> On 15 Feb 2019, at 16:12, Philip Thrift <cloudver...@gmail.com> wrote:
> On Friday, February 15, 2019 at 5:35:02 AM UTC-6, Bruno Marchal wrote:
>> On 15 Feb 2019, at 08:25, Philip Thrift <cloud...@gmail.com <javascript:>> 
>> wrote:
>> On Wednesday, February 13, 2019 at 10:40:32 PM UTC-6, cdemorsella wrote:
>> Two fascinating (and very different) approaches are presented to derive 
>> Quantim Mechanics main practical tool (e.g. Born's rule). Wonder what some 
>> of the physicists on here think about this research?
>> I find the argument that no laws is the fundamental law... and that the 
>> universe and its laws are emergent guided by subtle mathematical statistical 
>> phenomena, at the same time both alluring and annoying.... it is somehow 
>> unsatisfactory.... like being served a quite empty plate with nice garnish 
>> for dinner.
>> One example of emergence from chaotic conditions is how traffic jams (aka 
>> density waves) can emerge from chaotic initial conditions, becoming self 
>> re-enforcing within local domains of influence... for those unlucky to be 
>> stuck in them. Density wave emergence is seen across scale, for example the 
>> spiral arms of galaxies can be explained as giant gravitational pile ups 
>> with some fundamentally similar parallels to say a rush hour traffic jam, 
>> except on vastly different scales of course and due to other different 
>> factors, in the galactic case the emergent effects of a vast number of 
>> gravitational inter-actions as stars migrate through these arms on their 
>> grand voyages around the galactic core.
>> This paired with the corollary argument that any attempt to discover a 
>> fundamental law seems doomed to the infinite regression of then needing to 
>> explain what this foundation itself rests upon.... leading to the "it's 
>> turtles all the way down" hall of mirrors carnival house... head-banger. 
>> Perhaps, as Wheeler argued, the world is a self-synthesizing system, and the 
>> seeming order we observe, is emergent... a law without law.
>> Here is the link to the article:
>> https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/
>> <https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/>
>> One can (sort of) write all "physics" in a couple of equations: the Einstein 
>> Field Equation (EFE) and the Standard Model Equation (SME):
>> EFE: 
>> https://upload.wikimedia.org/wikipedia/commons/thumb/4/45/EinsteinLeiden4.jpg/620px-EinsteinLeiden4.jpg
>> <https://upload.wikimedia.org/wikipedia/commons/thumb/4/45/EinsteinLeiden4.jpg/620px-EinsteinLeiden4.jpg>
>> +
>> SME: 
>> https://www.sciencealert.com/images/Screen_Shot_2016-08-03_at_3.20.12_pm.png 
>> <https://www.sciencealert.com/images/Screen_Shot_2016-08-03_at_3.20.12_pm.png>
>> What caused this particular arrangement of expressions in these to be the 
>> "law" of our universe I suppose can be "explained" by it's being one of any 
>> number of possible arrangements.
> The tiny (sigma_1) arithmetical reality contains all “combinations” of all 
> programs, and your explanation is a bit like digital physics, where the 
> physical universe would be one special universal number, say U. That is 
> possible, but this can explain the origin of the physical laws, in a coherent 
> way with respect to the mind-body problem (the hard problem of consciousness) 
> only in presence of an explanation of why that program U is winning, that is 
> how such U can “multiply” you so much in the relative way that the laws of 
> physics get stabilised. Arithmetical self-reference explains consciousness 
> “easily”, but at the price of forcing us to derive the physical laws from any 
> universal machinery.
> The physical reality is not a mathematical reality among others, it is the 
> projective border of the universal mind, which is just the mind of the 
> universal machine. It is a complex many-dreams structure, and its quantum 
> aspects explain why negative amplitude of probability can play a role in 
> making the aberrant histories relatively rare, despite them being also in 
> that sigma_1 arithmetic.
> With mechanism, the idea that there is anything more than the sigma_1 
> arithmetical truth is absolutely undecidable. The sigma_1 truth emulates the 
> sigma_n believers for all n, and beyond. If the physics which is in the head 
> of the universal numbers departs too much from what we see, it will be time 
> to suspect that there is indeed something more. But not only there are no 
> evidence for that, but there are strong evidence for the completeness of the 
> sigma_1 truth with respect to the metaphysical questions.
> Bruno 
> Whatever brand of scientist - physicist, chemist, biologist, even 
> psychologist - it seems that they see any theory of whatever is within their 
> domain is to be composed of a finite number of sentences (e.g. equations, for 
> physicists). 

Yes, like a brain use a finite number of molecules, and mechanism eventually 
only assumes the finite number 0, s(0), s(s(0)), …, which actually will be used 
to code the finite things we are interested in.

But the meaning of those things are formalised by infinite structure, like the 
model (N, +, x), or like hide that a computable function associate any number 
to a number. The understanding of “red” should make you able to recognise *all* 
red things. With mechanism, such meaning are captured by nameable, and non 
nameable, number relations.

All theories assumes such potential, phenomenological, infinities. The concept 
of understanding is itself infinite, and more or less well captured by the 
comprehension axiom in set theories, or the abstraction Operation in Lambda 
calculus. Compute science is concerned by the behaviour of finite entities 
confronted to finite or infinite entities.

> To have a theory that is composed of an infinite number of sentences is sort 
> of outside of their way of thinking.

All theories contains an infinite set of sentences. Classical propositional 
logic contains as theorem “p -> p”,
“p -> (p -> p)”, “p -> (p -> (p -> p)), etc. Elementary arithmetic contains 
infinite propositions: 1+1= 2, 2+2=4, 4+4=8, 8+8=16, etc. That is why we use 
variables to say generalities, like Ax(x=x), that is, for all x it is the case 
that x = x. Or we use scheme of axioms. 
No need to put any ontology on this, with mechanism we need only 0, s(0), … 
Mechanism explains, using only the laws of addition and multiplication (and 
succession) how finite numbers get able to hallucinate other numbers, and why 
some sheaves of hallucination can become persistent and associated to deep and 
complex lawful histories.

I might disagree with you, everyone’s theory is infinite, but what you are 
perhaps saying is that at any moment of time, we consult only finite part of 
those theories, to figure out some reality we bet on. But that is not unlike 
the Turing machine, which consulte only finite portion of its tape, and asks 
only a finite number of query to some Oracle.

F=ma assumes already many infinite theories. Infinite theories are far simpler 
to use than finite theories, due especially to the abundance of very similar 
types of things, like photons, electro, water molecules, but also numbers, 
functions, relations, space, etc.

Digital Mechanism is a finitisme, not an ultrafinitism, to be clear. It also an 
indexical, it concerns your willingness to say yes to a digitalist doctor, or 
yes to a digital teleportation experience. I just show that in that case the 
mind-body problem reduce to a body illusion problem in arithmetic. It is more a 
problem asked in a theory of consciousness than in physics. Here the theory of 
consciousness is basically the whole theology of the universal machine, or the 
one common to all sound consistent extension of a little one like PA. PA 
assumes induction, which we can put already in the phenomenology. From the 
putself, we assume only RA(*).


RA = Robinson’s Arithmetic (often called Q):

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

An even cuter TOE is (without logic!):

1) If A = B and A = C, then B = C
2) If A = B then AC = BC
3) If A = B then CA = CB
4) KAB = A
5) SABC = AC(BC)

Both are finite theories, or can be easily viewed as shemes of proposition.. 
The second theory is purely equational.  We cannot prove that SK = KI in that 
theory, but that is not needed in the ontology, where they are indeed different.

Both theories emulate all Löbian machines, which you can define by any machine 
believing one of those  axioms, + logic, + corresponding axioms of induction. 
They are the machines we can interview on the theology, and the key proper 
theological proposition, well they can communicate them only conditionally to 
the computationalist hypothesis (of course), and some “dangerous” 
self-soundness implicit assumption. It is here that there is a theological trap 
(consistent in claiming that G* would necessarily apply to us).


> - pt 
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