4 ms·
> But that's precisely the point I'm getting at - if Pi is normal, you need to use base 2 for this to work because your codomain is just {0,1}. You can use any
by twanvl 8y ago
> But that's precisely the point I'm getting at - if Pi is normal, you need to use base 2 for this to work because your codomain is just {0,1}.
You can use any base that is a multiple of 2 (like 10) and then apply a parity function to the digits. If pi is normal, then the digit parity sequence is also normal.
Sure you lose some entropy, but in some sense the digits of pi have 0 entropy anyway since they can be calculated. And in the other sense of treating the digits of pi as an unknown random sequence, there is infinite entropy, so throwing away 70% of it doesn't matter.
- throwawaymath 8y agoYeah someone else pointed out a similar point about the bijection of evens and odds, good point. My initial claim is incorrect, so I'll concede that. I was operating from the idea that there is no bijection between the naturals and a parity check function, but you're right that if one sequence is normal the second set should also be normal regardless of invertibility.