Burn Math Class: And Reinvent Mathematics for Yourself (2016)
Act I
3. As If Summoned from the Void
3.7. Reunion
Let’s remind ourselves of what we did in this chapter.
1.Having extended the idea of powers from a meaningless abbreviation to a meaningful idea, we found that we had unwittingly created a bunch of different kinds of machines.
2.We had no idea how to differentiate any of these machines, but because of the way we invented powers, we knew how to relate them to simpler machines. For example:
3.Relating our new confusing machines to simpler and more familiar machines allowed us to “trick the mathematics” into telling us what the derivatives of the new machines were.
4.Along the road to figuring out the derivatives of our new machines, we invented several hammers: the hammers for addition, multiplication, and reabbreviation. These hammers allow us to shatter hard problems into simpler pieces.
5.Much to the author’s surprise, an unexpected dialogue occurred in the middle of the chapter, and we made a new friend. This may end up affecting the remainder of the book. I’m not sure the parts before it are safe either.
6.Full disclosure: the item above this scares me a bit.