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From: Martin Brown <'''newspam'''@nonad.co.uk>
Newsgroups: sci.electronics.design
Subject: Re: Quantum mystics
Date: Mon, 10 Jun 2024 20:16:10 +0100
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On 10/06/2024 19:52, john larkin wrote:
> On Mon, 10 Jun 2024 17:55:47 +0200, Jeroen Belleman
> <jeroen@nospam.please> wrote:
> 
>> On 6/10/24 10:14, Liz Tuddenham wrote:
>>> Jeff Layman <Jeff@invalid.invalid> wrote:
>>>
>>>> ... I was ok with mathematics in school until we started
>>>> on calculus. I could not, and still cannot, understand concepts such as
>>>> "vanishingly small".
>>>
>>>
>>> Calculus is to arithmetic what astrology is to astronomy.
>>
>> Now now, that's unjustified. Calculus is eminently useful
>> and perfectly rigorous.
>>
>> Mathematics is a tool chest. Unfortunately, the way it's
>> taught, few people end up being able to use the tools.

I'm not sure that it *is* the teaching. It is more a cultural thing. It 
is OK to be "bad at maths" but not OK to have not read Shakespeare.

I blame the teaching for the appallingly high proportion of electronics 
engineers that refuse to accept Special or General Relativity though.

>> Jeroen Belleman
> 
> How often do you use real, symbolic calculus?

Not quite daily but more than once a week. These days I tend to throw a 
lot of it at Maxima or Mathematica rather than do grunt work by hand. 
Even so mechanical tools need guiding towards the right answer.

Both have some annoying features/quirks that you have to work around.

> Solving differential equations?

Less frequently. Mostly I'm involved in finding faster rational 
approximations to awkward non-linear equations or linearising things 
that don't really want to play ball. The idea is to have a fast 
approximation that is good enough to act as a seed value for a 
NR/Halley/higher refinement step to always converge.

Much of that relies on calculus of variations which is another step 
above the sort of basic calculus taught in schools. It allows you to 
compute real world things like how a cable will hang between two poles.

Likewise for tensor differential analysis working in non-Euclidean 
curved coordinate frames (I haven't really used that in anger for 
decades now). OTOH being exposed to it broadens the mind.

-- 
Martin Brown