Use of geometrical methods in Babylonian mathematical astronomy (2016) | Hacker News Reader

Use of geometrical methods in Babylonian mathematical astronomy (2016)

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64 pointsAnon8444 comments

To flip this around: I have a chromatography textbook from only 20 years ago that teaches computing the area under the curve using what it called the “plate” method (i.e. draw rectangles inside the curve on the instrument’s printout and then add up their areas).

I had a physics professor many years back who told me about how they sometimes used to measure integrals by cutting out the areas of a plot they were interested in and weighing the resulting paper.

But negative area??? Maybe it was printed on complex paper

You could cut the paper along the X axis, and subtract the area below from the area above.

We like to think we know who did what in early mathematics, but we really only know about Greeks whose compatriots took the trouble to write down their names.

This particular result is contemporary with some of those selfsame Greeks. There is no telling which way advancements moved. Most likely it was both ways, by then. But there had been a long tradition of traveling to Egypt to learn geometry from the masters, and also of not naming foreigners one got things from.

Going on two millennia later, Francis Bacon was scrupulous about reserving credit to Al-Haytham for inventing Science as we know it today. People following Bacon were not, so much.

does it matter whether you have a heliocentric or a geocentric worldview when using this method?

No. Babylonian astronomers created arithmetical techniques for predicting key events of the moon and planets, such as the date that Jupiter reached a stationary point in the sky. (The stationary point is the positions where Jupiter starts its retrograde motion). They were not trying to explain the nature of the universe (cosmology). Ptolemy derived cosmological models based on geometry, but even he was interested in prediction, not explanation. In both cases, it does not matter whether the astronomer's view is helio- or geo- centric. Ptolemy used a geocentric model, but he did point out that a heliocentric version was a possible alternative.

Even Copernicus was not really that concerned with cosmology: he was showing an alternative to Ptolemy based on the heliocentric view of what he thought was the universe (now known to be the solar system).

In my view it was Galileo who really first proposed that these models went beyond prediction to describe the reality of the cosmos.

Do we know why they tried to predict, but not explain? Or would prediction simply be a prerequisite for explanation?

I heard (iirc in the “In our time” podcast) that they associated rare/unusual cosmological events (say, a solar eclipse) with signs from the gods. Hence, to better read the signs, you want to know what's normal/predicted.

Don't quote me on this, though :)

The most likely reason was because there was an obvious correlation between astronomical events and things that happened on earth. The most obvious are seasonal weather events, which are obviously important for agriculture. Having noticed that these earthly events correlated with certain astronomical events, it was natural to extend this to predicting other events based on astronomical "omens" such as conjunctions, risings, stationary points and so on. It is likely that Babylonian rulers used astrologers when making decisions such as the best time to attack a neighbour.

We know that, at various times, explanation was a strictly and vigorously defended priestly prerogative, and encroaching on that was a good way to get oneself dragged behind a chariot all through town.

The periodic back and forth movement of a pendulum can be modelled as a circular rotation with constant angular velocity. We "know" that it just goes over and back so we "know" that the circular motion is just a model. All the same, maybe in the future, they'll figure out that pendulums actually move in 4 dimensions. Then they'll look back at us and think "surely they should have known that pendulums really moved in 4 dimensional circles, because they knew about this model".

I'd imagine it's similar looking at the sky. If you "knew" the motion of the planets was related to some Gods moving around, you might expect that circular motion was just a model there too.

Orbits are always periodic functions, so quite amusingly heliocentric and geocentric models are equivalent (because of Fourier transformations).

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