Babylonian (Pre)Calculus!
January 29, 2016 1:01 PM   Subscribe


I was just reading this article in the nyt and I readily admit that I initially clicked on it because I thought the image was of a girl scout cookie and not an ancient nerd tablet.
posted by poffin boffin at 1:05 PM on January 29, 2016 [6 favorites]

And I thought my precal teacher in high school was ancient...(badum tshh)
posted by sallybrown at 1:15 PM on January 29, 2016

How do you say "When are we ever going to have to use this?" in Babylonian?
posted by thelonius at 2:06 PM on January 29, 2016 [6 favorites]

Walk Integrate like an Egyptian Babylonian
posted by Hairy Lobster at 2:25 PM on January 29, 2016 [3 favorites]

I initially clicked on it because I thought the image was of a girl scout cookie and not an ancient nerd tablet.

Technically, it could be both.
posted by GenjiandProust at 2:43 PM on January 29, 2016 [3 favorites]

Has anyone told BoB?
posted by pjsky at 4:03 PM on January 29, 2016 [2 favorites]

the thing that amazes me is that we can translate the writing cause as a completely untrained layman, I look at those tablets and think - well someone had fun.
posted by drewbage1847 at 6:36 PM on January 29, 2016 [2 favorites]

I didn't expect to get so caught up by this but by the time I got to "Additional tablets, including this one, show that the Babylonians realized that the area under the curve of a graph of velocity against time represented distance traveled" i literally yelled 'holy shit that's awesome' into an empty room sooooo

i mean i've had a beer but still

this is awesome, and considering the connections that had to be made to figure it out, a hell of a find

The Babylonians were calculating the distance Jupiter traveled in the sky from its appearance to its position 60 days later. Using the technique of splitting a trapezoid into two smaller ones of equal area, they then figured out how long it took Jupiter to travel half that distance.

i mean!!!!
posted by suddenly, and without warning, at 8:10 PM on January 29, 2016 [1 favorite]

Babylonians used areas in calculations in a lot of ways that we don't. There are huge jumps from "they used area in a calculation" to "they used graphs" to "they're finding under one particular curve" to "calculus!" And I really don't think of those jumps are warranted, let alone all of them. It's a really cool find, and some great translation work, but I'm pretty confident that the "OMG calculus!" aspects of this are really just science reporters being science reporters (overselling every minor thing)
posted by yeolcoatl at 11:42 AM on January 30, 2016

I don't think the claim is it's literally calculus, but the technique is one that wasn't used until the 1300s (IIR the article Correctly). I mean, Calculus proper didn't exist until the 17th century. But the fact that this particular technique is way older than believed, at least for one individual tablet (as the article I read points out, this wasn't a particularly widespread phenomenon from what little we know. Nothing like this was apparently used in any of the other calculations we know of from Babylonians).

Anyways, I think it's pretty cool. Wasn't part of it not just "they calculated area" but that they used the methods of calculating under a curve to figure out the rate of change over time as Jupiter moves across the sky and that aspect also tends towards Calculus (as opposed to just geometry/area).
posted by symbioid at 3:09 PM on January 30, 2016 [1 favorite]

The reason why I'm skeptical about "area under the curve" is that it essentially suggests that the Babylonians invented coordinate geometry. And while that's not impossible, it's a pretty big claim for something that is doesn't appear to be supported by any other tablet we have.
posted by yeolcoatl at 5:14 PM on January 30, 2016

The Babylonians were surprisingly good at astronomy. They had observations taken over hundreds of years, which let them calculate things like the mean lunar month to a ridiculously high level of accuracy. The Jewish calendar adopted that value and has been using it for the last 15-18 centuries without adjustment (I think). Almost all the present error reflects the actual change in the length of the moon's orbit, not the error of the original measurement.

The bit that I find mathematically impressive is that they had moved away from the concrete idea of areas representing land (or whatever) into an abstraction in which none of the of figures reflected physical units. There's a big conceptual leap between:
"Hammurabi wants to plant half his field with grain. The field is thirty cubits long, and it is twenty cubits wide at one end and thirty cubits wide at the other. How many talents of grain will he need?"
"This star has a motion over sixty days that is one degree each day at the start and half a degree each day at the end. How long does it take to go half the distance?"
If they had continued down that path (ahem) I suppose they would have discovered conic sections and then realised that their planetary observations matched some of those equations, and discovered universal gravitation two millennia before Newton.
posted by Joe in Australia at 9:04 PM on January 30, 2016


That part is not surprising to me. A large part of my whole point was that there were lots of other tablets that used area for abstract calculations that did not involve physical area. Yes, the Babylonians were very mathematically impressive. I'm not saying this wasn't impressive. I'm saying it's unlikely that it is impressive in the precise way that the reporters are claiming its impressive. It's impressive in other, less flashy ways.
posted by yeolcoatl at 8:17 AM on January 31, 2016

It's not the reporter who's making that claim, it's the researcher who published an article about it in Science. The article is literally called "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph."
posted by ultraviolet catastrophe at 10:17 AM on January 31, 2016 [1 favorite]

A large part of my whole point was that there were lots of other tablets that used area for abstract calculations that did not involve physical area.

Are there any examples you can point me to that are more sophisticated than "three men eat two loaves each per day over six days"?

I think the conceptual leap here is that the total period is described as being the sum of two dissimilar trapezoids of equal area. If you draw those trapezoids next to each other then you literally have a time-velocity graph. If you keep reducing the size while multiplying the number of those trapezoids you get a curve, and you almost necessarily arrive at the idea of infinitesimals and hence calculus.
posted by Joe in Australia at 2:27 PM on January 31, 2016

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