Alex's Adventures in Numberland - Alex Bellos [148]
The motivation behind my daily trip to the bakers was to chart a table of how the weights were distributed, and after ten baguettes I could see that the lowest weight was 380g, the highest was 410g, and one of the weights, 403g, was repeated. The spread was quite wide, I thought. The baguettes were all from the same shop, cost the same amount, and yet the heaviest one was almost 8 percent heavier than the lightest one.
I carried on with my experiment. Uneaten bread piled up in my kitchen. After a month or so, I made friends with Ahmed, the Somali manager of Greggs. He thanked me for enabling him to increase his daily stock of baguettes, and as a gift gave me a pain au chocolat.
It was fascinating to watch how the weights spread themselves along the table. Although I could not predict how much any one baguette would weigh, when taken collectively a pattern was definitely emerging. After 100 baguettes, I stopped the experiment, by which time every number between 379g and 422g had been covered at least once, with only four exceptions:
I had embarked on the bread project for mathematical reasons, yet I noticed interesting psychological side-effects. Just before weighing each loaf, I would look at it and ponder the colour, length, girth and texture – which varied quite considerably between days. I began to consider myself a connoisseur of baguettes, and would say to myself with the authority of a champion boulanger, ‘Now, this is a heavy one’ or ‘Definitely an average loaf today’. I was wrong as often as I was right. Yet my poor forecasting record did not diminish my belief that I was indeed an expert in baguette-assessing. It was, I reasoned, the same self-delusion displayed by sports and financial pundits who are equally unable to predict random events, and yet build careers out of it.
Perhaps the most disconcerting emotional reaction I was having to Greggs’ baguettes was what happened when the weights were either extremely heavy or extremely light. On the rare occasions when I weighed a record high or a record low I was thrilled. The weight was extra special, which made the day seem extra special, as if the exceptionalness of the baguette would somehow be transferred to other aspects of my life. Rationally, I knew that it was inevitable that some baguettes would be oversized and some under-sized. Still, the occurrence of an extreme weight gave me a high. It was alarming how easily my mood could be influenced by a stick of bread. I consider myself unsuperstitious and yet I was unable to avoid seeing meaning in random patterns. It was a powerful reminder of how susceptible we all are to unfounded beliefs.
Despite the promise of certainty that numbers provided the scientists of the Enlightenment, they were often not as certain as all that. Sometimes when the same thing was measured twice, it gave two different results. This was an awkward inconvenience for scientists aiming to find clear and direct explanations for natural phenomena. Galileo Galilei, for instance, noticed that when calculating distances of stars with his telescope, his results were prone to variation; and the variation was not due to a mistake in his calculations. Rather, it was because measuring was intrinsically fuzzy. Numbers were not as precise as they had hoped.
This was exactly what I was experiencing with my baguettes. There were probably many factors that contributed to the variance in weight – the amount and consistency of the flour used, the length of time in the oven, the journey of the baguettes from Greggs’ central bakery to my local store, the humidity of the air and so on. Likewise, there were many variables affecting the results from Galileo’s telescope – such as atmospheric conditions,