From: scerir (scerir@libero.it)
Date: Sun Mar 10 2002 - 08:02:44 MST
the famous conversation between a human
and an alien, in Carl Sagan's 1985 (*) novel
'Contact'
'Your mathematicians have made an effort to
calculate it out to ... let's say the
ten-billionth place. You won't be surprised
to hear that other mathematicians have gone
further. Well, eventually - let's say it's in
the ten-to-the-twentieth place - something
happens. The randomly varying digits disappear,
and for an unbelievably long time there's
nothing but ones and zeros ...'
'And the numbers of zeros and ones? Is it a
product of prime numbers?'
'Yes, eleven of them.'
'You're telling me that there's a message
in eleven dimensions hidden deep inside
the number pi? Someone in the universe
communicates by ... mathematics? ...
How can you hide a message inside pi?
It's built into the fabric of the universe.'
'Exactly'
She stared at him.
'It's even better than that,' he continued.
'Let's assume that only in base-ten arithmetic
does the sequence of zeros and ones show up,
although you'd recognize that something funny's
going on in any other arithmetic. Let's also
assume that the beings who first made this
discovery had ten fingers. You see how it looks?
It's as if pi has been waiting for billions
of years for ten-fingered mathematicians with
fast computers to come along. You see the Message
was kind of addressed to us.'
---------
(*) If pi is indeed normal, looking for a message
in its digits would be like searching for meaning
in Jorge Luis Borges' imaginary library of Babylon,
in which the books contain every possible combination
of letters and punctuation.
While there may be no cosmic message lurking in pi's
digits, if they are random they could be used to
encrypt other messages as follows:
Convert a message into zeros and ones, choose a string
of digits somewhere in the decimal expansion of pi,
and encode the message by adding the digits of pi
to the digits of the message string, one after another.
Only a person who knows the chosen starting point
in pi's expansion will be able to decode the message.
Bailey, D. and Crandall, R.
'On the random character of fundamental constant expansion',
in Experimental Mathematics, 10, 175 - 190, (2001).
http://www.nature.com/nsu/010802/010802-9.html
the Bailey-Plouffe-Borwein algorithm
http://www.mathsoft.com/asolve/plouffe/plouffe.html
http://www.cecm.sfu.ca/personal/plouffe/
http://www.eecs.umich.edu/~grbarret/pi/pi_links.html
http://www.joyofpi.com/pilinks.htm
http://www.escape.com/~paulg53/math/pi/links.html
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