[LINK] Numbers limit how accurately digital computers model chaos

[Bernard Robertson-Dunn]

On 26/09/2019 12:18 am, antonybbarry at gmail.com wrote:
>
>
> Antony Barry
> antonybbarry at me.com <http://me.com>
> Mob +61 433 652 400
>
> On 25 Sep 2019, at 6:51 pm, David <dlochrin at key.net.au
> <mailto:dlochrin at key.net.au>> wrote:
>
>> We could have a long debate about this!
>
> Been done.
>
> The Unreasonable Effectiveness of Mathematics in the Natural Sciences
> - Wikipedia
> https://en.m.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
>
Thanks Tony, good to see you again in this forum.

... "mathematical formulation of the physicist's often crude experience
leads in an uncanny number of cases to an amazingly accurate description
of a large class of phenomena".

Mathematical models can be used in two domains - one to describe and
explain in general, the other to predict behaviour in the specifc.

In the first, non-linearity hardly matters. In the second it is critical.

A classical example is the three body problem. A mathematical model can
be constructed that explains, at a conceptual and logical level, the
structure and relationships of three masses.

The equations are not solvable, analytically. When a specific example is
modeled numerically, the errors grow exponentially which make
predictions useless, beyond a certain limit.

Getting back to the original post, all this has been known for quite a
long time.

To quote from my first comment:

> Numbers limit how accurately digital computers model chaos
Gee, do these people not know how to research their subject.

IMHO, the issue is not mathematics or chaos, it's the state of what
passes for research today.

Bernard

-- 

Regards
brd

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