Here''s my two cents worth. First, to the original poster, random does not imply that all the digits pop up equally often. Nor does it, as some other posters clearly think, mean the number is "different each time". Random, in the mathematical sense, means that it is uncompressible, i.e. that it cannot be represented with 100% accuracy by any number (or combinations of numbers, as in formulas) smaller than itself.
Wether PI is in fact a random number is not known, but if what we''ve found out about it''s digits so far is any indication it most probably is.
As a sidenote I''d like to add that the fascination some of you have for finding more and more digits of PI is completely useless. Knowing PI to 34 digits is enough to describe a circle spanning the entire known universe with less margin of error than the size of a hydrogen-atom.
~Neophyte
-Death awaits you all, with nasty, big, pointy teeth
Is pi truely random?
Yeah, I guess finding Pi out to 10000 digits might not be useful in a practical sense. However, it makes an interesting problem that may bring out some interesting ideas in numerical analysis. Kind of like this: Although there exists a proof supporting Fermat''s Last Theorem, people still search for different ways to prove it. It''s just fun!
"... you act as if stupidity were a virtue."
-- Flight of the Phoenix
"... you act as if stupidity were a virtue."
-- Flight of the Phoenix
Hahaha that''s funny Buster. Is that the theory of pi relativity?
For some of you who don''t understand the discussion, pi, as it is used for measuring, is not a random number, but the digits themselves are in a random sequence as you go to smaller and smaller decimal places.
I think it is possible that the "randomness" of pi is not a question, but rather an answer to fit some mathematical law that we may not have discovered yet.
For some of you who don''t understand the discussion, pi, as it is used for measuring, is not a random number, but the digits themselves are in a random sequence as you go to smaller and smaller decimal places.
I think it is possible that the "randomness" of pi is not a question, but rather an answer to fit some mathematical law that we may not have discovered yet.
Everyone seems to agree that PI, the mathematical constant, is not random, nor is its decimal form to any precision. Now, for the distribution of 1s & 0s when pi is represented as binary, certainly you will get the same result everytime you approximate PI to the same precision. The original post asked about half of the digits being 1 and the other half being 0. It is generally held that PI''s digits are infinate in their amount when it is approximated (is there a proof of this) and taking half of infinity doesn''t make any sense.
...
The more I think about this, the more I believe that the distribution of 1s & 0s when PI is represented as binary must be random. Sorry I can''t explain it as I haven''t taken the proper courses in math. Now I''m pissed.
...
The more I think about this, the more I believe that the distribution of 1s & 0s when PI is represented as binary must be random. Sorry I can''t explain it as I haven''t taken the proper courses in math. Now I''m pissed.
About finding every string of numbers within pi, it''s similar to the thing about ''if you put a monkey in front of a piano and let him hit random keys for infinity, he''ll play every piece ever composed.''
messner
messner
Pi is not random. Nothing is random. However, after a certain point, it is impossible to predict something due to chaos theory, thus giving the appearance of randomness.
Furthermore, pi will never change; it will always be pi = C/D
and as a side note, e^(pi*i) = -1 proving e cannot be random either
Furthermore, pi will never change; it will always be pi = C/D
and as a side note, e^(pi*i) = -1 proving e cannot be random either
I believe what the original question was, that if you looked at the first 10,000,000 digits of pi, about how many of those would be 1''s, 2''s, 3''s, ect...
and it mostlikely would be that if you looked at the first 10million digits, you would find
about 1 million 1''s
about 1 million 2''s
about 1 million 3''s
ect...
so in that sense, pi is random, but of course pi itself is not random, for it is precisely defined.
Possibility
and it mostlikely would be that if you looked at the first 10million digits, you would find
about 1 million 1''s
about 1 million 2''s
about 1 million 3''s
ect...
so in that sense, pi is random, but of course pi itself is not random, for it is precisely defined.
Possibility
Ok everybody, let''s all join hands and start drawing conclusions from the empty set.
"... you act as if stupidity were a virtue."
-- Flight of the Phoenix
"... you act as if stupidity were a virtue."
-- Flight of the Phoenix
Author
Okay okay.. OF COURSE I didn''t mean to ask if pi is random in "rand()%10=next digit"-way. I just meant that can you find every possible finite pattern inside pi? And are the frequencies the same of getting 0 or 1? And obviously there is no answer to this..
I just thought about this because of that new formula with which you can calculate every digit of pi without calculating the preceding digits first.. but this only works in binary form (and other 2^n-forms I quess).
If you''re interested about the formula go to:
http://www.mathsoft.com/asolve/plouffe/plouffe.html
I just thought about this because of that new formula with which you can calculate every digit of pi without calculating the preceding digits first.. but this only works in binary form (and other 2^n-forms I quess).
If you''re interested about the formula go to:
http://www.mathsoft.com/asolve/plouffe/plouffe.html
HEY, wait, lets get back to messner''s post about the monkey...
If a monkey were to randomly hit keys on a piano for infinity, it wouldn''t play every piece ever made. That''s because a monkey would hit the keys with it''s fist and never play individual coords or sequence of keys. Some coords are difficult to play for a human and almost imposible for a monkey.
Common people, let''s not drift off the more important parts of the discussion!
E:cb woof!
If a monkey were to randomly hit keys on a piano for infinity, it wouldn''t play every piece ever made. That''s because a monkey would hit the keys with it''s fist and never play individual coords or sequence of keys. Some coords are difficult to play for a human and almost imposible for a monkey.
Common people, let''s not drift off the more important parts of the discussion!
E:cb woof!
This topic is closed to new replies.
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