The Sempiternal Count recites ALL the digits of pi!

It begins . . .

1. Introduction

For a kids' show, Sesame Street occasionally delved into some pretty deep subject matter. I'm sure you remember the 1983 episode where Big Bird visits the ancient Egyptian afterlife and defies Osiris to secure justice for the damned soul of a 4,000-year-old Egyptian prince.

Damned Prince Sahu, his demon visitant, and the great god Osiris are far from being the only ancient eldritch characters to appear on the show, though. It's a little known fact that the "Count" character is based on a mysterious but very real immortal entity known as the Sempiternal Count. This strange being, as his title denotes, exists within the time-stream like us mortals -- he is not atemporally "eternal" as some suppose God to be eternal -- and yet he has always existed and always will. (Hence his portrayal as a deathless "vampire.") And just as you've seen on Sesame Street, he really does spend the bulk of his time shouting out numbers and laughing.

The Count recently agreed to take some time out of his busy schedule to discuss this unusual pastime of his. Below is a transcript of our interview, lightly edited for clarity and to remove most of the ha-ha-ha-ing.

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2. Transcript

SC: Two! Six! Four! One! Ha ha ha . . .

WJT: If I may interrupt, my -- uh, is it "Lord Courtesy"? Forgive me for being a bit unclear on how to address a Count in English. I understand that you -- that Your Lordship -- enjoys a rank corresponding to that of an Earl, isn't that right?

SC: One! One false assumption! Ha ha ha . . . . As you would have realized had you thought about it, one can hardly claim noble birth who never experienced any sort of birth at all. I've always existed, which is why they call me Sempiternal. And do you know why they call me the Count?

WJT: Don't tell me it's really because you love to count things! I'd always assumed that that was --

SC: A gross oversimplification to make an ancient eldritch entity more comprehensible to the Sesame Street audience? Just so. There are only so many things around, you understand, and one has so much time to fill! No, I've hit upon a truly inexhaustible hobby, one that will keep me busy forever, and which is never boring because it is never repetitive. Surely you must have noticed that the numbers you caught me chuckling over when you came in were not in the sequence one normally uses for counting?

WJT: I was going to ask you about that.

SC: Digits of pi! I started back in the year 1742, and I've recited nearly nine billion of them so far.

WJT: Nine billion and counting! Just how many digits of pi do you intend to recite?

SC: All of them. After all, I have all the time in the world.

WJT: All of them? But pi has an infinite number of digits. If you recite them one by one, advancing one finite step at a time, you'll never reach an infinite number, even if you keep at it forever. You'll never reach the end.

SC: Two! Two false assumptions! Ha ha ha . . . . Suppose you told me you were going to recite all the months of the year, and I told you it was impossible because no matter how well you did it, you would never reach "Febtober." What would you say to that?

WJT: I suppose I would say that, since "Febtober" is not one of the months of the year, reciting all of them without ever reaching it is not only possible but to be expected.

SC: Now consider your implication that it is impossible for me to recite all the digits of pi because, no matter how many digits I recite, I will never reach the last one. But there is no "last digit" in pi any more than there is a "Febtober" in the year, so my failure to reach it is no failure at all and is in no way inconsistent with my reciting each and every one of the digits that are in pi.

WJT: Okay, maybe I worded that poorly. What I mean is that you can never recite all the digits of pi, because there are an infinite number of them, and you go through them one by one. No matter how many times you add one (or any other finite quantity), you can never reach infinity.

SC: But I don't have to reach infinity. There is no "infinitieth digit" of pi any more than there is a "last digit." I only have to recite the digits that are in pi. I don't have to reach "Febtober."

WJT: Poor wording again. I don't literally mean an "infinitieth digit." I just mean that because there are infinitely many digits, you can't recite them all.

SC: Because, although I have unlimited time, I have to recite them one by one?

WJT: Right. No process of adding up finite quantities can ever reach --

SC: Reach what? And remember that you can't say "infinity" or "the end." If I recite one digit after another a thousand times, I reach the thousandth digit. If I do it a quintillion times, I reach the quintillionth digit. Which of the digits of pi can I not reach by this process?

WJT: Well, for every digit of pi, it is true that it has a finite ordinality and thus can be reached by the iterative process of reciting consecutive digits. So you can reach each of the digits of pi -- but you can still never reach all of them.

SC: But what do you mean by that distinction? Do you mean that there may be two digits of pi such that reaching one of them by my method is inconsistent with reaching the other -- so that, while reaching either is possible, reaching both is not?

WJT: No.

SC: Or are you imagining some particular digit called "all the digits of pi" -- a close cousin to "the last digit," "the infinitieth digit," and the month of Febtober -- and saying that I cannot reach it?

WJT: No, not that, either.

SC: Let me help you. What you are saying is that, although I will recite each and every digit of pi -- that is, for every digit of pi it is true that I will eventually recite it -- I will never have recited them all. There will never come a time when I can say that my project is complete and that I have recited all the digits of pi.

WJT: Yes, that's just what I've been trying to say.

SC: Well then our disagreement is merely verbal. I never said that I will have recited all the digits of pi; I only said that I will. If that seems slightly paradoxical, such is the nature of sempiternity.

WJT: Okay, I guess we can agree that --

SC: But --

WJT: Yes?

SC: But suppose I told you that, as it happens, I have recited all the digits of pi. This task that can never be finished -- I have finished it. That's what I was doing for all those numberless eons before 1742.

WJT: But we've just agreed that that's impossible!

SC: Three! Three false assumptions! Ha ha ha . . . . We've only agreed that it is impossible, not that it always has been.

WJT: No, it is, was, and always will be impossible. No one -- past, present, or future -- can ever have recited all the digits of pi because there is no end to them.

SC: There is no end to them, quite right. But there is a beginning, isn't there? The first digit is three, the second is four, and so on.

WJT: But we're talking about finishing, not beginning. I don't see the relevance of --

SC: I recited them backwards.

WJT: You mean you started with the --

SC: No, that's just my point: I never started. I had always been reciting digits of pi in reverse order. At 10:17 a.m. on April 14, 1742, I recited the first digit of pi. Just before that, I had recited the second; before that, the third; and so on all the way back. I had always been doing it, for mahakalpas without number, until one day I finally finished.

WJT: But how could you have finished a finite time ago, if you began infinitely long ago and advanced step by finite step?

SC: I didn't begin infinitely long ago because I didn't begin at all. I have recited an infinite number of digits of pi, but each and every one of them was recited at a particular time only finitely antecedent to 10:17 a.m. on April 14, 1742. We have already discussed all this. Just reverse past and future and apply the same logic.

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3. Commentary

3.1. Bidirectional sempiternity

A typical definition of sempiternity, as a technical term in philosophy, is "existence within time but infinitely into the future, as opposed to eternity, understood as existence outside time." That is to say, sempiternity is like a geometric ray, or like the ordered set of all natural numbers -- or like the decimal expression of pi. It has a single endpoint and extends infinitely in one direction only. The Count, on the other hand, is what we might call bidirectionally sempiternal, like a geometric line, the ordered set of all integers, or the decimal expression of pi preceded by its mirror image.

I think many more people are willing to countenance future-only sempiternity than the bidirectional variety. This ultimately comes down to a very fundamental assumption about time -- namely, that the past actually exists but the future does not. A sempiternal future, these people would say, is boundless but not actually infinite. No matter how long one goes on living, one will always have lived for a finite number of years. The future is only potentially infinite, in the sense that that finite number will go on increasing indefinitely. Past sempiternity, on the other hand, is taken as meaning that an infinite amount of time has already elapsed, making it an actual infinity.

There is really no arguing with primary metaphysical assumptions, so I can only state that I do not share this one. Either only the present is actual ("presentism," as defended by Edward Feser here vis-a-vis Kalām), or the whole timeline is actual ("eternalism," which is what I believe due to the relativity of simultaneity and the fact of precognition). And either way, as I have tried to argue in recent posts, there is no question of an infinite amount of time elapsing because no point on the timeline is infinitely distant from any other.

3.2. A project which is neither completable nor hopeless

One of the things that used to bother me as a Christian youth was the idea that one day everything would be finished, every goal accomplished, and then -- an eternity of stasis and boredom? I used to think of John Lennon's infamous line, "Imagine there's no heaven . . . above us, only the sky," and reinterpret it -- thinking of "heaven" as a state of eternal rest after all has been accomplished, and Lennon as proposing that there is no such final state, only infinite potential. In Mormonism, this conception of heaven as an eternal sabbath -- when one has become "a pillar in the temple . . . to go no more out" (Rev. 3:12) -- coexists uneasily with the concept of "eternal progression." I was very much a proponent of the latter, finding the former unbearable.

But what's the alternative? Working forever to reach a goal that can never be attained? This is another sort of hell, that of Sisyphus. Still, suppose Sisyphus finally succeeded in getting his boulder into a permanently stable position at the top of the hill. Then what?

This sort of thing really used to bother me a lot, which I suppose made it emotionally easier for me to transition to atheism, since eternal extinction seemed no more futile or meaningless than any of the alternatives. Why want eternal life if it meant either chasing unreachable goals forever, or else reaching all possible goals and damning oneself to an eternity of boredom? All is vanity and vexation of spirit. As They Might Be Giants put it,

Now it's over, I'm dead, and I haven't done anything that I want --

Or I'm still alive, and there's nothing I want to do

Though the Sempiternal Count's specific pastime of reciting digits of pi would be mind-numbingly boring for us humans, it does provide a model for a tolerable eternity. Each goal is reachable, so one's efforts are not in vain; and yet there will never be a time when all the goals have already been reached.

3.3. Something new can happen, even after a sempiternity

In "What if there was no beginning?" I wrote,

If something has never ever happened through all the countless kalpas of our existence, shouldn't it be pretty obvious by now that it's never going to happen? Thus the thesis that we have always existed would seem to lead to despair.

But the example of the Sempiternal Count shows that this reasoning is not valid. The Count had always been reciting pi backwards without ever finishing -- until one day he did finish, and moved on to the next thing. So the thesis that we have always existed is not after all incompatible with the doctrine that "it doth not yet appear what we shall be" (1 Jn. 3:2).

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Note: I've been working on this post for a week or so. It's by pure coincidence that I finally finished it on Pi Day.