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* https://philarchive.org/archive/PACITT from https://codicalist.wordpress.com/2018/12/14/material-semantics-for-unconventional-programming/ - pt -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
