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Augie and the Topology of Leashes
Written December 13, 2004


About ten years ago, my neighbors brought home a new puppy, Augie the Doggie.  They tied him to a long leash attached to their front porch, and he eagerly explored their lawn while I watched the scene from my window next door.

It was a nice lawn, with landscaping and lush green grass.  But it wouldn't stay that way, not with Augie around.

The puppy was interested in only a few things.  He barked at any people he saw across the street.  (However, his bark was rather perfunctory unless the people were accompanied by another dog.)  And he loved to sniff the ground, examining it minutely for bugs or something.

However, he had no talent at all for mechanical engineering.  He would wander randomly across the lawn, investigating this shrub or that lamppost, trailing his leash behind him.  The leash had to follow his zigzag path, so it soon became wound around anything and everything that was above ground level.

Before long, the leash resembled a belt in a complicated pulley arrangement — except that one end of it was still tied to the porch.  At the other end, the pup couldn't pull it any farther.  In effect, he was on a very short leash, hardly able to turn his head.

Wild dogs don't have to deal with leashes, so canine evolution had not provided Augie with the mental tools needed to solve this puzzle.  Had he understood what had happened, it would have been simple for him to untangle the leash by following it backwards, retracing his steps.  But he didn't want to go that way.  He wanted to go to the porch!  The leash wouldn't let him!  All the poor puppy could do was bark for help.

The neighbors had to go out several times a day to untangle their pet.  They finally gave up and removed the shrubbery and other obstacles from the yard.  That was fine with Augie, because it gave him more grass to explore.

Once he found a loose piece of sod and tugged on it.  The turf pulled free from the soil underneath, and soon he had a fine divot, several inches wide and almost a foot long, still attached at one end.  He sniffed and prodded underneath it before letting the divot fall back into place.

Then he wandered over to the flower bed in front of the porch and began poking around in the dirt there.  About then, Mrs. Neighbor came out and saw what he was doing.  Augie didn't dig  deep holes for burying bones and such; he just liked to plow the top inch or so.  Nevertheless, he was messing up Mrs. Neighbor's flowers, and she knew he needed to learn a lesson.

She scolded him, grabbed his muzzle, and pushed his nose down into the dirt to point out what he had done wrong.  Now this method of reproof might work for some doggie misdeeds, but Augie actually liked having his nose in the dirt.  He had no idea what Mrs. Neighbor was trying to tell him.  In fact, he must have thought she was pointing out what a fine job he had done in turning over the topsoil.

When she let go of his muzzle, Augie thought, “You think that flower bed is something?  Wait till you see what I dug up over here!”  He trotted over to the divot, proudly picked up the loose end, and looked to her for approval.  Mrs. Neighbor just sighed.



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