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νοῦς

05/09/2021, 10:00 AMHey there! I study math, physics, and compsci independently. My interests focus on the (shared!) foundations of math, physics, and language. I want to develop computationally-rich environments where communities can gather and transmute their collective knowledge and catalyze discovery, learning, and teaching.
I am also interested in programming language design. I am very interested in dependent type theory, homotopy theory, higher categories, and how these ideas will influence the future of computing on increasingly-varied material substrates. To this end, I am trying to reimagine the entire information architecture, from MOSFET microarchitecture all the way up the abstraction layers. To this end, I want to extend the idea of formal structure (especially as implemented in category theory and functional programming languages) to include "formal substance", and to leverage the understanding which this affords to make more efficient metamaterial substrates for the observation and control of information flow, generally.
I got into math to learn physics, and then I got into computer science when I learned that my category theory knowledge should overlap significantly with the functional programming paradigm. I am currently reading SICP and learning Scheme, taking a break from Haskell so that I can better understand compiler and interpreter design. I'd like to push high-level interpretation further down in abstraction, and to find how information flow relates fundamentally to the shapes of our programs as physical control processes.

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Nick Smith

05/09/2021, 6:56 PMEspecially since you have a math background, you may not want to get too caught up in control-flow-based hardware and assembly languages. The hardware landscape is in the process of changing dramatically, with massively-parallel hardware of all kinds targeted at tensor operations and convolutions. Hardware is trending more towards math nowadays, and less towards the stuff you'll find in all the "standard" computer science textbooks 🙂. People might disagree with me here, but I'd wager 90% of all these textbooks will be obsolete in 20 years.

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And if you know category theory, then you already know what compilation is: it's just some kind of functor from one category (language) to another 😛. Compiler textbooks spend a lot of time talking about stuff like parsing and lexing, which is a trivial and unenlightening side-effect of demanding that our programs be serialised as text strings and manipulated as syntax *trees* (which I encourage people to challenge).

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(Categorical logic makes the same challenge to mathematical logic: maybe we don't need syntax trees)

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Pablo Donato

05/10/2021, 6:57 PMHello **@νοῦς**!
I am quite intrigued by what you mean by "formal substance" and "metamaterial substrates". Is this known terminology, your own way to frame existing concepts, or an intuition into a new way to conceptualize abstractions?
Also on the geometry of information flow in programs/proofs, you might be interested in the branch of proof theory called deep inference, which also seems to find connections with quantum physics (through category theory of course).

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νοῦς

05/10/2021, 7:30 PMThis looks exciting! Definitely in my interest vein! Today I started reading about quantum control flow, which seems to parallel the same domain of concern from a very different angle.
"Metameterial" is a real term, referring to synthesis of materials with specified properties. I think this domain will unlock many broad modes of information exchange. We are branching into spintronics, photonics, and I think the foundations of quantum computing will easily incorporate the variety of modalities by which energy, matter, and information inter-transduce. I am eager to learn how statistical mechanics and nonequilibrium thermodynamics fit into this too! It all has potential to synthesize, with the power of collected minds!
Biology is always a fantastic source of inspiration for our particular human adventures. Understanding the phenomenology of consciousness, will, and active becoming will require a more careful inspection of our planetary family. How do cuttlefish process their complex visual language??
I think the field of computation, especially its relationship to mathematics and physics, is in its youth. This time in history is a critical juncture, and we have boundless opportunities to help shape the future of human thought! I also want to build collaborative research and exploration tools for people to articulate, prove, invent, and explore mathematics together. Virtual reality will be a huge boon for education! Can't wait :D

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Pablo Donato

05/10/2021, 11:00 PMYes that's the kind of optimism and vision we want on FoC! I personally work on the collaborative tool side currently, where I try to design direct manipulation principles to perform mathematical proofs (you can read my intro for more info). I will look into this metamaterial stuff, looks really interesting!