It doesn’t even need to store the info indefinitely. It can calculate it on the fly to whatever precision is needed. It just has to be able to do it slightly faster than we can, which shouldn’t be a problem.
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Although notably it couldn’t forget. We can calculate it out to 62 trillion digits and then someone independently does it to 620 trillion digits and the first 62 trillion should be the same, so we might force them to have to buy a few extra terabytes off amazon
A good algorithm should be able to reproduce the numbers just fine. If somehow there is a difference that the humans notice, just convince them it was their mistake.
Well now we’ve just got to see if there’s a way to lag the simulation. Like everyone do pi calculations at the same time
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Not true. After I do math, my head hurts. Not much hurts after that other thing…
What would be the ramifications if pi turns out to be repeating or terminating after, say, 70 trillion digits? Or 700 trillion. Or 700 sextillion.
It would no longer be an irrational number, which I think would beg the question if any irrational numbers are truly irrational. And then amateurish math people like me would suddenly think the likelihood of us being in a simulation is a little higher.
If this is a simulation, someone just point out how we’re really in the bad place so this can get reset and we try a few things again.
TIA
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We’d have bigger problems, because the logical system that was used to prove that it is irrational, and that pretty much all of our understanding of mathematics is based on, would be broken.
Then again - pi being infinite and all, there probably is some N where the first N digits of pi are identical to the next N digits, so I don’t think simply seeing “look, those numbers repeat” is good enough evidence that the repeat will continue forever.
If the simulation can’t handle a simple pi algorithm, there are probably a lot of other more noticable things it struggles with…
Yeah that’s an interesting point haha. If it’s truly infinite then you’d think eventually as you figure out more digits you’ll get to a point where, by chance, the second half of your decimals matches the first half. Sort of like if you generate enough characters eventually you get Shakespeare. Although that relies on it being random.
Yeah - I guess there’s that too…
Not to get too existential but that infinite+random thing can sort of provide comfort too… like there was presumably an infinite amount of time before me and here I am, so presumably I’ve got an infinite of time to work with after death and so maybe my consciousness will be generated again? Of course heat death and that kind of thing doesn’t help.
And probably one where your consciousness is regenerated, but you also have x-ray vision, so that will be fun.
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Such a Pythagorean thought . . .
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Although I’ll probably just think of it as vision and seeing “normal colors” will seem very weird
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It only has to be a simulation for me, the rest of you are fake, and since I didn’t calculate pi to a bajillion digits this doesn’t impact the reality of the simulation to me.
Ha well jokes on u cause I know UR fake
And ur just trying to convince me we’re in a simulation because ur a simulation!
The technical term is normal, not random. A normal number is one in which any string of n digits has density (over the long run) of 10^{-n}. It isn’t known whether or not pi is normal, but is generally believed to be so and `almost all’ numbers are normal in the sense that numbers that aren’t normal have measure 0.
Having said that, for a randomly chosen number, the probability that the first N digits are repeated in the next N digits is 10^{-N}, and summing the geometric series shows that the expected number of times that that occurs is 1/9. So for most numbers in (0, 1), it is never the case that the first N digits exactly match the 2nd N.
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Will bridges fall down or spaceships blow up? If not, I don’t see what the big deal is.
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