taliesinb

8 ms·

31.
by taliesinb 3y ago
I have yet to find an adequate replacement for Mathematica and its graphics DSL. To create the visualizations in https://math.tali.link/classical-array-algebra/ takes a fair amount of interplay of code and data, I shu
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by taliesinb 3y ago
Does anyone know if Lean 4 has encoded much category theory?
33.
by taliesinb 3y ago
Exactly. Thought is prior to language, and much confusion happens when you conflate the them. In particular the surface syntax of language tells you next to nothing about the "syntax" of thought, which is hypergraphical, not tree-
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by taliesinb 3y ago
please clarify your suffix "which is natural language of the sentence"? are you referring to the positional encoding?
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by taliesinb 4y ago
Interesting article, though I thought this was going to be about the fact the the "phylogenetic tree" is not in fact a tree but a hypergraph, owing to the existence of sexual reproduction.
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by taliesinb 4y ago
Amazing! Even includes anagrams: a person called Charis Law who owns a company called Whirl Casa.
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by taliesinb 4y ago
I'd be fascinated to read these published things if anyone can point to them!
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by taliesinb 4y ago
I would love to have some pointers to the higher dimensional algebra you're referring to.
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by taliesinb 4y ago
Why is the submission URL using http instead of https? That just seems... bizarre.
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by taliesinb 4y ago
Yup. Genetic recombination means some genotypes are the result of crossover of two parents. Horizontal gene transfer has a similar implication. This means the true structure is a directed hypergraph.
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by taliesinb 5y ago
Interesting, but the video is only available at 480p for now, so it's hard to actually see any details in the demo. I assume this was uploaded very recently and YT is still processing the higher-quality versions.
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by taliesinb 5y ago
Very well put!
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by taliesinb 5y ago
> It also looks like you should have a strong plan to do something (hobby, hike, or work in another capacity). If you don’t, you may just stagnate and waste some of your prime years for growth and development. Having been on this journey
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by taliesinb 5y ago
I've had quite a journey since quitting, so sorry for the long post! I worked at a company writing mathematical software for 8 years. The work was interesting, but I kept feeling there was a deeper way of thinking about some particular
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by taliesinb 5y ago
A bizarre coincidence: this morning I was reading about a role for the Möbius strip in music, but it had nothing to do with this! It turns out orbifolds have an application in music theory. Orbifolds are a kind of generalization of a contin
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by taliesinb 5y ago
I read some of the recent submissions on the issues around C undefined behavior, which sound almost nightmarish. The common impression is "C is dangerous because it is so powerful" -- which makes it seem like an honest tradeoff, r
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by taliesinb 5y ago
A nice introduction! An interesting next step is to look at so-called cyclotomic polynomials. Wildberger's has a gentle introduction to this [0], though you'll have to tolerate his idiosyncratic notation ("polynumbers" i
48.
by taliesinb 5y ago
This site is an extraordinary labor of expository love! I've encountered it a couple times over the last 8 years or so. Page after page of detailed summaries, explanations, arguments, graphs, pictures, diagrams. It just keeps going. It
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Zig Showtime – AWS Rust(youtube.com)
3 points by taliesinb 5y ago|0 comments
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by taliesinb 5y ago
I agree, it's a high priority to build discrete versions of differential geometry, calculus, PDEs and so on. That's what I'm trying to do
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by taliesinb 5y ago
Wow, it looks extremely interesting! You know, it's bizarre, I recently pursued a similar approach, attempting to derive quadratic kinetic energy of an automaton controlled by a computer program (it used a circular tape to decide wheth
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by taliesinb 5y ago
Thanks for the link! I'd be curious if you know about other information-theoretic approaches to understanding phenomena even in say classical mechanics (let's put aside statistical mechanics where the connections are already well
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by taliesinb 5y ago
I largely agree about the book: I think there might be something there, but the case is far from being made. One small correction: the rewriting systems he proposes are not deterministic. As for how non-local entanglement can occur, I'
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by taliesinb 5y ago
> Aren't these multiway systems essentially what we see with ambiguous grammars... Yes. > One application of these might be to resolve the meaning of probabilities under the many-worlds interpretation... There's some ways to
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by taliesinb 5y ago
Shame, Atiyah was senile at that point. A sad note to end on after a brilliant career. But whatever you may think about him, Wolfram is not senile.
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by taliesinb 5y ago
I'm not an expert in Petri nets, but they are definitely used for modeling in various fields. Krohn-Rhodes theory also claims some successes if you read that article. As for the stuff I'm actively working on: even if it is success
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by taliesinb 5y ago
Some of the ideas in this post might pan out, some might not. Regardless, I do think token event graphs will turn out to be important. Of course, I'm biased: I coined the name TEG -- although the underlying idea originated with Max Pis
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by taliesinb 5y ago
Yes, I used Mathematica to author https://quivergeometry.net , but I had to write the markdown converter, katex generator, rasterization caching etc. myself. Took a while to set up but works quite well now. Some parts of it are q
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by taliesinb 5y ago
I forgot to say that if anyone hasn't seen it, RedBlobGames' tutorial on hexagonal grids is an extremely good resource that uses visualization and interactivity to great effect, and really helped me in early stages of my work:
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by taliesinb 5y ago
This doesn't involve traditional mathematics concepts, but I'm relying heavily on visual explanations in my mathematical explorations of discrete geometry, which you can find at https://quivergeometry.net . Probably t

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