One drizzly winter day several years ago, I lost my pencil.  I had gone out to take some notes off an irrigation pump station we planned on upgrading.  The roads were wet; I had to walk from my pickup about 10 minutes to the pump.  I took half the notes I needed to and lost my pencil.


I looked on top of the electrical panel, on the ground, behind my ear, and in every nook and cranny I could think of - no pencil.  I had taken half of the notes I planned to; no way had I forgotten the pencil to begin with.  I was by myself; no one could have stuck the pencil in their pocket and walked away.  I never got close to losing my temper; no chance that I threw the pencil in a childish fit of rage.  The pencil did not burst into flames; the pencil had to be there.  I looked for that pencil for half an hour before I gave up and got another pencil.


I spent too long looking for that pencil.  How long should I have looked for the pencil? A 12 pack of pencils costs about $4.00, or $0.33 each. My pencil was absolutely depreciated – worn down to less than half its original length and just the metal nubbin left on the eraser.  Let’s just assume that the value of the physical pencil was trivial compared to the value of time.  It is not as if my family had handed this pencil down from father to son for generations.


Walking to get another pencil takes 20 minutes.  If I had kept looking for the pencil I would have eventually found it, but I have no idea how long it would have taken me to actually find it.  My gut tells me that searching for about 30% of the time it would have taken to get a new one is the right play.  So I should have looked for 7 minutes before bailing and taking the defeated, shame filled walk to get another pencil.


If you smash that into a math formula:





S = time spent searching for pencil

R = the value of hope that I would find the pencil (basically an interest rate)

W = time spent making the walk of shame to get another pencil


In the example above, R works out to about 26%.  If you set S to 2 minutes, R works out to 10%.  10% fits better with the way these sorts of problems usually work out.  I guess this means I am irrationally confident in my ability to find pencils.  Not unrelated: I am bad at finding Easter Eggs.


If I had to do it all over again I would have used my phone to take pictures.  Because that’s what the cameras are for, right?