Some ChatGPT Sessions
No particular theme. Quoted text is me, rest is GPT.
2016 ML thoughts
(Old notes from 2016 that I stumbled upon).
My biggest takeaway from Redwood Research REMIX
I just finished a 1 month research program called REMIX (Redwood Research Mechanistic Interpretability Experiment).
finite, actual infinity, potential infinity
For a finite set, one can describe a uniform distribution. There isn't a natural way to do so for a countable set. But for a hyperfinite set, one can describe a uniform distribution through a probability density. So in some ways the countable is "bigger".
Actions and Flows
What is an action?
PSA: reward is part of the habit loop too
The usual setup of a habit is
a kernel of lie theory
just like how infinitesimals are useful because they're indiscernible from 0, but have the advantage of being able to be divided by.
The hyperfinite timeline
Take an interval. Cut it into H pieces, where H is hyperfinite. This serves as the index set of a stochastic process, among many other uses. Imagine that for each of the H steps, you flip a coin to get -1 or +1. Then move an infinitesimal distance left or right based on the sign. This is Brownian motion. Each infinitesimal piece of the timeline is profitably thought of as a Planck time.
Slick hyperfinite Ramsey theory proof
Blog power laws
August 2016: Jiuzhaigou, Sichuan Province, China[^maybe it should be timespace instead of spacetime, better to put the time first, what if the place identifier no longer exists? Plus timestamps are orderable.]
A Prince, a Pauper, Power, Panama
Instrumental convergence is an issue I think about a lot because it's so natural. Being rich and powerful almost never works against you.
Braindead Way to Derive Taylor Series of Exponential Function
$$e^x$$ was first defined by a formula for continuous compound interest:
What is the prime factorization of zero?
Fundamental theorem of arithmetic1: every whole number can be split into a product of prime numbers in a unique way.
Which deserves its name more than any other fundamental theorem, even the fundamental theorem of calculus. ↩
Use of emphasis in speech
Through a somewhat messed up example:
Generating a lot of language data with a theorem prover
I spent the last hour looking and failing to find the paper that made this specific claim: