Gpuccio: Functional Information Methodology

To follow up, something from another board in a universe far far away. To let @gpuccio see the why of this reference:

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!

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