[LINK] Numbers limit how accurately digital computers model chaos
dlochrin at key.net.au
Wed Sep 25 18:51:31 AEST 2019
On Wednesday, 25 September 2019 16:36:10 AEST Bernard Robertson-Dunn wrote:
> As you state, mathematics is a language, a model, of the real world. It may exist on its own in the real world (you can get a degree in the subject), but like any other language, its use is as a representation or reality, validated by experiment.
> And when you put numbers (data) in a model, it can become more than a generalisation, it can become highly specific - Apollo 11 on its journey to the moon and back.
We could have a long debate about this!
I suggest the axioms of any given system of mathematics are concepts derived from the real world. And as Kurt Gödel showed, no formal system can be complete because some _true_ propositions therein cannot be proved. This seems disappointing for something made in heaven.
But mathematics itself is not used to model the real world. Such models are the province of physics, where they're known as "theories". Mathematics is used to express and quantify these theories, but their substance is more like a fictional story with very special constraints; for example all observable aspects must accord with what we actually observe, and they must be consistent with other, established, stories.
Newtonian & Einsteinian gravitation constitute a classic example of two theories / stories which are wildly different in substance and in the mathematics used to express them. That's physics.
Well IMHO anyway...
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