the lighter side of financial mathematics

Engraved Portraits of Gauss for sale, just 40 dollars!

These are in fact 10 Deutsche Mark notes. I have the feeling that the seller, Acme Klein Bottle, sold them at a lower price before 2002.

I'm kind of tempted to order one, but forty bucks is forty bucks, and I'm a grad student. It kind of seems like a nice conversation piece, though. Besides, for two dollars more I could get a Klein bottle. Or I could get a Klein bottle hat. I knew someone who tried to knit one of these once; I don't remember if she succeeded. Acme also sells Mobius band scarves, which I suspect would be quite annoying because I like my scarves to have ends. These would have novelty value and keep me warm.

(You might also consider these portraits of Euler, or any of the portraits from this gallery. Rather strangely, all the portraits have numbers on them.)

But let's say, hypothetically, I bought the portrait of Gauss. I could hang it on my wall and people would wonder why I hung money on my wall instead of spending it. It would kind of be like a Knuth reward check -- Knuth pays a bounty of $2.56 for each error people find in his books.

In 2002, Knuth said in this article in the notices of the AMS, when asked what would happen if all his reward checks were cashed:

There's one man who lives near Frankfurt who would probably have more than $1,000 if he cashed all the checks I've sent him. There's a man in Los Gatos, California, who I've never met, whom I've never met, who cashes a check for $2.56 about once a month, and that's been going on for some years now. Altogether I've written more than 2,000 checks over the years, and the average amount exceeds $8.00. Even if everybody cashed their checks, it would still be more than worth it to me to know that my books are getting better.

Knuth didn't answer the question directly, but I assume he'd be okay if they all were cashed -- I have a feeling he's got some money saved up.

On the contrary, Erdos once said that he would not be able to pay out all the rewards he had put on various problems, and compared this to that the strongest bank would not be able to survive if all its customers simultaneously wanted their money -- but believed the bank run to be more likely. I'm kind of curious if there's a list of Erdos problems out there. This article indicates that people usually did cash Erdos checks, perhaps because the amounts of money involved are greater -- and back then, you got a cancelled check back from the bank anyway. Ronald Graham estimates that the total outstanding bounties on Erdos problems are about $25,000, although it seems he's not sure because as of that writing there was no list of them. I was able to track down a list of a couple dozen or so.

And while I'm talking about money: I previously wondered about the density of money, and I concluded that the density of U.S. coinage -- if we make certain reasonable assumptions about how change is given -- is $28.58 per kilogram. This was inspired by the fact that I had some change I needed to cash in.

I cashed in my change recently; I had 95 quarters, 126 dimes, 76 nickels, and 339 pennies, for a total of $43.44. This is also 2,052 grams, for a money density of $21.17 per kilogram. As I said in my earlier post, I tend to use quarters for laundry. One expects dimes, nickels, and pennies to occur in a 2:1:5 ratio in randomly occuring change; my actual experience is not too far from that. In randomly occuring change, though, one expects three-fourths as many quarters as pennies; I didn't have nearly that many quarters.