Puzzle Solving and Gestalt Shifts

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.