I have no idea why I've been looking into quaternions lately, or what I would ever use them for. I've been trying to use vectors to simulate elliptical orbits of planets in Geogebra, but it's been a lot of work. I don't even know if Geogebra handles quaternions. Reminds me of a Lisa Simpson line: "Bart, I'm NOT going to learn Ancient Hebrew!"
One positive thing it's led me to is the book Visual Complex Analysis by USF math prof Tristan Needham. He definitely sums up my opinion about how most math classes lose students: there's no attempt to link the abstractions with our experience of the world, and this applies to the disdain mathematicians feel for geometric reasoning, and worse:
More likely than not, when one opens a random modern mathematics text on a random subject, one is confronted by abstract symbolic reasoning that is divorced from one’s sensory experience of the world, despite the fact that the very phenomena one is studying were often discovered by appealing to geometric (and perhaps physical) intuition.
It's tough for a math nut like me to admit, but when I open most Dover math texts or those yellow ones in brainy bookstores, the ridiculous symbols and complete lack of visual appeal make my heart sink and I wouldn't carry the book home if it were free.
Another aspect of my Calculus Program Needham anticipates in the book is my lack of rigor. After giving credit to those who believe rigor strengthens the "precarious" structure of mental constructs, he suggests:
...that our mathematical theories are attempting to capture aspects of a robust Platonic world that is not of our making. I would then contend that an initial lack of rigour is a small price to pay if it allows the reader to see into this world more directly and pleasurably than would otherwise be possible.
Small price to pay, Prof.
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