Why is 13 such an unlucky number?

According to a norse legend, 12 gods once held a banquet, celebrating that everything in the world, except the mistletoe, which no one had bothered asking, had vowed to never harm beloved Balder. Loki, as always, being up to no good (therefore uninvited) and aware of the oversight, decided to crash the party, bringing a spear, deliberately crafted from that fateful plant. When the time came for drinking games, everyone thought, throwing things at Balder, just to see them bounce off, was a fun idea. After a few rounds, the trickster god, living up to his reputation, handed the mistletoe spear to Balder’s blind brother, who then, without intention, landed a fatal blow and took the blame for it.

Christianity offers a (somewhat) similar tale about 13 people attending their last supper, followed by the execution of their beloved leader due to the actions of a traitor (who later hung himself). When the religion spread through pagan Europe, it was seen to independently confirm the already existing belief that having a party with 13 guests spells disaster.

Cultural Impact The superstition of a 13th guest causing tragedy was so strong, that it later found its way into several fairy tales as well, e.g. Sleeping Beauty, Twelve Brothers and The Twelve Dancing Princesses by Brother's Grimm.

This explanation comes from “Extraordinary Origins Of Everyday Things”, p. 11, by Charles Panati. The book has been quoted ad nausea by columnists, but there’s a catch. Both stories only link 13 to a tragic event, but in neither is the number of persons present actually relevant to the unfortunate outcome. In other words, they merely incorporate a likely much older aversion. This puts the question right back on the table: what, if any, properties does the number Thirteen possess that makes it so disliked?

Let’s have a look at math and psychology.

The art of counting

In school, we learn numbers by raising fingers as a mnemonic device for remembering proper names of what is otherwise a purely abstract concept. Of course, there are only so many proper names, one can remember and eventually, we are forced to use compounding rules:

Note: Eleven and Twelve are only quasi proper names. They are derived from proto-germanic words, roughly meaning "one left over" and "two left over" respectively.

#	English	German
1	One	Eins
2	Two	Zwei
3	Three	Drei
4	Four	Vier
5	Five	Fünf
6	Six	Sechs
7	Seven	Sieben
8	Eight	Acht
9	Nine	Neun
10	Ten	Zehn
11	Eleven	Elf
12	Twelve	Zwölf
13	Three; Ten → Thirteen	Drei; Zehn → Dreizehn
14	Four; Ten → Fourteen	Vier; Zehn → Vierzehn
15	…	…

But why would there be 12 numerals with their own names when humans (in general) only have 10 fingers? Furthermore, why are 11 and 12 slurred remnants of a subtractive naming scheme, when all following number names are based on addition?

Finger-counting is intuitive, but hardly efficient. A more compact method, that has been around since ancient times, uses the thumb to point to finger bones, allowing one to count up to Twelve, on just a single hand. The other hand stays free to move things around (e.g. apples into basket), point to inventory, write the tally down, or even extend the count to 60 (mixed mode) and 144 (expert mode).

Touching knuckles to keep count is superior to raising fingers, but also requires some practise (which might be the reason why it fell out of favor in the western world). Nevertheless, the method was undoubtedly advantageous to merchants and mathematicians, who must have employed it throughout the centuries to the extend that a lot of (pre metric) trade units, phrases and conventions became duo decimal based:

• Grocers sell in dozens (12), grosses (144) and great grosses (1728).
• A troy pound consists of 12 troy ounces.
• Prior to 1971, 12 pence made up one shilling.
• A foot can be divided into 12 inches.
• The zodiac is made out of 12 signs, forming an early calendar system.

But if efficiency was the goal, why not assign the palm a number as well and increase the maximum possible count by one?

The knuckle counting method is most practical for taking (quick) inventory. That’s the realm of traders and merchants. A Merchant’s business typically involves buying in bulk and reselling in smaller quantities. Anything broken down into 12 equal piles can be recombined as 2, 3, 4 or 6 equal stacks. Ten piles only stack as 2 and 5, while 13 piles don’t stack at all.

Merchants had every reason to count to 12, none to go to 13 and they took the dozen to wherever they went to trade.

So, there we have it, two competing methods of keeping count. On one hand (pun intended) the efficient knuckle bone system, mandating proper names for the first twelve numbers, on the other, the more user friendly, but limited, finger counting and in between the medieval peasant, who is too uneducated to make heads or tail out of the decimal system. He knows how to express/understand numbers up to ten by raising fingers and maybe the words for 11 and 12 as well. After that, things get really difficult for him. It’s not hard to imagine that the poor guy would shun anything needing larger numbers, but what if he ended up in a situation requiring an exact count just one beyond his known number range (“13 bandits are on their way to ransack our village!”)? Wouldn’t that have been just… unlucky?