Tuesday, March 25, 2008

S n o w g r a p h

I have always been facinated by snow. The shape of a snowflake, its size, and the path it takes as it falls on the ground - each of this is the output of a complex mathematical equation that has thousands of variables. What would take a supercomputer a couple of hours to simulate is done by nature in a couple of seconds. And what more, there are billions of them snowflakes in one single day of snowfall. Each of them is uniquely beautiful.

After a long hiatus of 3 years, I resume to muse on this blog over the philosophy of snow. The topic of today's musings is what I call the snowgraph - the particular pattern describing which parts of the earth are covered by snow and which are not. Given a terrain with some variation of texture, windwardness and overboard traffic, nature solves a binary labeling problem - which parts of the terrain to cover with snow and which not.

The problem is interesting if the temperature of the earth is a little higher than freezing point, that is, so sufficiently high that a single isolated snowflake would melt away immediately after touching the ground. But when a crowd of snowflakes fall on the ground, a pattern will still emerge. The snowflakes will be floating islands of lower temperatures, sorrounded by a warmer ocean of atmosphere.

This accumulation of snow into a pattern will happen, if and only if the average frequency of a random snowflake hitting a portion of the terrain is higher than the time it takes on that terrain-portion for an averagely sized snowflake to melt away. Both the above variables depend on a complex assortium of factors such as the thermal conductivity of the terrain-portion, the windwardness of the terrain-portion and the thermal energy generated over the terrain-portion by traffic passing overboard (people/cars/water/..). Nonetheless, all these factors integrate with each other to produce the snowgraph. The snowgraph captures all the complex dynamics of this integration. This is nature's way of compressing information.

Now the interesting question is, can we discover the hidden forces that gave rise to the snowgraph (for example, by observing and analyzing an aerial photograph of the terrain) ? This is a fascinating piece of detective work. Given a photograph of a terrain in summer and in winter - one bare and one covered with snow, can we detect if either of them is fake ?

Most of the interesting questions of nature are of this kind. We have the snowgraph standing before us. But we have no idea why it is like that - why only parts of the terrain are covered with snow and why not the rest.

Why do we have five fingers on each limb ? Why do we have hair on top of the head but not on top of our palms ? Why are our palms soft and sinewy instead of hard and metallic ? Why do we have eyes on the top of the face, instead of having them over a prehensile object like our hands ? These are questions interesting not only to biologists, but also to roboticists who want to simulate these phenomena. Each of us is a snowgraph. Each custom in our society and culture is a snowgraph. Each object and each phenomenon in nature is a snowgraph - uniquely mysterious and uniquely beautiful.

The laymen amongst us abandon these mysteries and proceed with the daily routine. The believers amongst us give a ready answer - saying that it is God or whoever they believe in that did it all. But those few men amongst us who are bit by the curiosity bug, they dig deep and wide, and they unravel the mysteries of each snowgraph.

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