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

(Status: draft)

I’ve long held a view in my mind that the very well known Pythagorean “theorem” is not a “theorem” – in the sense of being able to be derived from a set of axioms through logical deduction. I want to jot down this thinking here because I think it is important for pedagogical reasons … but mostly I just want to get it off my chest even if the mathematical community considers this blasphemy. So I shall refer to this using “theorem” in quotes throughout this writeup.

I’ve never quite felt that I understood what “measurement” means in quantum mechanics and my recent engagement with quantum computing surfaced this rather starkly. I’m not talking at the handwaving level of “wavefunction collapse” and such esoteric things. I just want an ordinary close hand-lens view understanding of what measurement is, even if incomplete at some level. This post is an attempt at that. If any reader thinks I should read up X/Y/Z to understand this, I’d much appreciate any links/references.

(This post was originally posted on the Imaginea blog on 27 May 2016. That blog now no longer exists, so I’m reposting it here. I have The Internet Archive to thank for keeping a copy of the text and my colleague Srikant Patil for his help recovering the images originally presented in this post from an archive.)

Constrained randomness is useful in adding a dash of variety to computer composed music. Picking values that fit a parametric probabilty distribution whose parameters are used for control is therefore a common case. Here I describe how to do that given access to only a uniform random number generator in the unit interval.

There is no dearth of explanations of the Fourier transform on the internet. Being a believer in understanding a concept from as many perspectives as possible, I welcome all of them. Here I offer yet another perspective that is “intuitive” in its own way and yet is not something I’ve seen presented often or presented in yet more mysterious ways.

Kurals are posted in public transport in Chennai - trains as well as buses. When taking them pre-covid to work, I used to amuse myself by translating them into techie parlance. These are gathered from my tweets. Maybe I should expand the collection and maybe I will, but for now, here it is. I feel the fun of doing this is spoilt if I provide the actual translation in English too.

In issues of policy and negotiations between countries on actions to be taken to mitigate climate change, the country-level figures that get discussed are either total emissions or per capita emissions. While total emissions is an important figure, per capita emissions gets all the attention. I’m starting to think that might be the wrong number to focus on.

(This note on Alain Aspect getting the 2022 Nobel prize was shared by Prof. Sivakumar Srinivasan of Krea University. I’m posting this note here with his permission. I’ve taken a bit of liberty to split into paragraphs for easier reading. No other changes to his note.)

Alonzo Church’s insight that lambda is sufficient to express all of computation is a non-intuitive stunning revelation. Showing that numbers can be represented using lambda alone using what’s come to be known as “Church numerals” is also brilliant. However, subtraction was a problem with plain Church numerals. Kleene solved that by using a pair of numbers instead. However even Kleene’s construction doesn’t give us a representation for negative numbers. Here we’ll look at a possible way to use Brahmagupta’s formulation to represent integers using lambda.