#ultrafinite recursion

[king-of-men]

So I looked into buying options on BNTX, as one does, in the interest of gambling a little on it becoming a meme stock on the earnings today. Didn't happen which doesn't matter because those options are only sold in lots of a hundred (as far as my brokerage web interface knows anyway) and at 20 dollars a pop that's way beyond what I'm going to bring to a casino. It did however make me wonder: Is anyone selling options on these here options? And if not, why not?

[youzicha]

Maybe this depends on the details of the scenario? If you are a creature who evolved to live in a time loop (but how does evolution work if nothing changes..?) it would make most sense to think about things that way. But if we consider a mostly human-like brain, what would happen? You would remember something happening before, and also remember remembering it having happened before, etc. In real life, there’s the déjà vu phenomenon, which I think is exactly like this: you remember that the current moment has happened before, including remembering that it happened before! It’s like a fixpoint of your brain state. (Although, just like Yudkowsky’s law of ultrafinite recursion predicts, I actually don’t think you can clearly remember remembering remembering…)

I guess from the perspective of someone observing it from the inside, there’s no distinction between a loop in space-time and just a linear strip of space-time in which everything moves periodically, so you could think about the subjective sensation of being in a room looking at a pendulum or something like that. If we just go into the room, we will not instinctively identify memories with predictions about the future. But then, when we have just gone in it’s not perfectly loop-like, because we can remember going through the door and counting a finite number of swings.

Maybe that’s the answer to how you can evolve to live in a time-loop... just when you go into the room it is not yet loop-like, but as you spend more time there you gradually forget your memories from before the room, so your brain asymptotically approaches a perfectly periodic process where you get the same input and make the same response. It’s like the pumping lemma for finite state machines. I guess at the same time, you’d become more and more confident that the pendulum will keep swinging the same way, until you basically think about the future and the past in the same way. But at the end of this process, do you really end up with only one memory, or with a memory of a countably infinite series of swings? Or is there no actual distinction between the qualia of those, as some people have asserted about the inverted-spectrum thought experiment?

"if you were stuck in a time loop you would remember things happening an infinite number of times"? No, if you were stuck in a time loop you would remember things happening exactly once.

however, you would find there to be no distinction between thinking about the past and thinking about the future.

[rationalists-out-of-context]

Don't break the law of ultrafinite recursion unless you want to lose your pants.