PI: More mokeys with Typewriters?

[Namloh2000]

PI: More mokeys with Typewriters!?

There exists a recent post on the subject of an infinite amount of monkeys doing a lot of typing. You know the premise. I was going to post this there, but figured it might deserve to be a new thread altogether.

There's this number- Pi: 3.14159... and off it goes. It is irrational, meaning that it's digits are infinite, and that they never repeat in a cyclical fashion.

Studies have shown that Pi may also be "normal", meaning that it's digits are random in a certain statistical sense.

Lots of people study Pi. It's implications are more staggering than the average person would imagine. There is recent evidence suggesting that pi might contain just as many of any one number combination as there areany other number combination. Does that not imply that Pi has every number combination, including this post hidden somewhere within it's digits? Including Shakespeare?

Mind you: this is all within the realm of experimental mathematics.

But! (chuckle) If pi had every number combination, wouldn't one of those numbers contain infinite amount of zeros, making pi a rational number?

heh.

 

[wuliheron]

Infinity is not a number.

 

[Sven Tingblad]

I think pi has every finite number combination. It has only one infinitely long string of numbers: itself.

 

[hypnagogue]

I think pi has every finite number combination. It has only one infinitely long string of numbers: itself.

Not so, depending on how you count your strings. For instance, you can construct 2 infinite sets of numbers, one by stringing together the digits at pi's even decimal places, the other by stringing together the digits at the odd decimal places. In fact, for any number n you could construct an infinite string by counting every nth digit, so you can really construct an infinite amount of infinite strings from pi. Of course, once you start doing things this way it becomes pretty arbitrary what kind of strings you can find.

 

[vanesch]

Does that not imply that Pi has every number combination, including this post hidden somewhere within it's digits? Including Shakespeare?

Pi is the biggest copyright violation and software theft ever encountered. All the police services should be chasing it.



cheers,
Patrick.

 

[string_theory]

so is there any possibility that pi is rational?

 

[HallsofIvy]

No, it was conclusively proven long ago that pi is not rational. In fact, it was proved in the 19th century that pi is not an "algebraic" number either.

 

[HallsofIvy]

Studies have shown that Pi may also be "normal", meaning that it's digits are random in a certain statistical sense.

Lots of people study Pi. It's implications are more staggering than the average person would imagine. There is recent evidence suggesting that pi might contain just as many of anyone number combination as there areany other number combination. Does that not imply that Pi has every number combination, including this post hidden somewhere within it's digits? Including Shakespeare?

Note the use of the words "may" and "might". As far as I know the only numbers that have been conclusively proven to be "normal" are numbers that were specifically defined to fit that definition. On the other hand it has been proven that, in a strictly defined sense, "almost all" numbers are "normal".

 

[selfAdjoint]

Note the use of the words "may" and "might". As far as I know the only numbers that have been conclusively proven to be "normal" are numbers that were specifically defined to fit that definition. On the other hand it has been proven that, in a strictly defined sense, "almost all" numbers are "normal".

Once again showing that pi is likely to be a "typical" number. Almost all numbers are irrational, and so is pi. Almost all numbers are transendental, and so is pi. And now normality.

 

[Jared Prince]

there are 2^aleph null real numbers, and most of these are normal. But there are only aleph null numbers that can be defined by computer programs, and pi is one of them. This means that, to a good approximation, none of the numbers can be defined by computer programs (the percentage that can is infinitesimal). Pi is not a typical number, it is part of an extremely small subset of real numbers, the computable numbers.

 

[jackle]

Someone should write a book called "The PI Code" modeled on "The Bible Code". Remember to include predictions about the end of the world. There is a lot of money in it apparently.

 

[robert Ihnot]

Could monkeys be used to reproduce the works of Shakespeare? Here is a scientific project that clearly demonstrated that this is impossible:

The BBC reports that some scholars at the University of Plymouth wanted to test the theory, so they put a computer in the monkeyhouse of a zoo. After a month, "The Sulawesi crested macaques had only succeeded in partially destroying the machine, using it as a lavatory, and mostly typing the letter 's.'"

This cost the British taxpayer 2000 pounds, but the director of the project Mike Phillips said, they “learned an awful lot."

http://news.bbc.co.uk/1/3013959.stm

 

[matt grime]

I think you should have included the quote from the Zoo director about this "proving the mathematicians wrong", which led to the NTK caption of "zoo confuses infinite and eight".