Oddly enough my behavior ties in to my thinking on this.

Well, I read it from bottom to top instead of top to bottom, as I always found that easier, as conclusions are usually written better than introductions and I can unfold what’s in the conclusion easier as I read the paragraphs going up. I chuckled a bit when at my ending you wrote about rule-following at your beginning.Oddly enough my behavior ties in to my thinking on this.First programming language was BASIC. = means both assignment and also equality. LET A=4 and also 2+2=4.So for me, 2+2=4 means the number 4 can be seen as a variable containing 2+2 or 2+2 can contain 4. They are both an assignment and equivalent. It just so happens we have a special use for them as numbers too — it’s not all strings – so 2+2=4 is not only an assignment but it is also a “power statement” useful in mathematics, something a little stronger than arbitrary assignment.As what I intuited for mathematics I extended to logic — which had become a handicap in trying to understand aspects of logic that depend upon a full confidence (or belief) in the system as being much stronger than “a little stronger than arbitrary assignment”.It was a handicap in Geometry too for proofs as by then, it was all arbitrarily assigned and I viewed axiom/proof systems as games to play like I might program in my computer at home. Everything is an assignment, with a mathematical or logical game built in to some types, the context determined the usage for =.It wasn’t until I was well into my 20s that I started to wonder why other programming languages didn’t just have a simple =. I did ok but it was confusing.So by the time I came across learning about 1st order logic stuff, it was a different world where that = actually meant something quite serious to them. But my mind could not see it as more than a game one might program in with rules that are just as easily changed.

So for me the = is an interface symbol with multiple functions. There are other interface symbols too, each with different functions that establish relationships between things or create things or eliminate things. It can all be morphed and changed as needed, although the more you depend upon lower levels, the less free you are at modifying assignments and what functions are performed. A change of context (turn a number into a string) and a program won’t compile or will crash if running without safeguards.

Each chunk of logic in a computer program is evaluated atomically, line by line and two neighboring lines don’t need to have much to do with one another at all so long as they compile individually.

So, infinite regress is a loop that needs a BREAK statement.

There are many ways to write a program that are equivalent in function and can have entirely different schemes inside of them and if you put two programs side by side, the code may be entirely different, the logic and variables and functions seeming to have nothing at all in common and yet produce the same results.

You can’t determine the cause from the effect except in very simple cases with very strict rules as there are usually so many ways to arrive that backtracking is tricky to get correct consistently.

 ah my tl;dr: I don’t know if I can derive the pleasure you did from your discovery.This is sad to me as I can sense the satisfaction and pride in the product.But that is to say, I don’t have a starting point of firmness of axiom but quite the opposite, that of “arbitrary but functional”.I’m what comes from these revelations, having been built upon them as a “given” and so I don’t get the eureka because I can’t put myself in a place of working through the problems the way I’m supposed to.
My story starts with church and Turing and shannon. Godel and Peano is Old Testament, church, Turing, shannon the New.You experienced a prophecy fulfilled.
I remember being sad looking at mathematical puzzles and games as a kid. I would often solve them by folding the paper, poking a hole through them, tearing them, treating the paper as much as part of the solution as the ink pressed on top of it.
Lots of unwritten, unspoken rules out there. Axioms abound. Teachers expect you to figure out many of them.
There was a huge AI project, Cyc. It’s been going on my entire waking life just about. I’ve been aware of it since the 1980s. Throw as many microtheories as you can at it and watch the magic. An inference engine containing the sum of all human knowledge with the ability to reason.
It’s still ongoing and has found a number of applications.
But it was missing a few things they simply didn’t think about at the start and where it is weak is precisely in those areas, despite attempting to be as compact a complete database of facts and inferred microtheories that nevertheless stretches into the millions.
It cannot do what a 3 year old child does or even close. Its basis is different.
Jack Sinclair That is impressive. The stretching and folding is a smart approach. Give it enough flexibility in what it considers a viable ‘new section’ and I can envision how it lands in the right spot 8x out. Very cool stuff indeed.
I wonder if it’s being treated like a complete lattice each expansion. I can envision a full rotation through the complex plane ending you up with a similar but different yet compatible place. (with ‘compatible’ being ranges of valid potential chaotic expressions on a fixed lattice) Maybe the next chaotic section *is* hiding in the complex plane.
I experienced this working with genealogy and it took me a few days to figure out what was happening:
“In contrast to standard recurrent neural networks the input weights and connections within the reservoir are static”YES! Static. The complete lattice is fixed between the input connections and into the reservoir. Fixed connections. Fixed weights. Do something like a fourier transform but not that.Rate of flow has to be steady for it to work as it is flow rate that is the main feature it depends upon for reliability, for while the input and the entry into the resevoir is fixed, and the layout of the reservoir is fixed, the output is not.This isn’t to say it’s easy but I’m always looking for a trick that takes something common and does something uncommon with it.

OH this is practical.
Instead of assuming equations, which is what traditionally strange attractors are created from, do a time series and map it, ANTICIPATING a strange attractor, and successully seperating the linear from the non-linear components.
Data driven. Empirical. Equation free.
Oh I love chaos theory. and I’m laughing at the scale-free article – particularly the stuff about heavy-tail. It’s so true: they’ve been using scale-free so long (and now heavy-tail) that they’ve become buzz-words encompassing whatever they want it to mean.We’re moving away from beautiful-math algorithms towards data-driven modeling, which is messier but more accurate.
  I shouldn’t be so quick to say “data driven” either. Nothing’s data driven. Everything has a working theory behind it, guiding it along.,
 What all of these have in common, which I really like, is they’re all heavily timestamp and rate dependent. In short, streaming. That, like all streaming data, has its flaws (depending on fixed-rate dependable communication will only get you so far), BUT there’s enough algorithms out there to handle missed packets and such that it should be possible to incorporate more timing robustness into their reservoir and data-driven strange attractor state mappers.

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