Horseshoes and Social Distancing

Posted March 26, 2020

There’s a joking bargain that farriers often offer to novice horse owners:  They’ll shoe all four feet starting at one penny for the first nail and simply doubling the cost for the next nail at 2 cents, the next at four cents, and so on.  Total the fee for each nail and that’s the final bill.  

At first, this looks pretty good, there are eight nails in each shoe, and the cost for the first foot is a reasonable $2.55.  However, by the end of the second foot the whole thing looks like a rotten deal at $655.35 for just two feet.  Adding in the third foot brings the total to $167,772.15, and the final bill for all four feet is a whopping $42,949,672.95!

Mathematicians refer to the horseshoe nail bargain as an exponential progression; and the CDC website explains that is the same way the Covid-19 pandemic is growing.   According to their data, on March 15, 11 days ago, there were 3,487 cases in the United States, yesterday they reported 68,440.  If the number of cases continues growing like this, in a few days that will double, then double again and keep doubling.  

The current population of the United States is about 330 million, about 12-13 doublings away.    

Isolation and social distancing are the tools we have to combat this exponential increase.  It’s like putting only four nails in each horseshoe and spreading the sixteen nails over four feet.  The farrier’s bill would be high at $655.35, but that’s a lot better than 42 million!  

Please dear friends practice isolation and social distancing to help keep yourselves and everyone else safe—especially those valiant service workers on the front lines of this pandemic. 

[Thanks to son and mathematician Sam Ferguson and observant, IT friend Al Schumann for pointing out errors and suggestions to the first version of this post. I appreciate their corrections, and they have been included in the post as it now reads.}