Re:A Pixel Is Not A Little Square (1995) [pdf]
by jacobolus on Saturday July 27, 2019 @08:48PM
(#20545230)
> I find I think of vectors more often as a set of independent magnitudes for each of the coordinate system axes
Interesting. This is what Hestenes calls the “coordinate virus”, http://geocalc.clas.asu.edu/pdf/MathViruses.pdf ; very often any specific coordinate system is not inherent but is some arbitrary addition to the space made for convenience in some particular calculation. It is in my opinion a mistake to think of the coordinates as primary.
> operate on vectors, without caring for the exact coordinate system used
This is the opposite of the previous statement.
Re:A Pixel Is Not A Little Square (1995) [pdf]
by gsliepen on Sunday July 28, 2019 @06:27PM
(#20550164)
> This is the opposite of the previous statement.
Not really. I didn't say in the first statement that a specific coordinate system was used. In most systems, it doesn't matter how you choose your coordinate system, as long as the basis is orthogonal, treating the coordinates independently of each other will work.
Most calculations physicists do are the same as pure mathematicians would do. So we use for example in-product and cross-product operators to operate on vectors, without caring for the exact coordinate system used. Only when we have to come up with a final answer to a question like "what angle does the ball hit the ground and with what velocity?" will we convert our vectors into a magnitude and direction.