# Pocket AnthropologyJune 17, 2012 2:51 PM   Subscribe

Is there a way to find out approximately when I left this wad of money in my (very old) jacket pocket, using statistics and date/number info from the bills? What would be the minimum number of bills needed for such a thing?
posted by nile_red to Science & Nature (10 answers total) 1 user marked this as a favorite

The limiting case is:
"Well, it wasn't stashed before the newest bill in the wad."

(A wad of twenties fresh from the ATM might all be new, and thus might be freshly dated.)
posted by AsYouKnow Bob at 3:16 PM on June 17, 2012

I think the minimum number would be one (with last years date on it).
posted by DaddyNewt at 3:18 PM on June 17, 2012

As AsYouKnowBob says, I'm not sure this strategy will really work. Couldn't you have, like a banknote from the Tang Dynasty or something that you just put in there last week?
posted by box at 3:23 PM on June 17, 2012

This could totally be done, I think. It's definitely a stats question. If you could estimate the half-life of money in circulation and the influx of new money each year you could model the population of banknotes in circulation in any given year. Then given a sample you could test it against each of the populations to find which is the most likely source. The more banknotes you have in the sample, the higher the confidence in the result. Unfortunately I don't know enough stats to actually *solve* the problem, but I can definitely see a way.
posted by PercussivePaul at 3:41 PM on June 17, 2012 [7 favorites]

I think this would depend more on the habits of the person than the distribution of bank notes at large there are just too many other variables which can impact the distribution of dates on the notes. I don't think adding more bank notes would actually make this more accurate - in fact it might make things worse. For example

Take two banks one in busy urban center and another in a relatively quiet suburb. Do you really expect the distribution of bank notes would be the same? I don't. I would expect the flow and volume of hard currency through these banks would be very different. I know from experience that if I want to get a "new, crisp" bill going to the bank with the expected higher volume increases the chances.

So if at the bank level we have a distribution of notes which depends on many more variables than just the time, I would expect since people interact with different banks (and different merchants who interact with those banks) that it would be very difficult in general to use a distribution of dates on bills as an indicator of time...
posted by NoDef at 3:58 PM on June 17, 2012

Odd that you mention this. I had an assignment when I was in college to treat my room as if it were an archaeological dig and to figure ways to come up with dates. I took all the coins from my change jar and made a histogram of the frequency of date per coin. The pattern leads to a fairly obvious distribution that could be used to correlate a date at which point the collection was completed (which may have nothing to do with the date at which the collection was put in its location - ie, the collection was completed in 1987, but was bought at a garage sale in 2005 and buried in a garden in 2011).
posted by plinth at 4:04 PM on June 17, 2012 [4 favorites]

Oh, hmm, you need the banknotes to be a random sample from the population. However they'll almost certainly be correlated in some way. (What if they all came from the same batch at an ATM?) Well, it'd be fun to run the calculation anyway. Maybe you can make an incredibly sophisticated and complex model to handle all the intricacies...
posted by PercussivePaul at 5:06 PM on June 17, 2012

Definitely a stats question, but unfortunately one that requires you to have a little familiarity with mathematical statistics in order to solve it yourself.

You'll need two pieces of information: the date each bill was printed, and a probability density/mass function f(x) that describes the probability that a bill will be in circulation for x months. With that info, you can use maximum likelihood methods to calculate the most likely date that you left this wad in your wallet.

For example, in the case of a single bill printed on date d1, the likelihood that you left the bill in your pocket on date r1 is: f(r1-d1). In the case of eg three bills printed on d1,d2,d3, the likelihood that you left this wad in your pocket on date r1 is: f(r1-d1) * f(r1-d2) * f(r1-d3). You need to find the most likely date r1, ie the value of r1 that maximizes the product f(r1-d1)*f(r1-d2)...

You can do this with just a single bill, but you can feel more confident in your answer the more bills you have...
posted by JumpW at 5:39 PM on June 17, 2012

http://en.wikipedia.org/wiki/German_tank_problem
posted by joshu at 7:12 PM on June 17, 2012 [1 favorite]

It also depends on the denomination of the bills: 1's are replaced much more frequently than 50's: see FAQ alert for details.
posted by jenkinsEar at 8:30 PM on June 17, 2012

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