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Thursday, March 10, 2022

Review: When We Cease to Understand the World

When I was an undergraduate, I attended Kathy Yelick's "Denotational Semantics" graduate student seminar. There was a section discussion when people puzzled over the Y-combinator. On that day, I explained it as follows: when you want to write a recursive function, write it as though you had recursion as a native construct, and then at the end, wrap it with a Y. That's how you use it. (The lazy evaluation would expand on it as necessary when supplied with a concrete argument) One of the graduate students, not sure he understood what it meant, raised his hands and said, "Is that understanding sufficient to get us through the final exam?" Concrete manipulation vs intuitive understanding has always been a part of science and mathematics --- once you have a tool, it doesn't matter whether you understand how it was made as long as you know how to manipulate it. But of course, many people would disagree, and claim that if you don't understand how the tool works you don't know it. That's what this book is about.

When We Cease to Understand the World is a fictional account of various scientists and mathematicians: Karl Schwarzchild Fritz Haber, Alexander Grothendieck, Werner Heisenberg, and Erwin Schrodinger. It also includes mentions of Albert Einstein. While the mathematical theories are real, the events are made up, though how much I did not do the research on.

The book covers not mostly the mathematics and the science (though there's some explication and exposition), but the idea of what it must be like making a discovery that did not make sense at that time. It's also a reflection of the scientific and mathematical enterprise:

it’s not just regular folks; even scientists no longer comprehend the world. Take quantum mechanics, the crown jewel of our species, the most accurate, far-ranging and beautiful of all our physical theories. It lies behind the supremacy of our smartphones, behind the Internet, behind the coming promise of godlike computing power. It has completely reshaped our world. We know how to use it, it works as if by some strange miracle, and yet there is not a human soul, alive or dead, who actually gets it. (pg. 187)

Of course, I vehemently disagree with the book's premise and conclusions. Being able to exploit a quantum property means you do understand it.  That's the way science and engineering works. Just because you cannot manipulate the technology without tools (i.e., have an intuition about a system) doesn't mean you don't understand it. This sort of approach to thinking, science and technology is why we continue to have science denialists, and lots of people suffering from Dunning-Krueger.

The book showed up on a lot of "best of the year" series, but I'm afraid I cannot condone it for its conclusions. Get your science from the non-fiction section of the library or bookstore please!

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