Viewing profile — fiforpg

The use of computers in mathematics has been somewhat controversial from the very start. There are of course all the computer-assisted proofs (see 4 color theorem), as well as the …

On opening the article, I was somehow expecting a mention of the large deviations formalism, which was (is?) fashionable in late 20th century, and gives a nice information theoreti…

> much more performant compared to Linux alternatives is WinMerge I have found Beyond Compare to be very good on Linux, even on large files/directories.

While you can certainly argue that some texts have more substance to them than these literary works, you cannot deny that most texts have worse prose than the books.

> abusive language/notation basically everywhere in math In most cases it is not as much abusing notation as overloading it. If you think of the context of a formula (say, adjacent…

Right, I did realize after posting that close to numbers of the form 1{hidden bit} + (1-2^-52){mantissa with all ones} the relative accuracy — corresponding to the absolute accurac…

In the context of double precision the article says > the largest integer value that can be represented exactly is 2^53 — I am confused as to why it not 2^52, given that there are …

While the idea — of shuffling a societal system a little bit to prevent it from going stale — sounds important, I'm not convinced. Random shuffling leads to good results only when …

Not necessarily—in 3d there are uncountably many non-lattice packings. They all have the same density as the FCC lattice though. To construct these packings, shift horizontal layer…

That's true — time is a big place, and a lot of things are lost in it. I for one am rather more pained over disappearing of physical objects — genomes, books, art. Plus, it is all …

If you like this kind of language archeology, check out David Anthony's The Horse, the Wheel, and Language — for how the people that spoke the Proto Indo-European language were loc…

That paper by Wigner about mathematics really did originate an entire naming scheme for such texts, didn't it.

You are correct, after posting I realized the difference. The book is rather "theorems [formulated] without words". Which is why I added that the proofs are left to the reader :P

Nice. There's an entire book like this for geometric statements. Every picture is a fact, proofs are supplied by the reader: https://users.mccme.ru/akopyan/papers/EnGeoFigures.pdf …

I'd like to offer a contrarian view. Much of the NYT article can be explained away by the Gell-Mann effect. During most of human history it was hard to maintain multiple strong bon…

> the magic is the positional numeral system — of course. In the same way the (standard) Cantor set consists of precisely those numbers from the interval [0,1] that can be represen…

Vim Startify recently showed me a quip it attributed to Alan Kay. It went something like this: Modern software is similar to the pyramids: it consists of millions of blocks held to…

Nice example. You can avoid the issue with these being non-functions (because of the vertical segments) by rotating the picture so that the (0,0)-(1,1) diagonal is horizontal. That…

Yeah, the best part is that a woodpecker's tongue wraps all the way around the back of his head and attaches in the right nostril. The head effectively serves as a spool for the to…

Annnd, this is exactly how humanity figured out astronomy before the telescopes: by taking multi-year observations and keeping detailed records! See Antikythera mechanism, Tycho Br…

Looks like this kind of soft / euphemistic language dates back to even earlier than that. Here is a YT clip of George Carlin railing against it in his 1990 special: https://www.you…

> ritual-taboo programming I like to think of it as "cargo-cult programming", along the lines of the well-known essay by Feynman.

Yes, the title is comically non-specific. It is also mildly misleading: the table of contents/abstract mention boolean logic (after John Boole, 1815–1864), set theory (Georg Cantor…

Not only written text is a faster way to communicate information, it is so because it has much bigger context window: "A moment" in a video is exactly that, a moment of time, eithe…

There is a mildly related math puzzle I learned at some point in high school (iirc): someone comes to a subway station at (uniform) random times between 6p and 8p; he notices that …