De amicitia mathematica

A few days ago, a package arrived to our apartment in Bogotá. I looked at the stamp, and yes, it had stamps from Japan. I wondered for a second what it may be, and in a flash I remembered my friend Sakaé Fuchino had said something about needing my postal address, to send me his book. But it was so long ago that I was truly not expecting anything (our postal system in Colombia went, through privatization, from being very good to being virtually non-existent: a letter from Bogotá to Bogotá might now take three or four weeks, packages sent from abroad often get lost… there is no postal system anymore).

But a miracle happened, and after so many months, the book, the beautiful book written by Sakaé reached my hands in Bogotá!

Holding the book…

The book came accompanied with a letter (in Japanese and English) explaining how to reach the electronic version for use with translators. The letter and the book are just wonders to me.

The title is Linear Algebra in Self-Confinement (I), the first volume of a projected three-volume issue on linear algebra and related subjects in mathematics and physics. A book that Sakaé wrote during the confinement period.

Of course, I immediately started browsing and leafing the pages, jumping around and looking at the beautiful images, recognizing theorems here and there in the universal mathematical language, yet many times also wondering why such formula should be where it is. Occasionally, Sakaé gives the Latin-script original name of an author of a theorem, or of course universal mathematical function names such as , , , , etc.

The subject seems to be treated with such beauty and enthusiasm by Sakaé, that I really miss having learned Japanese [or at least enough for reading mathematics]. It is not everyday that a logician, a very accomplished model theorist + set theorist embarks on a project of writing a book on linear algebra; his perspective must certainly be very personal and enlightening!

There is (as expected) a kind of (almost) humoristic touch pervading the book, and clearly visible even to non-Japanese reading eyes. It is of course in the drawings at the beginnings of chapters (a small selection next!) but [am I correct, Sakaé?] also somewhat everywhere else in the text.

Sakaé (in addition to his set theoretic+model theoretic persona) is also a pianist and a composer of short contemporary pieces, an admirer of composer Toru Takemitsu and pianist Aki Yuji Takahashi, and also of the Catalan composer Frederic Mompou. None of these connections are in book (as far as I know) in a direct, obvious way. But his way of being attuned to contemporary expressions in music and art for sure must also enrich the tone of the book. (All of this is of course guesswork; my very basic sensations from holding the book in my hands, turning pages and pages, trying to decipher what goes on.)

The only image in color represents kernels and cokernels, in the shape of an egg, with the yolk of the egg playing centerstage:

Blurring of the subject (since I can’t read) was a way to browse, for me:

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Of course, I did try google’s «lens» to see what it gave. I didn’t expect too much of it. For starters, it doesn’t recognize correctly the author’s first name (gives Akira Fuchino once and later, inside the book, Chang Fuchino). My phone was for some reason translating to French, and it really, really turns out to be funny. Not just the translation, but the way it lays out the phrases, as in a kind of Oulipo composition of a book. The title becomes Ligne de période d’auto-isolement. Many strange phrases appear, such as modèles de modèles de pression, soit K un espace surfrappé, l’on considère K comme un poids conjoint, Puisque sin @ + cos 28 = 1, cela prouve, …

I just leave here those google lens photos (and the original of the last one, for comparison if you read Japanese)…

Anyway, it is such a pleasure to receive books, real books, from real people!

サカエさん、素晴らしい本をありがとうございました！

(Sorry for not spelling your first name correctly; google did it again!)