This is where we are distinct from other tensor web pages. We want to show you crazy things that will help you see what is being done in tensor calculus. This page will show one example of madness (your fall down the rabbit hole) and then invite you to explore the realm into which you fell.
The length 10 inches is equal to the length 25.4 centimeters. We will start with the first and arrive at the second.
Remember, anything can be multiplied by 1.
You’ve probably never seen units given their own numbers. It will look crazy:
10 in
10 (1 in)
[1] 10 (1 in)
[ (2.54) (1/2.54) ] 10 (1 in)
(2.54) 10 (1/2.54) (1 in)
25.4 (1/2.54) (1 in)
25.4 (1/2.54 in)
You have two choices. We could stop right now because what we have is true, or we could let someone in the audience tell us that (1/2.54 in) is the same thing as (1 cm).
25.4 (1 cm)
25.4 cm
We did all this because when you start working with vectors and one-forms, both the vectors and the one-forms have numbers.
The fall down the rabbit hole took us from 10 in to 25.4 cm.
If you found the fall into the rabbit hole interesting, we invite you to explore further , starting with “Sarcastic, Snarky and Skeptical”.
Appendix A
Vectoreverything 