May 152010

One of the most complex pieces of information I have ever tried to grasp is that of ancient cosmology, by which I mean that which prevailed as accepted knowledge before Kepler. Ancient cosmology has almost exactly the opposite ratio of complexity to modern cosmology: these days, the concepts are simple but the math is mind-bending; those days, the math was easy but the concepts were labyrinthine.

Imagine, if you will, what Ptolemy [the 2nd-century AD Greco-Roman whose works formed the basis of most medieval astronomy] and his Arabic successors were dealing with. Geometry, trigonometry, algebra (for the Arabs): we learn these as teenagers. But they were using these tools to explain and predict the actions of a cosmos they viewed as a vast and interlocking array of perfect circles which is nearly impossible for the casual investigator to envision, let alone comprehend its relationships. If you’ve ever seen an astrolabe, you will have a pretty good idea of what I mean, and an astrolabe is only a small and simplified model of the relationships obtaining between celestial bodies as the ancients understood them. (If you haven’t seen an astrolabe, may I recommend you visit the Museum of the History of Science in Oxford? It has as fine a collection of them as I’ve encountered.)

Ancient cosmology, like Aristotelian physics, has become a modern archetype for ‘wrong’ science, primarily because in our present-day arrogance we have applied Occam’s razor retrospectively and concluded that those old astronomers were idiots. (Funnily, Occam himself never applied his razor to astronomy, so there we are: we’re better at being Occam than Occam was.) But this is tremendously unfair, because actually the ancients weren’t wrong, at least not in the sense we usually mean.

Civilisations had been observing the skies for millennia and noticed certain patterns about the movements of heavenly bodies in the sky, none of which were wrong. The heavenly bodies really do move as observed thousands of years ago. Where they erred was not in the what, but in the how and why. Scientists then as now were keen to explain the mechanisms behind what they observed, and then as now they used as their test of correctness whether the mechanisms they hypothesised accurately predicted future behaviour.

And contrary to what you may have read or heard or taken on board in snooty science class where even Newton is ridiculed for being wrong, Ptolemy et al. came really close to accurate predictions in spite of their giant wrongness. Copernicus himself noted that Ptolemy’s mathematical tables resulted in predictions that were rarely more than 2 [geometrical] degrees off from observed measurements. Given that nobody at the time was relying on this information for anything really important – such as organising trips to the moon – this was an acceptable margin of error, and in the circumstances would not have mattered much but for the fact that (a) it was sloppy, and even pre-modern scientists found sloppiness annoying, and (b) more sophisticated tools for observing the heavens began to show us that ancient knowledge of the skies was, in fact, incomplete. Galileo saw things through his telescopes that the Egyptians never knew existed, because they didn’t have telescopes and couldn’t see them. The human eye is good, but not that good.

In the end, it was perfectionism and superior datasets that brought down the ancient cosmology, rather than its inherent ‘wrongness.’

And in fact the ancient cosmology was only wrong on one particular point: but it was a big, important point because it was the fundamental assumption on which everything else was based – and as we say today, garbage in, garbage out. You can have, as Ptolemy did, the most incredible and precise system for analysing data in the world, but if your inputs are crap, your outputs will be too. What’s astonishing and really worthy of admiration, in my view, is that Ptolemy’s outputs weren’t more crap than they were, considering how hilariously incorrect his starting point was. As noted before, he was always within 2 degrees of being accurate.

The reason Ptolemy’s system is the byword for bad science is actually the very thing that tells us what an incredible genius he must have been: the tortuous complexity of his data analysis system.

His point A, that incorrect starting point, was stationary geocentrism. His point B, those predictions, were mostly right. But the path from A to B is what gave us deferents, epicycles, equants, prograde and retrograde motions – terms which you only see used today, really, in astrology (which is one of the reasons why astrology is bunk).

You can’t exactly blame him, can you? To the naked-eye observer, it really does look as if the Earth stands still and everything else circles around it. We, who are so big on Occam’s razor, can hardly criticise the ancients for assuming this simplest of theories was the correct one. They saw what appeared to be the skies circling round the Earth. There was no good reason, at the time, to question this simple and elegant explanation of observed conditions.

Unfortunately, that simple starting point made it exponentially difficult to explain the mechanisms empirically or prove them mathematically. Every time someone thought they’d figured out the process, their predictions would turn out to be wrong – even if just a little – and then it was back to the drawing board to add on new layers of theories to account for those errors. Nobody thought to go back and examine point A, because why would they? Like good little scientists, they assumed the data were correct and the mistakes were theirs. They didn’t consider that stationary geocentrism was not a datum at all.

So the tiny fixes for the tiny errors built over time into a giant, interdependent, Escher-like edifice that was always just not quite right, a kaleidoscope picture just out of true no matter how one fiddled with it. Cosmology was a grand project, generation after generation always fixing, fixing, working away, convinced that just a tweak here, a jimmy there, and those minuscule errors would resolve into glorious perfection. After all, their margin of error was so tiny that their mistaken assumption must be tiny too. But in the process of fixing their tiny errors one by one, they hypothesised a cosmos that was no longer simple, no longer elegant, no longer perfect – instead it was complex, and virtually impenetrable, and exhausting: every scientist’s nightmare.

And that giant, unwieldy, hideous nightmare that was always not quite right turned out to be based on a fundamental assumption that was so mistaken it now occasions ridicule – and the vast unwieldy system is so archetypal that today we pretty much assume that the more complex your theory is, and the more tiny fixes it requires all over the place, the more likely it is you’ve made a mistake in your fundamental assumptions. You can alter this over here, and fiddle with that over there, and that will make everything more complicated, but nevertheless things will be better as a result, won’t they, and bring us closer to perfection, because we’re nearly there anyway, so surely that last step must be a small one.

Now, what does that remind you of?

Incidentally, I wasn’t re-reading my master’s dissertation before writing this post. I was reading Federalist No. 10.

  8 Responses to “Two degrees of Ptolemy”

  1. Ptolymeic epicycles – circles inside circles inside circles. Actually, Aristarchus managed to work it out – the lack of any way of explaining the movement of the Earth, his poor observations and a Platonic insistance that orbits must be circular.

    Just remember, Occam invented his razor as proof of the existence of God – he was, after all, a radical Franciscan, getting into quite serious trouble for complaining about Papal ostentation.

    • You have to wonder how he worked it out, though, if his observations were so poor that they suggested nothing of the sort to anybody else, and if his insistence on circular orbits undermined his theory. I mean, how did he arrive at such a conclusion? ‘Well, my observations contradict it and my maths don’t work, but I nevertheless hypothesise that the Earth goes round the sun because…’? Because the little green men say so?

      • Because he wasn’t as good an astronomer or mathematician as some other people – he was just a better theorist? IIRC, his calculations worked reasonably with his measurements, it is just that his measurements were wrong …

        And everybody insisted on circular orbits, it would be churlish to blame him for not being able to overthrow more than one of the gross misconceptions of his worldwide at a time :)

  2. Please insert “prevented his theory from gaining significant traction” at the end of that 1st paragraph! :(

  3. Nice read, thanks. Appreciate the time you put into this.

  4. You never know, perhaps the Large Haddock Collider really will prove the Big Bang theory. Just because more and more complexity* has been added to “explain” the discrepancies doesn’t necessarily means it’s all wrong. Perhaps it’s true that 96% of the energy of the Universe is Dark Matter & Dark Energy! And consider also Hawking’s assertion that the total energy balance of the Universe is zero.
    * The black stuff (about which we know and detect nothing) now has negative gravity!

    • Yes, that’s the point. The standard model is, although still consistent, getting rather too complex (and it doesn’t explain dark energy). Therefore, it is generally assumed that there is something more fundamental underlying it. Unfortunately, lots of things that are predicted by the standard model, such as the Higgs Boson – and anything that will appear in the cracks – like the SuSy partners of standard model particles that are one of the hypothesised dark matter components – do require higher potential particle mass, hence higher collision energies, to be detected.

  5. I’m not sure everyone got your point but I did and it’s genius. Such good writing!

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