Why do things break in a 2 element set?
The math jargon for a set where you can implement a 4 function calculator \((+,-,*,/)\) is a field. Fields can have a finite number of elements, and such fields always have a prime power number of elements, aka \(p^k\) where \(p\) is prime and \(k\) is a natural number.
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.
these are people who died
they were all my friends and they died.
(some writing without hesitation or editing. possibly with repetition and deviation.)
i went to kauai with my parents last summer. we walked across some trail that left me covered in mud, and near the entrance to the trail we saw a frog lying on its back, feebly twitching. i figured it would die. i left it there.
what it’s like to get nail phenolization
phenolization: (partially) destroying nail matrix with phenol to prevent ingrown nails.
Why 0 to the power of 0 is 1
A set/category theoretic interpretation.
Lines and Points are Circles
A space can be compactified by adding a point at infinity. The point of this abstraction, as with abstraction in general, is not so much generalization as unification.
Visual Programming, Functions, Copilot
Visual programming languages have not taken off in the mainstream. Languages like Scratch and Logo have mostly been known as educational tools and not for “serious” programming.
infinitesimals to atiyah singer
i learned some nonstandard analysis and clifford algebra, mostly through david hestenes’s ‘geometric algebra’.
The Soviet Dream I Miss
The youth of our region is gifting you, the young ones of the 21st century, with Koryazhma that has been turned from a small village into a modern town within ten years, Severdodvinsk that we built on land that used to be swamps, and the colossal wood industry of the North: Kotlass, Solombal and Arkhangelsk factories. We know that you will have better lives than us,” the letter continues. “You will do great things in our galaxy, will make our planet great. We are a little jealous of all you who are celebrating the centenary of our Soviet motherland. But we also know that you will be a little jealous of our restless young generation. We have a clear aim, a great future ahead of us and lots of things to accomplish. We have things that we can invest out hearts, brains, energy and labour in, and this is the source of our happiness.