Think in Math. Write in Code

Summary

Home GitHub Rss Think in Math. Write in Code. 6/8/19 Programmers love to discuss programming languages. We not only debate their technical merits and aesthetic qualities, but they become integrated into our personal identities, along with the values and traits that we associate with them. Some even defend a form of Linguistic Determinism that thinking is confined to what the language makes typable. Since we spend so much time writing code, a keen interest in language design is justified. However, the character of these discussions suggests that we think of them as much more, and have perhaps forgotten their primary role. Programming languages are implementation tools for instructing machines, not thinking tools for expressing ideas. They are strict formal systems riddled with design compromises and practical limitations. At the end of the day, we hope they make controlling computers bearable for humans. In contrast, thoughts are best expressed through a medium which is free and flexible. Thinking in Math The natural language which has been effectively used for thinking about computation, for thousands of years, is mathematics. Most people don’t think of math as free or flexible. They think of scary symbols and memorizing steps to regurgitate on tests. Others hear math and think category theory, lambda calculus, or other methods of formalizing computation itself, but these are hardly necessary for programming itself. I hope readers of this article have had a better experience regarding what math is about, such as a graph theory, algorithms, or linear algebra course; the kind that involves logic and theorems, and is written in prose with a mix of symbols (most symbols weren’t even invented until the 16th century). This kind of math is about creating logical models to understand real world problems, through careful definitions and deductions. If you don’t have a clear idea of what this looks like I recommend Trudeau, Stepanov, or Manber. Math allows you to reason about...