Miners Mills


Musings on Logic, Analysis, Decision-Making, and Other Elements of Natural and Artificial Intelligence

Predicting the Weather (And Other Chaotic Systems)

Complexity is all around us...

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This past weekend was my oldest son’s class camping trip.  Back when I was a kid in Pennsylvania, our camping trips were spent sleeping in sleeping bags outside on the ground, exposed to the bugs and elements, and probably easy to find for a bear or wolf.  At least that’s how I remember them.  In contrast, my son’s class does theirs at a campground, everyone bringing tents, so technically a little less exposed to bears and weather.

For the week leading up to the trip, I was regularly checking the weather forecast, uncertain if the trip was even going to be happening.  The forecast was consistently showing a 50% to 70% chance of rain or snow by Sunday morning… and two years ago, the trip ended a day early because snow ripped in unexpectedly (yes, there’s snow in May in the mountains outside Los Angeles).

But this past Thursday, we got the “all clear” signal.  “All clear” in that the trip was happening, that is — not “all clear” weather-wise, because the forecast was still showing a 70% chance of rain or snow Sunday early morning.

So, just like any concerned parent, I began thinking about how the weather is similar to other chaotic systems, such as traffic and macroeconomics.


We all get frustrated that our iPhones can’t tell us with 100% certainty what the weather will be like on any given day.  But we should be thankful that meteorologists can predict weather systems at all.  A physicist could explain how a particular water vapor molecule will react under the conditions in its immediate vicinity.  Perhaps the physicist could even predict with some degree of certainty where, under those conditions, the molecule might be in a few seconds.  But that’s about it.

If you’ve ever watched balls bouncing chaotically around a pool table, you know how difficult it is to predict where any ball will wind up… and that’s with only a few balls, and edges of the table to keep them in the same general location.  There are approximately 25,000,000,000,000,000,000,000,000 molecules in just a cubic meter of air, and no edges to keep them contained.  Our physicist would have absolutely no ability to determine how or where any individual molecule will be in 5 minutes, let alone 5 days.  The system is WAY too chaotic.

Yet somehow, using cool tools, meteorologists can predict that, in 5 days, there’s a high likelihood that some water molecules that came from somewhere will be dropping to the ground as rain (or perhaps snow) in a particular location at a particular time.  Wow!


So how is that like traffic?

Well, on the drive to and from the campground, there were a lot of cars on the road.  Each driver was obviously trying to get from Point A to Point B… most of them with very different Points A & B.  As they merged on and off the common roads and freeways, managing their own trajectory, the combination of vehicles created a complex pattern that somehow mostly flowed like a particle stream (complete with slow-moving rocks).  If I, or almost any particular driver, had decided not to drive on those roads at those time, the flow would likely still have been substantially similar.

But if, on any given day, many versions of “me” decide to either drive, or not drive, on a particular road, then the flow is much affected.  I may be driving on the freeway to go from my home to a campground, while thousands of other drivers may be on that same freeway to go from a different origin to a different destination for a different reason.  But the combination of those individual decisions, creates a collective outcome.  And, somehow, we can predict, with a high degree of certainty, that at certain times on certain days, certain roads will have high traffic or low traffic, even though we can’t predict whether any particular driver will be on that road, or not.


And what about economics?

“Microeconomics" focuses on decision-making by individuals (persons, companies, etc.).  “Macroeconomics" focuses on aggregate results (e.g. GDP, unemployment rate, inflation, etc.)  Metaphorically, if microeconomics is the study of individual drivers and molecules, then macroeconomics is the study of traffic and weather.

When the Fed raises interest rates a quarter percent, economists have no idea whether it’s going to prevent any particular company from buying a piece of equipment, or prevent any particular person from buying a house, but they can predict, with a high degree of certainty, that the increase will have some overall slowing effect on business activity and home purchases.  In 2011 & 2012, when the government cut social security withholding by 2%, they had no idea whether any individual worker would save the extra few hundred dollars, or spend it, but they knew that en masse, it would stimulate some additional spending in the economy.

Economic systems are obviously rooted in more complicated micro-dynamics than is weather.  There’s no analog to “consumer confidence” or behavioral factors in the meteorology world.  Air molecules don’t make decisions (quantum theorists stay out of this!), so weather is a chaotic aggregation of deterministic particle dynamics.  Yet somehow, even with individual behavior both unpredictable on the surface and driven by “choice-based" underlying dynamics, the macroeconomy is defined by largely predictable effects, at least over the short term.  GDP growth may vary a few percent here or there each year, but it doesn’t swing widely — even though on an individual level, the fortunes of any particular company or individual may.


All of these are examples of chaotic systems.  There are many others, of course — water molecules flowing in a stream, evolution via mutations, geographic population changes, electrons into current, etc.  All combine explainable actions and reactions on a micro level into countless complex interactions, which lead to incomprehensibly predictable aggregate outcomes.

To be clear, the outcomes are not “predictable" in an exact deterministic sense, but rather in a contained probabilistic structural sense.  No forecast can be perfect — and the degree of uncertainty usually increases significantly the further out the prediction, both because of the chaos, and possibilities of intermittent “shocks".  But the idea that an aggregation in a chaotic system is at all predictable with any degree of probability is pretty amazing.


Well, it did indeed start raining around 3AM Sunday morning, but by that point, all but one intrepid father and son (much braver than I), had departed the campsite.  Not ready to give up on nature though, we decided to stay in a cabin nearby, where my kids dragged me up the rain-soaked tree-lined mountain to look for fallen branches to use as weapons to protect ourselves from bears and wolves.

Then on the drive home, at one point, traffic came to an almost complete stop — apparently this was caused by people slowing to look at a few motorcyclists on the side of the road just hanging out and chatting.  Each person who slowed to watch only slowed a little… but in a complex system, that can (and did) accordion into a freeway jam.

And I’m not sure if anyone could have predicted that we would stop at the Subway in West Covina.  But enough unpredictable patrons stop at that Subway to provide a somewhat steady customer flow to keep them in business.  They may not realize it, but their business thrives on chaos.

Thanks for reading! Feel free to email me your thoughts.

David Chariton