Jon Webb's Blog

Sunday, March 27, 2005

Plants and Sight

All seeing things on the planet -- everything from mosquitoes to people (with the remarkable exception of some dragonfish) -- sense light by virtue of closely-related chemicals called rhodopsins. Three slightly different versions of rhodopsin give us the ability to perceive light as red, blue, and green components.
Rhodopsin originated in a bacterium. Salt-loving escendants of the bacterium still exist in the Red Sea. The bacterium's version of rhodopsin preferentially absorbed green light, like our eyes. That is why color digital cameras use the following mask to break light down into its red, green, and blue components:

That is, every other pixel is masked by a filter that lets through green light, and red and blue components are each half as frequent as green. The higher spatial sensitivity to green makes the color image appear to have higher resolution than it would if red, green, and blue were equally frequent, since our eyes have more retinal cells sensitive to green light than red or blue.
The bacteria's preference for green light and our eyes greater sensitivity to it have the same origin. The rhodopsin in bacteria was more efficient if it captured green light because that was what was left over in the pools of water it was swimming about it. At that time, the competitor for that light was algae floating on the surface of the pond. The chlorophyll in algae leave behind the green light -- hence their color. The bacteria therefore absorb green light, and look red as a result.
Our eyes, too, had to deal with green light in the forest environment that we evolved in. The forests and grasslands where we hunted gave good protection to our prey--but by having eyes that had high spatial sensitivity in this region of the spectrum, we could improve our chances of survival. So chlorophyll once again guided our evolution.
Algae evolved beyond the form of chlorophyll that absorbs just green light. More adept forms of algae absorb a wide spectrum of light, so that algae now comes in all colors. But the descendants of algae, which are the multicellular plants, were stuck with the early form of chlorophyll. So they are still green, and we, the descendants of the bacteria, see them with green-sensitive eyes.

Wednesday, March 16, 2005

Math puzzle

Here is a puzzle I invented. It is based on a similar puzzle, but mine is more difficult and trickier.
Two smart mathematicians, S and P, are given the sum and product of two numbers between 1 and 1000 (inclusive), respectively. That is, S is told the sum of the two numbers, and P is told their product, and they each know that they have been given the sum (or product) of two numbers between 1 and 1000 inclusive, and they know that the other mathematician has been given the product (or sum) of the two numbers, but neither one is told what the two numbers are.
They then have a conversation like this:
S (or P, if P goes first): I don't know what the two numbers are.
P (or S, if P went first): Neither do I.
S: I still don't know.
P: Neither do I.
Eventually, one of the mathematicians says "Now I know what the two numbers are!" and then the other one says "Now I know, too!"
I won't tell you how many times S and P went back and forth saying they didn't know what the numbers were, because if I did tell you that, you'd be able to figure out the two numbers.
What are the two numbers?

Monday, March 14, 2005

Athens and America

Like America, Athens used democracy as a tool of its foreign policy, during the Age of Athens (around 450 B.C.-404 B.C). It appealed to the serf sin neighboring city-states to revolt against their mostly monarchical governments. The idea, which worked for a while, was that the resulting governments would be more friendly to Athens. At the same time, the Athenians felt themselves to be fulfilling a historic and spiritual role in spreading democracy. History was on their side.
The parallel to America is striking. Like Athens, we believe that spreading democracy will create governments friendly to us, and that will be integrated into our economic system. We are doing on a global scale what Athens did in Greece.
The outcome for Athens was not so favorable, however. While it is impossible to untangle the various reasons, the fact is that Athens was overthrown by their neighbor Sparta in 404 B.C. Athens might have done better had it not worked quite so hard to promulgate its political system and tried to build alliances with its neighbors and their existing governments instead. Or not. It's impossible to say at this point.
However, had Athens not undertaken this effort at promulgating their political system, they might not be known as the model of democracy. Future governments, including ours, might not have been inspired by them.
Will we end up as Athens did? It is unlikely that a Sparta will arise to overthrow us in the same way--but it is quite possible that by adopting such an aggressive role in the world that we will find ourselves without allies when we need them. After all, America's economic dominance of the world will likely come to an end sometime in this century, once the Chinese economy is significantly larger than ours. At that point, we may wish we'd been more cooperative with our allies and less agressive about pushing our ideas. Turnabout is fair play.