What blew my mind is that it hasn’t been proven that pi contains an infinte number of ones, for instance. It’s not out of the question that there is a decimal place where the last 1 appears and there are none from then on.
It’s not really likely, but we simply don’t know and it is possible. It sounds weird given how many decimals of pi we’ve calculated, until you realise we’ve literally calculated 0% of them.
Yep! Pi might be a “Normal” irrational number, which is a really poorly named classification that basically means that the “random” arrangement of numbers in pi isn’t weighted and so you’ll end up with 1 in 10 digits being 1, and that that will be true for all bases. We’re kind of at a point where we think Pi is “normal”, but we can’t prove it.
If it is “normal” though, then that means that you could find any arbitrary sequence of numbers inside of pi, somewhere. Meaning that in base 128, pi would contain the ascii sequence for every book ever written, every book that ever will be written, every book that could be written, the accurate date of your death, and anything else you could ever imagine. Again, that’s not proven, but we think it’s the case
From a mathematical standpoint you’re right, but from the standpoint of application pi has an infinitesimal accuracy without going to 45 digits. At 3.1415926535, we’re more accurate than the distance between 3 atoms.
I don’t see how that’s relevant. Plus your last sentence sounds like you’re just repeating something you heard but forgot a part of it, because it makes no sense as it is.
The part they’re misremembering is that if you used 39 digits of pi as pi (not 45), it would be enough to calculate the circumference of the observable universe with a forward error of less than the width of a hydrogen atom (not the distance between 3)
What blew my mind is that it hasn’t been proven that pi contains an infinte number of ones, for instance. It’s not out of the question that there is a decimal place where the last 1 appears and there are none from then on.
It’s not really likely, but we simply don’t know and it is possible. It sounds weird given how many decimals of pi we’ve calculated, until you realise we’ve literally calculated 0% of them.
Yep! Pi might be a “Normal” irrational number, which is a really poorly named classification that basically means that the “random” arrangement of numbers in pi isn’t weighted and so you’ll end up with 1 in 10 digits being 1, and that that will be true for all bases. We’re kind of at a point where we think Pi is “normal”, but we can’t prove it.
If it is “normal” though, then that means that you could find any arbitrary sequence of numbers inside of pi, somewhere. Meaning that in base 128, pi would contain the ascii sequence for every book ever written, every book that ever will be written, every book that could be written, the accurate date of your death, and anything else you could ever imagine. Again, that’s not proven, but we think it’s the case
Whatcha got in that pi? Everything…
Yeah! It’s a really beautiful thing to think about. And exciting to imagine we may one day see a mathematician who works out the truth
From a mathematical standpoint you’re right, but from the standpoint of application pi has an infinitesimal accuracy without going to 45 digits. At 3.1415926535, we’re more accurate than the distance between 3 atoms.
I don’t see how that’s relevant. Plus your last sentence sounds like you’re just repeating something you heard but forgot a part of it, because it makes no sense as it is.
The part they’re misremembering is that if you used 39 digits of pi as pi (not 45), it would be enough to calculate the circumference of the observable universe with a forward error of less than the width of a hydrogen atom (not the distance between 3)