Introduction to "Pointwise Qualitative Factorization of 2-forms into 1-forms over ℝ^{4}, PDF format; 175K.
#### I just know Calculus III, or calculus-based physics. Does this paper have any use whatsoever to me?

Then you should know about the cross product **×**, and know what to feed into
a four-function calculator to compute it:

(a_{1}, a_{2}, a_{3})**×**(b_{1}, b_{2}, b_{3}) = (a_{2}b_{3}-a_{3}b_{2}, a_{3}b_{1}-a_{1}b_{3}, a_{1}b_{2}-a_{2}b_{1})
If you have memorized the formula in x-y-z coordinates, just change the subscripts from x,y,z to 1,2,3 to convert.
The coordinate formulation should look very similar to the coefficients I defined in the paper...in fact, the second part
rewrites (in the paper's notation) to

(c_{23}, -c_{13}, c_{12})
There's some "stratosphere math" that explains how things are defined so this works out.
Rather than go into that here, just use the result:

We can rephrase the entire paper to talk
about making inferences about coordinates a_{1..4}, b_{1..4} from the coordinates
of the four cross-products

(a_{1}, a_{2}, a_{3})**×**(b_{1}, b_{2}, b_{3}) = (c_{23}, -c_{13}, c_{12})

(a_{1}, a_{2}, a_{4})**×**(b_{1}, b_{2}, b_{4}) = (c_{24}, -c_{14}, c_{12})

(a_{1}, a_{3}, a_{4})**×**(b_{1}, b_{3}, b_{4}) = (c_{34}, -c_{14}, c_{13})

(a_{2}, a_{3}, a_{4})**×**(b_{2}, b_{3}, b_{4}) = (c_{34}, -c_{24}, c_{23})

Opinions, comments, criticism, etc.? Let me know about it.
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