You had me at ...
"geometry, music, mathematics, astronomy ...the writing of music is a hybrid activity between something very technical and rule based and computational and also pure chance and randomness and intuition and those things colliding allow us to evoke emotions…"

They tried this crap in my geometry/pre trig class....they called it "proofs"....forcing us to do mental gymnastics to spread out a problem from maybe three quick steps into 20. Asinine.
My last high school math class was advanced placement B/C calculus....I never found this a bit useful, because I was taught real math. By second grade we were expected to know up to 12 X 12 multiplication tables without hesitation, if they taught us by this method, we would have been years behind.

Since next to no one today is doing even moderately difficult math without a calculator/cellphone, I can't fathom why they bother at all anymore with more than basic math skills for non math or science majors...that said, my cousin still can't add 3 digit numbers or multiply or divide at all thanks to Waldorf schools, and that's really sad.

@Payback, I was accused of cheating in trig because I refused to show my work or do homework. I was separated from the class for a big test, and my score remained an A while the class average dropped by around one full grade. I never had to do homework or show my work in that class again, but did have to separate myself for tests so the class wouldn't cheat off of me. That was in boarding school.

It's part of common core. Supposedly it makes it easier to understand the theory behind math so later in higher level classes (algebra, trig, etc) they can easily break the harder equations down.

Beats me, I learned the old way and it worked for me through algebra 1/2, and geometry.

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Saw this story earlier today. Excellent work of art!

Why do Buddhist monks make sand mandalas?

When the mandala is finally finished, however long it takes for the monks to deal in this divine geometry of the heavens, they pray over it — and then they destroy it. ... Because the underlying message of the mandala ceremony is that nothing is permanent. Nothing.

Enlightenment, or, "DUDE! IT'S DOING IT TO YOU AS WELL!!!"

I felt sad when I found out non-euclidean geometry was only theoretical too.

Yeah, that doesn't sound like weed. No doubt, edibles can be powerful and I've definitely eaten some high doses that resulted in near inability to move & audio hallucinations/distortions. But, this sounds like he went through what they call ego-death, which is reliably found in moderate to high doses of psychedelics - "geometries from other Universes", in the void remembering that you had only dreamed that you were a human alongside extreme time dilation that feel infinite or like an eternity - are dead giveaways (pardon the pun). DMT is the best, of course. Get's one there in seconds and back in 10 minutes... instead of hours and hours....

Counter-rotating propellers sparked my curiosity when I first saw them on a British Seafire Mk46 at a flight show in the early nineties.

So my amateur's answer would be that it's about the problem of turning the engine's power into thrust. With increasing power, you can either increase the propeller's RPM or its area. So you either a) spin it faster, b) increase its diameter, c) use a more favourable blade geometry, d) add more blades.

a) and b) both lead to blade tips moving faster, and once they approach the speed of sound, wave drag sets in and ruins your day. b) also runs into issues in terms of ground clearance. Thus the Kim Jong-un blades on planes like the An-70: short and fat.

c) is rather difficult to do in terms of manufacture -- that's why more pronounced blade shapes are a relatively recent development.

d) on a single propeller decreases the efficiency of each blade as it passes through the previous blade's vortex. That's why, for instance, German planes in WW2 almost exclusively relied on 3-bladed propellers with increasing blade size, whereas Supermarine went to four and even 5 blades rather quickly. You can work the issue to a certain degree by modifying the blade geometry, thus the 8 blade props on a modern A400M.

Adding more blades by adding another propeller gets around d), although the aft prop still loses efficiency compared to the front prop. On the other hand, counter-rotating props massively reduces problems with torque, which can be rather horrendous for single engine prop planes. The Bf 109, for instance, is (in)famous for being difficult during take-off as it pulls to the side quite violently.

Oh ya, I miss-read your post. I think this fidelity is probably doable in games now, or maybe soon since games like Star Citizen are able to load SO MUCH geometry into a scene. Sounds like they are optimizing quite a bit by using vertex offsets for the face shapes instead of having to load all the extra geo as target shapes.

Well, that's what I was taught were proofs, even if just proving simple addition....but that shouldn't be an introduction to math, I got them in geometry/algebra 2 my sophomore year.
Well, kids not understanding basic math isn't new either, senior year remedial math existed when I was in school, but wasn't the norm. If your assessment is correct, that's pretty sad.

All that said, I got paddled in 5th grade for insisting 4-5=-1. My teacher didn't understand negative numbers. Just saying, poor educators aren't a new thing, but they do suck ass.

The big problem is education is so politicised now that it's near impossible to figure out what's actually being taught and what stories are pure hyperbole. Here in the U.S. we've heard all kinds of insane claims about 'common core', most of which were bullshit, because making a federal standard for education wasn't what many wanted (how dare they tell us the war of northern aggression was about slavery, these slanderous accusations will not stand, sir) so a movement was born to oppose it by all means possible, which usually meant outrageous lies.
I'm really glad I don't have kids in school, I would probably home school them if I did.

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