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> Computer computingpower?, Pi?
Isse
post May 31, 2007, 12:18 PM
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I wonder about what limits a computers ability to compute decimals of pi?
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Hey Hey
post May 31, 2007, 12:28 PM
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Time?
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Dragan
post May 31, 2007, 01:34 PM
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Until the floating point logic reaches his limits
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Rick
post May 31, 2007, 02:14 PM
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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
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Hey Hey
post May 31, 2007, 02:49 PM
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Just bump up the number of associated disks:

http://www.physorg.com/news5424.html
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Rick
post Jun 04, 2007, 10:21 AM
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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.
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Hey Hey
post Jun 04, 2007, 09:18 PM
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We'ed better get started then!

When/why would we ever need to have just an accurate definition of pi?
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Rick
post Jun 05, 2007, 09:31 AM
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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
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Hey Hey
post Jun 05, 2007, 10:45 PM
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QUOTE(Rick @ Jun 05, 2007, 06:31 PM) *
Because the decimal expansion of Pi is a pseudo-random number
How do you know? :
QUOTE(Rick @ Jun 04, 2007, 07:21 PM) *
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.

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Rick
post Jun 06, 2007, 08:38 AM
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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.
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Hudzon
post Oct 06, 2007, 05:25 AM
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QUOTE
The digit pattern of the digital expansion of any irrational number never repeats

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)
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lucid_dream
post Oct 06, 2007, 09:10 AM
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QUOTE(Hudzon @ Oct 06, 2007, 06:25 AM) *

QUOTE
The digit pattern of the digital expansion of any irrational number never repeats

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).

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Rick
post Oct 08, 2007, 02:50 PM
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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.
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TorusZL
post Oct 25, 2008, 08:28 PM
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QUOTE(lucid_dream @ Oct 06, 2007, 01:10 PM) *

QUOTE(Hudzon @ Oct 06, 2007, 06:25 AM) *

QUOTE
The digit pattern of the digital expansion of any irrational number never repeats

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).


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.
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carrie322
post Aug 07, 2013, 02:57 PM
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You don't keep the calculated variety as a sailing factor varying, but as a record of numbers. Provided that you don't run out of hard drive area, the record can be quite lengthy.
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Alan peterson
post Mar 17, 2015, 03:21 AM
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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.
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