I consider it the most beautiful piece of code I've ever written and perhaps my one minor contribution to human knowledge. It uses a method I invented, is just a few lines, and converges in very few iterations.
People used to reach out to me all the time with uses they had found for it, it was cited in a PhD and apparently lives in some collision plugin for unity. Haven't heard from anyone in a long time.
It's also my test question for LLMs, and I've yet to see my solution regurgitated. Instead they generate some variant of Newtons method, ChatGPT 5.2 gave me an LM implementation and acknowledged that Newtons method is unstable (it is, which is why I went down the rabbit hole in the first place.)
Today I don't know where I would publish such a gem. It's not something I'd bother writing up in a paper, and SO was the obvious place were people who wanted an answer to this question would look. Now there is no central repository, instead everyone individually summons the ghosts of those passed in loneliness.
Silvanus P Thompson | Calculus Made Easy (html book) - https://calculusmadeeasy.org/ (This shouldn't be your only exposure to Calculus. It is more for building intuition.)
The Discrete Mathematics course above is probably the most important for your work. In fact I would look for more Discrete Mathematics courses if I were you as it is far more important than anything else here.
Marco Taboga | Probability and Statistics & Matrix Algebra (html book, need calculus) - https://www.statlect.com/
On YouTube you can literally watch a good lecture course for just about any typical undergraduate course. You just need to know where to look. Also there are even some really good master's degree courses out there.
Of course the only way to really learn the mathematics deeply is to "learn by doing", aka problems and proofs.
There are a ton of channels starting to pop up like Grant's 3B1B (I find like a new one every week). He had a contest recently so maybe look at some of the winners.
Lastly this is pretty useful if you get into higher mathematics:
My list of recommended Youtube subscriptions, built from over a decade of curation.
No Particular ordering within the categories.
(D) means possibly defunct, hasn’t uploaded in awhile.
A tier educational / edutainment
3Blue1Brown - High level math, explained simply with good animation.
Captain Disillusion - Visual Effect explainers
Everyday Astronauts - Deep dive rocket science explainers (also a mix of news and live streams)
Game Maker’s Toolkit - Video Game design breakdowns
Jay Foreman - Mostly humorous looks at maps, best in video sponsor spots on Youtube
Kurzgesagt - In a Nutshell - Animated with a board science focus
Mark Rober - Engineer tackles interesting projects
Mathologer - Long and novel math explainers
Minute Earth - Ecology focused animation
Minute Physics - Physics focused animation
Numberphile - Math and number based curiosities
PBS Infinite Series (D) - Math
Primer - Simulated economy and behavior
Rare Earth (D, likely to pick up after the pandemic?) - Stories from traveling around the world
SmarterEveryDay - Science meets engineering, often meets highspeed camera
Stand-up Maths - Humorous math
Steve Mould - Everyday life curios phenomena underlined by physics
Technology Connections - Deep dives into non-computer technology in your home
Tom Scott - Interestings things, places, and ideas
Veritasium - General science, slight physics focus
Scott Manley - deep dives into space news, kerbal space program
Good educational edutainment (but not quite A-tier by my personal preference)
Ben Eater - Computing projects made with low level electronic components.
Code Bullet - Coding Projects, often automating video games
Colin Furze - Crazy physical builds by an insane Brit
EngineerGuy (D) - engineering explainers
Jill Bearup - Fight choreography
Jordan Harrod - AI / Machine learning
LeiosOS - Various computer science
Linus Tech Tips - Computer projects and products mostly with a gaming focus
Lock Picking Lawyer - See every lock in existence get easily defeated by an expert
Noclip - Video Game Documentaries
Objectivity - Archived objects from science history
PBS Space Time - Astrophysics
People Make Games - Video Game Documentaries
Periodic Videos - Chemistry, and a deep dive into every element on the periodic table
Practical Engineering - Civil engineering
Primitive Technology (D) - Ancient techniques for building and crafting, relaxing
Scam Nation - Small scale magic tricks
Sebastian Lague - Coding Adventures
Simone Giertz - Previously queen of shitty robots, maker style projects
SingingBanana (D-ish, appears on numberphile mostly now) - Math
Sixty Symbols - Astrophysics explained by professors
Stuff Made Here - Engineering/crafting projects
Think Twice - Math animations
Tom Stanton - 3d printer powered home engineering projects
Vihart - math
vlogbrothers - Mixed in with nerdy vlogs are some gems of thought and introspection on our world
Zee Bashew - Animated D&D spells and more
BrainCraft - Human psychology
Computerphile - Computer Science concepts, explained
SciShow / SciShow Space - Science news
Video Essayists
Errant Signal - video games
Joseph Aderson - video games
Mathewmatosis - video games
Writing On Games - videogames
Every Frame A Painting (D) - movies
The Royal Ocean Film Society - movies
Just Write - movies and literature
Humor
Brian David Gilbert - Surreal skits
Casually Explained - Witty introspection on life
CrackerMilk - Short, weird, to the point
David Mitchell’s Soapbox (D) - British rants
Felix Colgrave - Animation, probably tied to drug use
Joel Haver - skits/animation
videogamedunky - video games
Bisqwit's discussion of dithering is outstanding. He presents a very impressive algorithm for arbitrary-palette dithering that is animation safe.
> This paper introduces a patent-free positional (ordered) dithering algorithm that is applicable for arbitrary palettes. Such dithering algorithm can be used to change truecolor animations into paletted ones, while maximally avoiding unintended jitter arising from dithering.
He demonstrates it "live coding" style in this[1] video where he writes a demo in 256 colors of a "starfield" animation with color blending and Gaussian blur style bloom. The first animation at 6:33 using traditional ordered dithering has the usual annoying artifacts. The animation at 13:00 using an optimal palette and his "gamma-aware Knoll-Yliluom positional dithering" changed my understanding of what was possible with a 256 color palette. The animation even looks decent[2] dithered all the way down to a 16 color palette!
If that wasn't crazy enough, he also "live codes" a raytracer[3] in DOS that "renders in 16-color VGA palette at 640x480 resolution."
Loved the article, but loved even more to learn about MicroPython.
As an amateur programmer that has never actually physically handled hobby micro-controller type boards, but has read a lot about them, it was amazing to be able to try out the emulator at https://micropython.org/unicorn/
Make the leds blink, see how servo control works etc, all in the browser without having to actually buy any hardware! I had never seen anything like this.
Would love if others could point me to more advanced emulators of hardware micro controllers (if there is such a thing!)
I think my favorite (in terms of humor) is a commit from mpv complaining about locales and encodings. You can practically feel the committer's sheer frustration.
I feel obligated to mention in every one of these threads the wemos D1.
I actually have a tough time explaining just how incredible this board is. You can program it in the Arduino environment, meaning if you are doing any hobby electronics, you're probably already really familiar with the programming modalities.
It comes with a programmer, and power regulator. No fussing with anything like you might have to with a bare ESP8266.
It also has WiFi. It is the magic internet of things that I swear everybody was dreaming about 5 years ago. Go buy 10 of them. They're my favorite favorite favorite general purpose dev board right now, and actually they're so cheap that I have no problem putting them into "finished products"[1].
[1]: I build custom/one-off large scale installation pieces and hardware prototypes. Almost every single one of them has an arduino-ish device in it somewhere.
It does seem that RISC-V corrects a number of these design eccentricities. SPARC did not move the market an inch with an open release - perhaps MIPS will fail just as spectacularly.
You know who's awesome at Excel? Martin Shkreli. You know, the Wall Street asshole who's in jail now? A while back, someone told me "hey, dude, there are these videos on YouTube where Martin Shkreli uses Excel, and they're fucking magic. It's like the first time you watched someone who's really good at Vim. "
It's true: [0]. Say what you will about that little heartless douchebag, he's fucking awesome at using Excel.
You're right that many demos simply exist to showcase technical brilliance, but many in the demoscene are starting to trend further towards expressing artistic ability. Some examples off the top of my head:
Here are the first few exercises, all for while juggling 3. In all of the following X and Y should be taken as all possible combinations of Left and Right.
* Throw really high from hand X, catch in hand Y, and carry on;
* Throw one from hand X, hold up the ball in hand not(X), catch ball back in hand X and carry on;
* Do that twice in a row with the same hand;
* Do it with the left, then immediately with the right;
* Do it with the right, then immediately the left;
Email me when you've done all those a minimum of 10 times each.
I know a spelling corrector is not the same thing as a spelling checker, but this is too good an opportunity to pass to promote Martha Snow's hilarious poem 'Spell Chequer':
Eye halve a spelling chequer
It came with my pea sea
It plainly marques four my revue
Miss steaks eye kin knot sea.
Eye strike a quay and type a word
And weight four it two say
Weather eye am wrong oar write
It shows me strait a weigh.
As soon as a mist ache is maid
It nose bee fore two long
And eye can put the error rite
It's rare lea ever wrong.
Eye have run this poem threw it
I am shore your pleased two no
It's letter perfect awl the weigh
My chequer tolled me sew.
Donald E. Knuth cites it in TAOCP while discussing Balanced Ternary:
"Cauchy pointed out that negative digits make it unneccesary for a person to memorize the multiplication table past 5x5." [Comptes Rendus Acad. Sci. 11 (Paris, 1840), 789-798]
But he doesn't elaborate on it further, and neither does anyone else from what I can tell, and I have yet to figure out the trick. (I currently try to teach myself to EFFICIENTLY do all my mental arithmetic in balanced ternary - not an easy task!)
I was excited about this when it was all the rage. It speaks to me as a programmer. Some years later, I stumbled upon this excellent article by an artist considering the problem from the art perspective: http://www.dinofarmgames.com/a-pixel-artist-renounces-pixel-...
Which is a lot better than reading someone tell you about this new idea that is called "capsules" but doesn't go into detail. The only thing is that, when this presentation was given, it seems they hadn't worked much more than MNIST (so the new thing now would be the toys-recognition net).
I consider it the most beautiful piece of code I've ever written and perhaps my one minor contribution to human knowledge. It uses a method I invented, is just a few lines, and converges in very few iterations.
People used to reach out to me all the time with uses they had found for it, it was cited in a PhD and apparently lives in some collision plugin for unity. Haven't heard from anyone in a long time.
It's also my test question for LLMs, and I've yet to see my solution regurgitated. Instead they generate some variant of Newtons method, ChatGPT 5.2 gave me an LM implementation and acknowledged that Newtons method is unstable (it is, which is why I went down the rabbit hole in the first place.)
Today I don't know where I would publish such a gem. It's not something I'd bother writing up in a paper, and SO was the obvious place were people who wanted an answer to this question would look. Now there is no central repository, instead everyone individually summons the ghosts of those passed in loneliness.