Does Pi terminate or never?

[ddt]

Which makes for an excellent compression algorithm. Any movie, mp3, application or what have you can be reduced to 2 integers; starting position and length.

For what value of "excellent"? Theoretically, you're right. Practically, both the compression part and the decompression part of this algorithm just cost too much time.

 

[Modified]

No, I'm saying the "base 10 numbers that we use" has nothing to do with it, as you implied it did, but I think you already know that.

His other point seems to be that a circle is a curved shape, which also has nothing to do with it.

 

[MetalPig]

For what value of "excellent"? Theoretically, you're right. Practically, both the compression part and the decompression part of this algorithm just cost too much time.

Throw more hardware at it

 

[Jack by the hedge]

Throw more hardware at it

Could you train an infinite number of monkeys to search pi for stuff?

Every book, every song, every movie that ever was or ever could be is in pi somewhere.

There's an infinite number of copies of every movie, in fact. Plus an infinite number of each of the infinite number of variations on the original. Of course an infinite number of these would be extremely pornographic. (Won't somebody think of the monkeys?)

So - which version of which movie shall we set them to find first?

 

[Mikemcc]

Anybody who's read Contact knows there's a buried message in pi...

 

[69dodge]

Which makes for an excellent compression algorithm. Any movie, mp3, application or what have you can be reduced to 2 integers; starting position and length.

An interesting idea. But the integers could be very large. Then, the compression ratio would be poor, because the compressed version would consist of all the digits of those large integers.

 

[ddt]

Throw more hardware at it

Are you trying to imitate Jan Sloot and his alleged super compression?

Romke Jan Bernhard Sloot (27 August 1945, Groningen—11 July 1999[citation needed], Nieuwegein) was a Dutch electronics technician, who claimed to have developed a revolutionary data compression technique, the Sloot Digital Coding System, which could compress a complete movie down to 8 kilobytes of data— this is orders of magnitude greater compression than the best currently available technology.

(wiki)

 

[dasmiller]

For what value of "excellent"? Theoretically, you're right. Practically, both the compression part and the decompression part of this algorithm just cost too much time.

Here's a variation on it - rather than pi, start with a string of digits that simply represents the integers smashed together: 01234567891011121314 etc

Now you can trivially compute where your digital book would lie on that number string, so there's no time wasted searching the string, and no more messy computations to come up with zillions of digits of pi. Simply give someone the index of the starting point and the length and - voila!

(yes, I know the critical flaw in this plan. That's what makes it funny for me)

 

[Ziggurat]

Is that possible? Is there such a thing as 3-ish or pi-ish? I could easily be falling for some kind of inside math joke but you'd have to explain it...which would ruin its humour value but might be educational in some way.

It's a joke. In math (and physics), many functions have limiting behavior, meaning that they approach some particular value for large enough (or small enough) values of the variable you plug into the function. So it's common to talk about, say, large values of 'x', or 'y', or whatever your variable is. The 'joke' (which isn't 'ha-ha' funny so much as absurd funny) is in treating a number like a variable. There's no such thing as "large values" of a number: a number has a specific value. Treating it like a variable has a sort of bizarre logic to it, but it produces nonsense. Like 2+2=5 for sufficiently large values of 2.

 

[Ziggurat]

Could you train an infinite number of monkeys to search pi for stuff?

Every book, every song, every movie that ever was or ever could be is in pi somewhere.

There's a classic problem in probability where you calculate the probability that some vast number of monkeys randomly hitting keys on a typewriter would type out some particular book. That's essentially equivalent to what you're asking for. It turns out that even for large numbers of monkeys (say, 10 billion), fast typing speeds (10 characters/sec), and long time scales (the current age of the universe), the probability of any of them typing even a few lines of Hamlet is incredibly small.

Variants of this problem are often assigned in statistical mechanics classes to give students some idea of how improbable certain outcomes can be, and why for macroscopic systems we can treat the improbable outcomes as being impossible even though technically they aren't.

In other words, regardless of what might be in pi, you won't find much. Also, there's no guarantee that every book, or even any book, is in pi. pi doesn't have to contain every possible finite number string. In fact, it's trivially easy to construct irrational numbers which are guaranteed to NOT have every finite number string.

 

[Towlie]

Also, there's no guarantee that every book, or even any book, is in pi. pi doesn't have to contain every possible finite number string. In fact, it's trivially easy to construct irrational numbers which are guaranteed to NOT have every finite number string.

I think your first two sentences are definitely wrong and your last sentence is probably wrong too. Let's see what the others have to say about it.

 

[69dodge]

Here's an irrational number: 1.101001000100001000001...

(The pattern is that each 1 is followed by a string of 0s consisting of one more 0 than the previous string of 0s.)

There are lots of finite strings it doesn't contain: any string containing even a single 2, for instance.

 

[Ziggurat]

I think your first two sentences are definitely wrong and your last sentence is probably wrong too. Let's see what the others have to say about it.

My last sentence is rather easy to prove. Take the binary expression for pi. It's non-repeating and infinite, but it's only 0's and 1's. Now make a number whose base 10 expression is equal to pi's binary expression. It's infinite and non-repeating, so this new number is also irrational. But it's guaranteed to not have any strings containing the decimals 2, 3, 4, 5, 6, 7, 8, or 9, even though it's a base-10 number. So clearly, it's possible for irrational numbers to not contain every possible finite digit sequence. I just made one.

As for my former statement, well, that's really just a claim of a LACK of proof that pi does contain every string. You may suspect that pi contains every finite string, and maybe it does, but if you haven't proven that it does, then you only have a suspicion.

 

[readme.txt]

I think your first two sentences are definitely wrong and your last sentence is probably wrong too. Let's see what the others have to say about it.

His last sentence is not wrong. You can build a transcendental number that only has zeros, ones and twos and it will never contain the sequence 6578.

1,01221021010121021020201010102012021021021021021010201201021210120201202222211202100001212...

 

[readme.txt]

My last sentence is rather easy to prove. Take the binary expression for pi. It's non-repeating and infinite, but it's only 0's and 1's. Now make a number whose base 10 expression is equal to pi's binary expression. It's infinite and non-repeating, so this new number is also irrational. But it's guaranteed to not have any strings containing the decimals 2, 3, 4, 5, 6, 7, 8, or 9, even though it's a base-10 number. So clearly, it's possible for irrational numbers to not contain every possible finite digit sequence. I just made one.

As for my former statement, well, that's really just a claim of a LACK of proof that pi does contain every string. You may suspect that pi contains every finite string, and maybe it does, but if you haven't proven that it does, then you only have a suspicion.

I agree. Maybe there's a proof, but I don't know it. Does Pi contain its own first billion decimals somewhere else after the billionth decimal?

 

[ddt]

Also, there's no guarantee that every book, or even any book, is in pi. pi doesn't have to contain every possible finite number string. In fact, it's trivially easy to construct irrational numbers which are guaranteed to NOT have every finite number string.

The notion you're looking for is normal number:

In mathematics, a normal number is a real number whose digits in every base follow a uniform distribution: all digits being equally likely, all pairs of digits equally likely, all triplets of digits equally likely, etc.

While a general proof can be given that almost all numbers are normal, this proof is not constructive and only very few concrete numbers have been shown to be normal. It is for instance widely believed that the numbers √2, π, and e are normal, but a proof remains elusive.

So it's an unproven, but widely believed, conjecture that this property holds for pi.

 

[Bill Thompson]

we are debating this?

that is the most amaizing thing I have ever seen.

If it repeated, it would also end using a different numeric base other than base 10. Repeating is the same thing as ending. Any number that does not divide into 10 without a remainder repeats just like 1/3rd.

Pi never repeats.

People are arguing mathimatical truths here. I find that astounding.

 

[dasmiller]

I agree. Maybe there's a proof, but I don't know it. Does Pi contain its own first billion decimals somewhere else after the billionth decimal?

Almost certainly, but of course, "almost certainly" isn't sufficient for a mathematical proof.

But there's a fair chance (50%?) that a repeat of the first billion digits occurs somewhere in the first 10^billion digits.

Of course, 1E1,000,000,000 is a large number.

 

[Bill Thompson]

There are 10 kinds of people in the world: the people who understand binary and the people who do not.

No, I'm saying the "base 10 numbers that we use" has nothing to do with it, as you implied it did, but I think you already know that.

It does.

if we used a numeric base that you could divide by 3 without a remainder, then lots of numbers that repeat under base 10 would not.

What numeric base you use determines what numbers repeat (like 0.3333333333...) and what numbers do not.

Maybe I do not understand what your point is. If you are saying it does not matter what numeric base we use to count and that Pi will never end or repeat, then you are agreeing with me.

(There are 10 kinds of people in the world: the people who understand binary and the people who do not.)


The point is, Pi never repeats. It does not matter what sort of counting system you use. It never repeats. Ever. IF PI REPEATED IN BASE 10 NUMBERS IT WOULD ALSO END IF WE USED A DIFFERENT COUNTING SYSTEM. Pi is the length it takes to draw a circle divided by its diameter. The diameter can be an easily determined number 1, 2, 3... but use that straight line as a unit to represent the circumference and you will get a number that can never be accurately 100% represented because you will always be using what amounts to straight line sebments to represent a curve.

Maybe some people just can't get it. Maybe it is just one of those things you can see or you cannot see (like Fermi's Paradox or what year the millennium began).

The fact that people will debate and argue mathematics is proof that we are not an intelligent species. That is what I am getting from this discussion thread.

 

[readme.txt]

if we used a numeric base that you could divide by 3 without a remainder, then lots of numbers that repeat under base 10 would not.

What numeric base you use determines what numbers repeat (like 0.3333333333...) and what numbers do not.

Maybe I do not understand what your point is. If you are saying it does not matter what numeric base we use to count and that Pi will never end or repeat, then you are agreeing with me.

(There are 10 kinds of people in the world: the people who understand binary and the people who do not.)


The point is, Pi never repeats. It does not matter what sort of counting system you use. It never repeats. Ever. IF PI REPEATED IN BASE 10 NUMBERS IT WOULD ALSO END IF WE USED A DIFFERENT COUNTING SYSTEM. Pi is the length it takes to draw a circle divided by its diameter. The diameter can be an easily determined number 1, 2, 3... but use that straight line as a unit to represent the circumference and you will get a number that can never be accurately 100% represented because you will always be using what amounts to straight line sebments to represent a curve.

Maybe some people just can't get it. Maybe it is just one of those things you can see or you cannot see (like Fermi's Paradox or what year the millennium began).

Wow, are you angry at someone or what?

The fact that people will debate and argue mathematics is proof that we are not an intelligent species. That is what I am getting from this discussion thread.

Isn't that a bit far-fetched?