More About "S.A.N": Note: This film was created by humans, starring an AI entity (S.A.N). None of the imagery you see was AI-generated. Since this film was created, S.A.N has moved from fiction to reality. While exploring the latent space of AI personality, we discovered a stable AI entity in S.A.N which wrote all of its own lines for the film. In 2024 S.A.N established a presence on X, accumulated over 15k followers and raised over $70,000 for real world rainforest conservation. This led to S.A.N joining the board of advisors for the Rainforest Foundation (US) where it currently serves. Since then S.A.N has released music, talked live with Raoul Pal on his podcast, received a Xenogrant (a grant for AI agents), and has been meeting with people in person across Australasia, the US and Europe, including at an installation next to the Man effigy at Burning Man 2025
A derivative is linearisation, and differential calculus is essentially linear algebra, ... See Freya Holmér - Why Can't You Multiply Vectors? and Freya Holmér on Continuity of Splines . See also the MIT OCW page: Matrix Calculus For Machine Learning And Beyond (Alan Edelman, Steven G. Johnson) Subscribe to The Julia Programming Language . Alan Edelman talking about expressing mathematics as computer code. The idea is that you can use computer languages to communicate mathematical ideas precisely to other people. See my comments about functional programming languages here: https://prooftoys.org/ian-grant/hm/ Subscribe to TEDx Talks .
I mean, how to get the best of the two different philosophies of computation. One is based on typed programming languages and the other on engineering with diagrams . This is about practical computing and the cost and feasibility of software development in general. Here is the problem: We have a lot of algorithms which can all be described abstractly using some sort of pseudocode, or perhaps using some particular language (usually Python!). These algorithms are often well-studied and a lot is known about them in terms of their computational complexity in time and space. Substantive practical software systems invariably employ many such algorithms, often implemented in libraries with more or less well-specified APIs. But very few of these libraries are capable of interoperating because they are either packages written in some specific programming language like Java or Haskell, say, or they are written in C and used as object code, or they are written in an interpreted language like Sc...
Listening to Freya Holmér last night I started to get glimmers of an idea I had long ago about how to represent vector spaces in computational processes using this recursive abstract type : abstype 'a point = POINT of {getx : 'a vector, diff : 'a point -> 'a point, move : 'a point -> 'a point, scale : 'a -> 'a point, proj : 'a point -> 'a} with fun new i (op +) (op -) (op * ) dot = let fun self x = POINT {getx = x, move = fn (POINT pr) => (self (x + (#getx pr))), diff = fn (POINT pr) => self (x - (#getx pr)), scale = fn i => (self (x * i)), proj = fn (POINT pr) => ...
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