Tuesday, August 22, 2017

How to Predict a Solar Eclipse: a Guide for Ancient Egyptians --- and what it has to do with good economic analysis.

I had the fortune of watching the solar eclipse on August 21st 2017, slightly north of Bloomfield, Johnson County, Illinois.  No cloud disruptions, just two-plus minutes of total-eclipse gazing and an awe-inspiring event.  Magnificent!

Returning back to Chicago, I had to wonder whether ancient cultures, like the ancient Egyptians, the ancient Babylonians or the ancient Chinese, could predict solar eclipses, and how.  I searched the Internet, and I found http://www.haaretz.com/archaeology/1.808116 , which says, that they did, but not, how.   And I found https://image.gsfc.nasa.gov/poetry/ask/a11846.html by the NASA, no less, which suggests that those folks tried to find a discernible pattern in the recurrence.  The readings, in any case, made me feel that predicting a solar eclipse was rather impossible for these ancient people, or a somehow really amazing and hard-to-explain feat.  And they also make you feel, that those astro-observers back then had better try hard: if they missed one, their heads would be chopped off!  That’s a huge penalty for a type-1 error of rejecting a truthfully occurring eclipse.  I imagine that type-2 errors (“hmmh, there could be one”, and then there isn’t one) probably were ok for those guys, by comparison.  What an interesting problem in decision theory!

Having some leisure time in my car trip going back (which I should have spent thinking about more serious matters, probably), it then occurred to me that it really can’t have been all that hard to predict the few critical-solar-eclipse-times, within limits.  And I have to believe that these ancient observers indeed did.  Here is how.

Clearly, trying to extract some pattern from their occurrence will go nowhere. That method seems doomed from the get-go, right?  We get the next total solar eclipse in the US in 2024, then in 2045: where is the pattern in that?  I mean, fine, some surely tried.  And given enough data, one could learn some pattern in some mechanical fashion, it is bound to succeed.  The problem is: this takes lots of data, many tens of thousands of years: not wise. 

Instead those ancient astro-observers could have figured out and probably did figure out, that some structural modelling will go a long way.  First, it does not take a genius to figure out that the solar eclipse involves the moon and the sun.  Back then, the smartest scientist probably spend a large portion of their time observing the celestial bodies.  They knew about the cycle of the moon and the sun.  They knew about the new moon: there are days when you can see it faintly up in the sky.  They surely kept track roughly how high the moon would rise and how high the sun was.  The latter is known to practically all young kids today: the sun is high in the summer and low in the winter.  It is how you keep track of the year.  With the moon, I believe it always rises to the same height, but I might be wrong: in any case, surely, the ancients knew.  And surely, the ancients tried to measure these with some precision (How?  Not that hard either, but that could be a topic for another day). 

Armed with these two pieces of information, one now gets two intersecting patterns.  One is the up and down of the sun, due to the annual cycle.  The other is the lunar phase, changing from full moon to new moon and back.  If the new moon is too much below or too much above the sun, no solar eclipse.  It has to be close.  The “misconceptions” piece on https://en.wikipedia.org/wiki/Lunar_phase lays it out quite nicely, actually.  One probably needs a bit more: where the new moon rises that day and where the sun, and think about where their paths might cross.  Give an ancient astro-observer a few extra days of thinking about it, and they could probably figure that in as well.

Some rough measurement should then have been enough to predict when these close encounters might happen.  Would they be close enough for a solar eclipse?  If the measurement is too rough, then most of the times, an upcoming close encounter will not result in an eclipse.  So, the rougher the measurement, the more type-2 errors.  If those astro-observers warned of a potential eclipse, and it then didn’t happen, they can always tell the king that the gods were looking upon him kindly.  Who knows, perhaps they even got a raise that way!  But at least, they could avoid the type-1 error of not knowing of their possible occurrence. 

It really does not seem all that hard, right?  It would be nice to hear from a physicist, how precise the measurement needs to be to predict a solar eclipse correctly this way in, say, one of ten cases and have a warning in vain in the other nine.  Pretty precise, probably, and that may have been the main technical challenge then.  “When you cannot measure, your knowledge is meager and unsatisfactory” (Lord Kelvin, see https://bfi.uchicago.edu/news/mfm-feature/challenges-identifying-and-measuring-systemic-risk ).  So, precise measurement surely would have been important.  But the conceptual challenge, at least, seems reasonably simple, and certainly within the grasp of astro-observers back then, allowing them to make some reasonable predictions, even without the precise measurement equipment available today.

What does this have to do with good economic analysis?  Economists, too, need to predict events and need to discern effects from causes.  These days, machine-learning is all the rage for doing so.  Just takes lots of data, shove it into a computer, and it will detect any and all patterns, see e.g. https://scholar.harvard.edu/sendhil/publications/machine-learning-applied-econometric-approach and the work by Mullainathan at Harvard for econometric approaches, but also by many others.  One has to concede: remarkable achievements have been and are still being made, using that approach.

But the world is amazingly complicated.  Patterns are probably ultimately very tough to discern, unless they are guided by some theorizing.  So, structural modeling can go a long way.  The danger?  The theory and the structure might be wrong.  That can be a problem, sure.  But for those ancient astro-observers, that surely must have been well worth the risk, compared to the machine-learning approach of pattern detection and head-off-chopping.  And regardless of how little theory we pretend to us: we all use it anyway and all the time.  Perhaps that is a good thing, for the astro-observers back then and for economic analysts today just the same.  But it surely would be good to be explicit about it, when we do. 

IThat's it!  If you enjoyed this, I might tell you some other time how to calculate the diameter of the Earth, standing on the beach.  All that you need is your thumb, some waves, some plausible guesses and high school geometry.  Intrigued?

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