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- Are Shakespeare's plays encoded within Pi?
- The truth is, we don't know, but we suspect
- They're somewhere in those digits. And now I
- Will show why we don't know if we're correct.
- You see we think the digits do behave
- As if they were a random sequence, and
- And so many mathematicians try to brave
- This question, but we still don't understand.
- Pi isn't random. Each digit must be
- Exactly what the definition states.
- It's pseudo-random as far as we can see,
- But it's a subject of intense debates.
- Now I'll explain with this parameter:
- It's all in iambic pentameter.
- You may have heard of this scenario:
- A thousand monkeys type at keyboards 'till
- They write the words of Shakespeare. Even though,
- In one life, it's a task they can't fulfill.
- If you allow their kids to carry on,
- All through the generations, working hard,
- They will evolve before they come upon
- A single sonnet written by the Bard.
- But still the theory's sound! And it is true
- That with a random and infinite set
- Of letters, that eventually you
- Will find whatever words you want to get.
- However, on this thing you can depend:
- Before you do, the universe will end.
- Pi is a number, and that's why
- I can completely guarantee no part will be
- 9-1-3-7-5-2-2-8-ten
- 4-7-9-H-A-M-L-E-T.
- You'd have to make up something, like a code
- Where zero-one is A, Oh-three is C,
- Or you could also choose some other mode:
- Oh-2 could be "to be or not to be."
- But let's go with this system, where a Y
- Is 2-5, O's one-five, and R's eighteen,
- And next comes zero-nine, which is an I
- Oh-three, eleven. Yorick's name is seen!
- Does Pi say anything? How does it go?
- 1-4-1-5. I guess the answer's "no."
- If you desire to search Pi for a thing
- Like Hamlet, as if you'd 'discover' it,
- Without a copy used for referencing,
- You wouldn't know if you'd recovered it.
- In fact, it's almost certain, so beware:
- Before you get to Hamlet, if you slog
- Through all the digits, you'll find versions where
- There's just one thing changed: Hamlet is a dog.
- Dog Hamlet is so awesome, and he goes
- On infinitely many adventures.
- In this infinite space, everyone knows
- Dog Hamlet's king. Sometimes he has dentures.
- Unless Pi isn't normal. I'll admit,
- Pi might not have a single "Dog Hamlet."
- A normal number is a number where,
- If you take any pattern of length Z
- You'll definitely find the pattern there,
- And others that length with same frequency.
- Length 1 would just be every digit, so
- All digits happen infinity times.
- And all two-digit numbers also go
- In there somewhere. If you list all the primes,
- You get the Copeland-Erdős constant,
- which is one of few known normal numbers. Or
- Take every number in order and stitch
- Them all together. And we know there's more.
- Most numbers must be of the normal kind.
- But somehow, they are hard for us to find.
- We think that Pi is normal. Also e,
- And square root 2 and other stuff like that.
- We don't know how to prove that they must be,
- That Pi contains Macbeth where he's a cat.
- If you've got every combination of
- Digits of every length, that will include
- A Romeo and Juliet in love
- who meet in time and live and end the feud.
- And since this string of numbers must occur
- With equal frequency to other strings
- Of the same length, it don't matter whether
- You choose this code or other permutings.
- Perhaps somewhere, Dog Hamlet and Catbeth
- Are chillin', bustin' ghosts, avoiding death.
- There's simple open problems about Pi,
- Like whether every digit, oh through nine,
- Keeps happening. We can't figure out why
- 6 shouldn't stop appearing down the line.
- It seems ridiculous to think that 2
- Occurs finitely many times. I fear,
- That without proof, we can't say it's not true.
- Alas, poor Yorick may never appear.
- But the exciting thing is that I think
- These problems will be solved before too long.
- And then this video will really stink,
- Because all this not knowing will be wrong.
- Don't worry. I look forward to its fall.
- Till then, a Happy Pi Day to you all.