The best books on the biggest questions

This book is out to trick you. It presents itself as a compendium of charming puzzles and brain teasers that will make you scratch your head until you suddenly yell “Aha!”. But far greater trickery lies ahead, because these riddles are devilishly constructed to lead you --- with no additional effort --- to the most profound discovery in the history of mathematical logic. That discovery is Godel’s Incompleteness Theorem, which says that mathematics (and indeed even just arithmetic) defies logical description and therefore transcends mere logic. There are more things in heaven and earth than are dreamt of in your logical reasoning.

You could understand Godel’s Theorem by reading Godel, but that’s hard. Reading Smullyan is easy. It’s better than easy; it feels like playing a wonderful game against a bright and very funny opponent.

As a side note, this was the book that inspired me, decades after I’d read it, to imagine that I could teach economics through a series of brain teasers in my own book, Can You Outsmart an Economist? Smullyan died just as that book came out. I wish I could have sent him a copy.

Would you guess that the average daily temperature in San Francisco is above or below 558 degrees Fahrenheit?

I'm going to assume you guessed "below", because that's the right answer and absolutely everybody gets it right.

Now---what would you guess is the actual average daily temperature in San Francisco? If you are like just about everybody, your guess right now is quite a bit higher than the guess you’d have made a minute ago, before you saw my first (entirely ludicrous) question. This well-documented effect persists even when subjects are told about it and warned not to fall prey to it.

Perhaps I’m overestimating, but I believe this book contains about 14 billion equally fascinating and weird facts about how human minds process information. But although these facts are quirky, they are not quirks --- they are central to the working of the human mind, not just little mistakes we make around the edges.

Poundstone is a great storyteller and he regales us with one extraordinary experimental result after, but he doesn't stop there. Instead he invites us to ponder the implications for how we live our lives and how we understand the world. The tone is light-hearted; the subject is essential.

The number Pi, of course, has no history; like any other number, it is what it is and exists outside of time and space. But the human understanding of Pi has a rich history indeed, beginning with the discovery that the circumference of a circle is more than three times, but less than four times, its radius. The centuries brought better estimates, better ways of discovering new estimates, the discovery that Pi is irrational, the recognition that it has a habit of popping up in areas of mathematics that appear to have nothing to do with circles, and a slew of curious and beautiful formulas like this one.

Of course, a lot of other things were happening during those centuries, not all of them mathematical. Beckmann has not failed to notice this. His fascination with pretty much everything comes alive as he uses the history of Pi as a sort of jumping-off point from which to digress into four millennia of world events, all narrated from a unique personal perspective that I found thoroughly endearing. One minute you’re reading about how Wallis discovered that beautiful formula I mentioned, the next you’re reading about Wallis’s role in the English Civil War, then you’re on to some side comments comparing the English, French and Russian revolutions, a few words about Charles II (who “loved women more than he loved power”) and full circle back to Pi again.

It’s like that all the way through.

I vividly remember reading this book some years ago. You probably don’t remember it at all, even if you’re going to take my advice and read it tomorrow. That’s pretty odd when you think about. Why should we remember the past but not the future?

It does no good to echo platitudes like “the future hasn’t happened yet”. You could as well say “the past is already over”, which is equally true and equally irrelevant. The laws of physics tie the past to the present and the future to the present in exactly the same way. Any process that can run one direction in time can run in the other. So if the past can leave imprints on our memory, why can’t the future?

David Albert wants to make you appreciate the question, and then he wants to tell you the answer. Albert is that rarest of birds: A philosopher of science who both fully understands the science and has figured out how to explain it in a way that is clear, engaging, and not at all watered down.

Along the way to his big reveal, Albert illuminates a lot of modern physics. His unique philosopher’s perspective means that even professional scientists will learn something new. His unique prose style means that even those with no scientific background can grasp what he’s saying. No matter where you’re starting from, you’ll understand the universe better after you read this book.

Daniel Dennett is another of the handful of philosophers who combine a deep understanding of science with a prose style that draws you in and does’t let you go. His topic here is consciousness --- what it is, how it works, and how it’s possible. Dennett flits from psychology to neurology to computer science to philosophy, with punch lines coming every few pages. If you read the pages in random order, you’ll keep learning new facts you can't wait to tell your friends about. But that’s the wrong way to read this book, because Dennett is slowly building to a grand and coherent explanation of what consciousness is and how it’s possible. That destination alone makes the book a must-read; the fact that the journey is so enjoyable is icing on the cake.