January 6, 2023

Dear Nikola,

a) Thank you for your visit.

b) Thank you for your letter. From the time I received it, I have spent most of my waking hours reflecting on the issues about which you comment,

c) Rilkes Poem:
Ich fürchte mich so vor der Menschen Wort.
Sie sprechen alles so deutlich aus:
Und dieses heißt Hund und jenes heißt Haus,
und hier ist Beginn und das Ende ist dort.
Mich bangt auch ihr Sinn, ihr Spiel mit dem Spott,
sie wissen alles, was wird und war;
kein Berg ist ihnen mehr wunderbar;
ihr Garten und Gut grenzt grade an Gott.
Ich will immer warnen und wehren: Bleibt fern.
Die Dinge singen hör ich so gern.
Ihr rührt sie an: sie sind starr und stumm.
Ihr bringt mir alle die Dinge um.

was written when he was only 23 years old. I argue that in this poem words (Worte) and things (Dinge) are surreptitiously synonymous, and that this poem is inherently contradictory, in a manner analogous to Bertrand Russell's paradox, inasmuch as the poem presents itself as a set of words which repudiates all sets of words. I read it as a lyrical version of the liar's paradox: its message is true only if its message is not true. The assertion "dass wir nicht sehr verlässlich zuhaus sind in der gedeuteten Welt", (that we are not reliably at home in the rationalized world) is the consistent and pervasive theme of Rilke's poetry throughout his life. I find it a daunting challenge to interpret the evangelizing excursions of mathematicians and physicists into the realms of the irrational. All I know is to proceed step by step to try to understand.

d) Your reference to Georg Cantor's argument from the diagonal to the effect the "set of natural numbers" is not denumerable gave me to think. To enumerate is to count. If an entity is a number, it can be counted. Infinity is not susceptible to addition, subtraction, multiplication or division.  If one adds one additional guest to Hilbert's Hotel the infinity of existing rooms - and existing guests - collapses into a finite collection, because when one purports to add to infinity, it reveals itself as a fiction and collapses. Cantor's diagonal is meaningless except as a finite number.  The set to which that finite number might be added is demonstrated to be finite and ennumerable if only on account of that addition. Such is my worm's eye view of set theory.

Stay well and content. Let's keep in touch.
EJM