Crab Computing

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There is a recent arXiv.org preprint by Yukio-Pegio Gunji, Yuta Nishiyama, and Andrew Adamatzky called “Robust Soldier Crab Ball Gate”. It describes some experiments that demonstrate an ability to implement logical gates by behavior of crabs Mictyris guinotae.

The idea is based on the billiard ball computing, but swarms of crabs are used instead of billiard balls.

Andrew Adamatzky is a professor at the International Center of Unconventional Computing, Bristol; Yukio-Pegio Gunji and Yuta Nishiyama work at the Nonlinear Science Laboratory, Kobe University.

Here is a couple of figures from the article:

OR gate
OR gate

AND gate
AND gate

Here is also a video about soldier crabs:

The article ends with an “ethical note” that informs the reader that no crabs appeared to have been injured or adversely affected by the experiments. Phew.

Theorems are aristocratic, but proofs are plebeian

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Federigo Enriques

The famous phrase “Theorems are aristocratic, but proofs are plebeian” is credited to Federigo Enriques who was well known for somewhat nonrigorous proofs. Quoting the 3rd chapter of “The Unreal Life of Oscar Zariski” by Carol Parikh:

Enriques’ easy attitude toward life seemed to extend to mathematics, for Zariski described his third-year course in algebraic geometry as “just geometry, just playing around with curves and figures, very informal, no proofs. If somebody quizzed Enriques, he would plead, ‘Ah, come on.’ If something was missing in his proof, he would say, ‘Well, this is only “dubbio critico”—or, in a phrase still credited to him, ‘Theorems are aristocratic, but proofs are plebeian.’”

* Kunihiko Kodaira remembers Zariski quoting Enriques in a less eloquent form: “‘We aristocrats do not need proofs. Proofs are for you commoners.’” In the same article Kodaira speaks of his own admiration for the intuition of the Italian geometers, “which enabled them to derive correct results by obscure reasoning” (“Algebraic Geometry of the Italian School, A Japanese Mathematician’s Reminiscence,” Creativity and Inspiration, December 1987).

Lost in Translation

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Rokoku Kibun: Kashinchō Shiroku

Here is an amazing anecdote about translations of Alexander Pushkin (who is considered to be the greatest Russian poet). Quoting from Omry Ronen, The Triple Anniversary of World Literature: Goethe, Pushkin, Nabokov:

…the item in the history of world literature that seems to be especially appropriate as an allegory of Pushkin’s reception outside Russia during the first century since his death is the title of the first Japanese translation of “The Captain’s Daughter”: “A Diary of the Butterfly Meditating over a Flower’s Soul: Astonishing News from Russia.”

The first Japanese version of “The Captain’s Daughter” appeared under this title in Tokyo in 1883. In some Russian bibliographies it is listed as “Serdtse tsvetka i dumy babochki. Udivitel’nye vesti iz Rossii” (The Heart of a Flower and the Thoughts of a Butterfly: Amazing News from Russia): See A. S. Pushkin, “Kapitanskaia dochka”, izdanie podgotovil Iu. G. Oksman, “Literaturnye Pamiatniki” (Moscow: Nauka, 1964), 278.

I must admit that I had some doubts about this story (“The Heart of a Flower and the Thoughts of a Butterfly” is way too far from “The Captain’s Daughter” and completely unrelated to the book’s contents), but I was able to find another reference:

…the first actual translation was by Takasu Jisuke (1859–1909) in June 1883, when he did a partial translation of Pushkin’s “The Captain’s Daughter”, under the fanciful title (typical for translations of that time) “A Strange Story from Russia: The Thoughts of a Butterfly in the Heart of a Flower” (Rokoku Kibun: Kashinchō Shiroku).

— Tayama Katai, Thirty Years in Tōkyō.

It would be interesting to read the translation translated back to English or Russian.

Typing French accents

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I used to get on the basic Latin alphabet, but French requires to type diacritics and the “e dans l’o” ligature.

To set it up in X.org, one need to turn on ComposeKey in XKB options, e.g. write something like "compose:rwin". Then you can do the following:

  • aigu:
    ComposeKey ' e ⇒ é
    (catégorie, géométrie, idéal, mathématiques, schéma, variété)
  • grave:
    ComposeKey ` a ⇒ à
    (algèbre, idèle, paramètre)
  • circonflexe:
    ComposeKey ^ a ⇒ â
    (fête, fonction zêta, île, polynôme, tête)
  • tréma:
    ComposeKey " a ⇒ ä
    (ellipsoïde, naïve, Noël)
  • cédille:
    ComposeKey , c ⇒ ç
    (français, garçon, leçon)
  • e dans l’o:
    ComposeKey o e ⇒ œ
    (cœur, sœur, œuf, théorie des nœuds)

Actually, my dream is to get a laptop with some “French keyboard”—not AZERTY, but something that has separate keys for Ù, É, È, Ç, À.

A French keyboard

Soixante-dix et quatre-vingts

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As everybody knows, in French, numbers like 32 and 54 are made up as usual—”thirty two” (trente-deux), “fifty-four” (cinquante-quatre), etc.—while 70 is unexpectedly “sixty ten” (soixante-dix) and 80 is “four times twenty” (quatre-vingts). It is probably less known that there are separate words for 70 (septante) or 80 (huitante) and they are used in some countries, although it is still “soixante-dix” and “quatre-vingts” in France, because…
authors of the 17th century French dictionaries decided so:

C’est au xviie siècle, sous l’influence de Vaugelas et de Ménage, que l’Académie et les autres auteurs de dictionnaires ont adopté définitivement les formes soixante-dix, quatre-vingts, quatre-vingt-dix au lieu de septante, octante, nonante. Pourtant, les mots septante, octante, nonante figurent dans toutes les éditions du Dictionnaire de l’Académie française. Encore conseillés par les Instructions officielles de 1945 pour faciliter l’apprentissage du calcul, ils restent connus dans l’usage parlé de nombreuses régions de l’Est et du Midi de la France, ainsi qu’en Acadie. Ils sont officiels en Belgique et en Suisse (sauf, cependant, octante, qui a été supplanté par quatre-vingts (en Belgique et dans une partie de la Suisse) et huitante (dans le reste de la Suisse) tant dans l’usage courant que dans l’enseignement ou les textes administratifs). Rien n’interdit de les employer, mais par rapport à l’usage courant en France, ils sont perçus comme régionaux ou vieillis.

Septante est utilisé de façon majoritaire, en Suisse, en Belgique, dans la Vallée d’Aoste et en Français de Jersey, mais également de façon minoritaire en Savoie, parfois en Lorraine, en Franche-Comté, en Provence et dans la petite communauté acadienne, géo-linguistiquement isolée, de Wedgeport, au Canada. Il est également employé en RDC, au Rwanda et au Burundi, qui étaient colonisés et administrés par la Belgique jusqu’à leur indépendance. Le terme vient du latin septuaginta qui a aussi donné septuagénaire.

Hello world!

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My name is Lyosha Beshenov. I am a graduate student in mathematics.

A picture of me

I decided to create a stand-alone blog in English for discrete personal and mathematical notes.

The blog is called “Radical Ideals”, and it’s an obvious algebraic pun:

  • on the one hand, a radical ideal is an ideal I in a commutative ring that coincides with its radical Rad(I);
  • on the other hand, a “radical ideal” is an extreme standard of perfection :D

Let’s start.