I thought of a use for LLMs but I don't see myself having time to code it up for a few weeks. A touch typing tutor. It should be easy to take llama.cpp and adapt it to generate the next token based on which letters and words I need most practice with. So you get to practice with plausible sentences that still train you where you need it.
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.
@modularformsboy@dpiponi This wouldn't be a good choice anyway. You can compute {sin(π x), cos(π x)} to very high accurate with few term using a minimax approximation. Add in the symmetry of the problem and you kill off the range reduction that would be needed for a "standard" sincospi function.
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@dpiponi - "He's such a dyed in the wool Platonist, I can't stand it. According to him rational numbers "exist" but infinities don't."
What I find most annoying is that people who say some numbers exist and others don't never go into much detail about what it means for a number to "exist". I could be perfectly happy saying numbers exist, with one definition of "exist", or saying they don't, with some other definition. I can even imagine saying some numbers exist and others don't, with some more contorted definition of "exist". But most people who say some numbers exist and others don't seem to use a secret personal smell test for existence. Numbers that smell bad to them don't really exist - and they're shocked that I lack their sense of smell.
One of my favorite visual effects from pre-CG days was the shield effect in 1984's Dune. Lots of work with an optical printer. Underrated, I think, as I've never heard anyone talk about it.
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.
@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.
I know I must be a uniquely weird individual because in decades of using tabbed web browsers I've still never wanted to close tabs to the right and I've often wanted to close tabs to the left.
@dpiponi Yup. Two of my very frequently used features in Firefox: move tab to the right and close tabs to the left. I almost wish the move-to-front was automatic when switching browser tabs like with the alt-tab window order; maybe there's an extension for that.
For me, and presumably countless others, a computer has always been primarily a creativity tool. But I think this idea may be novel or unusual to a large segment of the population.
One of the weirder bugs I've experienced: you know how you're always being told to make sure caps lock is off when you enter your password? My Mac is currently enabling caps-lock at login and you can't disable it. It took a long time to deduce this was the problem but surprisingly I was able to log in after going round a few loops and realising an obvious trick...
@dpiponi I always remap caps lock to be another control key, just to go easy on my little finger. Side benefit, I guess I get to dodge mysterious and annoying bugs.
@4raylee@dpiponi I annoys me greatly that I still have to poke around in the guts of my OS in 2024 to get rid of Caps Lock. I don't want it, don't need it, haven't needed it since maybe the 80ies (and I'm not even sure then). And I don't change computers often enough that I can just do "whatever I did last time" - every new computer I have to learn a whole new set of nonsense to disable Caps Lock. 🙄
If some company made a decent keyboard that is exactly identical to all other keyboards but simply doesn't have a Caps Lock key, I think that would be a viable product...
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,
@dpiponi Heh, I almost had PTSD just reading your original post and seeing that screenshot. We had this ancient schoolmarm for our touch typing class and the teaching method was based on a DOS program where you had to touch-type in time to a recording of Bach playing from a cassette recorder (I wish I was joking--the DOS program was called PC Bach). Needless to say, it took me longer than it otherwise would have to fall in love with Bach when I matured, owing to that bad experience.
I have to admit I enjoy seeing familiar sci-fi plots appearing as papers. This one proposes that AIs cause civilizational collapse, explaining the Fermi "paradox".