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A Post about Stubbornness1

Submitted by John C on February 25, 2009 - 11:00

Let’s assume for the moment that the universe is completely, totally, 100% deterministic.

If this is the case, then given a complete understanding of the laws of nature and a total snapshot of the universe at some instant, a very dedicated individual (or machine, more likely) would be able to roll out the calculations and predict future states of the universe. In principal, anyway. I admit the details would probably get a little gnarly.

So let’s say modern science has figured out more or less how to do this: a means of predicting the future with 100% certainty. It’s a neat trick. Something to impress people at parties, anyway.

Now imagine a scientist—the stereotypical labcoat-clad clipboard-wielding boffin will do nicely. In fact, let’s pretend it’s Jen, circa strip 1. She has access to the skyscraper-sized supercomputer that Science has constructed for the purpose of brute-forcing its way through the mind-boggling infinitude of calculations necessary to predict the future. It’s pretty cool. She’s pretty happy about it.

One day the gang is at Razor Burger for lunch and they get to talking. Jen recently bought a new cat, and she’s rapturously describing it to Roy. In passing, she mentions that the universe is deterministic and that science has developed a method with which it can perfectly predict the future. But god is it a beautiful cat. Her name is Agnes and she’s a calico Japanese Bobtail. You really need to come over and see it one day.

In the meantime, Roy doesn’t really care about cats. I mean, they’re okay, but in his opinion Jen seems a smidge overenthusiastic. Then again, at least she’s not talking about her tuba again. So it could be worse. But wait, what was this whole thing about the universe being deterministic and science predicting the future? That sounds bad for Roy’s free will. Roy likes his free will. Quite a bit, in fact. If he has any say in the matter, he’d rather not part with it.

Roy says as much, and Jen replies, “Oh, free will? No, that’s a myth. A farce! Here, let me show you.” She whips out a handheld device from her coat pocket. It looks like a miniature Etch-A-Sketch with a retractable keyboard. “Have you decided what you’re ordering?”

“What? No. I’m trying to decide between the Shank-wich and the Shuriken Salad. I’ve been trying to watch my figure, but the Shank-wich is undeniably delectable…”

“Perfect! See, this unit is a portable interface to The Computer. I’ll just ask it to predict what you eventually decide to order. It’ll spit out an answer in a minute or two; you won’t even have to bother deliberating!” Thinking she’s doing him a small favor, Jen begins tapping away at the device’s keyboard. She’s hits SUBMIT before Roy can retaliate:

“No? What? That’s preposterous! I refuse to listen to your device. In fact, whatever it tells me to do, I shall do the exact opposite! Let’s see how this Compute-O-Whiz of yours likes that!”

And now we’ve come to the real crux of the story. If the machine can predict exactly how the future will unravel, then by definition whatever answer it yields must be the thing that Roy orders. But Roy is predicating his whole decision on the basis of doing the exact opposite of what the machine tells him to do. The machine cannot be incorrect, but Roy is infinitely stubborn. He would sooner be stricken dead than follow the whims of a capricious mechanical deity. The unstoppable object has run into its immovable wall. In short: a paradox. Therefore, it is logically impossible for Jen to tell Roy what he will be ordering.

Well, okay, fine. Just don’t tell Roy. Easy enough. Unfortunately, this doesn’t really fix anything. See, Milo’s been remarkably quiet this whole conversation. Actually, he’s been distracted. Daydreaming about the scientific consequences regarding the putative existence of leprechauns, mostly. But he catches the tail end of Jen and Roy’s exchange, and he finds Roy’s stubbornness amusing. He decides to try it out with his own portable interface to The Computer. If it tells Milo that he’s going to order the Cutlass Supreme Combo, he’ll get the Masamune Masher, and vice versa.

Now that the predictor and the stubborn person are one and the same individual, The Computer isn’t even allowed to generate a result. Think about it: how can The Computer calculate a correct answer if that answer is necessarily the one that will not come to pass? Back when it was Jen and Roy, Jen could feasibly make the query, secretly record the result somewhere, wait for Roy to place his order, and then reveal the (correct) prediction after the fact. There’s nothing logically inconsistent about that. In Milo’s case, however, knowledge of the prediction directly results in a paradox.

The weak conclusion of our little mental exercise is that it’s impossible for a stubborn individual to know their future. A stronger conclusion might be that it is generally impossible for a person to have 100% accurate information about the future. I can envision an interesting universe where the weak conclusion holds but the strong one does not: in this case, The Computer implicitly knows who is stubborn (and at what times, if we make the reasonable assumption that folks can be transiently stubborn) and fudges its responses accordingly. That is to say, The Computer occasionally lies. In point of fact, The Computer really does “know” the accurate answer—but it also “knows” that revealing this answer will self-defeat the prophecy. (Of course, we should be careful about personifying The Computer with words like know: although it is in a sense “omniscient”, it also necessarily lacks a certain degree of agency. It should, for example, be impossible for The Computer itself to be stubborn!)

The point is: in this theoretical world, stubborn individuals run the risk of getting a false prediction. Thus, in order to ensure that they’re always getting a true and correct prediction, they need to promise to themselves that they’ll follow whatever advice The Computer gives them. Talk about a self-fulfilling prophecy!

I’ll leave you with one last interesting corollary of the weak conclusion. It’s succinctly expressed as follows: If God exists and is omniscient, then it follows that God can’t be stubborn!

1 This post is largely based on an argument presented in Raymond Smullyan’s excellent book This Book Needs No Title.