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. 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, substraction, 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 keepin touch. EJM Cantors diagonal argument entails the premise that an infinite list might be denumerable or countable. Wer trägt des Himmels unzählbare Sterne ... https://www.google.com/search?q=Youtube+Beethoven+Die+Himmel+ruehmen+des+ewigen+Ehre+Fischer-Dieskau&client=ubuntu&hs=ibf&channel=fs&ei=Fq-4Y-2SJNav5NoPxauC4Ac&ved=0ahUKEwjt9YntjLT8AhXWF1kFHcWVAHwQ4dUDCA8&oq=Youtube+Beethoven+Die+Himmel+ruehmen+des+ewigen+Ehre+Fischer-Dieskau&gs_lcp=Cgxnd3Mtd2l6LXNlcnAQDDoKCAAQRxDWBBCwAzoECCEQCjoFCAAQogQ6BQghEKABOggIIRAWEB4QHToFCCEQqwJKBAhBGABKBQhAEgExSgQIRhgAUPtBWI_rAWChgwJoAXABeACAAYMBiAGMDpIBBDE2LjSYAQCgAQHIAQbAAQE&sclient=gws-wiz-serp#fpstate=ive&vld=cid:6c738455,vid:ZuV6W5hMqMI https://www.google.com/search?q=Youtube+Beethoven+Die+Himmel+ruehmen+des+ewigen+Ehre+Fischer-Dieskau&client=ubuntu&hs=ibf&channel=fs&ei=Fq-4Y-2SJNav5NoPxauC4Ac&ved=0ahUKEwjt9YntjLT8AhXWF1kFHcWVAHwQ4dUDCA8&oq=Youtube+Beethoven+Die+Himmel+ruehmen+des+ewigen+Ehre+Fischer-Dieskau&gs_lcp=Cgxnd3Mtd2l6LXNlcnAQDDoKCAAQRxDWBBCwAzoECCEQCjoFCAAQogQ6BQghEKABOggIIRAWEB4QHToFCCEQqwJKBAhBGABKBQhAEgExSgQIRhgAUPtBWI_rAWChgwJoAXABeACAAYMBiAGMDpIBBDE2LjSYAQCgAQHIAQbAAQE&sclient=gws-wiz-serp#fpstate=ive&vld=cid:6c738455,vid:ZuV6W5hMqMI Psalms Chapter 147 1 Praise ye the LORD: for it is good to sing praises unto our God; for it is pleasant; and praise is comely. 2 The LORD doth build up Jerusalem: he gathereth together the outcasts of Israel. 3 He healeth the broken in heart, and bindeth up their wounds. 4 He telleth the number of the stars; he calleth them all by their names. 5 Great is our Lord, and of great power: his understanding is infinite. 6 The LORD lifteth up the meek: he casteth the wicked down to the ground. 7 Sing unto the LORD with thanksgiving; sing praise upon the harp unto our God: 8 Who covereth the heaven with clouds, who prepareth rain for the earth, who maketh grass to grow upon the mountains. 9 He giveth to the beast his food, and to the young ravens which cry. 10 He delighteth not in the strength of the horse: he taketh not pleasure in the legs of a man. 11 The LORD taketh pleasure in them that fear him, in those that hope in his mercy. 12 Praise the LORD, O Jerusalem; praise thy God, O Zion. 13 For he hath strengthened the bars of thy gates; he hath blessed thy children within thee. 14 He maketh peace in thy borders, and filleth thee with the finest of the wheat. 15 He sendeth forth his commandment upon earth: his word runneth very swiftly. 16 He giveth snow like wool: he scattereth the hoarfrost like ashes. 17 He casteth forth his ice like morsels: who can stand before his cold? 18 He sendeth out his word, and melteth them: he causeth his wind to blow, and the waters flow. 19 He sheweth his word unto Jacob, his statutes and his judgments unto Israel. 20 He hath not dealt so with any nation: and as for his judgments, they have not known them. Praise ye the LORD. Psa 147:4 (LXX 146:4) ὁ ἀριθμῶν πλήθη ἄστρων καὶ πᾶσιν αὐτοῗς ὀνόματα καλῶν πλήθη πλῆθος • (plêthos) n (genitive πλήθεος or πλήθους); third declension (Attic, Doric, Arcadocypriot) a large number of things, a great number majority, main portion something of large size or magnitude specifically: a large group of people: crowd, multitude, throng, mob populace, people, general public magnitude, size, extent amount, quantity (of time) length obgleich man diesen begriff (unendlich) auslegen kann, wie man will, so ist er seiner eigentlichen bedeutung nach doch mathematisch. er bezeichnet das verhältnisz einer grösze zu einer andern als dem maasze, welches verhältnisz gröszer ist als jede zahl Kant 6, 117. ἄσβεστος • (ásbestos) m (feminine ἀσβέστη, neuter ἄσβεστον); first/second declension unquenchable, inextinguishable endless, ceaseless APEIRON/PERAS The Greek term Apeiron, meaning originally "boundless" rather than "infinite," was used by Anaximander for the ultimate source of his universe. He probably meant by it something spatially unbounded, but since out of it arose the primary opposite substances (such as the hot and the cold, the dry and the wet) it may have been regarded also as qualitatively indeterminate. Aristotle, summarizing the views of certain early Pythagoreans (Metaphysics A, 5), puts the pair Peras ("Limit") and Apeiron ("Unlimited") at the head of a list of ten opposites. Peras is equated with (numerical) oddness, unity, rest, goodness, and so on; Apeiron is equated with evenness, plurality, motion, badness. The two principles Peras and Apeiron constituted an ultimate dualism, being not merely attributes but also themselves the substance of the things of which they are predicated. From the Pythagoreans on, the opposition of Peras and Apeiron was a standard theme in Greek philosophy. Parmenides (fr. 8, 42ff.) seems to have accepted Limit and rejected the Unlimited for his One Being. The later Pythagoreans removed unity from the list of identities with Peras and argued that unity was the product of the imposition of the Peras upon the Apeiron, or else it was the source of both of them. Plato in the Philebus regards Peras and Apeiron as contained in all things, and supposes that it is through limit that intelligibility and beauty are manifested in the realm of Becoming. Exactly how the Ideas fit into this scheme is controversial, but in the doctrine of ideal numbers which Aristotle attributes to him Plato seems finally to have identified a material principle with the Apeiron and a formal principle with the Peras. Both principles apply to the ideal as well as to the sensible world. This leads in due course to the doctrine in Proclus (Elementa 89–90) that true being is composed of Peras and Apeiron, and beyond being there is a first Peras and a first Apeiron. The Christian writer known as Dionysius the Areopagite identified this doubled First Principle with God. Infinity The concept of infinity, for long wrongly regarded as contrary to the whole tenor of Greek classicism, was in fact a Greek discovery, and by the fifth century BCE the normal meaning of Apeiron was "infinite." Infinite spatial extension was implied in the doctrines of Anaximander, Anaximenes, and Xenophanes and was made explicit by the Pythagoreans (see Aristotle, Physics IV, 6). Denied by Parmenides, it was reasserted for the Eleatics by Melissus (frs. 3–4) and adopted by the Atomists. Plato, however (in the Timaeus ), and Aristotle (Physics III) insisted upon a finite universe, and in this they were followed by the Stoics and most subsequent thinkers until the Renaissance. Aristotle had, however, admitted that infinity could occur in counting and he stated the concept clearly for the first time. He also accepted infinite divisibility (Physics VI), which had been "discovered" by Zeno and adopted wholeheartedly by Anaxagoras. It was rejected by the Atomists. Plato rejected it in the Timaeus, although he seems to have admitted it at the precosmic stage in Parmenides 158b–d, 164c–165c. Aristotle accepted infinite divisibility for movements, for magnitudes in space, and for time. The concept of a continuum so reached has been a basic concept in physical theory ever since. The mathematical concept of infinitesimal numbers associated with infinite divisibility and also with the doctrine of incommensurables remained important until the development of calculus in modern times. Infinity is a wave function which collapses into unit with any measurement. thus Hilberts (heavenly) Hotel with its innumerable rooms (in my Fathers house are many mansions) collapses into an ordinary brothel in the Red Light zone of Scollay Square as soon as another room is added. One cannot identify an element of infinity without causing it to become finite. It is meaningless to puport to select an innumerable number.