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> You'll never run out of space again - π holds every file that could possibly exist! This isn't necessarily true, right? AFAIK this only holds if pi is normal

> You'll never run out of space again - π holds every file that could possibly exist! This isn't necessarily true, right? AFAIK this only holds if pi is normal, which we haven't proven.

hackernewds 3y ago
Thought John Lamhert did that in 1728 https://www.sciencefocus.com/science/how-do-we-know-that-pi-is-infinite/ https://www.sciencefocus.com/science/how-do-we-know-that-pi-...
- constantcrying 3y ago
  No, this proves pi can not be written as a fraction. But not being a fraction does not imply that a number contains all sequences of digits.
  - dragonwriter 3y ago
    As a fairly simple example, consider the number wirtten in decimal notation as: 0.101001000100001000001... (with an increasing-by-one sequence of zeroes between each successive 1.) It doesn't contain all sequences of digits, or even all digits, yet it cannot be written as a fraction.
    - constantcrying 3y ago
      >yet it cannot be written as a fraction. Is that trivial?
      - dragonwriter 3y ago
        > Is that trivial? My understanding is that it is a trivial (or at least well-known) result that a rational will always have a finite, infinitely-repeating terminal sequence in any base.
      - xigoi 3y ago
        Yes. It can quite easily (depending on your knowledge of basic number theory) be proven that a number is rational if and only if its digits (in any base) eventually become periodic.
ravi-delia 3y ago
Look we know that pi is normal. You know that pi is normal, I know that pi is normal. I'll give you 10,000:1 odds that we find any string you want with exactly the probability you'd expect from pi being normal, and before long you'll have forked over your life savings. It's annoying to prove, we barely know if any numbers are normal, but the idea of a normal number was invented to discuss what numbers like pi or e seem to be like. In math that's not enough, but this is CS! All encryption is built on weaker grounds than pi being normal.
- jakelazaroff 3y ago
  Okay, so I just have to find a sequence that hasn't yet been discovered to exist in pi? Or do I have to wait for a proof that pi isn't normal (if one exists) to get my money? My sequence is a trillion consecutive 0s, followed by a trillion consecutive 1s, etc, all the way up through a trillion consecutive 9s. Who wins the bet?
  - ravi-delia 3y ago
    > with exactly the probability you'd expect from pi being normal In this case you win it when you check enough digits of pi that, if pi were normal, the expected probability of finding your string. Probably not gonna happen, but if you ever do hit me up! If you do that work I'll have the opportunity to win lots of smaller bets edit: Wait that loses me catastrophic amounts of money. Keep checking until P<1/11,000, I think that's fair.

> You'll never run out of space again - π holds every file that could possibly exist! This isn't necessarily true, right? AFAIK this only holds if pi is normal, which we haven't proven.

hackernewds 3y ago

Thought John Lamhert did that in 1728 https://www.sciencefocus.com/science/how-do-we-know-that-pi-is-infinite/ https://www.sciencefocus.com/science/how-do-we-know-that-pi-...

constantcrying 3y ago
No, this proves pi can not be written as a fraction. But not being a fraction does not imply that a number contains all sequences of digits.
- dragonwriter 3y ago
  As a fairly simple example, consider the number wirtten in decimal notation as: 0.101001000100001000001... (with an increasing-by-one sequence of zeroes between each successive 1.) It doesn't contain all sequences of digits, or even all digits, yet it cannot be written as a fraction.
  - constantcrying 3y ago
    >yet it cannot be written as a fraction. Is that trivial?
    - dragonwriter 3y ago
      > Is that trivial? My understanding is that it is a trivial (or at least well-known) result that a rational will always have a finite, infinitely-repeating terminal sequence in any base.
    - xigoi 3y ago
      Yes. It can quite easily (depending on your knowledge of basic number theory) be proven that a number is rational if and only if its digits (in any base) eventually become periodic.

ravi-delia 3y ago

Look we know that pi is normal. You know that pi is normal, I know that pi is normal. I'll give you 10,000:1 odds that we find any string you want with exactly the probability you'd expect from pi being normal, and before long you'll have forked over your life savings. It's annoying to prove, we barely know if any numbers are normal, but the idea of a normal number was invented to discuss what numbers like pi or e seem to be like. In math that's not enough, but this is CS! All encryption is built on weaker grounds than pi being normal.

jakelazaroff 3y ago
Okay, so I just have to find a sequence that hasn't yet been discovered to exist in pi? Or do I have to wait for a proof that pi isn't normal (if one exists) to get my money? My sequence is a trillion consecutive 0s, followed by a trillion consecutive 1s, etc, all the way up through a trillion consecutive 9s. Who wins the bet?
- ravi-delia 3y ago
  > with exactly the probability you'd expect from pi being normal In this case you win it when you check enough digits of pi that, if pi were normal, the expected probability of finding your string. Probably not gonna happen, but if you ever do hit me up! If you do that work I'll have the opportunity to win lots of smaller bets edit: Wait that loses me catastrophic amounts of money. Keep checking until P<1/11,000, I think that's fair.