On Monday, January 28, 2019 at 6:27:37 AM UTC-6, Bruno Marchal wrote: > > > On 25 Jan 2019, at 14:53, Philip Thrift <[email protected] <javascript:>> > 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 <[email protected]> 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 <[email protected]> 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 <[email protected]> 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 <https://people.csail.mit.edu/sachour/res/pldi16_arco.pdf>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 system.* >>> *On a set of benchmarks from the biological domain, Arco* >>> *generates configurations with 35 to 534 connections and 28* >>> *to 326 components in 1 to 54 minutes.* >>> >>> >>> - pt >>> >>> >>> Intersting. >>> >>> Yet, that does not violate the Church-Thesis, even if very useful FAPP. >>> But such computations arise in arithmetic, either directly, or through a >>> infinite sequence of approximations. If all decimals of the analog >>> phenomenon needs to be taken into account, then we are out of my working >>> hypothesis, and even evolution theory becomes wrong, as evolution and life >>> becomes sequences of miracles. But the goal of the authors here is not >>> learning anything in metaphysics, just doing efficacious machine. In that >>> case mechanism explains the plausible necessity of such moves, including >>> quantum computations (which also do not violate Church’s thesis). >>> >>> Bruno >>> >>> >>> >>> >> >> >> I don't believe in (or know what are) miracles (although a real >> hypercomputer - one you could give any statement of arithmetic to - e.g. >> *Goldbach's >> conjecture* - and it could check through all - infinite number of - >> integers and tell you "true" or "false" within the hour - would be >> basically a miracle), but I do think that* substrate matters*. >> >> Hence in the PLTOS view (program, language, transformer/compiler, object, >> substrate), *substrate* can't be eliminated in the semantics of *program*. >> In other words, in *real programming*, there are no such things as >> substrate-independent programs. >> >> >> Because you assume some primary substrate. And then you need, coherently, >> to assume no-mechanism. No problem, but the current evidence favours >> Mechanism, and there has never been any evidence for substrate. Adding >> substrate in the picture makes the mind-body problem almost non soluble, at >> least without invoking some precise non computationalist theory of mind. I >> start from the computationalist of mind, shows that we have to derive a >> phenomenology of matter in a special (self-referentially based) manner, and >> nature seems to confirm this. The illusion of matter is easier to explain >> once we have a theory of consciousness, than to derive a theory of >> consciousness from some notion substrate (which are conceived usually as >> being inert). >> We are working in different theories. You might think about a way to >> motivate your ontological commitment in some primitive substance. The books >> in physics does not provide such motivation, as they do not aboard the >> mind-body problem (even if Everett Quantum Mechanics already look like a >> solution to the mechanist mind-body problem). >> >> Bruno >> >> >> >> >> > Just to note that the "substrate" terminology is used in computing (as > above): > > *Programmable analog devices have emerged as a powerful **computing > substrate* > * for performing complex neuromorphic **and cytomorphic computations. * > > It's a word combined with "computing" like love and marriage. > > > But those analog computations, although they could be very useful in > practice, do not change the consequence of the theory, unless you claim > that they provide us with a method to compute new functions, which would > violate the Church-Turing thesis (which I doubt very much). Keep in mind > that with mechanism, the physical reality has analog part, which might or > not be used by our bodies, although there are no evidences (that I know) > for this. I follow the idea of not adding any hypothesis in a theory, > unless there are strong evidences for them. > > Bruno > > > > "Analog" computing is a bit odd. Assuming real numbers (as commonly defined in math) do not exist in nature (which I don't think they do) then there is nothing in the Church-Turing sense of semantics that the analog computer computes differently. But in other semantics (like taking physical aspects into account - power consumption, for example - then analog substrate does matter.
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