As my wife ate her porridge this morning she asked "what exactly are oats?" and it turned out to be an interesting question because of Vavilonian mimicry.
When to automate a repetitive task:
NO-BRAINER: "This is obviously going to be faster to automate than to do it by hand _even once_. Let's automate it right now, and not do it by hand at all."
FORESIGHTED: "Doing it once by hand is faster than automating it, but I'm going to have to do it a lot of times, so it still saves time to automate it first."
NEED A RUN-UP: "I don't yet understand this task well enough to automate it, so I'll do it a few times by hand first to get the idea."
RAN OFF THE RUNWAY: "Great, now I've done this by hand a few times, I think I can automate it reliably! Oh, oops, turned out I only had one more case of it left to do."
TERRIFIED OF RUNNING OFF THE RUNWAY: "This is a one-off, so it would be a waste of time to automate it, I'll just do it manually."
[next day] "Oh, oops, I made a mistake and have to do it again. But it should be fine this time."
[a month later] "Even though I've had to redo it 25 times already, surely _this_ is the last time? So it would still be a waste of time to automate it."
Everybody knows from school how to solve a quadratic equation of the form $x^2-px+q=0$ graphically. But this method can become tedious if several equations ought to be solved, as for each pair $(p,q)$ a new parabola has to be drawn. Stunningly, there is one single curve that can be used to solve every quadratic equation via drawing tangent lines through a given point $(p,q)$ to this curve. In this article we derive this method in an elementary way and generalize it to equations of the form $x^n-px+q=0$ for arbitrary $n \ge 2$. Moreover, the number of solutions of a specific equation of this form can be seen immediately with this technique. Concluding the article we point out connections to the duality of points and lines in the plane and to the the concept of Legendre transformation.
Want to know how generating functions work?
How about proving the Ramanujan identities? How about doing all that, with *pictures*?
This course I've recently found and this excellent expository video of "The Art of Bijective Combinatorics" is an absolutely stunning way of doing all that!
For those who want to test their perception of colour, I made a little game called "What's My JND"
Half a year ago, I filled in some sorry's for the massive project [1] to formalize the Fields-medal winning proof that sphere packing in dimension 8 is optimized by the E8-lattice. Last week it was announced that all remaining sorry's were filled by Gauss, an autoformalization agent. Gauss was able to build on the blueprint and other scaffolding built by the community. A few days later, Gauss also formalized the proof in dimension 24, this time working directly from the published paper, without mayor community input [3].
Since Lean verifies the generated proofs, hallucinations are not a problem.
The community now processes the generated proofs to make sure it satisfies the community standards and remains usable in the future [2].
[1] https://thefundamentaltheor3m.github.io/Sphere-Packing-Lean/
a decade or so ago, I was writing a H.264 decoder (needed a custom one for stupid reasons which of course had to do with hardware reverse engineering).
the first order of business was to implement CABAC: the final entropy coding stage of H.264 (ie. the first layer I had to peel starting from the bitstream), a funny variant of arithmetic coding. the whole thing is quite carefully optimize to squeeze out bits from video frames by exploiting statistics. in addition to carefully implementing the delicate core logic, I also had to copy-paste a few huge probability tables from the PDF, which of course resisted copy-paste as PDFs like to do and I had to apply some violence until it became proper static initializers in C source code.
furthermore, testing such code is non-trivial: the input is, of course, completely random-looking bits. and the way bitstreams work, I’d have to implement pretty much the whole thing before I got to the interesting part.
so, a few hours later, I figured I’m done with CABAC and reconstructing H.264 data structures, and pointed my new tool at some random test videos. and it worked first try! the structures my program spit out looked pretty much as expected, the transform coefficient matrices had pretty shapes and looked just as you’d expect them to, and I was quite happy with that.
and then I moved on to actually decoding the picture from the coefficients, and this time absolutely nothing worked. random garbage on screen. I spent a long time looking at my 2D transform code searching for bugs, but couldn’t find anything.
and then it hit me exactly what “entropy coding” means. I implemented something that intimately knows and exploits the statistical properties of what video transform coefficients and other structures look like, their probabilities and internal correlations, and uses that to squeeze out entropy and reconstruct it on the other end. my “looks good” testing meant absolute jack shit: I could’ve thrown /dev/urandom into the CABAC decoder instead of actual H.264 video, and it would still look like good video data at this stage until you actually tried to reconstruct the picture.
and sure enough, it turned out I fucked up transcribing some rows from the PDF around a page break or something.
10 years later, I think of this experience every time I see a vibecoded pull request, or other manifestation of AI bullshit. all the right shape, and no substance behind it.
and people really should learn to tell the fucking difference.
RE: https://fosstodon.org/@BrunoLevy01/116131000728952901
doi2bib — give us a DOI and we will do our best to get you the BibTeX entry
RE: https://zeppelin.flights/@jsnell/116092888011247851
This was a great game! A really nice combination of crossword-style hints and Only Connect/Connections misleading categories. (The explanation of the rules makes it sound more complicated than it is)
Dan Piponi
Simon Tatham
Interesting Esoterica
ARBB
keithamus
Raphael APPENZELLER
Wanda
Andre Louis
DougMerritt (log😅 = 💧log😄)