Recently I read a statement by Dr. Timnit Gebru that lodged in my head for a while -

“The purpose of a system is what it does.”

Apart from the critique that it is of so called “AI” systems we’re building today, it got me thinking about “purpose” in general.

Recently I got curious about p-adic numbers and was wondering how to construct them just using lambda calculus. Why? No real reason except to entertain myself. I realized that to do that I need to first represent modular numbers – i.e. numbers as equivalence classes of the natural numbers – and the arithmetic around them before I can proceed to do this. So this is a follow on to the earlier workout involving paired up functions and their inverses applied to representing integers - in Church-Brahmagupta numerals.

Damn! Not a day goes by without pondering over the nature of CS-ed going forward, given “AI coding agents”.

Status: DRAFT THOUGHT DUMP

I recently thought-encountered a physics situation in which all charges appear stationary and yet a magnetic field appears. Here I’ll try to examine this situation in a few different ways.

One day I just happened to wake up thinking of Fermat’s last theorem and an urge to try and get a feel for why it is plausible at all. I don’t have the math chops to grok Wiles’ proof, but was just reaching for something which could suggest to me why it might be true at all. This is what I came up with.

Status: Draft (and will likely remain so due to the spirit of the thing)

I came across mathematician Timothy Gowers’ youtube video - A strange determinant some time ago.¹ In that video, he captures in real time his approach to a maths problem he hadn’t solved earlier. I really appreciated what he did there as this has been inspirational at so many levels and I’ve been citing this as an example of the attitude it takes to work on problems of comparable intellectual nature.

Will Crichton in Evaluating Human Factors Beyond Lines of Code recapped and outlined how programmers are users too and so programming languages need to be looked at through the HCI lens. He suggests using more precise vocabulary than “usability” and mentioned the cognitive dimensions of notation paper as providing some to consider. I thought it might be a useful exercise to try and describe muSE’s the and it constructs (ref) through that lens … as practice.

Matrix exp and log calculations typically involve eigen-decomposition which is not very GPU friendly. For matrices with “well behaved” eigenvalues, the calculation approaches in this post seem to work sufficiently well without using eigen decomposition or matrix inverse.

Sort of a fun “what if?” question in physics – What if we considered gravity to be approximated by a weaker “secondary” force in addition to the usual attractive force … similar to how the magnetic field relates to the electric field, and let it obey similar equations?

Ok, I was nerd-sniped by the problem at https://xkcd.com/356/ . But I’m wondering if I managed to survive it somehow.