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.
@BoydStephenSmithJr@dpiponi This has the same number of points on each circle around the origin, meaning the density goes to ∞ at zero.- definitely not uniform.
@dpiponi@BoydStephenSmithJr Yeah - I am definitely trouble coming up with the right words when it comes to ... "density"(?) of things. One of these millenia I'll write up where I think there's some missing nomenclature (and or ask whether maybe it exists and I'm just unaware of it)...
@Greenseer@Walrus@lowqualityfacts
It's definitely true that there are 35 atoms in the universe, though. Maybe even more. But certainly at least those 35.
@RubyTuesdayDONO
ChatGPT gives you the most plausible or most likely answer you could expect if you asked the same question somewhere on the internet (or, more precisely, that parts of the internet that was used for training). It is quite literally a mirror, that shows you what humans say and do.
When you see ugliness in a mirror, it does not behoove a self-aware being to try to blame the mirror.
Microsoft Teams continues to reveal its true nature as a billion sprint goals in a trenchcoat:
When you attach an image to a post, it's saved at the top of the Sharepoint folder belonging to the channel. (So the "files" tab becomes a cluttered mess, but that's not what I'm cross about now)
As well as restrictions on valid filenames, filenames of attachments have to be unique.
So if you've attached drawing.png once before, and upload another drawing.png, Teams asks if you want to replace the original, or keep both. If you keep both, it adds (1) to the filename.
... unless there's already a "drawing (1).png", in which case it asks you AGAIN what you want to do.
Is there a Big Brain Cloud Services reason it can't automatically find the smallest number that works?
"Vigo the Carpathian. Born 1505, died 1610. He was poisoned, stabbed, shot, hung, stretched, disembowled, drawn and quartered... Not exactly a man of the people"
I guess the best way to get spectacular improvements in the performance of your code is to do something spectacularly inefficient in the first version.
I’ve been working on a project that needs to perform computations on a quantity X along with several dozen of its derivatives wrt a parameter t, i.e. X'(t), X''(t), ... This is a form of “automatic differentiation”, but with a large number of derivatives.
There are simple rules for performing basic arithmetic on these vectors of derivatives; addition is trivial, and multiplication only grows linearly with the order of the derivative in the number of terms in each formula.
But the derivatives of 1/X and √X, written as sums of products of powers of derivatives of X, scale horrendously: the number of terms for the nth derivative is equal to the number of integer partitions of n:
And for a while, I thought, well, that’s just the way it is, I’ll have to live with it.
But luckily that turned out to be very naive! In fact, you can just write down the formula for the derivatives of a product, X(t)Y(t) = 1, and then solve that system by back-substitution to get all the derivatives of Y from those of X. Similarly for the square root, from Y^2(t) = X(t).
So the payoff for being dumb in the first place was the glorious feeling of seeing my code now running exponentially faster than before!
Properly photographing a 3.5" floppy disk for archival is annoyingly complicated. The label has THREE sides!
I've already built an automated system to take a picture of the front of a disk, but really I need to take THREE photos if I want to get the whole thing.
That means either three cameras or I need to rotate the disk 90° and then 180°, which is going to really stress the limits of my mechanical engineering skills.
@foone@The4thCircle I'm almost certain for the money you're spending on multiple cameras and 3d printed gadgets you could just hire a couple poor slobs on fiverr and make them take the pictures by hand...
Pals, what's the least egregious TV I can buy today, in the UK?
I want as little "smart" internet-connected nonsense as possible. Not bothered about 4k or massive size, but it should sound and look good.
You don't play the piano and you don't know anyone who does. What you do have is money. Lots of it. You are either a doctor or a lawyer by profession. The piano is likely placed in a prominent location in your expansive house, such as tucked under the stairs, where the sound can be muffled, or next to a bay window, where it can echo weirdly off the glass. The lid of your grand piano is always closed. There are photographs of you and your wife and kids arranged tastefully on the top and a soft accent lamp on the left hand side of the music desk which absolutely will not illuminate any part of the music adequately.