𝓙. 𝓜.

"Not everything written is important; not everything important is written."
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I strive to write about the mundane, the sublime, and all else in between. Sometimes unjustly accused of actually knowing what I'm talking about.
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Interested in consulting opportunities; DM me for further inquiries.

WordPress: https://tpfto.wordpress.com/
GitHub: https://github.com/tpfto
Shadertoy: https://www.shadertoy.com/user/tpfto
Ko-fi: https://ko-fi.com/pleasureoffiguring

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relay.momostr.pink

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Last Notes

2026-05-11 11:27:03 GMT

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I wonder if one might be able to use a percolation model to analyze this behavior...

2026-05-10 07:58:34 GMT

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in theory, the nearest university library uses LCC (https://www.loc.gov/catdir/cpso/lcco/); e.g. PL for Asian fiction, PS for American fiction, etc. In practice, as the semesters draw along, an author's body of work eventually get lumped together, even if they were originally in disparate classes.

2026-05-10 04:48:29 GMT

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In cases like these, a retraction feels not unlike closing the barn door after the entire herd has already fled.

2026-05-08 16:09:29 GMT

The thread on surprising facts you found out recently by @npub1nf4…nqe4 was getting a bit long, so I'm posting this entry separately: if I'm understanding https://en.wikipedia.org/wiki/Mohorovi%C4%8Di%C4%87_discontinuity#Exploration correctly, no manmade device has yet reached the Moho, the layer demarcating the boundary between the Earth's crust and mantle.

2026-05-08 00:34:50 GMT

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the carbon dioxide is why some wags point to Venus as what the Earth might eventually become if we don't curtail our release of greenhouse gases in the atmosphere.

2026-05-07 12:27:43 GMT

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Roland Bulirsch (https://en.wikipedia.org/wiki/Roland_Bulirsch), one of the two people who wrote a numerical analysis textbook I frequently refer to, as well as someone who wrote quite a bit on the subject of elliptic integrals, was apparently a gym buddy of Arnold Schwarzenegger. Bulirsch, along with their other gym friends, took up a collection to help Schwarzenegger emigrate to America.

2026-05-02 07:16:34 GMT

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all the focus on "growth" in various companies' quarterly reports sometimes reminds me of the "cancer cell" analogy; after all, if there's anything cancer cells are widely known for, it's unchecked growth. Unchecked, because the limits on cell division (e.g. telomeres) that are usually in place have been completely bypassed. You sometimes wonder if "we're doing okay, because this quarter, we earned just as much as the previous one" couldn't be ever considered enough.

2026-04-28 20:22:34 GMT

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one of my favorite biomimicry examples is the redesign of Japan's bullet trains based on the kingfisher's head and beak, which made them more efficient and streamlined. See e.g. https://biomimicry.org.nz/the-shinkansen-and-the-kingfisher-a-tale-of-biomimicry-in-high-speed-rail-design/

2026-04-23 23:44:52 GMT

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The last one not being threaded was actually deliberate, since it was a parenthetical remark at best. :) Thanks for checking!

2026-04-23 21:58:40 GMT

(This is all pretty well-known, but I kind of wanted to practice how to do threaded toots, the same way @npub1nf4…nqe4 sometimes does with various interesting topics.)

2026-04-21 11:32:44 GMT

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"trawling" and "trolling" are two completely different methods of fishing: https://alaskagoldbrand.com/blogs/news/what-is-the-difference-between-trolling-and-trawling-alaska-gold-seafood ; the latter is what lent its name to the annoying internet activity.

2026-04-20 23:26:47 GMT

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most people, when they think of green-colored gemstones, tend to prefer jade. I, for one, like peridot's colors more. :D

2026-04-19 23:55:08 GMT

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it's interesting that Seidel's wiki entry makes no mention whatsoever of the fact that she was about to be evicted from her residence a little while before she passed. I suppose it's the nature of the thing, but just how many wiki articles on people gloss over documented facts about their lives?

2026-04-18 21:26:41 GMT

Since @npub1nf4…nqe4 posted about tetrahelices (https://en.wikipedia.org/wiki/Boerdijk%E2%80%93Coxeter_helix) the other day, I thought I'd share something I recently made on Shadertoy: https://www.shadertoy.com/view/sfBXDR . If you look at the implementation closely, I generate the points of the tetrahelix through a recursion relation, instead of using the trig formulae in the wiki page. #math

2026-04-16 17:15:51 GMT

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at an extreme, consider the following (non-elementary!) hypergeometric function:\( a\, {}_4 F_3\left({{\tfrac15,\tfrac25,\tfrac35,\tfrac45}\atop{\tfrac12,\tfrac34,\tfrac54}}\middle|\frac{3125 a^4}{256}\right) \) which can be shown to be a root of the quintic \( x^5-x+a \) (see e.g. Glasser's paper, https://doi.org/10.1016/S0377-0427(00)00287-9 for details).

2026-04-16 07:46:24 GMT

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as someone who works with "special functions": I have a feeling someone (or multiple someones) is conflating "algebraic" with "elementary". Let me explain, starting with an analogy: in the so-called "casus irreducibilis" of cubic equations, we readily accept the use of trigonometric or hyperbolic functions (certainly elementary!) to represent the roots of a cubic polynomial. For quintics, we need theta functions or hypergeometric functions, which are most assuredly not elementary, but evaluate to algebraic numbers. (Then we need Riemann theta for roots of polynomials of even higher order!)

2026-04-13 09:23:31 GMT

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if the tetrahelix has unit edge length, the inner cylinder has radius \( \frac{\sqrt{18}}{20} \), and the outer cylinder has radius \( \frac{\sqrt{27}}{10} \) . So the circumradius-inradius ratio is \( \sqrt{6}\approx 2.4495 \), which is less than the corresponding ratio of 3 for the regular tetrahedron.

2026-04-13 02:13:06 GMT

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personally, I find the fact that you can inscribe and circumscribe cylinders on the tetrahelix very cute.
https://media.mathstodon.xyz/media_attachments/files/116/394/971/934/415/956/original/46e1754adb21cc02.png

2025-10-04 10:57:18 GMT

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if it isn't already apparent, the supramolecular guys have a most whimsical naming sense.

2025-10-04 10:45:37 GMT

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one very interesting analogue is the drug sodium nitroprusside (https://en.wikipedia.org/wiki/Sodium_nitroprusside), which is used in emergency situations that require lowering a person's blood pressure very quickly. A neat resource for looking up crystal structures of these beasties is the CSD, e.g. https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=DOJJAP05

2025-10-04 10:22:39 GMT

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...and well, if you or anyone else reading this thread has found host-guest chemistry (supramolecular chemistry) to be really interesting, I would then invite you to look up cryptands, calixarenes, scorpionates, pillararenes... it's a really deep and fascinating rabbit hole! ;D

2025-10-04 10:09:42 GMT

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in the bonding model I am familiar with, each oxygen is basically "sharing" an electron pair with the coordinated cation (i.e., a dative bond); I am not up to date with the supramolecular literature to check if they have refined this model since I last looked at it decades ago... :D

2025-10-04 10:06:13 GMT

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it took me quite a while to find a "nice" picture modeling the bonding in the cesium electrode (and also something you can cite, in case you want to go down this rabbit hole). Page 232 of Steed and Atwood (https://www.wiley.com/en-us/Supramolecular+Chemistry%2C+3rd+Edition-p-00029542) has the following lovely figure:
https://media.mathstodon.xyz/media_attachments/files/115/315/292/897/916/411/original/9446b78d26cfef37.png

2025-10-04 09:12:02 GMT

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and at one interesting extreme, you have electrides (https://en.wikipedia.org/wiki/Electride), where you have a large enough cation like cesium trapped in a crown ether, and a single electron serves as the corresponding anion. Pretty neat stuff!

2025-10-04 09:07:43 GMT

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most commonplace crown ethers are ultimately built out of ethylene oxide, which has two carbons and one oxygen; this is why they have crown sizes a multiple of 3 (12-crown-4, 15-crown-5, 18-crown-6, etc.)