In mathematics, we learn how to go to the first principles and perform a differentiation. This is when we go to the definition of a differential and get the result.
On a related note, here is an interesting quote from Elon Musk on first principles:
I think it is important to reason from first principles rather than by analogy. The normal way we conduct our lives is we reason by analogy. [When reasoning by analogy] we are doing this because it’s like something else that was done or it is like what other people are doing — slight iterations on a theme.
First principles is kind of a physics way of looking at the world. You boil things down to the most fundamental truths and say, “What are we sure is true?” … and then reason up from there.
Somebody could say, “Battery packs are really expensive and that’s just the way they will always be… Historically, it has cost $600 per kilowatt hour. It’s not going to be much better than that in the future.”
With first principles, you say, “What are the material constituents of the batteries? What is the stock market value of the material constituents?”
It’s got cobalt, nickel, aluminum, carbon, some polymers for separation and a seal can. Break that down on a material basis and say, “If we bought that on the London Metal Exchange what would each of those things cost?”
It’s like $80 per kilowatt hour. So clearly you just need to think of clever ways to take those materials and combine them into the shape of a battery cell and you can have batteries that are much, much cheaper than anyone realizes.