How would you describe the concept of infinity mathematically, scientifically, or psychologically?
Mathematically: Calculate and tell me something divided by zero.
Scientifically: Count and tell me the number of sand grains in your nearest sea shore. Or at least derive a formula to count it and tell me the exact figure!
Psychologically: Assume that all the thoughts of all the human beings in this earth are passing through your mind. And tell me what you feel!
Short answer: I punt.
Longer answers: 1) Having studied Calculus in High School and college, I did this too many times to remember. Or even think about coherently. The question is at the core of the differential calculus and the integral calculus.
2) Let me work on that one and get back to you.
3) My mind just exploded.
Longer answer: I've given this topic a lot of thought, and I even went to the trouble of researching and writing a Hub on the topic. The research I did was on Georg Cantor, and the contents of the Hub would be partly biographical, and partly about a couple "aha!" moments that I had many years ago. Cantor's diagonal is profound, and can be explained to a non-math expert. (Recently I saw an interview that Stephen Colbert (or more precisely, "Stephen Colbert" for another few days, anyway) had with the mathematician Terence Tao. During the five minute interview, Colbert made some debating point about infinity, and I could see that Tao was about to refine/correct what Colbert had said, but the explanation would not fit into a five minute interview.) Cantor can be explained to laymen, but it really deserves a bit more than five minutes. I wrote a lot on it, distilled it down, and ultimately gave up on the Hub, as there were too many loose ends that were beyond my abilities to communicate clearly (and, to be frank, beyond my understanding as well). The other "aha!" moment I had was with Zeno's paradox in my youth. Zeno is often brought out near the beginning of calculus courses, as an intro to the idea of limits. Turns out it wasn't so much an "aha" moment, more of a "these are not the droids you're looking for" moment. Zeno is thorny. Very thorny. Way over my head thorny. This one heads us deep into philosophy, physics, and psychology.
The Celtic circle works for me. It has no beginning and therefore no end. It confounded the Romans. Otherwise I have no idea how to describe or illustrate infinity.
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