When I was doing my Ph.D., my supervisor once came into my office and asked me how heavy the batteries I had in the lab were. I said, “Well, they are about 1kg each”, then he gave me a sly smile and asked me, “Is that when they are charged or when they are empty?” I assumed he was joking, but the question got me thinking. Does energy weigh? And if energy weighs, and given how information is stored, does information weigh? I stopped there, but physicist Antonio Padilla, author of the very fun-to-read book Fantastic Numbers and Where to Find Them (Penguin Random House UK, 2022), kept asking. If information really weighs, can my head collapse into a black hole when I think of or memorize the decimal representation of a very large number?
I am not sure if this reasoning is correct, but it is certainly fun to entertain. What are large numbers anyway? This and other interesting topics around very small and large numbers (Hollographic principle, quantum physics, Cantor’s infinites, conservation laws and symmetries, etc.) can be found in this fascinating book.
