How ignorance leads to more accurate results
When scientists measure something, the rule of thumb is usually: The more precise the measurement, the better the results. However, researchers from Göttingen have now shown that measuring too precisely can be a disadvantage. Deliberately ignoring part of the measurement accuracy can, contrary to common intuition, lead to more precise results.
Aljaz Godec and his team are interested in the mathematical determination of physical, in particular thermodynamic, properties from paths of individual particles or processes in a cell. Such calculations are very complex because the motion of the particles is subject to random fluctuations and thus individual paths yield different results. To describe this in theory, many scientists study local currents, for example in cells, derived from time averages along individual paths. Based on previous research, this works particularly well if the space being studied is divided into a grid. The smaller and finer the grid is chosen, the more precisely the paths of the particle and therefore the local currents can be determined, but the more complex the calculation becomes. What sounds logical, however, is not the whole truth.
In their tandem publication in Physical Review Letters and Physical Review Research, Cai Dieball, a PhD student in the Research Group of Mathematical Biophysics, and group leader Aljaz Godec showed how derived results can become more accurate if only a few, slightly larger grid points are used instead of a very fine grid when determining time averages along individual paths. And that, even though both, a part of the measurement accuracy and the rest of the considered space, are ignored. The authors were even able to determine that for each calculation there exists an optimal grid-point size at which the derived results become most accurate. This is far from intuitive, because a grid that is too precise, and therefore a measurement that is too accurate, will yield less accurate results. In the extreme case of an arbitrarily precise measurement, calculations even result in quantities that make no mathematical sense. The reason for this counterintuitive effect is that as the grid points become smaller, statistical expected values of local currents are dominated by more and more atypical events, and statistical fluctuations become larger in the process.
In addition to the systematic mathematical description and theoretical calculations that confirm the discovery, experiments in living cells also show that Godec and his team’s approach works. In the future, researchers could apply these new fundamentals in measurements with abstract dynamics in a high-dimensional potential and use them, for example, to study chemical reactions or protein or DNA folding.