Fortune

I got a fortune cookie today with the followng message:

Don't spend your time stringing and tuning your instrument. Start making music now!

American translation:

Git-R-Done!

Art?

I will leave the judgement to you. This art appeared in front of the IGB building. They are kind of interesting, but I do not think they fit in the environment that well. They are a little too bright. I think they are supposed be a 3-D (yes, they are 3-D, although the image I posted is a 2-D image) representation of some sort of biological molecule: either a protein or some enzyme. All three are the same shape, just different sizes. This could not happen in a chemical sense, it is just crazy talk.

Here I am sitting in the active site. The equation goes something like this:

Ugly art + Michael <=> odd sight.

The equilibrium constant favors the dissociated complex, but sometimes the thing is pushed to the right with the proper activation energy. This day it was some woman walking by, and I didn't want to look like an idiot by not getting in the active site...

Pennies: A day in the life

Penny Lane is in my is in my ears and in my eyes... Like most of you, I have a penny jar. It filled up yesterday (I filled it over the past year: 614 pennies + 2 Canadian pennies). As I was rolling the pennies to take to the bank, I asked a few questions. We all know that pennies are "useless" and "not worth the time." I have heard these arguments before, and there is some validity to them. Pennies cost more to make than they are worth (even though they are copper-plated zinc). They take up valuable transaction time (in this rush-rush world we live in you better not stand at a register for more than 2 seconds), and 2/3 of the coins minted in the US are pennies. But those are not the questions I asked. I think the "anti-penny" lobby is nothing but a bunch of Lincoln-hating, slave-owning bigots that wish the Great Emancipator never was president. They hate that his face is everywhere, but I digress...

I asked: What is the average age of a penny? How long does a penny stay in circulation? How many pennies are in circulation? What happens to pennies when they die?

Here I will answer these questions. The average age of a penny is simple to answer. I sampled my pennies, and measured how old each one was. (they come with the date minted stamped on them). And here are the results:

The average age of my pennies was 16.51 years, with a standard variation of 10.92 years. I can state with 95% confidence that the average age of a penny in circulation is 16.51 ± 0.86 years. However, the median age was 14 years, and the most probable age was 7 years (minted in 2000, 6.03% of all pennies). I had a lot of pennies from that year.

Those are simple statistics, and not that hard to figure out. Below I have posted a graph of my penny results. Overlaid with the results, I have a Gaussian function graphed with the average and standard deviation I measured earlier.

You may notice a few things about the data. First, it is not that regular of a population. The Gaussian does a poor job fitting the data (r squared = 0.48). It may do well as the pennies get older, but the fit is poor. I also noticed the data has some spikes in it at certain years, and dips at others.

I guessed the data was reflecting two things: 1. The mint produces different amounts of pennies each year. Some years they make more that others. For example, in 2000 (the year I graduated from Truman State) they minted 14.3 billion, compared to 9.8 billion in 1978 (the year I was born). This must be reflected somehow in the data. 2. Pennies leave circulation. Through some process, pennies are removed from circulation - I will speculate on this later, but for now we will say it is "magical."

If we account for these things, our data can be explained very well. If we assume that the pennies being removed from circulation is a first-order process, we can take the amount minted each year, and calculate how many are left in circulation this year (2007). I included numbers going back to 1940 in my data, including data from earlier than that is insignificant to the numbers. You can see the raw data with the modeled data over it.

WOW! That matches the data very well, no? The bumps and valleys are matched pretty well (r squared = 0.90). From the model, these are the numbers we get:

The half-life of pennies is 20 years. That is kind of cool, and it means that 25% of the pennies minted in 1967 are still in circulation (that's 750,067,654 pennies still around today). That does not necessarily answer our question "How long does a penny stay in circulation?" because we did not define what we meant by "stay in circulation." A half-life is a good place to start. We could ask which year pennies start making up the majority of the pennies in circulation

That question leads us to the following number: 95% of the pennies in circulation were minted after 1970 (both experimental and model). so, 95 % of the pennies are younger than 37 years. From this half-life, we can also estimate the number of pennies in circulation. By using the numbers of coins minted and their half-life, I came up with 219 billion pennies. Damn, that is a lot of pennies!

Without the half-life calculation, the graph does not match up well at all (r squared = 0.72), and the experimental and theoretical data had large differences between them. I did notice a lack of wheat pennies. They changed over to the Lincoln memorial in 1959 (150 years after Lincoln's birthday). In fact, I only has one of them in my 614 pennies. According to my model, almost 1% of the pennies I had should have been minted before 1959. That comes out to 6, but I only had one. There could be something else going on, but my sample is not large enough to say what. The other odd thing in the data, is I had a lot of 1969 pennies...is something going on there?

My last questions was, "What happens to pennies when they die?" Or, what are the mechanisms for pennies being removed from circulation? Collectors could store them, that removes them from circulation. Also, people could have penny jars all over the place, and never intend to spend the pennies. I also had a friend that would throw his pennies in the trash; that takes them out of the picture for sure (for the record, he was a left-leaning person). The government could collect worn coins and melt them down (do they do this?), and there are all of those fountains... I do believe in a penny heaven where all pennies are happy, wanted, land face up, and always shiny.

There are a few problems with my study. My sample may not be large enough to say much about the older pennies. And to measure a half-life of 20 years, we need to get more pennies. But it is interesting anyway. The other problem is that I collected these over the last year, meaning that 2007 will definitely be off. If I wanted to, I should have gone all over town and collected my pennies today, but that's just crazy.

Spelling

I cannot spell (or type), and I get called for it all the time. But everyone can make a mistake - check this out. Hillary cannot spell...all that Welsey education, and she is as dumb as I. Where is the media? Is this her "potatoe" moment?