[LINK] Numbers limit how accurately digital computers model chaos
dlochrin at key.net.au
Wed Sep 25 15:11:55 AEST 2019
On Wednesday, 25 September 2019 10:35:44 AEST Roger Clarke wrote:
> All mathematics involves intellectual models / mind-stuff.
> Mathematics is not, and not of, the real world.
Now that's a very brave assertion IMO. It can also be argued the reason why mathematics allows us to model the real-world so successfully is that it's a generalisation derived from the world we see around us. That's why the number "zero" was late to be recognised, for example.
The most beautiful equation of all is perhaps Euler's formula: e^(iϑ) = cosϑ + i sinϑ
where 'e' is the base of natural logarithms, 'i' is the square-root of -1, 'ϑ' is any angle, and ^ means to-the-power. If ϑ=pi this reduces to the wondrous equality e^(i pi) = 1 which is a relation between transcendental numbers. But even that doesn't imply that mathematics comes from some spiritual other-world.
> But the media, and the public, are very prone to confusion, because they've never heard Einstein's dictum 'God doesn't play dice with the world'.
On Wednesday, 25 September 2019 11:31:38 AEST Karl Auer wrote:
> Einstein was apparently wrong with is "Der Herrgot wuerfelt nicht". As Bohr said in response "Der Herrgott tut nichts ausser wuerfeln" - "God does nothing BUT play dice".
Karl, you beat me to it. However another explanation was recognised very early. It involves a seemingly far-out idea that all possible outcomes occur at any given moment, leading to a spectrum of realities or world-lines, and this results in quantum uncertainty at very small scales. It a form of multiverse.
> A new round of AI enthusiasm is prancing its nonsense around the world. And this one has associated with it a wave of artefact-autonomy.
> Unless we use our language very carefully, we're inviting:
> (a) simplistic scientists and engineers, and feeble-minded marketers, to over-believe and over-sell, and deliver horrible outcomes (of which Robodebt is merely a harbinger)
> (b) the media and the public will put up with the nonsense for a period of time, but public backlash will in due course wash away the hubris, and with it not just the badly-conceived and harmful models and artefacts, but also some that are of value to humankind
And an excellent one too.
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