Train of Thought #9: The Tessellating Traveller

It may seem a surprising admission, but I give a lot of thought to the problem of optimum packing density.  For some researchers, I am sure this is a fulltime pursuit; for me, it is an occupational hazard.  And when do I do my most productive thinking on the subject?  During my daily commute.

My analysis boils down to the quest for an answer to one fundamental question.  Do I line up, or do I tessellate?  I’ll explain my quandary.

In the morning, I alight my train at a busy railway station.  In the evening, the situation is the same.  Typically, I find myself one amidst the slow-moving rank and file of commuting humanity, hemmed in on all sides in a mass of bodies all moving in the same direction towards a common goal.  The exit.

And it is during these slow peregrinations that I noticed an unusual phenomenon.  Some people line up directly behind the person in front of them, whilst others slot into the gap between the two people directly in front of them.  A diagram may help to illustrate my point.

400 lining men

400 tessellating men

Effectively, one lot of people are lining up, whilst the others are tessellating.

So, where do I fit into this queuing system?

I realise that I am a tessellator.  It would be nice to think this is because I am instinctively falling into a pattern, which achieves the optimum packing density for human beings––as the diagrams above seem to illustrate, it is possible to pack more people into the same sized space when they tessellate as opposed to when they simply line up––but the truth is more mundane.

The truth is I am a tessellator because I am relatively short.  When I line up directly behind someone else I am usually left with no other outlook than staring into the middle of the back of the person in front, whereas if I tessellate I can obtain a longer view between the shoulders of the two people ahead of me.

That is until I reach the exit where all my patient tessellating is rendered worthless in the face of the regimented ranks of the automated ticket barriers, and I am forced to get back in line again.

© Simon Turner-Tree


Simon Turner-Tree continues his tiny daily battles against the system.


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