“I have the ability to travel from a world with a physical story to a world with the math tools needed to express that story.”
“We prefer it that when the Physicist comes looking, needing something, we can tell the Physicist that we already have it.”
When you studied Linear Algebra they taught you a method to do Matrix Multiplication.
You might remember it as something like “across the first matrix and down the second matrix”.
You should not be criticized if you wondered if “down the first matrix and across the second matrix”. In fact, we congratulate. You have some math DNA in you if you think like that.
One problem with matrix multiplication is that they just give you two rectangles with numbers (or functions, which become numbers when the functions are fed numbers). You aren’t given anything that provides instructions on what to with all those rows and columns.
There are more possibilities than just the two forms of matrix multiplication.
One extreme would have every possible combination being a term in a single summation:
The other extreme would have every possible combination being a separate component in the answer:
You’ve seen work with vectors [2×1] and [1×2]. Matrix multiplication was [2×2] and [2×2]. Let your imagination take you to things even bigger:
- [2x2x2] and [2x2x2]
- [2x2x2x2] and [2x2x2x2]
Does it make sense that with bigger math objects there would be more and more possibilities for the pair?
Of this begins a path (or hole) that leads to Tensorworld…
Vectoreverything 