Mimicry

January 13, 2008

The typical working mathematician is a Platonist on weekdays and a formalist on Sundays. That is, when he is doing mathematics he is convinced that he is dealing with an objective reality whose properties he is attempting to determine. But
then, when challenged to give a philosophical account of this reality, he finds it easiest to pretend that he does not believe in it after all.

(*)

From one of Reuben Hersh’s essays.

1+1

January 7, 2008

Page from Russel/Whitehead’s “Principia Mathematicae”

(*)

Particularly elegant proof of a well-known equality, excerpt from the infamous “Principia Mathematica” by Russel/Whitehead.

January 7, 2008

До—светания, — как бы прощаясь глухо,
Тело есть лишь продукт разложенья духа,
Слабый свет — продукт разложенья тела,
Но, как сказано кем—то, не в этом дело.

Из—за поля Хиггса* на берег Стикса
Выбираться, теряя остатки смысла,
Да и голоса, словно бельмо на глотке,
Так что не докричаться гребца и лодки,

Над водой, над которой еще светлеет
Слабый свет. Постепенно и он слабеет,
Потому что, подрагивая, уплывает с сетчатки на дно
Золотой пятак, медный обол, пятно…

(*)

Квантовое поле Хиггса — причина, по которой в ранней Вселенной изначально безмассовые частицы приобрели массу. В результате люди сделаны не из света, как ангелы, а из тяжелой материи. Выдумка трех нобелевских лауреатов, эквивалент первородного греха.

(**)

Yu. I. Manin’s poem “ In memory of Joseph Brodsky“, (*) is his as well.

Amalgames

January 2, 2008

Portrait-collage of Joseph Brodsky, by Dmitri Evtushenko

(*)

portrait-collage of Joseph Brodsky, by Dmitriy Evtushenko

Zero-summ games

January 2, 2008

Tarski told me the following story. He tried to publish his theorem [“For all infinite sets X there exists a bijection of X to X × X” implies “Axiom of Choice” – A.C.] in the Comptes Rendus Acad. Sci. Paris but Fréchet and Lebesgue refused to present it. Fréchet wrote that an implication between two well known propositions is not a new result. Lebesgue wrote that an implication between two false propositions is of no interest. And Tarski said that after this misadventure he never tried to publish in the Comptes Rendus.

(*)

From “A System of Axioms of Set Theory for the Rationalists”, Jan Mycielski

Земную жизнь пройдя до первой трети,
мне жребий пал покинуть город Пети

Saint-Petersburg bay