Abstract
A recent article by Faux and Godolphin explored issues of floating-point error in situations
relevant to classical dynamics, numerical integration, cellular automata, statistical analysis,
and digital timing. Examples were given that were suitable for discussion and student
project work. One of the examples explored the properties of an algorithm, described in an
IBM Knowledge Center document designed to convert a binary field representing the number
of counts of a quartz oscillator to integers for digital display. In Ref. 1 it was demonstrated
that the algorithm was vulnerable to rounding error resulting in an incorrect digital display.
Investigation associated with this example form the focus of this note.
The timing simulation results presented in Ref. 1 suggested that uncorrected rounding
error in stopwatch timer displays could be impactful if used for precision timing, such as
for race times or in experimental physics. Here we present and analyse race times obtained
from swimming competitions. The data give a clear demonstration of anomalous stopwatch
timing patterns, which can only be explained by rounding error. It is also shown that such
rounding error can result in a set of times being wrongly ordered. In the context of a sporting
event this could lead to the incorrect ranking of athletes and hence the incorrect awarding
of race positions. As a spin off of Ref. 1, this note may be of interest to educators, with
the results providing a resource for discussion and the approach providing a template for
additional student projects.