The Information Content of a Tornado

[swamidass (S. Joshua Swamidass)]

Continuing the discussion from Gpuccio: Functional Information Methodology:

@Art

Consider the tornadic thunderstorm. It consists of a number of integrated and essential components, all of which are needed to produce and maintain the tornado. The ground and upper-air windstreams (which must be oriented in precise manners), the precisely-functioning updraft, the supercell itself (which consists of more parts than I can possibly list), and the funnel cloud. By most accounts, an IC system.

Can we speak about the information content of a tornadic thunderstorm? I believe so. Recall that the informational content of genomes is usually estimated by “calculating” that fraction of all possible sequences (nominally, amino acid sequences) that can satisfy a particular specification. We can use a similar strategy to guesstimate the “information” carried by water vapor molecules in a storm. The hard part is deciding how few of all of the possible states that are available to a particular water molecule are actually “used” in a storm. Now, one can count up all possible positions in the storm, interactions with all possible partners, etc., etc., and realize that the number is probably rather small. But, for the sake of argument, let’s pick an arbitrarily large number – let’s propose that only 1 in 10^30 states of any given water molecule is excluded in a storm.

Starting there, we need only count the number of water vapor molecules in a storm and estimate the “probability” that the arrangement found in a storm would occur. If we arbitrarily think in simple terms - a storm that is 5x5x7 miles in size, a temperature of 30 degrees C, a partial pressure for water vapor of about 32 mm Hg, an overall atmospheric pressure of 1 atm - then the number becomes (roughly) 1x10^-30 raised to the number of water vapor molecules in the storm (which is about10^36). Which in turn is about 10^-10^6 (that’s 1 divided by 1 million!). Or, using the conversion @gpuccio does, about 3 million bits!

By focusing on the water molecules in a storm, @art nicely relies upon the fact that information content increases with the number of components in a system. This, however, does not demonstrate we will never observe natural objects with high information content. In fact, we see astronomically high FI in a commonly observed feature of the world.

[Argon]

I believe that point was driven home in The Hitchhiker’s Guide to the Galaxy using a ‘nice cup of hot tea’…

[swamidass (S. Joshua Swamidass)]

@Argon

nice cup of hot tea

Infinite Improbability Drive

The principle of generating small amounts of finite improbability by simply hooking the logic circuits of a Bambleweeny 57 Sub-Meson Brain to an atomic vector plotter suspended in a strong Brownian Motion producer (say a nice hot cup of tea) were well understood. It is said, by the Guide, that such generators were often used to break the ice at parties by making all the molecules in the hostess’s undergarments leap simultaneously one foot to the left, in accordance with the theory of indeterminacy.

Many respectable physicists said that they weren’t going to stand for this, partly because it was a debasement of science, but mostly because they didn’t get invited to those sorts of parties.

The physicists encountered repeated failures while trying to construct a machine which could generate the infinite improbability field needed to flip a spaceship across the mind-paralyzing distances between the farthest stars. They eventually announced that such a machine was virtually impossible.

Then, one day, a student who had been left to sweep up after a particularly unsuccessful party found himself reasoning in this way: If he thought to himself, such a machine is a virtual impossibility, it must have finite improbability. So all I have to do in order to make one is to work out how exactly improbable it is, feed that figure into the finite improbability generator, give it a fresh cup of really hot tea… and turn it on!

He did this and managed to create the long sought after golden Infinite Improbability generator out of thin air. Unfortunately, after he was awarded the Galactic Institute’s Prize for Extreme Cleverness he was lynched by a rampaging mob of respectable physicists who couldn’t stand him being “a smart arse.”