Twelve It Is
how many should I get?
MATH / NATURE
The Inspiration
When I started this post, it came as a result of another trek on the treadmill. Back when I posted about calendars, I learned a bit about the significance of the number twelve. Recently, I was sold on the topic when I came upon the tale of the baker’s dozen. On those occasions when I visit the bagel store, my favored location includes a 13th in your order to make it a baker’s dozen. What is that all about? In the 13th century, laws emerged to discourage cheating people as commerce centers and markets continued amidst burgeoning world trade. The penalty for cheating (short counting for example) a customer was amputation. Bakers decided it was better to save a hand and always include an extra item gratis. Seems a worthwhile plan if you value your hands. This is a working example of why I assume that our biases toward the “good old days” and guidance of the past are that I would prefer to forgo Afghan warlord-like ways to manage our modern world. The progress of the modern world should be embraced. Nostalgia is overrated in my opinion.
The Setup
Today my topic is the number twelve (a real dozen). Why do I care? I am not sure, but I find it intriguing enough to write about it. The number twelve recurs in our daily lives in a surprising number of ways. Months in a year, eggs in a dozen, flowers in a bunch. This is the sort of thing I ponder at times. If you are a frequent reader, you may recall my posts about calendars. The role of the Babylonians and Sumerian cultures played an important role.
So now, as a reminder, let us consider the two methods that developed early as counting systems. The Babylonians and Sumerians were early trading partners. The Babylonians favored counting the digits on their hand (five). The Sumerians favored counting the bones on their fingers (twelve). Of course, you must remember you have four fingers, not five as the opposed digit is your thumb! Combining five and twelve (multiplying) gave us the first sophisticated counting system in the world, base 60. They called it sexagesimal.
Sixty is Everywhere
While this may not be intriguing to everyone, I think that the results in our modern world that have become part of our daily lives around sixty and twelve are far-flung.
60 seconds in a minute
60 minutes in an hour
360 degrees in a circle
60 minutes in a degree
60 “seconds” in a degree minute
So the way we measure angles and keep track of time all comes down to 60
bagels, doughnuts, and eggs all are counted by the dozen
It seems that keeping time, paying attention to the sun and its angles as the year progresses, moon cycles, and elements of our modern calendar all owe homage to the combination of twelve and five (sixty). What is the use of the dozen and why is it handy. Twelve is pretty versatile because it is easy to split in half, thirds or quarters. That comes in handy when you are selling stuff or giving people their “share”.
So is this enough for a post? Probably not quite yet so it is time to dig deeper. One of my interests (yes this is anti-progress) is mechanical clocks. The precision we associate with what became something like a pocket watch is thanks to the magic of twelve and other numbers that are easily divisible. We might have to talk about gears and clocks in another post.
Gears have existed for a VERY LONG time. WE credit the Greeks and the mechanics of Alexandria for their origination. They were used to multiply our work effort and to provide the innards of early water clocks. Before we dig into water clocks, we have to step back a bit. Finally, I can make the case why this is worth talking about.
Figuring out what time it is and where we are in the world can be agreed upon as important by almost anyone. One breakthrough leads to another and often assists the construction of the next breakthrough. I can think of an interesting sequence of progressions like sundials » gears » clocks » compasses » celestial navigation. Now that might be a worthwhile trip and twelve will join us along the journey. There are really only six questions we can ask. They are referred to as the interrogatives and are who, what, where, when, why, and how. Twelve is critical to where (navigation) and when (time). That is good enough for me!
Sundials are at most, only 3500 years old. They were developed independently all over the world. Sundials are cool but have an unfortunate limitation. They only work in daylight. For that reason the early sundials marked the daylight hours and numbered them, you guessed it as twelve. The first sundials changed the length of the day each day as the number of daylight hours cycled through the year. An earlier post about calendars talked about the tilt of the earth on its axis and how that governs how much sunlight a given location gets in the summer and the winter. Sundials became more and more sophisticated and evolved to be latitude-specific. Finally, a sundial started getting accurate.
As our understanding of measuring full days became possible with the addition of timing devices, we moved to two 12 hour periods to comprise a full day. While it may just be me, I found that poking around to understand sundials turned out to be pretty interesting. If you want to learn more, here is a great site with an accompanying video for those with even greater interest. While I have a passion for mechanical clocks, sundials were never a thing for me and my backyard.
It turns out that we owe a lot to the Babylonians. In the same way, they were counting by 60s, they were also VERY INTERESTED in circles and figuring out how to make angular measurements. Tablets have been found that show a hexagon INSCRIBED in a circle. Since there are six sides to a hexagon and the Babylonians based their numbering on sixty, they chose to construct some measuring systems based upon the hexagons they could draw inside a circle. They broke up each of the six sides into units of sixty and we all ended up 3500 years later measuring a full circle as 60 X 6. That is why we ended up with 360 degrees in a circle (or a great acrobatic basketball dunk). Kinda cool, at least to me.
While I am wrapping this post up, the measurement of angles, coupled with the sundial and being able to figure out where you were in the world even when you’re moving (on a ship especially) allowed the world to enter the age of true mobility. Sailing the world’s seas and knowing how to get back is fodder for a future post. In the meantime, being able to sail the world and find your way back home inspires tonight’s song.
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