Ἥβα μοι, φίλε θυμέ· τάχ´ αὖ τινες άλλες
   γῠναῖκες, ἐγὼ δὲ θανὼν γαῖα μέλαιν´ ἔσομαι.

...with apologies to Theognis.

Damned numbers, redux; or, a last[ing] gift for Gaby

A few days ago I did a bit of drive-by blogging to lodge a mild complaint against my occasional arithmomania. At the time, my goal was eluding me and the problem seemed altogether intractable, thus my irritation.

I have since, however, succeeded. (Yes, I know, it surprises me, too, but miracles happen sometimes!)

Pretending for a moment that Adler was incorrect in the earlier quotation, I will attempt briefly to explain what I've done. At the most basic, I've discovered a new prime; technically, a "titanic prime". Well, perhaps not "new", as surely the number existed in some abstract sense before any of us were aware of it, but it has never before been known in the literature or records, and it's a peculiar beast in its own right.

One of the things that makes it so is its sheer size: written out, the number is 7,993-digits long! While there is an infinity of primes, according to the database of largest known prime numbers, there are only 5,383 known prime numbers larger than this; and while 5,383 might seem a large amount, considering there are millions of known primes, it's a relatively tiny fraction.

Adding to the oddments, this is a star-congruent prime. What that means is that if you write the digits out in the positions and shape of the 37th star number (with the index, 37, itself being a star number, and chosen as, unfortunately, it will be my age next October), the seemingly random jumble of digits comprising this number reveal obvious, unmistakable patterns.

Specifically, it will be seen that the number takes on the shape of a hexagram (for Siouxsie and JJ), and spiraling around the center is the number 2011, the current year. If you go out from there, you'll find 1988, then 3, then 11—the date, 11-3-1988. While already a meaningful date, in terms of primes it has even another meaning in that November 3rd is the anniversary of the discovery of the first titanic prime in 1961. Moving farther out, we find the number 22, the current age in 2011 of someone born on that 11-3-1988 date. And going to the outermost edge of the figure, we find the whole surrounded by the number 7—chosen as the seventh letter of the alphabet is "G", an initial. The rest of the star is filled with zeroes.

The figure is too large to demonstrate within the constraints of blogger, but as seeing it makes it far more understandable than reading about it, I have a temporary presentation available here. I will flesh out the page later into something more presentable and move it to a more public URL, as Dr. Pickover has already asked about publishing and linking to it. Once the formal primality proof certificate is completed, it will also turn up on the prime number database's Prime Curios page.

"So what do acorporeals do, instead?"

Yann sat up and leaned against the side of the bed. "All the other things the embodied do. Give gifts. Show affection. Be attentive."

"What kind of gifts?"

"Art. Music. Theorems."

"Original theorems?"

"If you're serious."

Tchicaya was impressed. Mathematics was a vast territory, far more challenging and intricate than physical space. Reaching a theorem no one had proved before was a remarkable feat. "That's positively... chivalric," he said. "Like a knight riding off to the edge of the world, to bring back a dragon's egg. And you've done that, yourself?"

"Yes."

—Greg Egan, Schild's Ladder, chapter 8.

Sorry, yes, I'm a "bit" of a geek.

Consecutive vowels?

I'm not at all sure I buy today's XKCD theory. I mean, I say things like euouae, Aissaoua, Guauaenok, egueiite and homoiousia all the time, and that never happens to me—and all he has to say is "queue"? Maybe he just uses some form of Couéism.

Damned numbers

In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.

—Alfred Adler

I suppose that explains a lot.

Mathematics is a dangerous profession; an appreciable proportion of us goes mad.

—J. E. Littlewood

Though perhaps that explains more.

Hipsters! Argh!

Rilke, "On Love - and other difficulties"

I am of the opinion that "marriage" (partnership, union, etc.) as such does not deserve as much emphasis as it has acquired through the conventional development of its nature. It does not occur to anyone to expect a single person to be "happy,"—but if he marries, people are much surprised if he isn't! [...] Union is, in many respects, a simplification of one's way of life, and the union naturally combines the forces and wills of two people so that, together, they seem to reach farther into the future than before.—Only, those are sensations by which one cannot live. Above all, a partnership is a new task and a new seriousness,—a new challenge to and questioning of the strength and generosity of each partner and a great new danger for both.

It is a question in union, to my feeling, not of creating a quick community of spirit by tearing down and destroying all boundaries, but rather a good partnership is that in which each appoints the other guardian of his solitude, and shows him this confidence, this trust, the greatest in his power to bestow. A togetherness between two people is an impossibility, and where it seems, nevertheless, to exist, it is a narrowing, a reciprocal agreement which robs either one party or both of his fullest freedom and development. All companionship can consist only in the strengthening of two neighboring solitudes, whereas everything that one is wont to call "giving oneself" is by nature harmful to companionship: for when a person abandons himself, he is no longer anything, and when two people both give themselves up in order to come close to each other, there is no longer any ground beneath them and their being together is a continual falling. So, there is scarcely anything more difficult than to love one another. That it is work, daily labor, God knows. For one human being to love another: that is perhaps the most difficult of all our tasks, the ultimate, the last test and proof, the work for which all other work is but preparation. But, once the realization is accepted that even between the closest human beings infinite distances continue to exist, a wonderful living side by side can grow up, if they succeed in loving the distance between them which makes it possible for each to see the other whole and against a wide sky!

Therefore this too must be the standard for rejection or choice: whether one is willing to stand guard over the solitude of a person and whether one is inclined to set this same person at the gate of one's own solitude, of which he learns only through that which steps, festively clothed, out of the great darkness.

[...]

Love consists in this, that two solitudes protect and touch and greet each other.

[...]

I hold this to be the highest task of a bond between two people: that each should stand guard over the solitude of the other. For, if it lies in the nature of indifference and of the crowd to recognize no solitude, then love and friendship are there for the purpose of continually providing the opportunity for solitude. And only those are the true sharings which rhythmically interrupt periods of deep isolation...

—Rainer Maria Rilke, Letter to Emanuel von Bodman, Aug 17, 1901 (while Rilke was 26).

Shawshank Epictetus

οὐκ οἶδας, ὅτι καὶ νόσος καὶ θάνατος καταλαβεῖν ἡμᾶς ὀφείλουσίν τί ποτε ποιοῦντας; τὸν γεωργὸν γεωργοῦντα καταλαμβάνουσι, τὸν ναυτικὸν πλέοντα. σὺ τί θέλεις ποιῶν καταληφθῆναι; τί ποτε μὲν γὰρ ποιοῦντά σε δεῖ καταληφθῆναι. εἴ τι ἔχεις τούτου κρεῖσσον ποιῶν καταληφθῆναι, ποίει ἐκεῖνο.

—Ἐπίκτητος, Αρριανου των Επικτητου Διατριβων, III.5, "Πρὸς τοὺς διὰ νόσον ἀπαλλαττομένους".

Don't you know that both sickness and death must eventually surprise us, no matter what we're doing? They'll surprise the farmer in his field, the sailor at sea. What do you want to be doing when they come for you? For make no mistake, you will be overtaken. If you have anything better to do before then, get to work on that.

—Epictetus, Discourses, book III, letter 5.

Or, to use the paraphrase from Shawshank Redemption, "Get busy living, or get busy dying."