Burn Math Class: And Reinvent Mathematics for Yourself (2016)
Act III
The Infinite Beauty of the Infinite Wilderness
6. Reunion
In this chapter, we did a bunch of fun stuff, including:
1.By using the analogy between vectors and machines, we managed to extend calculus to “cannibalistic” machines that eat an entire machine and spit out a number.
2.Since functions can be thought of as vectors with infinitely many slots, we could think of this new cannibal calculus as calculus in an infinite-dimensional space.
3.We showed that the operations of cannibal calculus are essentially the same as those in single-variable and multivariable calculus.
4.We checked the validity of our new cannibal calculus by using it to reinvent some things we already knew, such as the fact that the shortest distance between two points is a straight line. In doing this, we gained more confidence that the odd infinite-dimensional calculus we’ve invented in this chapter behaves essentially the way we hoped it would.
5.Throughout the chapter, we continued the discussion with which we began the book: without exception, at all levels of mathematics, the underlying ideas are extremely simple, and their apparent opacity and difficulty results not from the ideas themselves, but from poorly chosen notation, arcane terminology, and backward or sloppy explanations. I cannot claim to know with certainty whether any particular reader will find the explanations in this book “better” or “worse” than those in the standard textbooks, but the point remains true. Any persistent confusions you may have experienced in the course of reading this book are the fault either of the explanations I have offered or of my own clumsy choice of words, not the fault of the underlying mathematical ideas themselves. In every case, the widespread lack of understanding and appreciation of mathematics in our society is not the fault of mathematics, but the fault of mathematics educat—
Mathematics: I THINK I’VE HAD ENOUGH OF THIS.
Author: Uh. . . I was in the middle of writing someth—
Mathematics: I’VE LISTENED TO YOU COMPLAIN ABOUT MATHEMATICS EDUCATION FOR THE LAST 371 PAGES, AND YOU STILL HAVEN’T DONE ANYTHING ABOUT IT! ENOUGH WITH THE WHINING! IT’S TIME FOR ACTION!
.ωActions Speak Louder
Mathematics: THAT’S BETTER. AS I WAS SAYING. YOU’VE COMPLAINED ABOUT THESE “MATHEMATICS TEXTBOOKS” AND “MATHEMATICS COURSES” IN EVERY SINGLE CHAPTER.
Reader: But you weren’t even here until the third cha—
Mathematics: SO PUT YOUR MONEY WHERE YOUR MOUTH IS! YOU’VE WRITTEN US INTO EVERY SITUATION EXCEPT THE ONE YOU SEEM TO CARE SO MUCH ABOUT CHANGING. I’VE MET ANTHROPOMORPHIZED COMPUTING MACHINES AND CREEPY SILENT META-ENTITIES AND BEEN TO SOMETHING CALLED ABEWEIS BAR, BUT I STILL HAVEN’T SEEN A SINGLE ONE OF THESE MATHEMATICS CLASSROOMS THAT SEEM TO BE MASS-PRODUCING MISUNDERSTANDING ABOUT ME! IF MATHEMATICS EDUCATION IS SUCH A JOY-KILLING, BACKWARD ENTERPRISE, THEN WHY DON’T WE STOP GOOFING AROUND AND DO SOMETHING ABOUT IT?
Author: I. . . well. . . I mean, I’ve tried to help out a little bit by writ—
Mathematics: I DON’T WANT TO HEAR ANY EXCUSES! IF YOU WON’T DO SOMETHING, I WILL!
(Mathematics rips the characters out of this chapter and into the next.)