Multiplying by i…
Recently I did a series of posts about how the complex numbers arise from a natural progression of math realizations. I’ve done posts in the past about how the natural numbers lead through the integers and rationals to the real numbers. (And I’ve done posts about how weird the real numbers are, but that’s another topic.)
I recently came across another way a progression of obvious natural questions directly leads to the necessity of a new type of number, and this progression takes us all the way from the naturals to the complex numbers.
All by asking, “What do you get when you…”
In my family, we were rather casual about birthdays and other event days. It wasn’t unusual to celebrate a birthday, not on the exact day, but on a nearby day. We were fairly poor, so birthdays mostly consisted of a cake and a token present of some sort. (Put it this way: I can’t recall a single birthday present I ever got. We just weren’t that into birthdays.)
But I don’t recall ever not celebrating Christmas or Easter on the day. That may be as much due to my father being a pastor and having to do his thing at church on those days. The religious upbringing — and the strong streak of anti-materialism that went with it — likely accounts for downplaying birthdays and other gift-giving occasions.
Which is all to say that I missed posting on John Venn‘s birthday!