Given a random number generator that generates points uniformly in the unit interval [0,1] can you generate uniformly distributed points in the unit circle using only algebraic functions? In a finite number of steps - so no rejection sampling, loops, recursion. No "almost always" finite either.
Just wondering about sitiations where it seems you can't avoid trig functions.
Despite Wildberger being a bit off the usual conventional paths in mathematics, he's influenced me to the point where every time I write a line of code using an angle I ask myself if I could use an alternative "rational" representation.
@BartoszMilewski Yeah, I find ultrafinitists who actually believe in way more numbers than me weird. Maybe I should call myself a zeroist. But people often do interesting math despite weird philosophy.
Saw a clip of the Agatha series actors bragging that the show has very little CG. The magic was all…practical. Who cares? What is this obsession? CG is only an issue for the director and creative people on the movie and accountants, and if it distracts by looking unreal while watching a TV show or movie. An unhealthy focus that feels anti-VFX worker, when there’s so much VFX in media that nobody realizes. This series captures the issue: https://www.youtube.com/watch?v=7ttG90raCNo&t=937s
Looked up speed of snails on Google to see if my USPS package "moving through network" from San Francisco is literally going at a snail's pace. Looks like snails would have to be 3 times faster to beat my package.
When I first came across Voigtländer's paper on speeding up free monads [1] and some of the methods that Hinze mentions [2] I was a bit bemused about why category theory had anything to say about program optimization. But now it seems obvious. Much of optimization is a lot like algebraic manipulation where you're rearranging while hoping to keep the value the same. But in particular, a really common optimization move is to write f(g(x)) as (fg)(x) where (fg) is somehow simpler (or more reusable than) than just applying g then f. Ie. associativity - which is one of the laws of category theory. I think this step also accounts for almost all of the computational reasons for using linear algebra. Eg. graphics pipelines make good use of this kind of associativity.
@pervognsen I got a bit obsessed with parallel prefix scan too after reading Danny Hillis' survey of Connection Machine techniques. Especially the parsing methods. I've noticed them resurfacing recently.
@davidphys1 I haven't thought about Feigenbaum's constant much since I was an undergraduate so I looked at wikipedia to refresh my memory and I learnt that it also arises from the rate of convergence of the size of the circles in the Mandelbrot set and I'm wondering how I got this far through life without learning this fact.
There's a retired couple living in my mom's apartment complex who seems to spend 12 hours every day sunbathing outside during the summer months. They did this when we were visiting last year and they're continuing the streak apparently. After you've lived in a warm climate for a while, the whole idea of sunbathing starts to seem obscene, but this is something else.
@BartWronski@pervognsen@neilhenning Living in NYC is my fantasy but I don't think it's ever going to come true. Maybe it's better to always have the fantasy and never be disappointed.
@BartWronski@pervognsen@neilhenning Having moved recently my wife is missing friends just 20-30 miles away whereas I'm a bit antisocial and could happily move thousands of miles. Things are changing though - she really wants to give up driving and now she's seen the reality of living close to rural areas she's beginning to understand why I like cities :)
I hate typing practice. Seriously. I've been programming computers since before most of you were born. But I need to move on from being a two fingered typist, even if a fast one,
I kept saying to myself "he's gotta be an alien", "surely he's not human", but in my heart of hearts I didn't really believe it...until...well I'm not giving you any spoilers...