### Paradox: This Title is a Lie

I recently finished *Paradox, The Nine Greatest Enigmas in Physics* by Jim Al- Khalili (which I got for free! This honor was accorded me because of my character, charm, good looks, and because ~~the medical department contributed four gallons of grain alcohol to the contest~~ I have a blog and said I’d write up a review.)

This is a book, as the title implies, about so-called paradoxes in physics, but the opening of the book actually takes us through logical paradoxes (including the “this statement is a lie” paradox I’ve modified for the thread title) and mathematical puzzlers such as the Monty Hall paradox. The difference between the logical paradoxes and the remainder, as Jim explains, is that a logical paradox is a true paradox — something that cannot logically stand. The mathematical and physics paradoxes he discusses have a resolution, it’s just that the answer is not obvious because you tend to get different answers if you look at the problems in different ways and you aren’t careful enough in your assumptions and analysis.

It was the resolution of the Monty Hall problem that told me I was going to like this book. I had heard it before, but it’s a clear explanation that points out why it’s such a puzzler the way it is usually presented.

In light of “I’ve heard this before” I will offer up my standard disclaimer (standard in the sense that I’ve stated it once before): since I’m a physicist, I can’t tell you that this book made me understand any new bits of physics. All I can tell you is that I found the explanations to be pretty clear. Explaining physics of this sort without equations isn’t easy, and there are times where the explanation has to end up with a “trust me, this is what the math says,” in part because quantum mechanics and relativity are not intuitive.

Al-Khalili takes us through some ancient paradoxes from Zeno, some thermodynamics in discussing Maxwell’s Demon, several paradoxes in relativity owing to the difficulties in simultaneity, and the weirdness of length contraction and time dilation, and into quantum mechanics with Schrödinger’s cat. Also included are some cosmology issues from Olber’s paradox and Fermi’s question and he also covers Laplace’s demon.

In each of the discussions he explains the underlying physics, though you’ll have to be patient, as the paradox is set up and discussed before the physics discussion happens, and I suspect that in some chapters this might cause some confusion as to why there is a paradox. All I can say is to trust that you will get to your destination. However — and this is one of the really enjoyable things about the book — the path to the destination contains many side treks to metaphorical scenic overlooks and other interesting places to visit, and (in my opinion) there aren’t any tourist traps — all of his tangential discussion has some value to it, in explaining some physics or history of physics.

There are a couple of minor nits I’ll mention. A couple of the paradox resolutions weren’t completely satisfying to me (such as one of the time-travel arguments that ends up looking circular: paradoxes aren’t permitted, so there is no paradox), and some details that matter only to a physicist (gravitational time dilation depends on the potential though he says strength of gravity, which is at best ambiguous but I always take to mean the acceleration, g; he also implies that GPS signals go both directions between receiver to the satellite when it’s only a broadcast from the satellite) and one detail that only matters to someone in a job like mine, which is that he associates the famous Hafele-Keating clocks-on-a-plane experiment with the “United States Naval Research Observatory” which sounds like a hybrid of the Naval Observatory and Naval Research Labs. I’m sensitive to that because people mix us up, or think we’re the same place, all the time. Fortunately he gets the attribution correct later in the book.

But, as I said, those are minor things. Overall it was an enjoyable book to read. I definitely give it a “spin up” rating.

I enjoyed the book also, and like you were sent a copy to evaluate.

A few minor things:

The statement “this statement is a lie” isn’t a paradox. It’s just shows that natural language (in this case, English) is inconsistent.

” The difference between the logical paradoxes and the remainder, as Jim explains, is that a logical paradox is a true paradox — something that cannot logically stand. The mathematical and physics paradoxes he discusses have a resolution, it’s just that the answer is not obvious because you tend to get different answers if you look at the problems in different ways and you aren’t careful enough in your assumptions and analysis.”

Mathematics and logics are just formal systems. The only real difference is that logics deal with values and mathematics deal with quantities. I’m not sure how you can say logical paradoxes are different enough from mathematical paradoxes to make the above quotation true.

“(such as one of the time-travel arguments that ends up looking circular: paradoxes aren’t permitted, so there is no paradox)”

That’s an odd way to go about it. I’d just say that time travel is a matter of geometry and there’s no meta-time, so if you did go back in time, you were there the one and only time it happened. You cannot change the past.