Indeed there are! As new technology becomes part of a scientist's experimental arsenal, the accuracy of a particular measurement will improve.

If you take the measurements and plot them on a graph versus time, then often you will see some pattern. In this case of the measurements mentioned in the article, the authors probably used a log-log plot of the difference between the measurements and their asymptote. A log-log plot tests if data is following polynomial behavior.

Looking at the paper you mention, the authors must have found that the data appears to be converging to an answer where the error at a polynomial rate. So they guessed that in the future the error will decline at the same rate.

Of course that does not prove that the error will continue to decline at that rate: new technologies might make the rate go down even faster! Or the existing methods might run into an unanticipated problem that means the existing measurements are as good as they are going to get. Most predictions based on this type of argument are only good for a few years or so into the future at best.

By the way, one famous example of this type of observed technological progress law is Moore's law which gives the trend for the number of transistors that can be put in an integrated circuit. This empirically observed law has actually worked for decades!

Mark Huber
Associate Professor of Mathematical Sciences, CMC