2023 September 22


Sigils of our name

William Shatner - Common People

Joy Oladokun & Noah Kahan - We’re All Gonna Die

Continuing my obsession with the Monty Hall problem, from Paul I learned of ChatGPT’s difficulties with handling things that sound like but are not the Monty Hall problem.

Many centuries ago there were four small islands in the bay of Algiers. While long gone – they joined the African mainland in 1525 – their legacy remains in that Algeria, the largest country in the world with no inhabited islands1Kazakhstan is larger and land-locked, but has an island in the Caspian sea with a population of 5, has a named derived from al-Jazair, arabic for “the islands”. In other potential etymological confusion, Niger and Nigeria to the south are unrelated to the latin niger “black”, but rather come from the River Niger, whose name likely comes from the local Tuareg egereou n-igereouen, also known in arabic as nahr al-anhur “river of rivers”.

What is the meaning or purpose behind obscure character ⍼ U+237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG ARROW, also called “angzarr” ⍼? No one knows. Records of how it was added to unicode show that it indirectly came from a private organization’s database of symbols, but the organization is now defunct and how it got added to that database is lost. The earliest known glyph for it appears second from the left in the image above. (Note: above image is black-on-transparent and invisible if viewing this page in dark mode; open in a new tab.)

Motzkin’s polynomial, discovered in 1967,

x^2y^4 + x^4y^2 - 3x^2y^2 + 1

is the first known polynomial that is nonnegative everywhere but not a sum of squares. (Nonnegativity follows from the AM-GM inequality on (1, x^2y^4, x^4y^2) or by multiplying by 1 + x^2 + y^2 and then expressing as a sum of squares.) The existence of such polynomials was proven by Hilbert in 1888. Indeed, testing for SOS is efficient but testing for nonnegativity is NP-hard.

Expansion of an ideal gas into vacuum is isothermal, but for real gases it is believed there is an “inversion temperature” below which Joule expansion is cooling, and above which Joule expansion is warming. For helium this is 40 K, for hydrogen this is 200 K, and for other gases it is too high to have been measured.

Gorillas spend an hour building a new nest every day, even if they plan on sleeping in the same spot.

GitHub Copilot” is a context-aware code autocompletion tool that was trained on a huge repository of publicly-available code. It may be a little too overfit to its dataset, however, because given little more than the prompt “// fast inverse square root” it produces the exact source code for the inverse square root function famously used in Quake III Arena – comments and all. Nonetheless, while I am skeptical of its actual utility, it is capable of some very flashy results.


The build and testing of a lego submarine made with a glass food container for floatation, magnets, and ballast. The radio receiver and power supply are inside the container to keep dry, and are coupled to the propellers with magnets.

The Marsh Screw Amphibian (video) used giant screws instead of convential wheels, going on water or land, and could travel sideways as capably as forwards; it got up to 20 mph on packed snow but struggled on soil or roads. Another exotic off-terrain vehicle prototype was the Rolligon (video): it had giant, deformable, low-pressure tires the width of the vehicle.

Five time world scrabble champion Nigel Richards, the only player to have won more than once, started playing scrabble at the age of 28 because his mother wanted to find a game she would beat him at. A computer analysis of 919 moves he’s made in scrabble endgames (where there is perfect information because all tiles have been drawn) showed he made suboptimal moves only 11 times; the best scrabble AI made 41 errors in those positions, whereas top 10 players on average error 47% of the time. Unrelated: a tournament scrabble game with no words.


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