All hail and beware the linear, time invariant system

Okay, I’m an engineer, a gearhead, a nerd.  Glad we got that over with.

Now, one of the things that engineers can’t stand is mathematics that you can’t do anything with.  We learn a lot of math, but when the stuff is just esoteric and we can’t use it, it pisses us off (technical term).  We do like math that allows us to do stuff, to build things, understand nature, fix things.

To that end, we learn to love an idealization of math known as the linear, time-invariant system.  The idea is that a lot of things can be modeled using math.  Things that move are often modeled using what is known as differential equations, where the change in the behavior of something is a function of where it is.  Now, a lot of this is complicated and hard to solve, but when that function is linear and doesn’t change over time, it opens up a lot of nice tools to us.  Like protomatter for Captain Kirk’s son, David Marcus, it solves a lot of problems.  So, we tend to try to beat a lot of problems into areas where we can whip out our linear, time-invariant system tools.

Here’s the thing:  those are idealizations.  Nature isn’t really that way in any detail, but we can get a lot of things done if we assume that it is.  Engineers that work in the real world are very cautious about this, though, because real world stuff tends to break those assumptions.  We know that friction, and grease, and wind, and crap (that isn’t modeled by our linear, time-invariant math) is in our real system.

So, why bring this all up?  Because a lot of the rhetoric that we hear is based on similar idealizations of nature and human behavior.  Folks tell you that all we need to do is cut taxes or rich people or give every slacker the same level of living as every hard worker, and everything will be fine.  And they would be if those people and the world were linear and time-invariant.  But they aren’t.

People are definitely nonlinear and they do vary a lot over time. So any idealized model of human behavior is BS.  There is always friction.