I got involved with the Alternative Natural Philosophy Association back in the late 1990s when I hired one of the attendees of the Dartmouth Summer of AI Workshop, Tom Etter, to work on the foundation of programming languages. ANPA was founded on the late 1950s discovery of the Combinatorial Hierarchy (CH). The CH is a pure combinatorial explosion of discrete mathematics that appeared to generate the 4 dimensionless scale constants of physics <https://github.com/jabowery/ANPA/blob/main/CombinatorialHierarchy.py>, the last 2 pure numbers (137 and 2^127-1+137) corresponding to α aka Fine Structure Constant <https://en.wikipedia.org/wiki/Fine-structure_constan> and αGproton aka ratio of proton to planck mass. I've been recently working with David McGoveran <https://en.wikipedia.org/wiki/David_McGoveran> before he passes away, on generalizing the aforelinked Python code for the CH to produce his derivation of the proton/electron dimensionless mass ratio under a particular interpretation of the CH and the way its levels interact. If we get that done, we'll a computer program linking up the first two numbers of the CH (3 and 10) with the last two under an interpretation of discrete mathematics McGoveran and his colleague Pierre Noyes call "program universe". On the strength of that work I applied for a job with xAI since it bears directly on the mission of xAI. I, of course, was turned down for any of a variety of reasons but I did ask them to at least try to pick David's brains before maggots pick them.
Tom was, when I hired him, editor of the ANPA-West journal. I hired him because he'd found a way of factoring out of Quantum Mechanics what he called "the quantum core" as a theorem of relational combinatorics in which relational extensions aka relation tables could, if one treated them as *count* tables, in turn, be treated as a kind of "number". These "relation numbers" have *dimensions* and *probability distributions*. By "dimensions" I mean the things we use to characterize numbers arising from *measurements* like the number of chickens per the number of sea cucumbers as well as the number of kilogram meters per second square. That was one thing I demanded (going back to my 1982 work at VIEWTRON) fall out naturally from the mathematical foundation of any programming language. In other words, I absolutely hated with a UV hot passion the fact that the existing foundations for programming languages always ended up with kludges to deal with units and dimensions. Another thing I demanded was the treatment of procedural programming (1->1 mapping by statements between subsequent states) as a degenerate case of functional programming (N->1 mapping ala 3+2->5 & 1+4->5...) as a degenerate case of relational programming (N->M mapping). So he'd handled that as well. Another thing I demanded was some way of naturally emerging sqrt(-1), as a pure number, in the treatment of state transitions so that what physicists call dynamical systems theory emerges as naturally as dimensioned numbers. The fact that he handled fuzzy numbers/logic was beyond what I demanded but, hey, there it was! Tom's "link theory", introduced in the PhysComp 96 conference did all of the above by the simple expedient of permitting the counts in his count tables to include negative counts (ie: a row in a table being an observational case counting as 1 measurement and a -1 measurement being permitted). Tom was friend of Ray Solomonoff's (although I didn't discover that until years after both Tom and Ray had passed away) and they apparently arrived together at the Dartmouth Workshop early together. So I'm not here to deny that there is nothing of value to AGI to be found in the search for the minimum-length descripton of the origin of pure number parameters in natural philosophy, but let's be practical here. Statistical mechanics was not necessary for the Navier–Stokes equations, even though the foundation of both in *calculus* existed well before either. Wolfram can palaver all he wants to about "computational irreducibility" -- something that was recognized by mathematicians and physicists centuries before he coined that neologism -- but that is a red-herring when considering the foundation of AGI in Solomonoff's Algorithmic Information Theoretic proofs or in my own search for a programming language with which one might code said algorithms. The fact that it is hopeless to construct a "shortest program" that predicts what the universe will do for any of a variety of reasons (including that it is "computationally irreducible" in the sense that its predictions can't be computed prior to observing what they predict) is neither here nor there in a practical sense. The universe is constructed in such a manner as to permit us to make *useful* predictions without making *perfect* predictions. But we have to admit that, for some strange reason, Solomonoff's proof that the shortest program is the most likely program, applies at multiple scales of *im*perfect models. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Teaac2c1a9c4f4ce3-M7b5ff5fb972647f1b83dc15f Delivery options: https://agi.topicbox.com/groups/agi/subscription
