[extropy-chat] Role of Observer is not Relevant

[Mike Dougherty]

On 4/3/07, Jef Allbright <jef at jefallbright.net> wrote:
> Amplifying John's point here, if you were to imagine throwing a dart
> at a perfect number line representing the range from 0 to 1, you would
> have zero chance of exactly hitting a rational number.

A perfect number line?  Is that a line of 6's?  Wait a minute, there
are no perfect numbers from 0 to 1...

Actually, given the relative fatness of the dart i'm pretty confident
there is a nonzero probability that more than one rational number lies
within the interval of the width of the dart.  For the sake of
argument, lets draw the target line after the dart is thrown so we
don't have the requirement of landing to either side of the
unidimensional line.

on a tangential note...

A friend of mine once explained to me an idea he encountered for
encoding an [arbitrarily long | infinite] library of knowledge:
Represent each byte of a data stream as the next decimal place of a
Real number between 0 and 1.  Using a very accurate mark on a unit
measure, you would have completely encoded the data stream.  Of course
the limitation of physical reality makes this impractical to carry
around an actual object - but mathematically my first impression of
this 'scheme' was to remind him of the pervasiveness of phi as a
candidate to suggest this encoding may already be done, he just needs
to figure out the decode.

just in case you haven't already encountered this amazing irrational
number: http://en.wikipedia.org/wiki/Golden_ratio