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] <javascript:>> > 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. But matter is a mystery (this I've learned from Galen Strawson), so I do think there are mysteries. - 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
