Jeff Hawkins on Kepler and misguided taste for simplicity and beauty

The best scientists are often motivated by seeking beauty and simplicity. Historically, this drive has served humanity pretty well and many of the core discoveries in physics were, as Schmidhuber puts it, driven by compression progress.

But it seems to me that, while beauty and simplicity can make for a good initial compass, it’s good to pursue a mixed strategy and check direction with a more systematic, analytical approach.

In my mind, the two main reasons are:

  1. It’s easy to kid yourself. Our brain sees beauty in patterns, in analogies, in stories. The drive is useful in expectation but very unreliable unless you have a good bullshit filtering mechanism. There was a nice study on how using analogies and case studies make people more confident without improving their judgment. Note to self: look up.
  2. The drive doesn’t care about others. There are many other things I value besides beauty and curiosity – long-term sustainable thriving of humanity, for instance. By default, the drive to compression progress is very nearly orthogonal to those. Fortunately, I’m gradually finding ways of directing this energy better. I’ll report on those when I achieve Perfect Inner Harmony.

A good example of (2) you get people like Jurgen Schmidhuber, whom I consider to be among the most dangerous people alive.

More (or less, depending on your view AI defaults) extreme examples are scientists serving totalitarian regimes and developing weapons. Pick your favorite one, I don’t want to draw comparisons.

Anyway, as the title promised, here’s Hawkins, On Intelligence:

False analogy is always a danger. The history of science is rife with examples of beautiful analogies that turned out to be wrong. For example, the celebrated astronomer Johannes Kepler convinced himself that the orbits of the six known planets were defined by the Platonic solids. The Platonic solids are the only three-dimensional shapes that can be constructed entirely out of regular polygons. There are exactly five of them: tetrahedron (four equilateral triangles), sextahedron (six squares, aka a cube), octahedron (eight equilateral triangles), dodecahedron (twelve regular pentagons), and icosahedron (twenty equilateral triangles). They were discovered by the ancient Greeks, who were obsessed with the relationship of mathematics and the cosmos.

Like all Renaissance scholars, Kepler was heavily influenced by Greek thought. It seemed to him that it couldn’t possibly be a coincidence that there were five Platonic solids and six planets.

Sorry to intervene, but… What?

This seems to me like “It can’t be a coincidence that our genome uses four nucleotides, which is suspiciously close to Pi?”

I can empathize though. It’s hard not to think about Plato when you look at viral structures.

2019-07-24 16_44_07-Platonic solid - Wikipedia.png
A virus shaped as an icosahedron.

Anyway, Hawkins…

As he put it in his book The Cosmic Mystery (1596): “The dynamic world is represented by the flat-faced solids. Of these there are five: when viewed as boundaries, however, these five determine six distinct things: hence the six planets that revolve about the sun. This is also the reason why there are but six planets.” He saw a beautiful but entirely false analogy.

Kepler went on to account for the orbits of the planets in terms of nested Platonic solids that were all centered on the sun. He took the sphere defined by Mercury’s orbit as his baseline and circumscribed it with an octahedron. The tips of the octahedron defined a larger sphere, which gave the orbit of Venus.

Around Venus’s orbit he circumscribed an icosahedron whose outer tips yielded the orbit of the Earth. The progression continued: a dodecahedron drawn around the Earth’s orbit gave the orbit of Mars, a tetrahedron around Mars’s orbit gave the orbit of Jupiter, and a cube around Jupiter’s orbit gave the orbit of Saturn. It was elegant and beautiful. Given the limited precision of astronomical data in his day, he was able to convince himself that this scheme worked! (Years later, Kepler realized he had been mistaken after he got hold of the high precision astronomical data of his deceased colleague Tycho Brahe, which proved that planetary orbits are ellipses, not circles.)

It reminds me of the state of Hawkins’s current field, theoretical neuroscience: it’s waiting for its Brahe (or more likely, thousands of them). Admittedly, they have a much larger job than astronomers.

Kepler’s excitement serves as a cautionary tale for scientists, and indeed for all thinkers. The brain is an organ that builds models and makes creative predictions, but its models and predictions can as easily be specious as valid. Our brains are always looking at patterns and making analogies. If correct correlations cannot be found, the brain is more than happy to accept false ones. Pseudoscience, bigotry, faith, and intolerance are often rooted in false analogy.

And now for something completely different… Empiricism? Math? Prediction markets?

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