[SystemSafety] Faults in maths proofs
Les Chambers
Les at chambers.com.au
Sat Dec 12 20:35:08 CET 2020
Yes. Scepticism, the restingplace of the philosopher on a lazy day.
But one thing this discussion proves is the essential difference between the mathematician and
the engineer.
Mathematicians are edgy dudes obsessing over truth for all cases for all time for all space.
Engineers are more relaxed operating on a limited segment of that curve.
Newtonian mechanics works for us most of the time until it doesn’t. Then we go find Einstein so
we can build a GPS system.
Personally I’m relaxed as long as I have faith that, in my current scope of works, the truth I’m
working with will not crack and kill someone. Childlike, I am dependent on mathematicians for the
warmth of that feeling.
The mathematician in the slide pack announced he has given up. What a pussy. A good dose of
Stoicism is required here. Doesn’t he know that our approach to truth will be forever asymptotic,
for the truth lies at infinity. All one can do is munt on and endure.
Take the Americans. Having got rid of Trump they’re on their way, giving more credibility to
Churchill’s Lemma that Americans can be counted on to do the right thing ... after they’ve tried
everything else.
Les
> Another gem of scepticism from Derek. This time he is due unambiguous
> thanks. (There's condescension for you!)
>
> Yet one does not need to turn to complex mathematics to find examples of
> potentially perfidious proofs.
>
> Consider the equation: ax^3 e^-x = 1.
>
> With only a little wrangling, it is easy to *see* that this equation has
> exactly one root when a = (e/3)^3 . Now, according to Galculator, this
> quantity is approximately equal to 0.743908774934. Hence one *expects*
> that the equation
>
> 0.74391x^3 e^-x has exactly two real roots very close together - as can
> be found by numerical solution using Newton's method. ... But the
> question now arises as to *what would constitute a rigorous proof* that
> this equation has exactly two real roots?
>
> I'll leave this as a teaser for the more mathematically literate on this
> list.
>
> Olwen
>
> On 10/12/2020 15:54, Derek M Jones wrote:
> > All,
> >
> > "What is Mathematics?"
> > https://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf
> >
> >
> > A discussion involving recent examples of 'proofs'
> > that may or may not be correct, starting at slide 5.
> >
> > There is some discussion of the use of programs to create proofs,
> > and the problem that software contains faults, just like mathematical
> > proofs.
> >
--
Les Chambers
les at chambers.com.au
+61 (0)412 648 992
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