Daniel Dockery

animî nostrî dêbent interdum âlûcinâri

Home of published musician, recording artist, mathematician, programmer, translator, artist, classicist, and general polymath.

The Gabriela-star prime: a last and lasting gift

January 28th, 2011

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

“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.

My arithmomania flaring the last few nights, I’ve been sleeplessly pursuing an elusive goal—one I frankly had no hope of achieving, yet one from which I couldn’t seem to pry myself. For reasons I can’t explain, even to myself, my most recent relationship has been punctuated by an urge to create. At times it’s been the usual Muse instinct of simply being inspired in some direction or other, but it’s also had manifestations of a blind urge: no particular inspiration, just the feeling that I ought to be making something. Often, I’ve been unable to help myself recalling the Current 93 lyric, “I wanted to write for you—songs, poems and bibles” for it’s very like the urge I felt, though I’m no poet or prophet (despite the name) and perhaps only rarely more than a mediocre musician. Still, there was the urge. And our time together did produce several pieces of music, from short, simple things, to some of my better recordings; some writing here and there, a few translations of my own; even some effort at returning my long out of practice hand to sketching, among other attempted acts of creation. But none have truly satisfied me; and I guess by this point, it’s obvious none satisfied her either.

I do not imagine this will fare better for either of us, but I felt myself again driven to produce something, and as it would be the last, I wanted to produce something lasting, something that could well outlive the both of us and any memory of us. Most of what I do, what I know how to do, is of fleeting interest and will scarcely outlive most times the time it takes to create it, much less wider swathes of time. But there is one field in which I sojourn from time to time that has a firmer bedrock, one that once chiseled tends to remain so, and so it is to that I turned.

It is no new theorem, alas, I have hewn out, but perhaps a unique thing nonetheless. From the infinite sea of prime numbers, I have fished out a heretofore unknown specimen with a number of distinct qualities I wanted to enshrine in it.

One of the first things to set it apart is the sheer size. While the number of primes is infinite, according to the database of largest known primes, only 5,383 known primes are larger than this 7,993-digit creature. On its own, 5,383 might seem a large number, but given the known primes tally in the millions, it’s a relatively tiny fraction.

There is a class of numbers known as the “star numbers“. They’re figurate numbers in the shape of a hexagram. The number of digits, 7,993, makes this a star number itself; specifically, the 37th—and 37 too is a star number—which number I chose as it will be my age this next October. While written out like a normal number, this looks like an odd jumble of random individual and runs of digits, if we write it out instead in the shape of the star, its mystery unfolds itself clearly.

Looking at it in that form—as you may do here, for the nonce, until I’ve time for a better presentation—you will see that the center is formed of the digits of the current year, 2011, radiating around to the points of the hexagram. Jumping out from there you find the numbers 1988, 3 and 11, which constitute the November birth date of my ex. In the context of primes, the date has a further significance in that it’s the anniversary of the 1961 first discovery of a titanic prime (in which group this prime also belongs). Continuing out, we find 22—her current age. At the edge, surrounding the whole figure, is the number 7. While it’s traditionally the number of Venus and signifies love, I chose it more particularly since the seventh letter of the Roman alphabet is “G”, her initial.

I will need at some point to draft a more formal, and better looking, web page to demonstrate the number than the one linked above; and once the formal primality proof certificate is completed, it will also turn up on the prime database’s Prime Curios page.

It may ultimately mean little, but it will definitely outlast me. Long after we’re forgotten, the number will remain, enshrining its little mystery, recalling somewhere how we were in this last year we had.

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

J. E. Littlewood

Desiderata

December 17th, 2010

Missing someone tonight, I wrote a small new piece for piano, which you may hear on Facebook or here:

[This piece is not currently available on this site, though it may still be heard at thesixtyone.com and heard on her album on Last.FM.

Ἐρατώ

February 27th, 2010

Εἰ δ᾽ ἄγε νῦν, Ἐρατώ, παρά θ᾽ ἵστασο, καί μοι ἔνισπε…

Long already a muse and inspiration to me, as I have mentioned here before, I have written and released this newest piece to acknowledge that she has also inspired me in ways and directions I’d no longer thought open to me.

It’s but a little thing, I know, but we work with what gifts we have and this is mine. Thank you, my dear, for everything: my life is better with you in it.

With all my love, then, I present for you, Gabriela, your track “Ἐρατώ”—the Greek’s muse of love for the muse of my own:

This track may also be listened to or voted on at thesixtyone.com and heard on Last.FM.

Catullus: “How many kisses?”

November 3rd, 2009

quæris, quo mihi basiationes
tuæ, Lesbia, sint satis superque.
quam magnus numerus Libyssæ harenæ
lasarpiciferis iacet Cyrenis
oraclum Iouis inter æstuosi
et Batti ueteris sacrum sepulcrum;
aut quam sidera multa, cum tacet nox,
furtiuos hominum uident amores:
tam te basia multa basiare
uesano satis et super Catullo est,
quæ nec pernumerare curiosi
possint nec mala fascinare lingua.

G. Valerius Catullus (84–54 BCE), carmen VII

Translated:

You ask how many of your kisses, love,
would be enough—or more!—for me?
As many as the grains of Libyan sand
lying along silphium-bearing Cyrene
between the oracle of sweltering Jove
and the sacred sepulchre of old Battus;
or as many as the quiet night’s stars
which see the secret loves of men:
to kiss you with that many kisses
might be enough to sate your mad lover!
So many that the curious cannot count
nor evil tongues disdain them.

Happy birthday, Gabriela!

segadora de mi canción de atardecer

October 24th, 2009

In 1924, Neruda published the volume Veinte poemas de amor y una canción desesperada (Twenty love poems and a song of despair). Among the pieces, number sixteen stood out to me tonight,

En mi cielo a crepúsculo eres como una nube
y tu color y forma son como yo los quiero.
Eres mía, eres mía, mujer de labios dulces
y viven en tu vida mis infinitos sueños.

La lámpara de mi alma te sonrosa los pies,
el agrio vino mío es más dulce en tus labios:
oh segadora de mi canción de atardecer,
cómo te sienten mía mis sueños solitarios!

Eres mía, eres mía, voy gritando en la brisa
de la tarde, y el viento arrastra mi voz viuda.
Cazadora del fondo de mis ojos, tu robo
estanca como el agua tu mirada nocturna.

En la red de mi música estás presa, amor mío,
y mis redes de música son anchas como el cielo.
Mi alma nace a la orilla de tus ojos de luto.
En tus ojos de luto comienza el país del sueño.

I’ve tried my hand at it, with middling results:

You’re like a cloud in my twilight sky
and your color and form are how I love them.
Oh, sweet-lipped woman, you are mine, mine,
and in your life live my endless dreams.

Your feet are rosy before the lamp of my soul,
my sour wine is sweet on your lips:
oh, harvester of my evening song,
how my lonely dreams feel you are mine!

You’re mine, I go shouting in the evening breeze—
mine!—and the wind sweeps my words away.
You hunt through the depths of my eyes, what you find
holds back your nocturnal glance like water.

You are caught in the net of my music, my love,
and my musical nets are as wide as the sky.
My soul is born on the shore of your sad eyes.
In your sorrowful eyes, the land of dreams begins.

2009/10/28

As Neruda indicates the poem is a paraphrase of a poem in Rabindranath Tagore‘s 1913 collection The Gardener, I will present that here for contrast:

You are the evening cloud floating in the sky of my dreams.
I paint you and fashion you ever with my love longings.
You are my own, my own, Dweller in my endless dreams!

Your feet are rosy-red with the glow of my heart’s desire, Gleaner of my sunset songs!
Your lips are bitter-sweet with the taste of my wine of pain.
You are my own, my own, Dweller in my lonesome dreams!

With the shadow of my passion have I darkened your eyes, Haunter of the depth of my gaze!
I have caught you and wrapt you, my love, in the net of my music.
You are my own, my own, Dweller in my deathless dreams!

no. 30

That same Muse evoked this small work, and so I cast my net again and hope for a catch like Tagore and Neruda’s.

This track may also be heard at Last.FM.

Dark nights, bright inspirations

October 22nd, 2009

Si te ves herido, no temas llamarme. No, llámame desde donde te halles, aunque sea el lecho de la vergüenza. Y yo iré, yo iré aun cuando estén erizados de espinos los llanos hasta tu puerta.

No quiero que ninguno, ni Dios, te enjugue en las sienes el sudor ni te acomode la almohada bajo la cabeza.

¡No! Estoy guardando mi cuerpo para resguardar de la lluvia y las nieves tu huesa, cuando ya duermas. Mi mano quedará sobre tus ojos, para que no miren la noche tremenda.

Gabriela Mistral, “Poemas del éxtasis”, VIII

This track may also be listened to or voted on at thesixtyone.com and heard at Last.FM.

Daniel Dockery

animî nostrî dêbent interdum âlûcinâri

Home of published musician, recording artist, mathematician, programmer, translator, artist, classicist, and general polymath.