Zero

Zero is about nothing. By which I mean, it's about the idea of a void, a lack-of-thing, as being a sort of thing itself. It's written by Charles Seife, who also wrote Proofiness. Zero is similar to A Brief History of Infinity, by Brian Clegg, in that it's more of a history book than it is a math or science book. They're also similar because they talk about infinity, because zero is "infinity's twin."

The first six chapters of Zero (or the first seven, depending on how you count them) are about the idea of nothing slowly working its way into the mainstream, followed closely by the idea of the infinite. There was actually a lot of resistance to both of these ideas, especially in the West, which is made even more interesting by Seife's flowery writing. I'm not entirely sure what "flowery writing" actually means, but I'm pretty sure it happens in this book. Zero does technically go into some math, but never in much detail. There's just enough math to make sense of all the pretty pictures.

The last three chapters are about zero in physics, where it likes to cause problems. This second part seems much weaker than the first part; Seife uses quite a bit of hand-waving, and never shows us a single equation. I think that if Seife would show us the actual equations and where the zeros are, we would better understand why zero is to blame for these quirks. That said, I'm sure some people will be glad that the math all but disappears when the physics comes on.

If you wonder how ideas take hold, or like history, or are somewhat confused about zero yourself, then maybe give Zero a try. For what it's worth, I finished it in just three days, so it can't be all that boring. (Although, that probably says more about my schedule than it does about the book.) I think the best way to understand what Zero is like is probably just to read the introduction (which Seife calls "Chapter 0"), so I've just typed it up here. This might be illegal. Don't tell anyone. The point is, he remains that flowery throughout the book, and if you like that section, I think you can enjoy the rest.

Flatterland

Flatterland is full of puns and science. Really, if it weren't for the name "Ian Stewart" on the front, I'd suspect it had somehow been written by me. Flatterland is a "sequel" of sorts to Edwin A. Abbott's Flatland, which I suppose you should technically read first, although I think Flatterland stands perfectly well on its own. Still, a quick review/summary of Flatland is in order.

Boop. Just did a quick review. Two paragraphs. It doesn't even have a picture of the cover. Go read it, if you'd like.

Anyways, back to Flatterland. As the tagline says, it's like Flatland, only more so. And with a healthy helping of Alice in Wonderland to boot. Flatterland is set about a hundred years after Flatland, and follows the adventures of Victoria "Vikki" Line, a woman who finds her some-number-of-greats-grandfather's book, which is entitled Flatland. (Yes, they are actually the same book.) Anyways, Vikki reads Flatland, and in it finds instructions for summoning a being from Spaceland, in a way that is kind of hilarious.

So, Vikki summons someone from Spaceland. However, she gets a bit more than she bargained for. Instead of the stuffy, boring old Sphere from Flatland, she meets a loud, energetic, grinning creature known as the Space Hopper, who can travel through much more than just stuffy, boring old Spaceland. The Space Hopper equips Vikki with a Virtual Unreality Engine, or VUE, and takes her on a tour of all sorts of spaces and geometries, meeting many strange people along the way. They pay special attention to a strange place called Planiturth, and the fact that its inhabitants don't really know which space they're in.

Personally, I really liked Flatterland. I'm a big fan of puns, and math, and paradoxes, and big toothy grins, and winks directed at the fourth wall, so what's not to like? I think Ian does a good job of describing and explaining all the spaces, and why they're all cool. If I had one complaint, it would be that there aren't enough pictures. Actually, I do have that complaint. A book about geometries should have more pictures in it. But, besides that, it's a fun read, and it stays crazy enough to always keep you guessing. If you like bending your brain a bit, and you don't mind a good pun every once in a while (or a bad pun (or twenty)), then I think you should try Ian Stewart's Flatterland.

Flatland

Flatland, by Edwin A. Abbott, is a memoir written by one A. Square, who inhabits the two-dimensional universe known to us as Flatland. The first half of the book is about Flatland itself, and the lives of the people inside it, who live in a strictly ordered society where social class is determined by the number of sides you have. Women, all of which are lines, have the lowest status (even though they are technically really thin quadrilaterals). There's also this freaky thing where kids are beaten into being more regular, and color is not allowed, and it's kind of terrible.

The second half of the book is about A. Square's experience of being visited by a Sphere from Spaceland, which has a third spatial dimension. As A tries to wrap his head around the fact that there can be a third dimension, the reader gets to try to thing about what a fourth dimension could mean. The Sphere also takes A through the first and "zeroth" dimensions, which is fun. Then the Sphere takes A back home, at which point A is promptly thrown in jail for being a lunatic. If you like dystopias and/or thinking about higher dimensions, then Flatland is a book you might like.

Our Mathematical Universe

Our Mathematical Universe is about big questions: Why are we here? What made it all? What's it all made of? Where did we come from? Where will we go? Where did we come from, Cotton Eye Joe? and so forth. More specifically, it is about Max Tegmark's answer to all those questions.

Tegmark takes us on a tour of the extremes of physics, from the epic scales of our entire universe to the smallest scales of atoms and space. The part about cosmology and the beginning of the universe is especially good, because Tegmark has personally worked with the data from satellites investigating the Cosmic Microwave Background Radiation. He also talks about the possibility of multiverses, and identifies four different "levels" of multiverse. I like that he stresses that there is no such thing as a "multiverse theory" in physics; multiverses are not a theory, but a prediction of other theories.

Then he talks about his idea that, in the end, the entire universe is a mathematical object. He makes quite the compelling case for the idea, essentially arguing that for physics to mean anything it has to be true, but in the end he didn't convince me. It's kind of a nice idea, though. A good effort. Anyways, if you'd like to see the structure of the entire book, it's something like this:

Yep. That's taken right out of the book. Tegmark did some of my job for me. Nice of him.

When Tegmark says "my quest for the ultimate nature of reality," he means it. The book is about his quest. Our Mathematical Universe could equally accurately be called Max Tegmark is a Nerd, although I doubt that would sell quite as well. The book is filled with personal anecdotes and little asides, which I think adds to it a lot. Then, of course, there's the whole "reality is math" thing that he believes. Still, he's an interesting person with interesting ideas, so it's fun to go on the "quest" with him. He certainly kept me to the end, at least. If you're also interested in the big questions about what it's all about, and you don't mind having a friend along for the ride, then you would enjoy reading Our Mathematical Universe.