Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

Even when the market seemed to be doing great, the Vancouver Stock Exchange Index continued to drop. By November 1983 it closed one week at 524.811 points, down by almost half its starting value. But the stock market had definitely not crashed to half its value. Something was wrong. The error was in the way that computers were doing the index calculations. Every time a stock value changed, which happened about three thousand times a day, the index would be used in a calculation to update its value. This calculation produced a value with four decimal places, but the reported version of the index used only three; the last digit was dropped. Most important, the value was not rounded: the final digit was simply discarded. This error would not have occurred if the values had been rounded (up as often as down), instead of truncated (always down). Each time there was a calculation, the value of the index went down by a tiny amount.