Grains of sand

When you upend an hourglass and watch the grains of sand trickle out to form a little pyramid below, it is not possible to predict the progress of any individual grain. You know that the sand will fall in always the same amount of time but the rules of fluid mechanics, and possibly chaos, govern the paths taken by each grain.

I had some practical experience of this today. My Metropolitan to Baker Street was no more crowded than usual but we had a rather slow journey in, and a very large number of people converged on the hopelessly inadequate stairs linking down to the Jubilee and Bakerloo platforms. Just like the sand, we formed an inverted pyramid, each person jostling and inching forward as the people at the apex got into the top of the steps. You could not predict the order in which people moved. Once inside the huddle one had to keep on moving, because the pressure behind was gentle but remorseless. Also another train was close behind and nobody wanted to be on the platform when another hundred people joined in.

For some moments I barely moved, then it was possible to take a half step, and another, and suddenly there were just a few backs in front of me. Yet still people were pressing on both sides, some moving straight into any gap that allowed, others hanging back a little and so we continued in this chaotic fashion until I in turn reached the steps and at once surged forward into the relatively empty space ahead.

I guess that if you take a given number of people, say 80, they would always take the same amount of time to pass down the stairs. It is an odd feeling to be part of this process, subject to the same forces that make hourglasses work.