[FOM] throwing darts at natural numbers (reply to Arnon Avron)

[Thomas Lord]

On Sun, 2009-08-02 at 09:25 +0300, Arnon Avron wrote:

> Well, believe it or not, but this is what will happen also
> when your two friends throw darts at the real numbers between 0 and 1...

A problem with this discussion is the
application of a physical intuition
to a situation which can not be physically
realized.  There is no such thing as a 
dart with a perfect point tip.  There is
no such thing as measuring where a dart hits
with arbitrary precision.  Our mammal brains
and their sense of space and mechanics fail
us at that fine a level of detail.  Unsurprisingly.

People are making apples v. oranges
comparisons between "what it's like to throw darts"
and "what sentences are true in certain formal
systems".

The dart-throwing family of analogies to 
reals is handy because using it we can often
guess things that can be proved about the reals.
The reals are handy because they can often be
used to formally compute some empirically 
verifiable facts about dart throwing.

All that we have here in this quasi-paradox
is confirmation that reals are not a perfect
model of dart throwing and vice versa.

-t