Precisely how do you measure?

I am reading a book with an intriguing title. "How round is your circle?" which discusses measurement and engineering mathematics (among much else). The authors point out that experimental science progressed in step with the ability to make accurate measurements. This was especially the case in astronomy, which in turn led to Newton's laws and the law of gravity being demonstrated.

I have mentioned my concern about over-precision in measurement in other blogs. Recently, Exeter, where I live, has erected signposts for the benefit of pedestrians. Distances are measured in time. This is a method often used, but is prone to abuse and error. Jokes abound about the hotel that is "two minutes from the beach" (provided you are an Olympic runner and there is no traffic in the streets), or the house for sale that is "ten minutes drive from the city centre" (when there is no other traffic, you ignore speed limits and stop signs). The problem with some of Exeter's distances is that they are too precise. One reads 19 minutes to the university campus, which is so large that it takes over 20 to cross it. There is a case for defining a set of walking times that can be used, to allow for the variation in pace, and the problem of where do you measure to. What do you think the set should be: 1,2,3,4,5,8,10,15,20,25,30,40?

Operational Research and Psychology

Well, actually, as many people have pointed out in the past, psychology is part of O.R., so my title creates a false split.

A part of my education in O.R. was the apocryphal story about the O.R. consultants and the problem of the lifts in the skyscraper. Occupants of the building complained about the time they spent waiting for the lifts to get from the upper floors to the lobby. So the consultants looked at the options, they built models of the consequences of extra lifts, faster lifts, dedicated lifts from the upper floors, etc., etc. The reduction in mean waiting time was always very small. Then the psychologist in the team suggested that the company place mirrors in the waiting areas for each lift shaft. He explained why. Why? (see the end of this blog)

I had the same sort of problem at the weekend. Each year, on the second Saturday in September, I take part in a prayer walk around the churches of the city of Exeter, my home. The idea is that a group will start early in the morning, follow a winding route around the city, stopping to pray in about 25 different churches, praying for the city and its people. I have the responsibility of planning the route; for several years we have used the same route. This is not a TSP, of course, because the walkers don't end at the start point. It is not quite minimal but is quite close to the best.

In 2008, two new churches came into the list of city churches. We decided to include one of them, miss the other, and omit another, because it was linked strongly with these two. But the selected new church would add so much extra mileage to the old route that we needed a new plan. So we made the walk have two starts, with two groups starting at 8am and converging on the cathedral at 10am to walk for the rest of the day together. So I devised such a route; the two initial legs had minimal lengths for the churches that they visited, given the fixed end at 10am. However, I had forgotten the psychology. The second route had a lot of road walking, and went past the main railway station, so there was traffic. The consensus was that it would be better to walk a little further (about 300 to 400 metres) and walk beside the river on a footpath, away from the traffic. So that is what we will probably do next year -- alter the start and route to give more traffic-free paths.

Why the mirrors? The reason was that it was not the actual waiting time that people notices, but the perceived waste of time. Mirrors distracted people; some could admire themselves and tidy their clothes and appearance, others could watch. (In the 1970's there were sexist stereotypes for these activities, which I will not repeat.)