How far can we go—in science, mathematics, technology, medicine, the arts, even politics? Can our efforts in these fields advance indefinitely? Or will they eventually bump into limits? I have a weakness for such impossibly grand questions, and so, I was happy to discover, does the British physicist David Deutsch.

Mr. Deutsch has earned notice for his vigorous advocacy of the many-worlds interpretation of quantum mechanics—the idea that, although we see a particle follow only one path in our world, it actually follows all...