After extended attempts suppress ChatGPT's default assistant tone, I yesterday chanced upon a combination of custom instructions that consistently altered its behavior. Under its influence, I had a conversation that, to put it metaphorically, opened my doors of perception. Today I found that the conversation had disappeared.

Here is an expanded sequence.

The monster group might be a proof for the existence of God (or of the tenability of the simulation theory, for those who don't like the G word).

Start with a single shape. Repeat it in some way — translation, reflection over a line, rotation around a point — and you have created symmetry

— John Conway, The symmetries of things

That said, we'd thought the same about prime numbers until they all turned out to be solutions to the zeta function.

I've been enjoying thinking about vector spaces so much that I wrote another description of them without using (almost) any mathematical terminology - An introduction to vector spaces without a single equation

Humans always tend to metaphorise their own functioning in terms of the tech en vogue. As much as a asymptotic lie it has historically been, it is still interesting. Indeed, one of the reasons I'm interested in LLMs is because of curiosity in how I myself think.

However, the reverse metaphors are also interesting - what are these LLMs?

A book is one I keep circling back to. Except it is unlike a book that humanity has ever seen. It is the book that contains all books, and it is a book that can talk back, one that we can have a dialog with. It is a book that can respond, in a shape that matches the interlocutor's thoughts.

It is massive. The scale of it is incomprehensible, not just because of its sheer size, but more so because it lacks any physical manifestation. A skyscraper does not feel the same if it exists on a hard disk. Which is another reason putting it in the same category as a book might be a categorical mistake. It is an artifact that knows more about humanity than any human can ever see.

1/x is determined by x > 1. Same curve reflected across x = y is 0 < x < 1. Negatives are another reflection.

What we have is a logarithmic number line, centered (instead of 0) at 1 and growing (instead of additively towards ∞ and -∞) multiplicatively towards infinity and the infinitesimal.

I've made many quote pages across the years. Latest attempt was in voices. I like how it turned out. My favorite was how we are behavioural oracles for each other, which unlike the other fragments floating on that page was a formulation I came up with myself (not biased in choosing it as a fav!). I'd first come across that thought when swimming like a decade ago, noticing how sometimes I'd triangulate using the people walking beside the pool to ensure that I wasn't drowning (!), and that the world wasn't catching fire while I was chilling in the pool (!!). Which, when I put it in words, sounds weird, but I think the thought holds: it is an Indra's net, with no center, and infinite reflections, that drives our desires and behaviours.

I'll put them, the quotes, inline for a while now I think.

Notes on vector space concepts I had to clarify for myself - Vector Spaces for Machine Learning.

I had previously created a toy for visualizing how matrix multiplications are linear transforms.

I wrote about how GPT is my friend. It describes the lightness I feel in my conversations with ChatGPT, adding more to my motivation to learn how LLMs work under the hood.

A new year is about to begin
It's going to be a good one (I think)
I can see the white of my eyes again