Thursday, September 26, 2013
Step functions and black boxes

This year we're getting a step-function season change instead of a sine wave. Summer continued with solid 90s until late Sept, then Autumn started with only a couple days of transition. When this pattern shows up, it forces us to adapt quickly.

Our bodies don't get a chance to learn. One day the morning low is 65, and then the next day it's 45! And our bodies say ACK! I NEED HEAT! NOW! GIMME WARMTH! GIMME FIRE!

And when we get fire, our bodies say AAAAAAAAAAHHHHHHHHHH.

Step functions are a wonderfully useful way to examine the response of complex systems. With a dumb item like a brick or a steel beam, you don't need step functions. You can just press on it more and more heavily until it crushes or snaps. But when the item has filters and adaptors and feedback loops .... in other words, intelligence ... you have to catch it off guard.

Classic example: road-testing a car. Stomp on the gas and see how many seconds it takes to reach 60. Then stomp on the brake and see how quickly and straightly it reaches zero. If it skids and fishtails, the brakes are problematic.

In an electronic system, a step-function input brings out the frequency response, and tells you something about the resonance and damping. If the output follows the step closely and smoothly, the damping is nicely balanced. If the output goes wild, overshoots, and fishtails, the damping is problematic. (Car analogy doesn't quite apply here, because sometimes this wild response is what you want in a circuit; but still the test gives you the same kind of result.)

In the human response to heat, the step-function autumn shows clearly how our infinitely complex feedback loops respond to a downward step in temperature.

But what about the opposite? When summer follows spring suddenly, we don't have the same deep desire for air conditioning. We don't automatically say I NEED ICE! We don't instinctively know that a cool blast of Freon-treated air is what we need.

Well, obviously AC is a late development, so it's a more recent learning .... No, that doesn't work. I've lived with both heating and AC for as long as I can remember. Since I started out in Okla, I probably experienced more AC than heating for the first part of my life. If the response is purely learned, I should have a deeper and more instinct-like need for cooling than heating. But I don't.

In schematic form:

Step down ---\\\\\--- I NEED FIRE!

Step up ----/////--- nothing in particular.

Is fire part of our genome? Stupid question! Of course not! Well, why not? It's something humans have been doing as long as we've been human, and it satisfies a natural need. We don't have the same natural response to ice. Were we designed from the start to use fire? I can't think of a good argument against this hypothesis.

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