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:
"Litany Against Fear" in Present Tense
I love the Litany, but think it could benefit from more present tense. A litany is an entreating. That's why they're recited over and over. It tells one how to treat something as they are currently experiencing it.
When it's time to party we will party hard
The best feeling in a party is just sinking into a chair and talking about whatever you feel like with another. The best feeling in a party is doing something you've never done before and finding you enjoy it, or glorious wipe out like in that motorbike scene in 10 Things I Hate About You. The best feeling in a party is discovering someone strange in the same ways as you and feeling understood and not broken but just different and being ok with that.