Re: how do I get more numbers past the decimal?

Gordon Burditt wrote:
aroused an awareness that these equations were sensitive to very small
changes in input. This is from page 16 of Gleick's book:
And if his machine had stored 50 decimal places, he would have gotten
yet different results.

It doesn't matter what language you are using - you will NEVER get exact
results for a random number in any language. That's what random is all
about. You will also never get exact results for some math operations,
like (1/3) * 3 will never equal 1. It doesn't matter what language you
use - it's a fact of digital life.

What you need to do is determine how much accuracy you really need.

Understood. I guess I'll take that question to a forum focused on
math. I've no idea what level of precision is considered meaningful in
this context, though I imagine there are forums where people can offer
some insights into that subject.

Question: is Chaos Theory the theory of roundoff errors?

No.

In other
words, if you do the math EXACTLY (e.g. using algebra, not reducing
everything to numbers immediately, so at least the errors cannot
cascade. Hint: this will be time-consuming.), do all the wierd
things described still happen?

Yes.

Chaos theory is about the incredibly complex solutions possible from very simple equations.

Even if they are exact solutions.

And its also about sensitivity.

The bullet that misses by a hairsbreadth and doesn't kill you, and the one that gets a slight gust and does..

Its also about the mathematics of edges, because edges are binary things in an analogue world.

If you like the simplest example of a chaotic system is balancing a pencil on its point, and working out which way it will fall.

Never mind the maths, you know it depends on the draught that sets it in motion, or the precision with which you can balance it.

If a set of equations has a widely varying solution depending on small variations in its terms, you know its a very unstable description. Plenty of life features things like that. Just not for long..:-)
.

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