Nickel and Dime

When I was a little kid, I had a lemonade stand for a day. An early brush with capitalism. My mother made the lemonade, we put a table and chair at the sidewalk, and placed the pitcher and a small sign on the table. 

I set the price at two cents a cup. 

My brother was my first customer. He handed me a dime and asked for his change. I wasn't sure what to do. My brother looked at the change I had, and picked up a nickel and three pennies.

I knew that wasn't right. He's giving me one very small lightweight coin and taking away four larger heavier ones? I told him I wasn't born yesterday, and I knew that wasn't fair.

My brother was quite amused. He explained the arithmetic, but I wasn't buying it. He was clearly trying to cheat me. No one would create a currency in which a small coin was worth ten times as much as a heavier larger coin. That doesn't make sense.

Perhaps that's why my brother is a physicist-turned-economist and I'm a (too logical) mathematician.

When I ran the above story past my brother, he replied (bemusedly, according to him, which led to a bemusing discussion about what "bemused" actually means):

Logically, though, the conclusion should be the other way around. Your little kid self argued in terms of size, i.e., in physical terms, while my teenage self argued in symbolic, i.e., mathematical terms. And I didn't try to cheat you, which my present economist self finds surprising.