I saw something recently that got me thinking about Kuhn's distinction between normal science (which he describes as "puzzle solving") and revolutions (which he likens to Gestalt shifts). The thing I saw was a puzzle (hence the connection to puzzle solving). The puzzle consisted of this: six toothpicks are laid down on a table in groups of three. Each group of three forms an equilateral triangle with a base near the puzzle-solver and the opposite apex pointing away. Here's the puzzle: move one (and only one) toothpick to form four triangles. If you really want to get into the spirit you should go get yourself six toothpicks and try this yourself before reading any more....
... no, seriously, it will help you get what I'm talking about ...
OK, so the trick ends up being that you move one of the toothpicks on the left triangle so that it forms a representation of the number 4 (i.e the numeral 4). (Try it - you just have to slide the right side of the triangle so that it become perpendicular with the base.) The other triangle remains a triangle. So the result if 4 triangles. Now, you can argue that it should be "4 triangle" not "4 triangles", but I saw people solve the puzzle so it's not totally off the wall.
My point is this: solving that puzzle involves something like a Gestalt shift. Kuhn would probably not disagree. After all he says it is persistent failure of normally good puzzle solving strategies to solve a seemingly valid puzzle that leads to crisis and ultimately revolution in science. He might argue that it was only after you had exhausted all possible ways of actually forming 4 separate triangular shapes with the toothpicks that you would make the Gestalt shift to thinking about the numeral 4. Maybe this is right (I wasn't one of the ones who solved the puzzle so I don't know).
What strikes me is that this is a Gestalt shift that is taking place on a very low level. The Gestalt shift needed to solve that puzzle is not one that will alter my view of the Universe, or force me to cast out all of my previous notions of puzzle solving. Yes, it may now add a tool to my puzzle-solving arsenal that simply wasn't there before. But if this is a revolution it is a microrevolution. And a revolution on this scale would not lead to any incommensurability. Actually, visual Gestalt shifts usually don't produce incommensurability - you can still see the rabbit even after you've seen the duck, and you can usually coach others to see what you now see.
Kuhn says (in The Structure of Scientific Revolutions) that revolutions take place on many scales. But he always seems to talk about the big ones. His distinction between normal science and revolutions implies that normal science is what takes place without interruption for years and years until BOOM there is a revolution. But if revolutions can take place on ALL scales (from a new way of seeing a highly specialized problem in a particular area of technical research, all the way up to revolutions that involve major cosmological or metaphysical consequences) then revolutions must be happening ALL THE TIME. Granted, the big ones only come around occasionally, but little ones occur almost non-stop. It's a scaling law behavior - think earthquakes (big ones are rare but devastating, little ones happen all the time but may be unnoticed).
If this is true then the distinction between normal science and revolutions becomes much less clear. The idea of incommensurability doesn't seem to hold up either (or maybe it only applies to the biggest of revolutions, but I'm not even convinced of that). Something to think about.
Sunday, August 10, 2008
Friday, August 1, 2008
The Realism of Copernicus
I've been doing some reading in preparation for teaching a course on the Copernican Revolution this Fall (currently I'm reading Alexandre Koyre's "The Astronomical Revolution"). In the process I've been struck by Copernicus' apparent motivation for developing his new system of astronomy. It wasn't so much that he was trying to devise a system that would match up better with observations (and he didn't). It wasn't that he really was convinced that the Earth moved independent of astronomical considerations (at the time you would have had to be crazy to believe that). It was that he was absolutely, utterly committed to the REALITY of uniform circular motion in the heavens. I guess this can be attributed to Platonic (or maybe Pythagorean?) influence, but he seems to have believed that uniform circular motion was the only thing that could possibly REALLY be going on up there in the skies. He states clearly that his major motivation for devising his system was to get rid of the equant, which was Ptolemy's great heresy against the Platonic (and Aristotelian) doctrine of uniform circular motion. He was so committed to ridding astronomy of equants that he was willing to consider the absurd notion of a moving Earth!
It is interesting to contrast Copernicus' metaphysical commitment to the truth of uniform circular motion with the phenomenalism of Andreas Osiander, who wrote the controversial preface to Copernicus' "De Revolutionibus". Osianders view, as stated in that preface, is that the job of astronomy is to "save the appearances" and that one should use every mathematical trick available, even one as silly as making the Earth revolve around the Sun, in order to make the calculations match the appearances of the sky. This view is actually quite sophisticated and modern, and is not much different from the logical positivism that dominated philosophy of science (and philosophy generally) during the first half of the 20th Century. But this is obviously not Copernicus' view. He is willing to throw out a very useful mathematical trick (the equant) in order to get back to what he KNOWS is the TRUE motion of the celestial bodies, namely uniform motion in a circle.
So Copernicus has the less sophisticated philosophical point of view, as well as a strong metaphysical commitment to a scientific idea that turns out to be totally wrong. And it is exactly because of this that he, rather than Osiander and others like him, revolutionized astronomy and paved the way for modern science. It turns out he didn't need to be so revolutionary. He could have gotten rid of equants and stayed with a geocentric universe by throwing in a few more epicycles (as Kepler later showed). But either he was unaware of this, or decided to give the heliocentric view a shot and became convinced of its beauty (and thus its truth, since he held that kind of Platonic view).
It is also interesting that it was Copernicus' devout commitment to uniform circular motion that led him to the first major breakthrough in astronomy since Ptolemy. But it was Kepler's ability to see past this view and consider non-uniform non-circular motion that led to the next major breakthrough. I doubt very much that Copernicus would have been pleased at what Kepler did to his astronomical system. It just goes to show that sometimes "bad" ideas lead to "good" results.
It is interesting to contrast Copernicus' metaphysical commitment to the truth of uniform circular motion with the phenomenalism of Andreas Osiander, who wrote the controversial preface to Copernicus' "De Revolutionibus". Osianders view, as stated in that preface, is that the job of astronomy is to "save the appearances" and that one should use every mathematical trick available, even one as silly as making the Earth revolve around the Sun, in order to make the calculations match the appearances of the sky. This view is actually quite sophisticated and modern, and is not much different from the logical positivism that dominated philosophy of science (and philosophy generally) during the first half of the 20th Century. But this is obviously not Copernicus' view. He is willing to throw out a very useful mathematical trick (the equant) in order to get back to what he KNOWS is the TRUE motion of the celestial bodies, namely uniform motion in a circle.
So Copernicus has the less sophisticated philosophical point of view, as well as a strong metaphysical commitment to a scientific idea that turns out to be totally wrong. And it is exactly because of this that he, rather than Osiander and others like him, revolutionized astronomy and paved the way for modern science. It turns out he didn't need to be so revolutionary. He could have gotten rid of equants and stayed with a geocentric universe by throwing in a few more epicycles (as Kepler later showed). But either he was unaware of this, or decided to give the heliocentric view a shot and became convinced of its beauty (and thus its truth, since he held that kind of Platonic view).
It is also interesting that it was Copernicus' devout commitment to uniform circular motion that led him to the first major breakthrough in astronomy since Ptolemy. But it was Kepler's ability to see past this view and consider non-uniform non-circular motion that led to the next major breakthrough. I doubt very much that Copernicus would have been pleased at what Kepler did to his astronomical system. It just goes to show that sometimes "bad" ideas lead to "good" results.
New Approach to the Blog
Up to this point I've been trying to post relatively well thought-out essays. But as any hypothetical reader could tell, I've kind of dropped the ball recently. It's not that I haven't had things I wanted to write about. I just didn't have time to do a full-fledged essay.
So from now on I am going to start writing quick little ideas that pop into my head. I may muster up a genuine essay or two (with actual research, though not as much as if I was really going to publish). But for the most part I will post short descriptions of things I am thinking about in regards to the history and philosophy of science, and teaching physics and astronomy. Mostly these will be questions or ideas I want to explore in greater detail someday (who knows when?). Or they may be just offhand comments that will be carried no farther. If I ever have any readers, I hope they will be sympathetic to this approach.
So from now on I am going to start writing quick little ideas that pop into my head. I may muster up a genuine essay or two (with actual research, though not as much as if I was really going to publish). But for the most part I will post short descriptions of things I am thinking about in regards to the history and philosophy of science, and teaching physics and astronomy. Mostly these will be questions or ideas I want to explore in greater detail someday (who knows when?). Or they may be just offhand comments that will be carried no farther. If I ever have any readers, I hope they will be sympathetic to this approach.
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