11–20 of 143 posts
Everyone should learn some of the tools of Geometric Algebra sometime in high school, and it would save a whole lot of confusion. http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
The problem with textbook for all levels (other than them being outrageously expensive) is that they contain many level of abstraction, or what one may call self-censure, presumably in order not to scare kids off. One level is the general consensus of how should a topic should be taught, another layer is the author's view of how it should be taught In practice there's the third layer, where the teacher presents them in a certain way. This results in a long chain of Simon Says where the final, safe stuff that's taught, for the benefit of the students, mind you, may become very detached from the reality and excitement of the topic. Unfortunately, students always sense this and they tune it out, leading to so many people not liking math, physics, signal processing, you name it.
The joy of access to a person who is infinitely (compared to you) knowledgeable in atopic and is willing to interface you on multiple levels and telling you as it is is enormous. Best known such example, of course, is Feynman but physics SE and some other boards come close.
I am humbled by the clarity of this answer! The problem with textbook for all levels (other than them being outrageously expensive) is that they contain many level of abstraction, or what one may call self-censure, presumably in order not to scare kids off. One level is the general consensus of how should a topic should be taught, another layer is the author's view of how it should be taught In practice there's the t…
Everyone should learn some of the tools of Geometric Algebra sometime in high school, and it would save a whole lot of confusion. http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
I like the linked paper a lot so far (still reading it) even though I disagree that everyone should learn this just so that physics majors and similar can avoid some amount of confusion.
For anyone dealing with computer vision, graphics, or modeling type fields, I recommend the more recent book “Geometric Algebra for Computer Science”. http://www.geometricalgebra.net/
The title statement is meaningless. "Imaginary numbers" are not "multiply" by "90°". What does it even mean to "multiply" by an angle? Correct statement: "*i is equivalent to a 90° rotation in some contexts." Which is kind of obvious to anybody who has done some maths or physics at some point?
Trivially, this result is clearly obvious.
Here is an even better discussion on the same topic, and the HN thread from last year: http://betterexplained.com/articles/a-visual-intuitive-guide... https://news.ycombinator.com/item?id=2712575 One great conclusion from this approach is how intuitive it becomes to understand the square root of i . I always thought you'd need another dimension to describe that, and another dimension for the square root of that unit,…
Imaginary numbers are an artifact of how our number line is constructed. We could construct alternative number lines where imaginary numbers do no exists. The computations involving such alternative number lines would be different, but the outcome would be the same.
If someone asks what is an imaginary number the correct answer is "z = a+bi, where a and b are real numbers, and i^2 = -1".