[X] My Assistant

[Rob Pinnegar]

Several years ago, when I was still at U of Western Ontario, I was browsing through some of the old books in the astronomy section of the main campus science library. One of these dated from the late 1800s and contained a couple of hypotheses, current at the time, that are worth passing along. (I don't think I've posted these before... apologies if I'm repeating myself.)

The first of these had to do with the number of moons around each planet. After Asaph Hall discovered Phobos and Deimos in 1877, no planetary satellites were found for another fifteen years. This book must have been published during that time, because the author pointed out that Earth had one moon, Mars two, Jupiter four and Saturn eight. This had apparently led people to speculate that Uranus had sixteen moons, and Neptune thirty-two, most of them waiting to be discovered. (It seems that Bode's law died very, very hard.) My guess is that this probabaly dates the book to just before 1892, when Amalthea was discovered, as it would have taken people a while to start thinking that all the moons out to Saturn had been found. The death blow came six years later, when Pickering picked up Phoebe.

The second hypothesis was the really neat one. In the late 1800s, Jupiter and Saturn's axial tilts were well known because Jupiter's bands were clearly visible, and of course Saturn's rings provided even better evidence of its tilt. However, since Uranus and Neptune are so bland and so far away, estimates of their axial tilts had to be based on satellite orbits. As a result, although Uranus' axial tilt was pretty well determined, the estimate at the time for Neptune was terribly wrong because it was thought to be same as the plane of Triton's orbit. Since Triton's orbit is circular, everyone (quite reasonably) thought Triton was a regular satellite. In fact, there weren't any irregular satellites known then -- Iapetus and Luna would've had the largest known orbital inclinations. And Proteus hadn't been discovered. So there was no way of telling that this assumption was wrong.

This gave estimates of the axial tilts of Jupiter, Saturn, Uranus and Neptune as 3, 27, 98 and 160 degrees. At this point, someone had the bright idea that there was an unknown process operating in the outer Solar System that was causing the outer planets to flip over from the outside in. I thought this was terrific. Naturally, when better telescopes were invented, this was found to be wrong... but it was still a great idea.

Although it's unscientific to say so, in a way it's always a pity to see a brilliant idea blown out of the water by fact. Nonetheless, even if we can't keep wrong ideas around for sentimental reasons, at least we can appreciate them for the merits they had, given the information that was available at the time.

[JRehling]

Although it's unscientific to say so, in a way it's always a pity to see a brilliant idea blown out of the water by fact. Nonetheless, even if we can't keep wrong ideas around for sentimental reasons, at least we can appreciate them for the merits they had, given the information that was available at the time.

These are great anecdotes, Rob!

In fact, some of the core work in science started with simple pattern-matching.

There is a (nascent) branch of artificial intelligence that tries to reproduce human scientific reasoning. It's not too hard to write a program that can take the appropriate data and spit out Kepler's Laws very quickly -- much faster than Kepler came up with them.

My grad advisor Douglas Hofstadter has pointed out that this is a specious result because the really important insight -- what it took Kepler years to come up with -- is being handed to the computer. And that important insight is... natural laws tend to be expressible to a decent approximation with polynomials.

At the beginning of the 17th century, that wasn't known. Kepler spent a lot of time exploring the ratios found in the regular polyhedra looking for mathematics that explained the orbits of the planets. Eventually, polynomials were found to express their motion... and polynomials were found to provide good models of many other scientific phenomena.

As a consequence, we now learn polynomials as a cornerstone of our mathematical education. And those AI researchers can build "polynomial smarts" into their programs. But it was basically trial and error work that led to the original observation that polynomials are so useful... we can derive the reasons why with hindsight, but the usual caveats regarding highsight all apply.

Likewise, we now understand that the basic distribution of stuff in the solar system was the result of some stochastic nature of the initial distribution. Certainly, dynamics constrained certain final hypothetical statuses from occurring, but we all can assume that there could have been one fewer big satellite around Jupiter, and Mercury could have been smaller, Saturn probably could have been a little farther out, etc. But without a really solid model of solar system formation that could be "run" computationally, that wasn't so obvious in 1891 -- maybe the solar system was the way it had to be, just as the sequences in chemical-element families follow unbreakable rules. The periodic table was discovered within a decade of the discovery of Phobos and Deimos. The meta-level regularities in the natural world were just being established.

[dvandorn]

My grad advisor Douglas Hofstadter...

Yes, that explains a great many things, John. I may occasionally disagree with your assumptions, but I always find your logic impeccable.

-the other Doug