fiforpg

7 ms·

1.
by fiforpg 3mo ago
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 partially-assisted ones (see Viazovska et al on packing prob
2.
by fiforpg 6mo ago
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 theoretic view of the CLT. Or something like that. There's a to
3.
by fiforpg 9mo ago
> 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.
4.
by fiforpg 1y ago
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.
5.
by fiforpg 1y ago
> 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 paragraphs) as its implicit arguments (think lambda
6.
by fiforpg 1y ago
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 accuracy of a single bit in mantissa — is about 2^-53. The hidden b
7.
by fiforpg 1y ago
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 52 bits of mantissa, so relative accuracy is 2^-52, which
8.
by fiforpg 1y ago
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 it is combined with a good fitness estimate (see: natur
9.
by fiforpg 1y ago
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 layers of FCC horizontally with respect to each other. It is conj
10.
by fiforpg 1y ago
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 the more exciting to think about what caused some langu
11.
by fiforpg 1y ago
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 located in time and space.
12.
by fiforpg 1y ago
That paper by Wigner about mathematics really did originate an entire naming scheme for such texts, didn't it.
13.
by fiforpg 1y ago
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
14.
by fiforpg 1y ago
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 Caution: proofs of some of t
15.
by fiforpg 1y ago
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 bonds anyway; long distance communication pre-internet was
16.
by fiforpg 1y ago
> 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 represented using only 0 and 2 in their ternary expansion (repeat
17.
by fiforpg 1y ago
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 together by nothing but sheer weight and the labor of thousand
18.
by fiforpg 2y ago
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 way you are talking about a sequence of continuous function
19.
by fiforpg 2y ago
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 tongue. Awesome technology.
20.
by fiforpg 2y ago
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 Brahe, etc. Arguably the entire Greek epistemology was so soli
21.
by fiforpg 2y ago
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.youtube.com/watch?v=o25I2fzFGoY
22.
by fiforpg 2y ago
> ritual-taboo programming I like to think of it as "cargo-cult programming", along the lines of the well-known essay by Feynman.
23.
by fiforpg 2y ago
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, 1845–1918), Curry-Howard correspondence (middle 20th
24.
by fiforpg 2y ago
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, either a frame or a couple of seconds that will stay in
25.
by fiforpg 2y ago
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 the first train he observes arriving at the same station is
26.
by fiforpg 2y ago
Just as the author of this blog, I found Dark Sky UI uniquely concise and informative. I managed to somewhat replace it with not one, but two apps (on Android): - OpenWeather for a dense, one-page view of short-term upcoming conditions (tem
27.
by fiforpg 2y ago
From a quick reading of the footnote, it seems that Turing uses optimal transport distance rather than the Hausdorff distance. Convergence in the latter implies convergence in the former, but not the other way round.
28.
by fiforpg 2y ago
This Quanta trickled through my head Like water through a sieve.
29.
by fiforpg 2y ago
One thing I remember liking in this post was his personal homepage (a little further down). There has been a recent HN discussion of Glance, a personal dashboard, but Wolfram's seemed more effective.
30.
by fiforpg 2y ago
Nice work! Emacs folks may also like the Maxima mode, a very capable interface to a full-blown CAS: https://www.emacswiki.org/emacs/MaximaMode

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