Re: Hello There?
Robert Low wrote:
Nam Nguyen wrote:
A sequence of 2 decimal digits could represent any value, between
0 and 100: plenty of room for representing any alphabet from a-z, A-Z,
0-9, a blank, and some more. So in the infinite decimal expansion
of a transcendental such pi or e, I wonder if there would exist
a meaningful sentence or phrase such as "Hello There"?
Assuming that pi is normal, any
(finite) message you are interested
in is encoded there, in the
encoding of your choice.
I actually don't know (or remember) the definition of a transcendental's
being "normal". Of course we certainly could create a transcendental
containing "Hello There" simply by putting it there, say, in front
of pi's decimal expansion. The motivation for asking the question is
that "Hello There" is too short; so pi may "accidentally" contain it.
But, in the name of abstract mathematics, let's assume we have a DVD
huge enough to contain a very high resolution audio-video movie-frames
of the Earth for the past 65 million years. [In brief, the DVD also
contains many intelligent-conversations]. Now, the longer this
_finite_ DVD is, the more difficult we could imagine that pi
(in the binary format now) could contain it. But pi is still an
infinite number, so it's equally hard to see why pi couldn't
accommodate such a finite DVD. Also, pi is algorithmic; so *if*
such DVD exist in pi, could we say then *in principle*, we can
formalize biological life processes and human intelligence, through
the algorithm that generates pi? Just a curiosity though.
.
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