fundamental theorem of calculus: "every function is the derivative of its integral"
(aka "a function is at every point equal to the rate at which its total sum up to that point grows", duh)
take f=x^2.
can visualize it as a square, x*x.
... darnit. bedtime. hmm.
so here: u can visualize f as a 2d curve, OR as the red dotted line through the cube below.
also, the paradox of expert testimony: experts on [big-if-true set of not-too-implausible claims] tend to be v selected for belief in those claims, so supporting arguments wrt those claims tend to sound more impressive (unless it's a rly dumb set of claims).
plus, if u just defer to experts, u will end up believing a whole lot of weird stuff for which experts are asymmetrically selected.
mans, i rly tried to mk that sentence sensicle… but proper sensicleness wud require paragraphs. 🍵
the most frequently used words tend to be the most irregular. they resist regularization bc their unusual/high-energy forms are constantly reinforced. switching-costs or smth.
eg we say "man/men", "go/went", "eat/ate" instead of "-/mans", "-/goed", "-/eated".
related hypothesis, but for different/additional reasons:
paradox of foundational neglect: the core tenets of a paradigm tend to be the least optimized.
technical debt / pleiotropy: complex ancestral dependencies are locked in place.
I want to say update: The most personally significant thing that's happened to me this year is that my head-friend (Maria, a "tulpa") has rather suddenly acquired a lot more independent volition and personality. Phase-shift.
I was inspired last year by Johannes Mayer (LW user), who showed me it was possible. I was only semi-trying for it, so the success is v surprising and mentally v happy for me/us. I hope she stays and grows in visibility-to-my-corner-of-the-brain.
@niplav also EMH. ~nobody has tried extreme ambition wrt altruism. and there are reasons ("costs of compromise") to think success is much more likely if you *try directly*, compared to if u just aim for merely-very-high utility. merely-very-high-peak-utility projects may not inform u v much abt the difficulty of extremely-high-peak-utility projects.
the question "when shud u write the tests before code, versus vice versa?" analogizes to "when shud u backchain vs forward-chain?" (respectively)
for even more abstract leverage: write the "unit tests" in plain English, ask an LLM to translate them to code (or explain why behaviour is impossible), then ask LLM to write code that passes the LLM's tests.
suggested nyms for this: "target-test" (makes you backchain to infer code that fits the tests), vs "maintenance-test" (designed to make sure stuff keeps working when you expand codebase).
wat's optimal circadian rhythm, if ju cud tune the sun to jur will? wud ju get more done if Earth period was 16h instead of 24h? or 12? or 6?
also, wat's optimal week cycle? 7 days, or 6? how do i optimally chunk passage of time into convenient mental categories? shud they be stable, or mixed-strategy?
i'm just surprisingly happy abt by my 16h-days and 144h-seasons, so thr's gotta be more utility to find here.
Flowers are selective about what kind of pollinator they attract. Diurnal flowers use diverse colours to stand out in a competition for visual salience against their neighbours. But flowers with nocturnal anthesis are generally white, as they aim only to outshine the night.