Can we return to the subject of pi please, now who wants apple and who wants cherry? Do you want cream with that
Is anyone surprised by the above? I'd only be surprised if Pi did not appear random in such a fashion.
Well, you can say that... and I cannot argue as I cannot prove that any other possible universe does not exist. But mathematics is the language of our universe, this much we know to be true. If you want to insist on other possible universes, then you should be the first to accept that patterns can be imbedded into mathematical constants as these constants would change for another "possible" universe.
Whether other Universes actually exist or not is irrelevant. Mathematics is the languages of all possibilities of existence, regardless of whether such possibilities are actualized - witness our recent discussions of Newtonian universes, and SR-only universes. I suggest that while physical constants may change, mathematical constants may not.
Point accepted. However, I do contend that the alien circle pattern as mentioned by SL is possible given then infinite length on the digits of pi. Some local pattern is bound to happen just by chance. I wouldn't put any meaning into this as the ficticious aliens apparently did, but nevertheless, it would be cool to find.
Pete, I totally agree with you. No matter what universe you inhabit, curvature is curvature. If you set up the mathematical construct called a plane (of zero curvature) and describe a closed curve of uniform constant curvatrue on the plane, and divide the perimeter length of this closed curve by the distance between two points that are diametrically opposed, you will always get the ratio pi. (that would be a CIRCLE for those of you not living in my universe...)
Is there an algorithm to get any digit of π in binary without knowing any of the preceeding digits - similar to the BBP formula for hexadecimal?
I think the binary immediately follows from the hex... Every hex digit corresponds to 4 binary digits, so if you know the nth hex digit, you immediately know the 4n-3 to 4n binary digits. eg if the billionth hex digit is B, then the binary digits from the 3,999,999,997th to 4,000,000,000th are 1011.
I guess the question is what the chances are of finding said pattern within the first n digits. Or, what is the chance of the first set of 1s and zeros of length greater than 20 being a set of 121 that represent an 11x11 picture of a circle?
Argh, now I have to figure out how this hexadecimal mathematics works in computer language. Damn you.
You can find about any code you want in a book of sufficient length. So I imagine you can find any code you want in the digits of pi given a sufficient length of the digits.
Yes, of course... but that's not relevant to what I said. What is the probability that said pattern (11x11 picture of a circle) could be found in (say) the first 10<sup>100</sup> digits of Pi? Not even worth considering! What is the probability that the first sequence of 1s and 0s of length 20 or more occurring in Pi would be of length greater than 100? Not even worth considering!
Please Register or Log in to view the hidden image! What language / environment are you working in? Often you can represent hex numbers using the 0x prefix: eg 0xC is the same as 12 (but I don't know if that helps!)
Any reason why you chose a google digits? I'd say the probability is ~100% Please Register or Log in to view the hidden image! I got lost in the middle of that sentence. Reading from the beginining of the sentence to the end does nothing for me. Let me try end to beginining... Yeah, that makes no sense. Try it: considering worth even not 100 than greater length of be would pi in occuring more or 20 length of 0s and 1s of sequence first the that probability the is what?
And how did you calculate your wild-ass-guess? I know you can do it! Imagine that you search the digits of pi from the beginning until you find twenty digits in a row with nothing expect ones and/or zeros. What is the probability that these twenty digits are the first in a group of 121 that represent a picture of a circle? Do you get it yet? In the novel, the surprising thing was not that such a sequence could exist in the digits of pi, but that it is was found so early. This was spelled out pretty explicitly... have you read it?
Something about an approximation to a circle using a polygon with google line segments wouldn't fit inside the universe. So someone said once anyway. OK - there in lies the problem. I was considering the binary digits of π, not the decimal digits. 0. No I haven't Please Register or Log in to view the hidden image! Again, in what base? I'd only consider binary.
I've heard there's a two-line hymn in the language Sanskrit, which gives the value of pi/10 upto a certain number of decmal places, using a system which substitutes the letters of Sanskrit with the 9 digits. That's not very surprising. What is surprising is that apart from the fact that it can be read in two ways, as hymns to two different Hindu Gods, it also contains a formula for extending the value to any number of decimal places. Unfortunately, I don't know Sanskrit, and so cannot verify this. Is there anyone here who does?
And there are vimanas buried with the ancient cities of India as well. I suspect that the meaning of life can be found in Sanskrit too Please Register or Log in to view the hidden image!
