Recently, the physicist Sabine Hossenfelder, who maintains a wonderful blog, posted her thoughts about "infinity," its necessity as a mathematicians' tool, on the one hand, but its unreality from the point of view of the science of physics, on the other. Her point is that a physicist only regards something as real if it is necessary in order to explain an observation. Infinity, she says, will never fill that bill. She also went a bit into the mathematics of infinity, and the fact that not all infinities are the same. The real numbers are a different sort of infinity from the integers. I used the co mment section under her blog post to ask a question that has long been on my mind. I remember when I was a kid, many decades ago, some of us nerdy types excitedly read "One, Two, Three, Infinity" by George Gamow. Gamow covered some of the same territory you just did although I'm guessing progress has been made in the last half century or so. If I recall corr...