On Friday, February 15, 2019 at 12:01:26 PM UTC-6, Bruno Marchal wrote:
> On 15 Feb 2019, at 16:12, Philip Thrift <cloud...@gmail.com <javascript:>> 
> 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> 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/
>> 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
>> +
>> SME: 
>> 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(*).
> Bruno
> 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).
> Bruno
I was really talking about every theory considered has a *finite 
specification*. In Robinson Arithmetic (*RA*) above there are only 7 
sentences listed. Of course an infinite number of sentences can can be 
produced from these via rules of the specification. 

One can have the axioms of True Arithmetic (*TA*):

   A sentence S is an axiom of *TA* if S is evaluates to be true over the 
natural numbers.

That would be an "infinite" theory.

(Consider a theory of physics that just accumulated all sentences S that 
passed an experiment.)

But also what I am talking about are theories with *non-quantitative 
domains* (are not numerical at all, but are experiential).

*The Enactive Approach to Qualitative Ontology*


- pt

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