I recently mentioned that the culture we get the word “algorithm” from (the Abbasid Caliphate and its House of Wisdom in Baghdad) didn’t invent the concept and doesn’t own it. I don’t think that’s a controversial claim or anything; I’m sure the Abbasids would’ve agreed. They were building on work from India, and knew it. What we call “Arabic numerals,” the Abbasids called “Hindi numerals.” But I don’t think that means the ancient Hindi culture owns math either. The first algorithms were invented in prehistory; the oldest mathematical artifacts are ten times older than the oldest written artifacts. So what would they have been for?
This will be a series. Possibly just a series of two, since I only have two ideas so far, but I bet there’ll be more.
You Need To Stop Calling Them Lunar Calendars, My Dude
You’ll find plenty of people arguing that the earliest mathematical artifacts were calendars. This was long, long before agriculture, but hunter/gatherers would still have been interested in seasonal cycles. If you can predict when winter is coming, you can store food and/or travel towards the equator. If you can predict other celestial events, you can really impress your friends and maybe be a shaman. Maybe it helps make plans to meet up later if you have a shared understanding of “what day is it today?”
But would that really be the first use-case for calendar-like reasoning? You need to be getting pretty sophisticated before calendars are more useful than just…looking. You can tell when winter is coming because it’s autumn. It’s not like you can predict it down to the day with a calendar. If the seasonal cycles aren’t obvious where you are, how important can they really be?
Ditto, with emphasis, for lunar calendars. Can you imagine trying to sell someone on your amazing new invention that tells you what the moon looks like right now? “I can just look up.” “But what if it’s day?” “Then I can remember what it looked like last night and it’ll still look basically the same?” “But what if it’s cloudy?” “Then the moon doesn’t look like that, now does it.” You have to be very sure where your next ten meals are coming from before you can start being interested in predicting what the moon will look like ten days from now.
But what if there were some cycle that was invisible most of the time, quasi-regular, and very important? That seems worth tracking. Hypothetically.
So let’s look up what the oldest known “mathematical artifact” is.
That would be a tiny bone (about the length of a business card or lipstick tube) found in the Lebombo mountains in southern Africa. It’s part of a leg bone from a baboon, and it has 29 notches in it, with different sections carved in visibly different styles. There was probably pigment involved too, but that hasn’t survived.
It looks as though somebody went to a fair bit of trouble, using multiple different cutting tools, to create a travel-size device that keeps count from 1 to 29. What a strange thing to do. The bone’s discoverer, Peter Beaumont, sent the bone to archaeologist Alexander Marshack for analysis. Marshack wrote that the bone was too “clumsily made” to be decorative and had no apparent practical function, so it was probably a ritual object of some sort. As more artifacts of this sort were discovered, from tens of thousands of years apart and different continents, Marshack noticed that it was very common for them to have about 29 notches, or else more but in groupings of about that amount. So he refined his theory—a ritual object to do with the lunar cycle. Ancient Man, he argued, seems to have been very obsessed with the moon.
For example, there was the 25,000-year-old wolf bone found in Dolní Věstonice. It has 25 notches, then a double dividing line, then 30 more notches. From which we can conclude, I guess, that the lunar cycle was more irregular in the past. Or the Ishango bone, found in Congo, which is too processed for us to be sure what kind of bone it was. That one has 168 etchings, made at different times or at least with different tools, which Marshack took to mean it was a six-month lunar calendar. Sure, six lunar cycles are 177 days long, but maybe the moon came early one month. Or the one found in a different site in Dolní Věstonice. Three human bodies, two male, one female, had been buried with, we assume, their possessions. That one has 29 notches in it too, divided into phases. They only found one notched bone in that grave, so maybe only one of the three was really into moon-watching.
And, okay, I’m sure some of these were lunar calendars. Lunar calendars are a thing. But the earliest ones? I doubt it. I think it’s pretty obvious what they were, unless your mind is so limited by your cultural taboos that you can’t even go there. Different women (an imprecise term but “period-havers” is too awkward) have different menstrual cycle lengths. 28 days is the median, 29 is the mean, it can be much shorter or longer. Knowing when you’re at your most or least fertile helps you know when to have sex. Knowing when you’re likely to bleed or have cramps helps you plan travel. Knowing when you’re very late gives you valuable information too. So making your own personal notched baboon bone that tracks your own personal cycle would be worth some trouble.
I’m hardly the first to think this, but looking around, it seems like archaeologists (male ones, anyway) get so stuck on the lunar ritual idea. When someone points out that 29 days is the average length of a menstrual cycle, they say “oh, okay, so maybe the bones were for tracking the alignment of the menstrual cycle with the lunar cycle? FOR RITUAL PURPOSES, PROBABLY?”
Also the lunar cycle isn’t 29 days long, it’s a little over 29 and a half days long, so after a few months, the “29 notches on a bone” method would’ve crashed and needed to be reset. Whereas the “look up” method would continue to be reliable. Some menstrual cycles are very regular, some aren’t, but everyone has the same inconstant moon.
The Modern Period
The state of our medical knowledge is often disappointing. Especially, perhaps, when it comes to women’s health. Knowledge was lost in the Enlightenment, when “old wives’ tales” were discarded in favor of rational scientific investigation conducted almost exclusively by men. Lingering sexism and lingering taboos continue to hobble us—there are still some pretty basic facts about women’s bodies that we either don’t know or don’t teach.
As a man, I don’t think I’ve benefited from sexism. Oh, I’ve definitely been advantaged, privileged, by sexism. But on net? I’m sure I’m much worse off from the marginalization of women in STEM. Women, evidently, were the first mathematicians, the first technologists. I’d rather live in a world they’d been more allowed to co-invent, even if it meant having to compete on a more level playing field.
But no, I live in a world where not only do we deny the existence of early period trackers, we’ve started to erase the more sophisticated ones we have now. There are apps that don’t only serve the same function as a tally stick—they can tell you what sex ed misses about what symptoms are normal and how cycles tend to vary. They’ve probably saved some lives. But reproductive health is becoming so criminalized that period-havers are deleting their period trackers, lest the data be used against them by the government.
Somehow, we’ve taken a wrong turn, and ended up back in our prehistoric cave, right before the first mathematician took up her blade.
I wonder if other women reading this thought--before you got to it--oh, I know what that was tracking! I like this piece, thank you, Aaron.