Tuesday, May 18, 2010

Calculating the Irritation Threshold.

We've talked about tolerance a lot lately.  That made me think of something that I've worked with for a long time.  I call it Area Under the Curve.

The unauthorized biography of Bill Gates tells a story about one of billg's personality quirks.  He's known to say, frequently, "That's the stupidest thing I've ever heard."  Well, when one says that as often as billg does, then one has to start questioning the veracity of the statement.  I mean, "ever"?  Really?  Each day the new Stupidest Thing is more Stupid than the previous?

The author explains how billg's mind works.  There is a certain attenuation over time in billg's consideration of The Stupidest Thing Ever Heard.  As time passes, the Stupid Value naturally decreases by some fraction.  As Time goes to Infinity, the Limit on Stupid approaches zero.  As such, each new day, each new hour, each new moment brings a new opportunity for something else to supplant the most recent Stupidest Thing as the new Stupidest Thing.

Elegant simplicity that could only be developed by a programmer.  Even back in the days when the world didn't really know what a programmer was.

So, that started me thinking.  I'm assaulted with Stupidest Things all the time.  There are days when each tick of the clock brings something new and Stupid.  That's got to have an effect on me.

After some careful self observation and soul searching (drinking) I determined that I am not inclined to react to each individual Stupid Thing as it assaults my sensibilities.  Rather, I am inclined to respond to the residual effect of the most recent Stupid Thing assaults combined.  Everybody has a limit, as the saying goes, a point at which patience runs out: over the edge, end of the rope, straw that broke the camel's back, those sorts of things.

So, I've figured out that it is some collection of Stupid Things that goads me to a reaction.  But how?  Basic math.

Consider the present moment in time as (0,0) on an x-y grid.  I know, it's math, but this will make sense.  The X-axis measures time with the future on the right and the past on the left.  I know that makes the past, with which we are most concerned, negative numbers for X, but you're all smart people: get over it.

On the Y-axis, measure the value of the Stupid Thing as some level of assault on my sensibility.  A little Stupid Thing will have a small spike on the Y-axis, a monumental assault on my sensibilities will have a very large spike.

As time moves forward on the X-axis, those spikes move into the past.  Connect the dots of those points, and suddenly you have a line that represents a level of irritation over time.  Beautiful.

Math and Physics geeks will immediately see where I'm going with this (and its inherent flaw, which I will address).  Whenever you have a line over some zero-value baseline, the first thing one should try to do is calculate the area under that line (curve) to see how much "stuff" you've carved out in your graph.  Yes, it's calculus. 

Use a certain "lookback" period (beyond which the data are irrelevant) and you can calculate the value of residual irritation based on the area under the Stupid Things curve.  When that area calculation reaches a certain value, you can expect me to do something really unacceptable like yell at a random minion, put a hole in a wall, quit my job, or tell my boss to go fuck himself.  Yes, those are all real examples.

There's a problem with the straight-up lookback period, though.  It doesn't take into account the signal attenuation.  The value of the Stupidest Thing decays over time.  So, in this model, there's no accounting for the decay of the spikes as time moves to infinity (the values should approach zero).

Enter a third axis.  (Math and Physics geeks, smile knowingly.  You knew where I was going with this.)  Floating above our x-y grid is a plane that represents the signal attenuation value at any time.  When it is flat (parallel and non-intersecting), there is no attenuation.  However, dip this attenuation plane towards the negative-X side of the graph and it will, eventually, intersect with the x-y at some point.

Now, instead of a two-dimensional area-under-the-curve calculation to predict when my head will explode at you, it is a three-dimensional VOLUME-under-the-curve. 

If you want to keep me from randomly biting your head off then you have to do one of two things: make sure you do not bring me something that is going to be the Stupidest Thing I've Ever Heard, which would generate a new data point spike, and risk exceeding the Irritation Threshold.  Or, make sure that the Attenuation Plane is at a steep enough angle that recent Irritations quickly decay to zero.

There you have it.  "Be brief.  Be bright.  Be gone."

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