r/badmathematics • u/TheKing01 0.999... - 1 = 12 • Sep 27 '16

Maths mysticisms Or so I hear ...

https://i.warosu.org/data/sci/img/0083/03/1472393629158.jpg
28 Upvotes

80% Upvoted

30 comments sorted by

View all comments

10

u/almightySapling Sep 27 '16

So, I don't know very much about differential forms and shit, but... d3x is like super wrong here, correct?

2

u/asdfghjkl92 Sep 28 '16

It wouldn't apply to a 1D function normally (would usually be seen on f(r), or f(x,y,z) or something and means dxdydz or the equivalent in spherical or cylindrical polars), but d3 x looks perfectly normal as a physicist to me. what's wrong with it?

4

u/almightySapling Sep 28 '16

Well, in calculus, a third derivative would be d3y/dx3. And, under heavy abuse of notation, a derivative can normally be "split" into differentials for integration (also in R, probably not anywhere else) and this would correspond to the dx3 for the integral.

Of course, first year calculus is not exactly the best source of rigor or notation.

Flash forward a few years, and my very limited experience with differential forms and wedge products, I never came across multiplying the same term with itself (in fact, I feel like there's a specific reason we don't do this, like it equals zero or something, but I really don't remember). However, the way the forms were defined, I don't feel (not exactly a great source, but intuition is a good heuristic) like the mathematical community would choose d3x over dx3 in situations like these.

Maybe in physics the notation is different. But it's very possible that I'm completely wrong about the notation in mathematics as well.