[LINK] Numbers limit how accurately digital computers model chaos

Bernard Robertson-Dunn brd at iimetro.com.au
Tue Sep 24 22:48:51 AEST 2019

On 24/09/2019 5:10 pm, Stephen Loosley wrote:
> Numbers limit how accurately digital computers model chaos
Gee, do these people not know how to research their subject.

Michael V Berry wrote about this subject in 1978 and was quoted by
Nassim Taleb in the Black Swan.

"On a billiard table, if you know a set of basic parameters concerning
the ball at rest, can compute the resistance of the table (quite
elementary), and can gauge the strength of the impact, then it is rather
easy to predict what would happen at the first hit. The second impact
becomes more complicated, but possible; and more precision is called
for. The problem is that to correctly compute the ninth impact, you need
to take account the gravitational pull of someone standing next to the
table (modestly, Berry's computations use a weight of less than 150
pounds). And to compute the fifty-sixth impact, every single elementary
particle in the universe needs to be present in your assumptions! An
electron at the edge of the universe, separated from us by 10 billion
light-years, must figure in the calculations, since it exerts a
meaningful effect on the outcome. (p. 178)"

The cause is non-linearity not chaos. Chaos is the result. The problem
is not just the accuracy of the numbers used to represent real values,
but any source of error, perturbation or simplification.



Bernard Robertson-Dunn
Canberra Australia
email: brd at iimetro.com.au

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