19
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Arithmetic contains or executes (in the block-statical way) all computations. Your first person is distributed on all computations going through your current (relative) first person state. To make any prediction on the future of your possible inputs, you need to take all the computations into account, and the laws of physics is what is invariant in all consistent extensions. 
See the entire UDA argument in my papers. 





I know physics (fundamentally) is a disaster today (2019),

Let us not exaggerate perhaps. Quantum Mechanics is a jewel, and GR is not bad. But a fundamental theory is still lacking. But it could be found, even without Mechanism. The advantage of mMechanism is that we get directly (almost) a theory of qualia, with a theory of quanta as special case.



but how does the hodgepodge Standard Model and haphazard unification (w/GR) attempts point to anything but an idiosyncratic Matter (which it is up to physics to "model")? 

Noether’s theorem explains already a lot. You might take a look at Vic Stenger’s book “The comprehensible universe”.

But time and space are perhaps too much taken for granted, even and especially in string theory. I do think that string theory progresses in the good direction, from a pure physical point of view. But QM (without collapse) might require Mechanism and its extraction of the wave, and strings. It certainly does if we want to have both qualia and quanta, and decent relations between them.

As long as theology is not back in science, science has not yet even begun. But I do think that the standard model will not be overthrown. It will be unified from our understanding on the nature of space, and later, perhaps unified through arithmetic, group theory and number theory. It will take some times. Before that, let us remain open to all possibilities, including the possibility that Mechanism is true, in which case we do have the TOE, and a lot of work to test it in a  better and more precise way than today.

Bruno






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Philip Thrift

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Aug 21, 2019, 2:40:24 PM8/21/19
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The "symmetry" perspective, like that Victor Stenger in The Comprehensible Cosmos 


is at odds with Lost in Math / The Ugly Universe (Sabine Hossenfelder 


Physics is confused by its attraction to beauty and symmetry. 

@philipthrift





Brent Meeker

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Aug 21, 2019, 3:17:33 PM8/21/19
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On 8/21/2019 1:28 AM, Bruno Marchal wrote:
> So A explains why there is only one M possible

So what is the one possible M?  Physicist build 10 billion dollar
machines to try to find out.  If you can do it from your desk, let's
hear about it?

Brent

Bruno Marchal

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Aug 22, 2019, 4:34:02 AM8/22/19
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A part of this has been already done, and I have explained it here. Once you assume Mechanism, it is conceptually very simple, the physical reality emerges from the conditional statistics on all computations, and it works already by justifying the quantum shape of the physical reality. Only the future will show if what they found with the 10 billion dollars machine could have been deduced from arithmetic; or if it belongs to some geographical type of reality.
In most case, you can bet that observation will be quicker than deduction in arithmetic, but that has nothing to do with the conceptual question. Arithmetic already explains why observation provides information more quicker than the very hard derivation that Mechanism makes obligatory, if we want to keep both the quanta and the qualia.

The key, is that when we assume digital mechanism, there is just no choice in the matter (sorry for the pun).

Bruno



>
> Brent
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Philip Thrift

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Aug 22, 2019, 5:32:59 AM8/22/19
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On Thursday, August 22, 2019 at 3:34:02 AM UTC-5, Bruno Marchal wrote:

> On 21 Aug 2019, at 21:17, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:
>
>
>
> On 8/21/2019 1:28 AM, Bruno Marchal wrote:
>> So A explains why there is only one M possible
>
> So what is the one possible M?  Physicist build 10 billion dollar machines to try to find out.  If you can do it from your desk, let's hear about it?

A part of this has been already done, and I have explained it here. Once you assume Mechanism, it is conceptually very simple, the physical reality emerges from the conditional statistics on all computations, and it works already by justifying the quantum shape of the physical reality. Only the future will show if what they found with the 10 billion dollars machine could have been deduced from arithmetic; or if it belongs to some geographical type of reality.
In most case, you can bet that observation will be quicker than deduction in arithmetic, but that has nothing to do with the conceptual question. Arithmetic already explains why observation provides information more quicker than the very hard derivation that Mechanism makes obligatory, if we want to keep both the quanta and the qualia.

The key, is that when we assume digital mechanism, there is just no choice in the matter (sorry for the pun).

Bruno



 

Even if Arithmetic "explains" (all) Matter, exactly in the sense of your theory:

From a pragmatic POV, to make things (new computers, robots, vehicles, foods, ... ) there is no such thing as arithmetics stores to go to and get what is needed to build things out of. You have to go to materials stores to actually get what is needed to make anything.

@philipthrift

Bruno Marchal

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Aug 22, 2019, 10:49:14 AM8/22/19
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You are right. To use computationalism to make a physical prediction would be like to use the LARC in Geneva to taste a pizza. The goal of metaphysics is not the same as the goal of physics. Those sciences are related, even differently in fiction of the metaphysical assumptions, but they have quite different goals. Physics try to make efficacious predictions, Metaphysics try to explains where we come from, what we can hope or fear, where we ara going, why matter seems to hurt, and who are those “we”, etc.

Bruno






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Russell Standish

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Aug 23, 2019, 6:54:17 PM8/23/19
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On Wed, Aug 21, 2019 at 10:28:39AM +0200, Bruno Marchal wrote:
>
> On 20 Aug 2019, at 19:38, Philip Thrift <cloud...@gmail.com> wrote:
>
>
>
> The reason to suspect that arithmetic comes from matter (M→A) vs. matter
> comes from arithmetic (A→M) is that with A→M there many Ms.
>
>
> On the contrary: Arithmetic (A) explains why there is many geographies and
> history, but only one physics, the same fr all universal machine. That is due
> to the fact that Physics (Matter, M) emerges from the first person
> indeterminacy on *all* computations.
> So A explains why there is only one M possible, and why the physical reality is
> the same for all universal machine/number.
> With A, the physical laws are justified being laws, and we get some criteria
> (lacking in physics+physicalism) to distinguish physics and geography.

This answer is a bit glib IMHO. In some ways it echos the statements I
give in section 9.3 of my book "Theory of Nothing", but which I freely
admitted I felt were provisional and too hand-wavy. However, I believe
that Markus Mueller has since provided an answer in the form of a
theorem (Thm 2.3 "Emergence of an Objective Reality") in his paper
arXiv: 1712.01816.

That paper to me is probably the most significant result in this area
since I published my book.

Cheers

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Philip Thrift

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Aug 24, 2019, 1:24:47 AM8/24/19
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So how does one get from (simple)


to (complex)

   (the Lagrangian Standard Model equation)

?

@philipthrift
 
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Bruno Marchal

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Aug 24, 2019, 5:14:32 AM8/24/19
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> On 24 Aug 2019, at 00:54, Russell Standish <li...@hpcoders.com.au> wrote:
>
> On Wed, Aug 21, 2019 at 10:28:39AM +0200, Bruno Marchal wrote:
>>
>> On 20 Aug 2019, at 19:38, Philip Thrift <cloud...@gmail.com> wrote:
>>
>>
>>
>> The reason to suspect that arithmetic comes from matter (M→A) vs. matter
>> comes from arithmetic (A→M) is that with A→M there many Ms.
>>
>>
>> On the contrary: Arithmetic (A) explains why there is many geographies and
>> history, but only one physics, the same fr all universal machine. That is due
>> to the fact that Physics (Matter, M) emerges from the first person
>> indeterminacy on *all* computations.
>> So A explains why there is only one M possible, and why the physical reality is
>> the same for all universal machine/number.
>> With A, the physical laws are justified being laws, and we get some criteria
>> (lacking in physics+physicalism) to distinguish physics and geography.
>
> This answer is a bit glib IMHO. In some ways it echos the statements I
> give in section 9.3 of my book "Theory of Nothing", but which I freely
> admitted I felt were provisional and too hand-wavy. However, I believe
> that Markus Mueller has since provided an answer in the form of a
> theorem (Thm 2.3 "Emergence of an Objective Reality") in his paper
> arXiv: 1712.01816.
>
> That paper to me is probably the most significant result in this area
> since I published my book.

Which results? Can you elaborate on this? From memory, I think he does not distinguish the 1p from the 3p in his account, so he has no mean to distinguish the qualia from the quanta. But his paper was indeed very interesting, but with no clear distinction between physics and geography, nor quanta and qualia, a bit like ignoring (like so many) the mind-body problem.

Bruno



>
> Cheers
>
> --
>
> ----------------------------------------------------------------------------
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> Visiting Senior Research Fellow hpc...@hpcoders.com.au
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Russell Standish

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Aug 25, 2019, 12:26:54 AM8/25/19
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A partial answer is explored in Stenger's "Comprehensible Cosmos". In
brief, its a combination of symmetries and symmetry breaking. But, as
they say, the devil is in the details.

Cheers
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Philip Thrift

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Aug 25, 2019, 4:13:27 AM8/25/19
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Ironically (and I thought this at the time almost 20 years ago now when I was interacting with Vic on his old group [ https://groups.google.com/forum/?hl=en#!forum/atvoid ]) is that "laws from symmetry" and "symmetry-breaking were contradictory to his anti-Platonist philosophy of science. It was his way to address  the idea of a universe not created by God, but a way I think both unnecessary and wrong.

A universe born of pure randomness and so-called symmetries forming which are merely contingent that gives a universe we just happen to be in makes sense instead: It is the opposite of symmetry-breaking. It is happenstance symmetry-forming. That there is a prior symmetry that is then broken is pure Platonism. 

@philipthrift

Brent Meeker

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Aug 25, 2019, 1:56:57 PM8/25/19
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On 8/25/2019 1:13 AM, Philip Thrift wrote:


Ironically (and I thought this at the time almost 20 years ago now when I was interacting with Vic on his old group [ https://groups.google.com/forum/?hl=en#!forum/atvoid ]) is that "laws from symmetry" and "symmetry-breaking were contradictory to his anti-Platonist philosophy of science. It was his way to address  the idea of a universe not created by God, but a way I think both unnecessary and wrong.

A universe born of pure randomness and so-called symmetries forming which are merely contingent that gives a universe we just happen to be in makes sense instead: It is the opposite of symmetry-breaking. It is happenstance symmetry-forming. That there is a prior symmetry that is then broken is pure Platonism. 

Vic's view of the major symmetries were that they were picked out by us because we wanted physical laws that applied at all times (time-translation->energy conservation  spacial-translation->momentum conservation).  He didn't say this was free choice, but one constrained by nature.  In other words we abstracted away some "geographic" problems to reach them.   Then he extended this idea to Point Of View Invariance.  It's application to the internal symmetries of particles was not so clear.  We not only had to choose the thing conserved by also the transformation which conserved it.

Brent

Philip Thrift

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Aug 25, 2019, 2:27:55 PM8/25/19
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But symmetries don't exist in some absolute, static Platonic realm and we just "pick them out". They are not a priori (except perhaps in the Kantian synthetic a priori sense). 

There are no symmetry breakings  because they were broken already.

That Vic put "man" here at the center (POV invariance) of the laws of physics is completely contradictory to almost everything else he wrote. Whatever symmetries there are accidental and contingent, not heavenly decree.

@philipthrift






Bruno Marchal

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Aug 26, 2019, 5:42:18 AM8/26/19
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The physics of the digital machine has an important symmetry at its core (derived from the fact that “p -> []<>p” is satisfied in S4Grz1, Z1*, X1*: the material modes).

The breaking of symmetries is brought by the subject invariance, mainly present in the two modes with “& p”, which brings some antisymmetry in the picture. SGRz1 proves an antisymmetry formula the Grz formula
[]([](p -> []p) -> p) -> p.

I have thought wrongly that this symmetry + antisymmetry makes the S4Grz1 theory collapse, but I was wrong. The quantisation []<>p does not collapse (we don’t have []<>p -> p).

Here “man” is replace with “universal machine”. Mechanism sides with Vic on this. 

Bruno









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Philip Thrift

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Aug 26, 2019, 6:04:18 AM8/26/19
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On Monday, August 26, 2019 at 4:42:18 AM UTC-5, Bruno Marchal wrote:

On 25 Aug 2019, at 20:27, Philip Thrift <cloud...@gmail.com> wrote:



On Sunday, August 25, 2019 at 12:56:57 PM UTC-5, Brent wrote:


On 8/25/2019 1:13 AM, Philip Thrift wrote:


Ironically (and I thought this at the time almost 20 years ago now when I was interacting with Vic on his old group [ https://groups.google.com/forum/?hl=en#!forum/atvoid ]) is that "laws from symmetry" and "symmetry-breaking were contradictory to his anti-Platonist philosophy of science. It was his way to address  the idea of a universe not created by God, but a way I think both unnecessary and wrong.

A universe born of pure randomness and so-called symmetries forming which are merely contingent that gives a universe we just happen to be in makes sense instead: It is the opposite of symmetry-breaking. It is happenstance symmetry-forming. That there is a prior symmetry that is then broken is pure Platonism. 

Vic's view of the major symmetries were that they were picked out by us because we wanted physical laws that applied at all times (time-translation->energy conservation  spacial-translation->momentum conservation).  He didn't say this was free choice, but one constrained by nature.  In other words we abstracted away some "geographic" problems to reach them.   Then he extended this idea to Point Of View Invariance.  It's application to the internal symmetries of particles was not so clear.  We not only had to choose the thing conserved by also the transformation which conserved it.

Brent



But symmetries don't exist in some absolute, static Platonic realm and we just "pick them out". They are not a priori (except perhaps in the Kantian synthetic a priori sense). 

There are no symmetry breakings  because they were broken already.

That Vic put "man" here at the center (POV invariance) of the laws of physics is completely contradictory to almost everything else he wrote. Whatever symmetries there are accidental and contingent, not heavenly decree.



The physics of the digital machine has an important symmetry at its core (derived from the fact that “p -> []<>p” is satisfied in S4Grz1, Z1*, X1*: the material modes).

The breaking of symmetries is brought by the subject invariance, mainly present in the two modes with “& p”, which brings some antisymmetry in the picture. SGRz1 proves an antisymmetry formula the Grz formula
[]([](p -> []p) -> p) -> p.

I have thought wrongly that this symmetry + antisymmetry makes the S4Grz1 theory collapse, but I was wrong. The quantisation []<>p does not collapse (we don’t have []<>p -> p).

Here “man” is replace with “universal machine”. Mechanism sides with Vic on this. 

Bruno




 
The way I see this is there is first a cauldron of random syntax soup from which some "symmetries" are formed (by happenstance).

"How then does one find (some) mathematics useful in science? The key concept is that matter has codicality: It has a programmatic, or codical, nature. It follows repetitive behavior that can be described programmatically. (Possibly, matter that does not have this nature would fall apart and could not form a universe.)"

But even if some symmetries are present in all possibilities of matter (that does not fall apart), they were not dictated from above.

@philipthrift
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