Tag Archives: book review

Textbook Review: Exploring Black Holes

I’m bringing a box of textbooks with me to Denmark. Most of them are for work: a few Quantum Field Theory texts I might use, a Complex Analysis book for when I inevitably forget how to do contour integration.

One of the books, though, is just for fun.


Exploring Black Holes is an introduction to general relativity for undergraduates. The book came out of a collaboration between Edwin F. Taylor, known for his contributions to physics teaching, and John Archibald Wheeler, who among a long list of achievements was responsible for popularizing the term “black hole”. The result is something quite unique: a general relativity course that requires no math more advanced than calculus, and no physics more advanced than special relativity.

It does this by starting, not with the full tensor-riddled glory of Einstein’s equations, but with specialized solutions to those equations, mostly the Schwarzschild solution that describes space around spherical objects (including planets, stars, and black holes). From there, it manages to introduce curved space in a way that is both intuitive and naturally grows out of what students learn about special relativity. It really is the kind of course a student can take right after their first physics course, and indeed as an undergrad that’s exactly what I did.

With just the Schwarzchild solution and its close relatives, you can already answer most of the questions young students have about general relativity. In a series of “projects”, the book explores the corrections GR demands of GPS satellites, the process of falling into a black hole, the famous measurement of the advance of the perihelion of mercury, the behavior of light in a strong gravitational field, and even a bit of cosmology. In the end the students won’t know the full power of the theory, but they’ll get a taste while building valuable physical intuition.

Still, I wouldn’t bring this book with me if it was just an excellent undergraduate textbook. Exploring Black Holes is a great introduction to general relativity, but it also has a hilarious not-so-hidden agenda: inspiring future astronauts to jump into black holes.

“Nowhere could life be simpler or more relaxed than in a free-float frame, such as an unpowered spaceship falling toward a black hole.” – pg. 2-31

The book is full of quotes like this. One of the book’s “projects” involves computing what happens to an astronaut who falls into a black hole. The book takes special care to have students calculate that “spaghettification”, the process by which the tidal forces of a black hole stretch infalling observers into spaghetti, is surprisingly completely painless: the amount of time you experience it is always less than the amount of time it takes light (and thus also pain) to go from your feet to your head, for any (sufficiently calm) black hole.

Why might Taylor and Wheeler want people of the future to jump into black holes? As the discussion on page B-3 of the book describes, the reason is on one level an epistemic one. As theorists, we’d like to reason about what lies inside the event horizon of black holes, but we face a problem: any direct test would be trapped inside, and we would never know the result, which some would argue makes such speculation unscientific. What Taylor and Wheeler point out is that it’s not quite true that no-one would know the results of such a test: if someone jumped into a black hole, they would be able to test our reasoning. If a whole scientific community jumped in, then the question of what is inside a black hole is from their perspective completely scientific.

Of course, I don’t think Taylor and Wheeler seriously thought their book would convince its readers to jump into black holes. For one, it’s unlikely anyone reading the book will get a chance. Still, I suspect that the idea that future generations might explore black holes gave Taylor and Wheeler some satisfaction, and a nice clean refutation of those who think physics inside the horizon is unscientific. Seeing as the result was an excellent textbook full of hilarious prose, I can’t complain.

Book Review: The Invention of Science

I don’t get a lot of time to read for pleasure these days. When I do, it’s usually fiction. But I’ve always had a weakness for stories from the dawn of science, and David Wootton’s The Invention of Science: A New History of the Scientific Revolution certainly fit the bill.


Wootton’s book is a rambling tour of the early history of science, from Brahe’s nova in 1572 to Newton’s Optics in 1704. Tying everything together is one clear, central argument: that the scientific revolution involved, not just a new understanding of the world, but the creation of new conceptual tools. In other words, the invention of science itself.

Wootton argues this, for the most part, by tracing changes in language. Several chapters have a common structure: Wootton identifies a word, like evidence or hypothesis, that has an important role in how we talk about science. He then tracks that word back to its antecedents, showing how early scientists borrowed and coined the words they needed to describe the new type of reasoning they had pioneered.

Some of the most compelling examples come early on. Wootton points out that the word “discover” only became common in European languages after Columbus’s discovery of the new world: first in Portugese, then later in the rest of Europe. Before then, the closest term meant something more like “find out”, and was ambiguous: it could refer to finding something that was already known to others. Thus, early writers had to use wordy circumlocutions like “found out that which was not known before” to refer to genuine discovery.

The book covers the emergence of new social conventions in a similar way. For example, I was surprised to learn that the first recorded priority disputes were in the sixteenth century. Before then, discoveries weren’t even typically named for their discoverers: “the Pythagorean theorem”, oddly enough, is a name that wasn’t used until after the scientific revolution was underway. Beginning with explorers arguing over the discovery of the new world and anatomists negotiating priority for identifying the bones of the ear or the “discovery” of the clitoris, the competitive element of science began to come into its own.

Along the way, Wootton highlights episodes both familiar and obscure. You’ll find Bruno and Torricelli, yes, but also disputes over whether the seas are higher than the land or whether a weapon could cure wounds it caused via the power of magnetism. For anyone as fascinated by the emergence of science as I am, it’s a joyous wealth of detail.

If I had one complaint, it would be that for a lay reader far too much of Wootton’s book is taken up by disputes with other historians. His particular foes are relativists, though he spares some paragraphs to attack realists too. Overall, his dismissals of his opponents are so pat, and his descriptions of their views so self-evidently silly, that I can’t help but suspect that he’s not presenting them fairly. Even if he is, the discussion is rather inside baseball for a non-historian like me.

I read part of Newton’s Principia in college, and I was hoping for a more thorough discussion of Newton’s role. While he does show up, Wootton seems to view Newton as a bit of an enigma: someone who insisted on using the old language of geometric proofs while clearly mastering the new science of evidence and experiment. In this book, Newton is very much a capstone, not a focus.

Overall, The Invention of Science is a great way to learn about the twists and turns of the scientific revolution. If you set aside the inter-historian squabbling (or if you like that sort of thing) you’ll find a book brim full of anecdotes from the dawn of modern thought, and a compelling argument that what we do as scientists is neither an accident of culture nor obvious common-sense, but a hard-won invention whose rewards we are still reaping today.