Non-Linearity

We don’t  do very well with predicting the future because we fail to anticipate non-linearity.  This is apparent almost anywhere you look.  Most people when they hear that the average temperature of the earth might rise by a couple of degrees, seem to have a mental image of a slightly warmer summer and maybe a bit less snow in winter (if you live in a place that has snow in winter).  Very few people associate such a seemingly small change with the possibility of deserts in places that are lush today.  Yet with non-linear systems that’s exactly what you can get from a small change.

Here are some other recent examples that I have run across.  Apparently the plane that crashed in Buffalo was on auto-pilot during much of the time that ice built up on the wings.  Aerodynamic lift is a perfect example of highly non-linear system.  If you lose attachment of the airflow to the wing due to excessive icing or due to too high an angle of attack, lift does not decrease gradually, it simply disappears.  The easiest way to think about this is by imagining a glass on a table.  As you push the glass closer to the edge of the table, the glass stays at the same “altitude.”  That’s even true if part of the glass is already hanging over the edge.  But push just a tiny bit further and the glass drops to the floor.   Even in this seemingly trivial example it appears that we don’t have a “built-in” safety model, as kids will inevitably put plates and cups down at the edge of a table and learn not do so only after considerable breakage.

The current financial crisis is of course another massive case of non-linearity.  I have posted previously about how leverage vastly amplifies risk in a completely non-linear fashion.  The overall financial system is full of feedback loops and most of them are positive loops, meaning that effects are amplified resulting in non-linearity.   For instance, as the stock market drops people are less wealthy.  When they are less wealthy their tolerance for risk goes down and many stocks that previously seemed acceptable no appear too risky resulting in more sales.  That of course drives the stock market down further.

Yet another great example is server load.  We were talking to one of our portfolio companies yesterday that is experiencing rapid growth.  One of the founders observed that their database server has fairly low load and even during spikes does reasonably well.  He seemed to infer from that that they could handle much higher loads.  But such an inference is deeply flawed and ignores the many fundamental non-linearities in server load.  Let’s use a coffee shop as a simple example.  As long as folks arrive at a rate that is less than the rate at which the barristas can make espressos, lattes, cappuccinos, etc there will be no build up of a line (for simplicity I am assuming a deterministic coffee shop, i.e. folks arrive at exactly the same interval and it takes exactly the same time to serve them).  The second the arrival rate of customers exceeds the service rate, a line will start to form and that line will continue to grow as long as the arrival rate exceeds the service rate.  So a tiny change in arrival rate will result in a huge change in wait time!  So just because your server can handle current spikes does not mean it won’t completely croak on spikes at only a slightly higher level.

I have been reading a lot about education recently and how poorly it prepares us for a rapidly changing world.  I was looking for examples of that from my own life and it struck me how little I learned about non-linearity in school or even in college.  Given our apparent lack of built-in understanding of non-linearity this is a huge omission!

Posted: 24th February 2009Comments
Tags:  education development learning systems financial markets

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