“Soon enough,” Alice Dreger writes at the beginning of her romp of a book, “I will get to the death threats, the sex charges, the alleged genocides, the epidemics, the alien abductees, the anti-lesbian drug, the unethical ethicists, the fight with Martina Navratilova and, of course, Galileo’s middle finger. But first I have to tell you a little bit about how I got into this mess.”

As is so often the case, what got ­Dreger into trouble was sex. A historian of science and medicine, she criticized a group of transgender activists who had attacked a sex researcher for his findings on why some people want to change gender. Having hounded the researcher mercilessly, the activists attacked Dreger too. The bad news is that this was hard on ­Dreger. (More on that momentarily. For now, I’ll just note they called her son a “womb turd.”) The good news is that from this mess emerged not only a sharp, disruptive scholar but this smart, delightful book.

“Galileo’s Middle Finger” is many things: a rant, a manifesto, a treasury of evocative new terms (sissyphobia, autogynephilia, phall-o-meter) and an account of the author’s transformation “from an activist going after establishment scientists into an aide-de-camp to scientists who found themselves the target of activists like me” — and back again.

As its title suggests, the book is also a defiant gesture aimed at those who would deny empiricism. Yet this middle finger (Galileo’s actual middle finger, in fact, which Dreger stumbles across in Italy) is raised in affirmation as well. It points toward the stars that confirmed his cosmology — and toward empiricism’s power to create a fairer, more rational society. For Galileo is famous not just because he saw how the stars move. He’s famous because he insisted we see for ourselves how the world works, share what we see and shape our society accordingly.