With Friday the 13th coming up, it’s hard not to wonder about the number 13. Is that number really a source of bad luck, or is that just in the imagination? Various reasons have been given for 13’s reputation, some of which are related to Christianity and the Christian Bible[1]. Also there are various discussions of “perfect” 12 being more common, like for the number of months. But the calendar is more of a long-term thing. I’m looking for a more practical everyday reason.
First of all, what should be considered bad luck – or even good luck – in a STEM context? Previously, I basically described good or bad luck as being mysterious self-inflicted good or bad outcomes in “Ghosts, Luck, And Curses.”[2] The same thing could be happening with 13, but when the influence of people is removed from the situation, what’s left is just the number 13. Can the number 13 itself lead to a higher occurrence of bad outcomes than other similar numbers?
Looking at different group sizes, I tried dividing the total count by subgroup size and using the remainder. When looking at group sizes 3-20 and subgroup sizes 2-6, I found that the most nonzero remainders were found for group sizes 7, 11, 13, 17, and 19, each of which has 5 nonzero remainders. It’s not surprising that these are all prime numbers, since they all have the most remainders. Note that I opted not to divide a group count by a subgroup count that was larger than it, but that wasn’t particularly significant.
Maybe there’s some other measure that makes the number 13 stand out most. Does remainder proportion highlight 13? I tried looking at each remainder as a fraction of the subgroup size and then took the total for each group. While the results for the same prime numbers are highest, they are no longer tied. But the highest 5 proportion totals do not include 13. So that’s not it either.
Maybe it’s nothing so deep or analytical. With Christmas around the corner, there will be many food treats to eat. It’s common to prepare such treats in batches. As it turns out, 12 is a nice size with 4 rows of 3 each fitting nicely into a rectangle. Cookies on a baking sheet come to mind. The same could be said of the number 6 being nicely rectangular, but more is seemingly better. Not surprisingly, muffin baking tins often have recesses for exactly 12 muffins. Try sharing 12 cookies or cupcakes among 13 people. Someone isn’t getting a whole one.
Why does not getting a treat have to do with luck? How do you distribute delicious treats among a sizeable group of people (especially kids)? Have them stand in line. But if there are 13 potential recipients of 12 cookies, someone is getting less than one or maybe none. If the person at the end of the line gets none? That person was “unlucky.” Or if a kid has to share with a younger sibling? There could be bad feelings between them. Maybe someone pushed past the others to avoid being last. That person could be viewed as selfish or be liked less. Someone might decide to right the injustice wrought by someone unfairly getting a whole cookie when they didn’t. Any of that negativity could lead to bad outcomes (such as harassment or a fight), which again would be unlucky. To avoid all that, if the host/hostess has to cut a piece from each treat to try to ensure even portions for all recipients, that would be unlucky for them. The same with having to prepare an extra batch just so that thirteenth recipient could get a treat.
On the other hand, suppose there are 13 treats but only 12 recipients. Who gets the last one? Some among the 12 might fight for it. The lucky recipient might be seen as unfairly favored. Even if someone does not want the extra treat at the moment, do they deserve something extra later, to compensate for not getting the extra treat this time? Looking for that opportunity could distract one from more important thoughts, possibly leading to an unlucky outcome. How fair is it if there isn’t a next time, so that taking turns to get the extra treat doesn’t work out? Granted, there are likely to be fewer complaints about extras than a shortage. Maybe the host/hostess should secretly eat the thirteenth treat and avoid any bad luck from 13.
A more modern example, suppose several people need transported, including the drivers. 12 people could fit into 3 cars that can comfortably take 4 each, but a thirteenth person would require either another car or for someone to sit in the middle in the back seat. (The middle seat of the second row is sometimes known as the “hump,” alluding to space traditionally carved out for a driveshaft. Why is that seat still so uncomfortable in spite of front-wheel drive not requiring space for a driveshaft running the length of the car?) Having to be the middle person in a back seat could be considered unlucky, not to mention any discomfort from stuffing 3 people into the back seat, where they likely don’t fit to begin with.
While I don’t exactly consider the question settled, I think I did manage to shed some light on the subject. I briefly tried finding a strictly mathematical reason for 13 being unlucky. At best, I showed it could be less efficient than similar numbers, though not always as bad either. I came up with a few examples – maybe contrived – that show 13 can lead to negative feelings or at least some inconvenience or discomfort. I also showed how 13 could look worse than 11 if someone has to do without. More traditional explanations have merit as well. While trying to put 13 people around a rectangle table that seats 12 doesn’t help, highlighting the bad actions of a thirteenth person in religious history could make the event (and number) more memorable. In the future, if it makes sense, I’ll avoid the number 13. Or any number, if avoiding it makes sense. Why push my luck?
References
[1] https://www.mentalfloss.com/article/23266/13-reasons-people-think-number-13-unlucky
[2] https://oddstem.com/2018/10/13/ghosts-luck-and-curses/
Copyright 2024 by Mike Ferrell
Odd STEM 