The Case of the Missing Pi Day 4s

Yesterday was Pi Day, 3/14 (those who prefer days before months can have Pi Approximation Day, 22/7) and in celebration of this momentous annual event, I invited several of my American colleagues (who have learned to tolerate my numerical eccentricities) over to my house in Canada for an International Pi Day Pie Party, which was a great success.  And, of course, as befitting this event, we had Pie, complete with Pi (to two decimal places) on top:

It's blueberry!So far, so good.  (And for the record, it was very good).  There was only one problem: the local dollar store I went into had a very odd distribution of candle numerals: it had tons and tons of 0, 1, 2, and 9, some 3s, but no 4s, 5s, 6s, 7s, or 8s.  As a professional numbers guy, and also as a guy who needed a 4 for his pi(e), this was deeply disconcerting.

After a moment, I figured out why. Ordinarily, when stores buy products that come in different varieties from wholesalers, the default is to order the same amount of each variety.   In this case, the store had obviously ordered an equal amount of each numeral, but they were being purchased by consumers at different rates.    Now, there is nothing about the properties of the natural numbers that would lead to this observed distribution (if it were Benford’s Law in action, it would be 1 and 2 that would be in short supply). Rather, the explanation is a social one:   Many parents do not buy birthday candles for their child’s first, second, or third birthday, because, while, as my (thankfully childless) brother noted, “Babies love fire!”, parents of toddlers do not.    At the other end, by the time your kid is about 9, and certainly by the double digits, they’ve probably outgrown the ‘giant novelty numeral candle’ phase of their lives.  Ages 4-8 are the sweet spot, and thus these sell out much more quickly.

I also note that, for adults, decadal birthdays like 20 and 30 tend not to attract much numerological attention, whereas 40, 50, and 60 certainly do (not so sure about 70 and 80), and by 90 most of the clientele is deceased.    This doesn’t explain why there were so many 0s available – perhaps purchasers are aware of this phenomenon and order extra zeroes, but don’t take account of differential demand for the tens digits.

Now, if we lived in a perfect world where suppliers and store owners had full information about their stock and made perfectly rational decisions, purchasers would notice such discrepancies and perhaps order more of the missing numerals.  The local dollar store, however, does not occupy such a world.  Fortunately, this being Windsor, Ontario, there was another dollar store across the street, and while it also had a skewed distribution, lo and behold, it did have one lonesome 4 for purchase (seen above).   Thus my Friday Pi Day pi display supply foray was saved.  Yay! (Try saying that in Pig Latin.)

Actually, this is not the first time I had encountered this phenomenon.  Back in 2008, when American gas prices first regularly began to hit $4.00 a gallon, the New York Times reported on, of all things, a shortage of numeral 4s, because their number sets were purchased with an equal distribution across all ten digits (presumably with extra 2s and 3s purchased individually to deal with those dollar amounts).  Once that leading digit got to 4, there was a temporary shortage, leading to some store owners writing their own makeshift 4s until new ones could arrive.

Thus, while we think of linguistic and symbolic resources like numerals as being effectively infinite, in contexts like these, you can indeed have shortages and surpluses.   Thankfully, now that we’re on to the Ides of March and our Pi Day shortage is dealt with for another year, I can store these candles for future use, if I want.  The pie, on the other hand, has gone to a better place.  Because, while you may sometimes need to ration your fours, let’s hope we never live in a world where we have to ration pie.

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