"Natural" basis for the hour?

I’m reading an article on the Sphinx in the February issue of “Smithsonian.” They’re talking about who built it, what its function might have been, etc. (Hey, cool, it’s online also.)

So I’m reading along, and I get to this:

Is there any reason that the day is divided into 24 hours? Would the ancient Egyptians have hours similar to ours?

I think the fact that there are 365 days in a year (close to 360) and 13 moons in a year (close to 12) led to 12 and 24 being used as common divisors in time-keeping. And to the 360-degrees-in-a-circle convention, too.

I believe the Romans divided the day (i.e., from sunrise to sunset) into 12 hours, but the night into four watches. Thus a summer hour was longer than a winter one (and a summer watch correspondingly shorter).

I do not think that there is anything very “natural” about the hour (except, perhaps, that 12 has a lot of divisors for such a low number). It is just a tradition that caught on widely.

The Egyptian division of the night (sunset to sunrise) into twelve parts is attested as far back as the late third millennium BCE, and the corresponding division of the day was made a while later.

Ancient Mesopotamian astronomy divided the whole day (sunset to sunset) into twelve units known as “beru”. One-sixtieth of a beru was an “USH”*. This was influenced by the base-sixty number system that they’d had since at least the late third millennium, so there were lots of sixties and twelves and so forth floating around in their metrology.

However, the division of daytime or nighttime into 12 units seems to have originated in the Egyptian practice, whence it was borrowed by Greek astronomy and became standardized in the western tradition.
(See John David North, Cosmos, and Hunger & Pingree, Astral Science in Mesopotamia.)
*(capital letters for sumerograms as opposed to syllabic Akkadian words like “beru”.)

The original hours were so-called “seasonal” or “unequal” hours, namely equal divisions of the daytime or nighttime period. So as the length of day and night changed during the year, the length of the hour changed.

Equal hours originated in classical astronomy (possibly influenced, I think I remember, by the Babylonian beru which were of fixed length), because unequal hours were such a pain in the ass to work with.

Interesting! Thanks, all.

So the point in the material quoted in the OP – 24 pillars representing 24 hours – would be wrong. Unless you have 2 pillars/hour, I guess.

Well, 24 pillars (or 24 anything) could certainly symbolize the 24 hours of the day. But that doesn’t mean that the 24 pillars would actually serve any significant astronomical or timekeeping function.

In general, the archaeoastronomy speculations in that article seem to be a bit overblown. Yes, if the temple is laid out on an east-west axis, that in a way “symbolizes the movements of the sun”, since the sun does rise and set more or less due east and west, respectively, at the equinoxes. But there’s nothing very sophisticated about that.

Nor is it remarkable that if you stand at some vaguely specified location in the midst of a number of built objects at sunrise or sunset on a solstice (or any other day, for that matter), there’s a good chance of seeing the sun and/or shadows positioned in ways that seem to symbolize something meaningful. The question is, how many orientations couldn’t be interpreted as symbolizing something meaningful?

It’s worth noting that this is true absolutely anywhere on the Earth. If you set up something aligned east-west, then it’ll correspond to the equinox sunrise and sunset. That doesn’t mean that’s necessarily the reason you aligned them that way, though.

But not if the day doesn’t have 24 hours.

12 is a useful number in the days before calculators. Generally, for people not accustomed to math and especially decimal points (when did that appear, 1400’s or later?) 12 could be divided into 1, 2, 3, 4, 6, or 12 pieces. That’s a lot of the smaller numbers, and so convenient. This is also why things would be sold by the dozen.

Make it 60 or 360, and the number of divisors is even more.
60 - 1,2,3,4,5,6,10,12,15,20,30
360 - 1,2,3,4,5,6,8,9,10,12,15,18,20 etc.

What did early man tend to do for “practical math”? Divide things up several ways. 12 was a really convenient number for this.

24 does divide 360 without a remainder (360/24 = 15), so celestial bodies move through the sky by an integer number of degrees each hour.
1/4 of a degree per minute, or 15 degrees per hour would have been less of a hassle for ancient astronomers to deal with than 0.2963 degrees per minute and 17.778 degrees per hour.

Looking at the prime factors of 360: 3 X 3 X 2 X 2 X 2 X 5, there aren’t all that many choices for hour length with that work out as neatly. These are the possibilities: 2,3,5,6,9,10,12,15,18,20,24,30,40,45,48. (Yeah, I may have missed one, so shoot me!)

Twenty might’ve worked out well, but 30 would’ve given us an hour that was too darn short to get anything done in.

Duodecimal (base 12) and sexagesimal (base 60) systems of counting and arithmetic were in common use because of the ease by which they can be factored (having factors of 1,2,3,4 and 1,2,3,4,5 respectively), allowing division without resulting in fractions or remainders. This was critical in early systems of measurement, architecture, and engineering prior to the innovation of positional notation of fractional quantities (i.e. what we would consider today to be numbers to the right of the decimal place in the nearly ubiquitous base 10 counting system). Counting units of time in these numbers is therefore “natural” insofar as it is easy to make different divisions of time; as an example, look at historical naval and guard watches, that are often broken into six divisions across the day, some of which are broken into half or “dog watches” for convenience.

As far as the question of an hour being a natural unit of time, there are some physiological and psychological reasons why a period of about an hour is a convenient use of measurement. For instance, most people can only focus on an intellectual learning task for about an hour before needing a break. Ninety minutes to two hours is about as long as most people can exert themselves at an exhausting physical task without break. Similarly, something on the close order of minutes is convenient for counting units of brief action, and the sixty seconds in a minute is about as long as most people can self-calibrate their internal time measurement with any degree of precision. (Try this one for yourself; most people can maintain a decent correlation with a clock up to about 45-70 seconds, and then start diverging significantly.) That doesn’t mean that these divisions are universal, only that they are convenient and happen to align with numbering systems that can be factored numerous ways.

Stranger

My own theory is that people in the ancient world had 12 fingers and 12 toes. Somewhere along the line these were lost.

Some guy named Cecil has addressed this question, as well.

Oh, him. :rolleyes:

And if a loss of digits means a loss of precision, does that mean our ancestors were super-dexterous?

I know you’re kidding, but there is a point here.

We moderns count on our fingers. Ten fingers gives us base ten.

The ancients counted on the spaces between the fingers. four spaces per hand, eight total. And the outside surfaces of each hand, two per hand. That gives six counting points per hand and twelve total. For them base twelve is equally natural.

Yes, counting finger spaces and using base twelve is unfamiliar to you and me so it feels a lot more awkward, but that’s just an effect of practice.

Gotta cite? There certainly exist various non-decimal (contemporary and historical) finger counting systems, but I’d like to see some evidence that duodecimal finger counting was the norm for “the ancients” (by which I presume you mean Mesopotamians and/or Egyptians in or before the fourth/third millennia BCE) and that that norm gave rise to their base twelve metrology.

[On theory that ancestors had six fingers per hand]

Yes, but they were also super-sinister.

Makes me wish that the metric system was base 12. Add a base-12 number system, and we have the best of both worlds!