Thoughts on <What We Now Call Computers>

Opening

A channel I deeply respect recommended this book, so I bought and read it directly — my first time doing that in a while. The recommendation came with a note that anyone interested in computers, artificial intelligence, and mathematics would find it fascinating — so I had high expectations. But honestly, I don't think I properly understood even 50% of the content.

As the title suggests, this is a book that explores the past — the ideas of which geniuses gave rise to what we today call a "computer." While reading, I found myself dozing off when confronted with difficult concepts like logical systems, transcendental numbers, and infinity. Even so, now that I've closed the book, I feel something I didn't before: that what we call a "computer" is more meaningful as software than as hardware. Put another way, a computer feels less significant as a physical "object" you can see in front of you, and more meaningful as an "existence" that came to be because of what certain geniuses of the past were pursuing.

I didn't understand everything — but I've done my best to summarize below the key ideas of the geniuses highlighted in the book and how they each contributed to the concept of the computer.

About the Book

The book unfolds the thoughts and lives of these geniuses in the following order:

Leibniz → Boole → Frege → Cantor → Hilbert → Gödel → Turing

Through this progression, the book tells us that the computer we know today wasn't created by any one person who decided "I'm going to build a computer" — rather, it's an idea that emerged at the end of a long development of philosophy and mathematics. Here's a concise summary of each figure's leading thought and contribution:

1. Leibniz: "Thoughts and logic can be represented as symbols."
2. Boole: "Logical judgments (True/False) can be calculated mathematically."
   1. This resulted in boolean logic and the formalization of AND/OR/NOT operators.
3. Frege: "Meaningful sentences can be expressed as symbols."
   1. Frege's logical system is a subject still studied in computer science today. Through this step, the logical foundations of programming languages were born. (Example: sentences like "If x is a horse, then x is a mammal" can now be expressed symbolically.)
4. Cantor: "Some infinities are larger than other infinities."
   1. This became the occasion for mathematics to deal with the concept of infinity and for set theory to develop.
   2. (To be honest, Cantor was the part I found hardest to understand...)
5. Hilbert: "Mathematical problems can be solved by rules."
   1. From this concept, a program became a set of rules, and an algorithm became a way of solving a problem.
6. Gödel: "No matter how well you construct the rules, there will always be statements that cannot be proven true."
   1. This defined the limits of programs and automation.
7. Turing: "You can build a machine that computes."
   1. The idea evolved: the process by which humans think is simpler than we realize, and if you build a machine that follows that process, you can create a computing machine that performs — as well as or better than — any calculation a human can do.

Closing

Writing it out this way, the roots of each genius's ideas seem to faintly connect — showing how they built on each other to become the computer of today. Compared to before, when I only knew their names, this feels like a significant step forward. Personally, after reading this book, I want to re-watch the film . When I watched it before, all I could think was how much I loved Benedict Cumberbatch — but this time, I think I'll be able to enjoy a deeper layer of connecting what I've read here about Turing as a human being to what I see on screen.

If there were a few keywords in this post that caught your attention, reading this book during a long holiday might be a good recommendation.