🚀 go-pugleaf

On Sun, 30 Mar 1997 21:49:49 -0500, Chris Wagner
<wagnerc@ucunix.san.uc.edu> wrote:

>Haplo wrote:
>> 
>> >So it would seem, Ivo, but if so then the ancient philosopher Zeno must be
>> >correct. Zeno proved logically that motion was purely illusion, not really
>> >existing at all.
>> 
>> >To understand his argument, picture yourself against the
>> >wall of a room preparing to walk to the other side. As you walk, you pass a
>> >point halfway to the opposite wall. Then you pass a point half of the
>> >remaining distance. Then you pass another point . . . ad infinitum.
>> >Mathematically, you will ever reach the wall because you will only continue
>> >getting halfway from where you are.
>
>Mathematically he is correct.  


Nope. Actually Zeno's paradox pointed up a deficiency of the
mathematics of his time which, corrected, formed the basis of
calculus.

The point is that the series of steps each takes a corespondingly
shorter time. So if the time it really takes to cross the room is 1
second then the first step takes 1/2 seconds, the second 1/4 and so
on. The total time up to the nth step is 1 - 1 / (n + 1) ergo we don't
reach the wall because the description doesn't reach the _time_ when
we reach the wall.

Zeno assumed, in effect, that the sum of an infinite sequence of
positive numbers (the time for each step) must be infinite while
correctly pointing out that another infinite series (the movement) has
a finite limit.

---------------------------------+----------------------------------
I was born weird:  This terrible | Like Pavlov's dogs we are trained
compulsion to behave normally is | to salivate at the sound of the
the result of childhood trauma.  | liberty bell.
---------------------------------+----------------------------------
Malcolm