Chapter 5. Category Theory

Thomas Watson was famously quoted as saying, "I think there is a world market for maybe five computers". That was in 1948. Back then, everybody knew that computers would only be used for two things: math and engineering. Not even the biggest minds in tech could predict that, one day, computers would be able to translate Spanish to English, or simulate entire weather systems. At the time, the fastest machine was IBM's SSEC, clocking in at 50 multiplications per second, the display terminal wasn't due until 15 years later and multiple-processing meant multiple user terminals sharing a single processor. The transistor changed everything, but tech's visionaries still missed the mark. Ken Olson made another famously foolish prediction when, in 1977, he said "There is no reason anyone would want a computer in their home".

It seams obvious to us now that computers are not just for scientists and engineers, but that's hindsight. The idea that machines can do more than just math was anything but intuitive 70 years ago. Watson didn't just fail to realize how computers could transform a society, he failed to realize the transformative and evolving powers of mathematics.

But the potential of computers and math was not lost on everybody. John McCarthy invented Lisp in 1958, a revolutionary algorithm-based language that ushered in a new era in computing. Since its inception, Lisp was instrumental in the idea of using abstraction layers—compilers, interpreters, virtualization—to push forward the progression of computers from hardcore math machines to what they are today.

From Lisp came Scheme, a direct ancestor of JavaScript. Now that brings us full circle. If computers are, at their core, machines that just do math, then it stands to reason that a math-based programming paradigm would excel.

The term "math" is being used here not to describe the "number crunching" that computers can obviously do, but to describe discrete mathematics: the study of discrete, mathematical structures such as statements in logic or the instructions of a computer language. By treating code as a discrete mathematical structure, we can apply concepts and ideas in math to it. This is what has made functional programming so instrumental in artificial intelligence, graph search, pattern recognition and other big challenges in computer science.

In this chapter, we will experiment with some of these concepts and their applications in everyday programming challenges. They will include:

With these concepts, we'll be able to write entire libraries and APIs very easily and safely. And we'll go from explaining category theory to formally implementing it in JavaScript.