My First 1000000 Years

Limites
Hay una línea de Verlaine que no volveré a recordar,
Hay una calle próxima que está vedada a mis pasos,
Hay un espejo que me ha visto por última vez,
Hay una puerta que he cerrado hasta el fin del mundo.
Entre los libros de mi biblioteca (estoy viéndolos)
Hay alguno que ya nunca abriré.
Este verano cumpliré cincuenta años:
La muerte me desgasta, incesante.
                      —Jorge Luis Borges, 1923 English

Limits
There is a line of Verlaine I shall not recall again.
There is a nearby street forbidden to my steps.
There is a mirror that has seen me for the last time.
There is a door I have closed until the end of the world.
Among the books in my library (I am looking at them now)
There are some I'll never open again.
This summer I complete my fiftieth year.
Death wears me down, incessantly.
                      —Jorge Luis Borges, 1923 Español

Passing half a century is a landmark for those who count on 10 fingers, but as a bit-player I celebrate powers of 2. Today I turn 2⁶, which is a mega-milestone: 1000000₂ years. It’s a special occasion in several ways. Need I point out that it’s the last power of 2 I’ll ever see? Also, other than 0 and 1, it’s the only sixth power I’ll visit in my lifespan, and hence it is the only age that’s both a square and a cube.

As a young man—well shy of 50—I admired that poem by Borges, but as I grow older I find its mood of lugubrious foreboding less attractive. Yes, it’s true: There is a line of Borges I’ll never read again. But if my time is so limited, I shouldn’t be spending too much of it stuck in a tight loop, rereading the same lamentations over and over. Let the last time pass; I’ll move on to something new—something I haven’t yet done for the first time.

Life is all too full of never-to-be-repeated moments, right from the outset. Even the silly numerology of birthdays makes this apparent. Long before I reached my last power of 2, I celebrated my last Bell birthday (52), my last Catalan birthday (42), my last perfect birthday (28), my last factorial birthday (24), my last pair of birthdays satisfying \(x^m - y^n = 1\) (\(2^3 = 8, 3^2 = 9\)). Never again will my age be an even prime number, a multiplicative identity, an additive identity. But I can live with that!

And I still have a few treats to look forward to. In a couple of years I come to my next triangular birthday—and that one may not be my last. Then of course there’s \(3^4 = 9^2\). At the end of my eighties there’s a Fibonacci waiting for me, if I can make it. And, nearer at hand, I have marked my calendar for May 22, 2018, when I will celebrate my 25,000th spin around the earth’s axis. Maybe I should try to spend the day in orbit.