Numbers and their meanings: A short history

Today, let me dabble a bit on numbers, where they come from and what they mean.

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Yeah, I didn‘t know what to write as an introduction this time. Sorry.

Now that I ruined it, let‘s begin!

Outnumbering our limits

First and foremost, numbers fascinate us because we are hilariously ill-prepared to understand them. Sure, we can probably grasp how one apple and two oranges differ, yet numbers thrive on scale… and we do not. Take the problem of automobile accidents. For years, the US government has scarcely awakened public concern on the subject. It‘s not that we don‘t know that a car crash is deadly nor is it because we don‘t know that such accidents happen. Rather, we don‘t realize just how common they are. In the USA alone, more than 45 000 people are killed each year in car crashes. That statistic has been shared with the public for years now. And that‘s exactly the problem: it is a big number and therefore it means absolutely nothing to most of us. Never mind that this represents more deaths every year than all American dead during the Vietnam War, the common man is not too happy to dismiss it and continue on his merry way.

This issue is largely related to our insufficient capacity to understand probabilities (see my post on the subject). As Stalin is supposed to have said: “One death is shocking news. A thousand is a statistic.“ I have very few in common with that man, but I sadly have to agree with the sentiment. We see small numbers as clearly distinct concepts, but large numbers end up as an utterly incoherent mush. The pressing issue here is that we do not comprehend how the first interacts with the latter. As Archimedes pointed out, any number - no matter how large - can be matched and exceeded by adding together sufficiently many smaller numbers. That statement, no matter how simple it was, took centuries to become commonly accepted by mathematicians supposedly much more acquainted with numbers than most.

Speaking of scale, we are especially bad at comparing scales outside of the linear. Anything that grows more quickly than straight addition quickly loses all sense and concreteness. Mozart once wrote a waltz published as a game by Simrock in 1796. It contains eleven variations for fourteen of the sixteen bars of the waltz. Such a small partition, yet it would take about the age of the Earth itself to play it all out. In the same vein, take the classic chess puzzle where a scholar asks the prince for one grain of rice on one square and double that amount for each successive square of the grid. Another seemingly simple demand that was truly asking for more rice than what the whole Earth contains. We don‘t appreciate just how large such tidy packages can be. Never mind comparing them to each other.

Some tribes of South America use a numerical system consisting of only three numbers: one, two and a lot. Maybe that numerical system would be better suited to our capacities. As I said, numbers work on scale and we do not.

Numbers and us

So we don‘t understand math. What about it? Well, ignorance brings forth strange responses from us. Uncertainty and anxiety certainly (as many of you might have experienced during math classes). But more importantly, awe, wonder… and worship. Almost every culture, historical or not, attributes a sort of power over us and by extension our environment. This section will focus on describing some common number symbology around the world. Keep in mind, that almost everything I will describe below is far entrenched in the speculative. Take it with a grain of salt.

We first need to consider where numbers originate. Do we know exactly when humans started using numbers? Of course not. But we do think that the integration of numbers was gradual. As such, numbers could first arise with the need to count things. The important nuance here (and a fascinating theory frankly) is that just like us when facing a new concept, our ancestors would have associated numbers with what they knew. Take video games for example. At first, they were profusely compared to movies and board games since those were well established in the 1950s. We can even argue that such comparisons are still used today (it is fair to say that many PS3/360 games still tried to be movies). In any case, our ancestors probably associated such an extravagant concept as numbers with what they knew - concrete and reassuring things. As far as we can go back in time, the number 2 was associated with ideas of duality. Whether we look back to Sumerians, Egyptians or Hebrew cultures, they all share in some way our “two sides of the same coin“ view.

Interestingly the theorized original meaning of 3 seems associated with the number system I mentioned (1, 2 and many). In most historical cultures, 3 became associated with repetition, law and continuity. For example, in Greek mythology, it is said that Atalanta dropped 3 golden apples. It could have been 4 or 7, but 3 sufficed to express to idea of multitude. In other words, she dropped many (read 3) golden apples. Since 3 was analog with the previous concept of “many“, this would be the number that would most be associated with divinity. After all, deities exceed our understanding - just as many encompass more than we can chew.

Let‘s continue down numbers. Some time later, as human society became more sophisticated and its mathematical needs grew, the concept of 4 would also have been established. For its part, 4 would acquire a very strong attachment to the natural world. This could be because human society would have realized that the Earth extends in 4 directions. 4 cardinal directions, 4 winds and 4 kingdoms are common concepts across cultures demonstrating the cardinality of the number 4. It is probably this association between the Earth and 4 that explains why 4 also comes up in astrology. After all, if 4 encompasses everything on the horizon, why not what is above it too? This could explain why lunar months are made of 4 weeks of all things. This could, in turn, explain the relation between 7 and astrology (as dividing a lunar month into 4 makes weeks of 7 days). As the seventh day of the fourth week of a lunar month marks the apparent death of a moon, this is often seen as why 7 acquired a certain gravity in Sumerian society. This association would follow in successive cultures (7 deadly sins anyone?).

I could continue forever on such speculations. Frankly, you don‘t need to remember exactly any of this. Rather, I find it much more interesting to keep in mind that numbers (and mathematics in general) were shaped by human concerns… but that they also shaped us in turn. I will only mention 3 (or should I say many?) other theories.

The popularisation of finger counting could explain the association between 5, the human hand and then the human itself.
The adoption of the decimal system probably explains the association between 10 and a sense of completeness in many cultures. This could also explain why 40 is an extremely common number used in Abrahamic religions to mark the change of an era. After all, 40 is the completeness (10) all over the world (4).
Finally, this view of 10 could explain why 9 is often seen as “almost complete“. Remember that the siege of Troy lasted 9 years.

One last curiosity for the road

I could go on and on. But let me end on the theory of one of the most famous “bigger“ numbers: 666. The association between that number and the devil is theorized to come from a remark from John the Apostle stating that “this number designates the name of the Beast of the Apocalypse, the Antichrist“. Yet, you probably don‘t know that he was talking about a specific person and not a religious entity! Indeed, in the Hebrew system (which assigns numbers to letters and words), the name of “Caesar Nero“ (a Roman Emperor who persecuted Christians) has a value of 666. In that way, 666 became a common political graffiti in Rome!

In any case, I know this was hard to follow. Yet, I also hope it showed just how much you can deep dive into numerology. Moreover, I scarcely mentioned the Hebrew system! Those Hebrews sure had a knack for numbers. I leave this to you to explore. I also encourage you next time you see a number to go look up what is associated around the world with that number. You WILL learn something. Trust me.

See you next time.

References

Innumeracy: mathematical illiteracy and its consequences, John Allen Paulos, 2011.
Medieval number symbolism: its sources, meaning, and influence on thought and expression, Vincent Foster Hopper, 2000.