I wonder about what limits a computers ability to compute decimals of pi?

Time?

Until the floating point logic reaches his limits

You don't keep the computed number as a floating point variable, but as a list of digits. As long as you don't run out of disk space, the list can be quite long.

http://www.geom.uiuc.edu/~huberty/math5337...pe/welcome.html

Just bump up the number of associated disks:

http://www.physorg.com/news5424.html

Assuming each decimal digit of Pi takes one byte to store (actually, we can do it with 4 bits, or two digits per byte), then we could have 10^18 digits. If we can read 10 digits a second, it would take only 3 million years to read the number.

We'ed better get started then!

When/why would we ever need to have just an accurate definition of pi?

Because the decimal expansion of Pi is a pseudo-random number. Very useful. So is the binary expansion and also any digital expansion of any irrational number. Pick your special number. Then pass the expansion through a decrypter and read the secret messages.

http://teamster.usc.edu/~fixture/Robotics/PrivCrypt.html

How do you know? :

The digit pattern of the digital expansion of any irrational number never repeats (or it would be rational). The next digit in the sequence is not predictable, it must be computed. Unpredictability is one of the definitions of randomness. Even distribution is usual, but not required. That is, there might be twice as many 3s as 5s in the expansion of Pi, and it would still be random, just with an uneven probability distribution. Maybe you should do a digit frequency analysis of Pi and e. I'm busy working on the pseudo-prime factoring problem.

Was there a mathematical proof of this? (Not that I doubt that it's true, I'm just curious to see what the proof would look like)

it's follows directly from the definition of irrational number.

On a side note, Stephen Wolfram says in his New Kind of Science that human life, which he equates with a cellular automata, is as meaningless as the digits of Pi. Some food for thought (though not much).

I thought Wolfram's book was a bit tedious.

"Life's but a walking shadow; a poor player,
That struts and frets his hour upon the stage,
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury,
Signifying nothing." --William Shakespeare, Macbeth

However, for the full brunt of the meaninglessness angle, see nightrover's posts.

Hm...is Pi an endless cellular automata? Certain cases of cellular automata cannot be predicted (as Wolfram says). They have to be computed and thats about all you can do. Maybe there is a way to model Pi as a cellular automata.