Unpredictable Afternoon Tea

In which I have far too much fun

After Douglas Hofstadter

Tortoise and Achilles are taking tea in the garden.

Tortoise: Achilles, why do you exist?

Achilles: Good morning. It’s lovely to see you too.

Tortoise (insistent): No, really, why do you exist?

Achilles (sighing): Well, if we assume that everything follows from what came before, then I exist because my parents met, and they existed because their parents met, and so on back to the beginning. But this answer isn’t correct because the world isn’t really like dominoes. It's more like rolling dice, where many different things could happen at any moment, and somehow I ended up being one of them. Or so the physicists say.

Tortoise: …That is not really what I meant by my question. Sorry. I think I phrased it badly.

Tortoise sips some tea, staring off into the distance.

Tortoise: The weather today seems perfect for tea drinking, doesn’t it?

Achilles: Yes, it is rather nice out. Not too hot, not too cold.

Tortoise: And isn’t it remarkable how temperatures on Earth are usually suitable for tea-drinking?

Achilles: Not so. The very fact that we can drink tea so often means that it must be the case that the laws of nature often result in tea-drinking weather. It is not remarkable at all.

Achilles (thinking): Ah, I see what you were getting at earlier. I suppose that… one could say that one exists because one exists? If I am able to observe my own existence, then it must be the case that the universe’s laws allow for my existence…

Achilles: Why, you sneaky little—I’m not falling for that again!

Tortoise (smiling): Whatever do you mean?

Achilles (animated, arms waving wildly): Strange things happen when things talk about themselves! If a mathematical system asserts its own consistency, that itself proves that the system is inconsistent! There is no way this works! Surely you cannot explain the fact of my existence on the basis of my existence!

A theoretical neuroscientist with crazy hair materializes between Tortoise and Achilles.

Dr. Karl Friston: Excuse me. Actually, you can. I’m Karl, by the way. (Karl looks around, adjusts his glasses and determines that he is in some Hofstadter-adjacent universe. Oh good. He can certainly survive—ahem, minimize his variational and expected free energy—here.)

Tortoise: Karl, I am skeptical of your claim.

Dr. Karl Friston: Let me be more clear. If you state mathematically that things exist over some timescale, then it is necessarily true that things maintain their own existence over that timescale.

Achilles: Wait, wait, wait. What do you even mean by “thing”?

Tortoise: And how is this useful? It sounds as if you are simply stating x = x. This is obviously true.

Dr. Karl Friston: Achilles, a thing has an inside, an outside, and a blanket that separates the inside from the outside. And Tortoise, I think you’ll answer your own question by the end of this conversation.

Tortoise: Okay, but suppose that the thing we’re talking about is a very strange organism that only has one cell, a cell membrane and a very strange protein inside of it that is either curled up or flat. Suppose further that most of the time this protein is flat, but today suddenly the protein has changed such that it is now curled up most of the time. The inside, the outside and the blanket all remain unchanged, but arguably, the thing itself has changed!

Dr. Karl Friston: Yes, you are certainly right. For a thing to remain the same thing over some timescale, it must also have a constant phenotype, in addition to having the same blanket and the same inside.

Tortoise: So what exactly happens when you formalize these conditions?

Dr. Karl Friston: A neat little theorem pops out that says things must minimize a quantity called variational free energy during the course of their existence. I would show you the math, but I don’t see a whiteboard around here.

Achilles: But what does that actually mean?

Dr. Karl Friston: It very roughly means that things are constantly making predictions and then changing either the world through action or their predictions through perception to minimize how surprised they are.

Achilles (on the brink of tears, very confused): So are you saying that we somehow got useful information out of nothing but observing that “things exist over time which means that they must exist over time”? How? (Voice cracks.) How is that even possible?

Dr. Karl Friston: (Karl pats Achilles gingerly on the shoulder.) Well, erm… to apply the Free Energy Principle you need to specify a generative model. That is, you need to describe what the states the thing you’re describing usually occupies. The Principle only tells you in a formal way that the thing will continue maintaining the states that define what it is, not what these states actually are—as the modeller of the system, you have to specify that information. It doesn’t just materialize out of nowhere!

Achilles (visibly calmer): That makes more sense.

Tortoise: So the meta-conclusion here is that making very obvious statements in very specific, formal ways and then shuffling the statements around is an unexpectedly useful exercise?

Dr. Karl Friston: That is certainly one meta-conclusion you can take away from this conversation, yes.

Achilles: Then I wonder when being very vague and imprecise is useful.

A poet with graying hair, sharp eyes and a flamingo scarf emerges through a rip in spacetime.

Achilles: Who are you?

Anne Carson: I am what I am by being what I am not.

Tortoise (gaping, fish-like): I—I—I—cannot parse your claim.

Dr. Karl Friston (panicking): That is logically impossible. If you exist over time, then you must continue maintaining the states that characterize you—if you are what you are not then you are simply—not—

The teacups sprout hips and begin to wiggle them side by side.

Tortoise: Oh dear. We seem to have created a paradox.

Achilles (gritting teeth): Not again…

Anne Carson: Reality, you are my strict Mother.

Dr. Karl Friston: My guess is that this simulation can no longer minimize its variational free energy because Anne Carson has a self-contradicting generative model.

Anne Carson: So this is all my fault?

Anne Carson (exasperated): You lot. Learn to not take everything so damn literally.

Achilles, Tortoise, Dr. Karl Friston: (Puzzled staring.)

Anne Carson (sotto voce): Orpheus turned back. So must all who seek truth in mirrors.

The garden flickers out of existence and then back into existence.

Tortoise and Achilles are taking tea in the garden.