Comment: I'll concede your point on starting to count at one

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I'll concede your point on starting to count at one

I was trying to point out the importance of zero, but I didn't do it very well. I think that saying 10 is comprised of 1 + 0 = 1 is a bit of a stretch numerically. The concept of 10 is 1*10^1 + 0*10^0. That only works using base 10. I just tried the same exercise (with the number circle and doubling starting at 1) in base 8 and base 12, and the results don't look nearly as pretty. Just for fun, I decided to try base 20, since the Mayans used base 20. The start of the pattern doesn't look too good, but the pattern will be very complex and I don't have time to complete it right now, so I'll reserve judgement on that one. The problem is that any number base we impose is essentially an artificial organizational mechanism that we (necessarily) impose on numeric concepts. The concepts themselves are independent of how we organize numbers. That's why I am fascinated by pi and other natural numbers like it. Their meaning goes beyond the numerical systems we impose.