Preposterous Universe

Wednesday, March 02, 2005
The formula for all the future

For the last two months I've been pretty good at staying in Chicago, with only the one jaunt to Aspen and DC. Now it gets hectic again, with multiple trips per month for the foreseeable future. But it's going to be quite the world tour this year: France, India, Turkey, Canada, Korea, and China, not to mention various exotic domestic locales.

The fun begins today, when I fly to Santa Barbara for the previously-mentioned conference on Theoretical Physics in Drama and Narrative, where I get to pretend to be a literary critic. To set the mood, here's a short excerpt from one of the central texts of the conference, Tom Stoppard's Arcadia. (Thomasina is a precocious thirteen-year-old, and Septimus is her tutor; the year is 1809.)
Thomasina When you stir your rice pudding, Septimus, the spoonful of jam spreads itself round making red trails like the picture of a meteor in my astronomical atlas. But if you stir backward, the jam will not come together again. Indeed, the pudding does not notice and continues to turn pink just as before. Do you think this is odd?

Septimus No.

Thomasina Well, I do. You cannot stir things apart.

Septimus No more you can, time must needs run backward, and since it will not, we must stir our way onward mixing as we go, disorder out of disorder into disorder until pink is complete, unchanging and unchangeable, and we are done with it for ever. This is known as free will or self-determination.
He picks up the tortoise and moves it a few inches as though it had strayed, on top of some loose papers, and admonishes it.

Thomasina Septimus, do you think God is a Newtonian?

Septimus An Etonian? Almost certainly, I'm afraid. We must ask your brother to make it his first enquiry.

Thomasina No Septimus, a Newtonian, Septimus! Am I the first person to have thought of this?

Septimus No.

Thomasina I have not said yet.

Septimus `If everything from the furthest planet to the smallest atom of our brain acts according to Newton's law of motion, what becomes of free will?'

Thomasina No.

Septimus God's will.

Thomasina No.

Septimus Sin.

Thomasina (derisively) No!

Septimus Very well.

Thomasina If you could stop every atom in its position and direction, and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra you could write the formula for all the future; and although nobody can be so clever as to do it, the formula must exist just as if one could.

Septimus (pause) Yes. (Pause.) Yes, as far as I know, you are the first person to have thought of this. (Pause. With an effort.) In the margin of his copy of Arithmetica, Fermat wrote that he had discovered a wonderful proof of his theorem but, the margin being too narrow for his purpose, did not have room to write it down. The note was found after his death, and from that day to this--

Thomasina Oh! I see now! The answer is perfectly obvious!

Septimus This time you may have overreached yourself.
They hadn't, of course, read my ideas about the arrow of time. What I'm not quite sure of is, should they have been talking about "atoms" in 1809? (And I still don't understand what's up with the tortoise.)

Ideas on culture, science, politics.
Sean Carroll

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