Book Review: The Math(s) Fix - Part 1 of 2
Do we need a new subject?
In the real world, computers carry out these, um, computations! This doesn't mean that computers have replaced mathematicians. This means that the role of a mathematician is no longer what it used to be.
Anyone for a course in photography?
Wolfram says that, until recently, a course in photography would have to include film processing. In fact, it would start with the essential skill of loading a film into the camera. Digital photography has shown us that this skill was incidental to the technology of the day, not something essential to the art itself.
Similarly, what we continue to consider as the essence of mathematics is a collection of skills that were appropriate before the advent of the digital computer.
Our author is afraid that the subject of mathematics, unless updated, will go the way of latin in British schools!
Why make it compulsory?
The problem in one paragraph
The mechanics of inverting matrices, but not the use of machine learning. Sketching graphs of functions, but not the ability to construct models from observations of the real world. Calculation of statistics by hand, but not the filtering of large datasets to extract relevant information to process (p. 119).
The process to rule them all!
I will summarise my understanding of each of these 4 steps with an emphasis on the second and fourth, only because they may be the least obvious ones.
Abstract (to computable form)
- Translate the problem into a language conducive to computational solutions. While Wolfram does not specify such a language at this stage of his book, I would think that he had something like "pseudocode" in mind. Pseudocode is a way of writing algorithms so that they can then be implemented in various programming languages.
- The abstraction should address the general case of the problem rather than one specific instance of it.
In the next instalment, I will talk more about the proposed new curriculum, what the author has termed a computer-based computational subject. I have a few disagreements with him on that part of the book, while still sharing his overarching view.