Joshua Bell wrote:
>
> There's a great quote I came across somewhere: "Average
> weather is a myth." That is, weather is chaotic, and
> while you can point to an average over time
> the fact is that unlike a nice bell curve, very few
> years will have "average weather".
>
Hmmm... I think this "Average weather is a myth" comes
from the new mathematics tools developed after Chaos
was analysed. It might be something related to the
fact that certain numerical series can't have an
average, in other words, that the numerical series
generated by taking the average of the previous
elements is again a divergent series.
A trivial example is the series:
x[1] to x[9] = 0
x[10] to x[99] = 1
etc
[or x[10^n] to x[10^(n+1)-1] = 0 if n is even or
1 if n is odd]
If we define the series
y[n] = (x[1] + ... + x[n]) / n
Then y[n] oscilates from 0 to 1 - in other words,
the initial series has no average [well, actually,
I guess y[n] oscilates from 0.1 to 0.9; but the
idea is the same, and we can change x so that y
will oscilate from 0 to 1]
Alberto Monteiro
