Everyday entropy: averages

The speed of molecules at 25 degrees C.

It is impossible to know more than half of the information about anything.  At large scales, most of the information is hidden from view, and at smaller scales it begins to suffer from quantum uncertainty.  Realistically, you can only know a tiny fraction of the information about any given thing, but that’s where the genius of statistical mechanics comes in.  If you have a representative sample of the information, it will mirror the probability density of the total information, so that even with only a billionth of a trillionth of the total information, you can get a very good picture of the average temperature, density, velocity and momentum of a body.  The danger of this method is the belief that the average is the truth, and this is where entropy enters stage left and stage right in a pincer action that explains why science isn’t saving us from ourselves.

From the one side, your sample of information is always selected from the information that makes itself available, and this information may be statistically different from the unavailable information.  If you think of a boiling pot of water, you can see the bubbles but not the water, so  your information is dominated by the rising of the bubbles and not the sinking of the water.  Given the visibly available information, it looks like the stuff in the pot should jump out.  This is pretty typical of situations where there is a high-intensity flow surrounded by a low-intensity counterflow.  Within the filaments of an unstable fluid boundary the filament flow may well be the reverse of the average dynamic flow or pressure change.  This disconnect can lead to profound misunderstanding of the dynamic if the filaments are the only measurable feature.  War reporting will feature battles won or lost, but not the tide of people, materials and opinions that make the difference over time at geographic scales.  Likewise, the moments of conspicuous environmental conservation are puny compared to the flood of deforestation and development, and commuter rail is insignificant next to the waves of suburban traffic.

From the other side, unless your system is isolated and in perfect equilibrium, which is impossible, there is a transformation taking place that will eventually render your information obsolete, no matter how perfectly representative your sample was at the time of observation.  This is particularly obvious where things are in resonant flux, like the tides rising and falling.  It looks for all the world like a flood is coming if you measure the movement of the water at maximum flow.

It’s easy to be glib and flippant about Heisenberg’s uncertainty and the fundamentally unmeasurable nature of real things, so it’s important to remember that averages and probabilities are measurable.  When you have a large group of nearly identical things, like a macroscopic clump of matter, you can precisely measure the average location, momentum and density of the group.  Averages and probabilities unify ontology and epistemology for anything that has enough identical neighbours or phenomena with enough iterations that an average or probability can be established.  And this is the key.  Where parameters are constant or repetitive, we can have knowledge.  Where parameters are in flux or will only happen once, all we have is an aesthetic.  This is the fundamental problem of climate change.  It can’t be treated scientifically.  We have only one shot with this planet.  The important thing about entropy is that it gives you an unscientific image of how systems evolve, and in particular how much space and time they need to adjust to an input of energy or a change in chemistry.

Allegiances in war, like the carcinogenesis of an individual cell in a living organism, cannot be known to exist or not exist until they have played their part in a cascade of events.  The quality of a striker in football cannot be known until they either score or do not score, because no matter how many times they have scored in the past they may never score again.  These things are indeterminate because they depend on unpredictable things that depend on unmeasurable things, but local averages build up and stabilise one another over many interactions to the point were, on average, half of the universe is not chaos.


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s