"Imaginary numbers exist in electrical engineering"

Stormtroper

You know how when some high school kid asks about whether non-real numbers 'exist' in some physical sense, one of the go-to answers is that voltages, currents etc. can be 'complex'. I've always found this very misleading, as it conceals the fact that what is being talked about is merely sinusoidal functions with different phases and not some sort of 'alternative voltage' or anything. If the kids aren't convinced by looking at a complex plane or vector rotations or something, they wouldn't be convinced by that if they understood it, the same way they wouldn't be convinced by, say, two dephased mass-spring systems.

Bluesy_Cowgirl

I am not convinced.

glennmagusharvey

So clearly, numbers like 1, 5, 761, and 1438902 show up in nature and can be found growing on trees and underneath rotting logs, while all fractions and decimals were produced by humans, originally hand-crafted but nowadays churned out in factories.

Also, e and pi make no sense at all.  Totally unreasonable.  Why the hell are there numbers with non-repeating decimal patterns?  It just doesn't make sense!

Stormtroper

All numbers are made up except for positive integers smaller than 12 or so.

Our statics professor had some philosophical vendetta against negative numbers and how they were 'unphysical' and warned us that if we put a negative force somewhere in our exams, he'd grade it as 01 (the lowest grade), so we had to figure out the forces' sign/direction beforehand so we'd know how to make a free-body diagram. Thankfully in the problems we got they weren't hard to figure out.

lrdgck

Let me remind you of this picture which feels relevant to this thread.



(Haven't had a smaller one.)

Stormtroper

A logical Platonist professor of mathematics and a prominent member of
the anti-NatSoc party was teaching a class on foundations of mathematics
and Kurt Godel, a known opponent of logicism.

"Before the class begins, you must get on your knees and worship Russell and accept that he was the most highly-advanced logical thinker the world has ever known, even greater than Frege!"

At this moment, a brave, formalist, intuinitionist, pursuer of true mathematics who had edited 1500 pages of Deutsche Mathematik in Nazi Germany and understood the necessity of restricted comprehension and fully supported all expulsion of all unintuitive mathematics stood up and held up a copy of the
transcripts of Hilbert's 1930 radio address

"How intuitive should mathematics be?"

The arrogant professor smirked quite Platonically and smugly replied "as
intuitive as the logical framework it is grounded on allows it to be.”

"Wrong. Unrestricted logical foundations of set theory has been shown to yield
pathological results and even paradoxes that one cannot resolve without
appealing to higher order logic. If mathematics were as intuitive, as
you say, as the axioms that ground it… then we should be able to
subdivide and arrange a set in such a way that it reassembles into two
identical copies of the original set in nature."

The professor was visibly shaken, and dropped his chalk and copy of Principia Mathematica. He stormed out of the room crying those logicist crocodile tears. The same tears logicists cry for "the destruction of Cantor's
paradise" (which has been shown to lead to many pathological counterexamples in analysis) when they try to corrupt the pure and aesthetic theorems from the intuinitionists. There is no doubt that at this point our professor, Schlomo Von Freudman, wished he had pulled
himself up by his own type-theoretic bootstraps and become more than a
Platonic logicist professor.

He wished so much that he could find the Devil's Staircase in nature in order to prostrate himself off of, but he himself had endorsed the proof of its zero measure!

The students applauded and all converted to intuinitionism that day and accepted Hilbert as their role model and beacon of intuition for mathematics. An eagle named “finitism" flew into the room and perched atop the finitely generated Sierpinski's pyramid and shed a tear on the chalk. The radio address was played several times, and Poincare himself showed up and forbidden the set theoretic construction of the natural numbers from publication.

The professor lost his tenure and lost his tenure the next day. He died of caffeine overdose and was forced to watch physicists summing divergent infinite series for all eternity.

Wir müssen wissen,
Wir werden wissen.

Stormtroper

Relevant Hitler:

lrdgck

Well, I'm still here, so obviously he didn't get rid of all of them. Anyways, one of the better Hitlers I have watched, for sure. I personally never got the point of that contour stuff. Just counted the residues and did that two pi i calculation and it kind of worked out most of the time.

Stormtroper

I can't say I understand much of what they're saying. I still run into trouble where I end up doing algebra things that are true of real numbers but not necessarily so of complex ones (oddly enough I don't have this problem with quaternions, I think it's because it's more obvious that they don't work the same way).

This is my favourite math Hitler, in an alternate universe where he did take topology like Stalin: