Work

I will be working this week-end: proof.

Defining nematic viscosities: Mięsowicz and Leslie-Ericksen

Isotropic fluids only have two viscosities, intervening in shear and extensional deformations. For anisotropic media, such as nematic liquid crystals, more coefficients are needed, as shown by Mięsowicz in the late '30s: three shear viscosities, labeled \(\eta_1\) to \(\eta_3\), a fourth one \(\eta_{12}\) introduced later by Helfrich and a rotational viscosity, \(\gamma_1\). We do not worry here about extensional deformations.

The whole topic was put on a solid theoretical basis in the '60s by Leslie and Ericksen [brief and clear presentation here] who introduced six coefficients (\(\alpha_1\) to \(\alpha_6\)), only five of which are independent. As one can expect from dimensional analysis, the two sets of viscosities, \(\left \lbrace \eta_i, \gamma _1 \right \rbrace\) and \(\left \lbrace \alpha_j \right \rbrace\) are linearly related.

I only recently realized, while discussing with my former PhD advisor, that the difference between the two definitions is deeper than an arbitrary linear transformation. Mięsowicz had in mind clear experimental configurations, defined by the relative orientation of director, velocity and velocity gradient, while Leslie and Ericksen adopt a more formal approach, based on generalized hydrodynamics, as in the paper of Martin, Parodi and Pershan.

The twist (so to speak) is that the theoretical approach gives a clearer view of the various modes and the constraints on the coefficients, while the Mięsowicz configurations are very difficult to achieve in practice, precisely due to the coupling between flow and director orientation.

Reproducible experiments (again)

Last year I discussed a psychologist's essay on "the emptiness of failed replications". I'm returning to the status of experiment replication because a few days ago Science published a paper of the Open Science Collaboration, which was only able to confirm less than half of the 100 psychological studies it replicated. The study is very interesting in itself, but I'll only comment here on the reaction of psychology professor Lisa Feldman Barrett in a New York Times op-ed. She makes the point that attempting to replicate an experiment in different conditions can lead to different results and, by that fact, point to the importance of previously neglected parameters: context is important.

She illustrates her position by three examples, one of them taken from physics :

[...] when physicists discovered that subatomic particles didn’t obey Newton’s laws of motion, they didn’t cry out that Newton’s laws had “failed to replicate.”

Prof. Feldman Barrett confuses here the epistemological function of experiment and theory. A physical theory cannot be replicated, but it can be tested using (hopefully, reproducible) experiments. Obviously, performing an experiment with elementary particles cannot be seen as replicating one that uses macroscopic objects.

There is, however, a more alarming problem with her position, summarized by the phrase :

Much of science still assumes that phenomena can be explained with universal laws and therefore context should not matter.

There are very few completely general natural laws. Scientific results are "universal" precisely in the sense that the necessary context should be fully specified : A occurs every time conditions B, C, and D are fulfilled, irrespective of parameters E, F and G that are not mentioned.

Of course, the more general the applicability, the more interesting the result, as the psychologists very well know : they say "X correlates with Y and Z in adult humans", and not "X correlates with Y and Z in this set of 58 adults" that they used to infer that particular correlation. The latter finding will not be published in high-profile journals.

Fully specifying the context is certainly more difficult in the social sciences than in physics, but the solution is adding more rigour, not claiming for psychologists the right to generalize their results arbitrarily (what holds for a few dozen psychology undergraduates in an American research university may not apply to all mankind). If the generalisation is shown to be incorrect, this is not proof of a new and exciting result, but simply a sign that the original authors oversold their findings.

Reproducible experiments

Yesterday evening, after having spent my day trying (and failing) to reproduce somebody's published research, I stumbled (via Soylent News) upon a psychologist's essay on "the emptiness of failed replications". Jason Mitchell, psychology professor at Harvard, states that failing to replicate somebody else's experiment does not represent a meaningful scientific contribution. Well, thank you, Prof. Mitchell !

All jokes aside, it took me quite some time to parse the text, and even more time to realize that this difficulty is likely due to the implicit assumptions that I brought from my own field of work (experimental physics), which are quite different from those of the author, an experimental psychologist. Ultimately, I learned more from trying to separate these two viewpoints than from the text itself, which makes a rather simplistic argument.

The argument

Mitchell's main point appears to be that one cannot learn from negative arguments, since not finding something cannot prove it doesn't exist. This sounds entirely reasonable, and is certainly true in the case of the "black swan" example the author uses, but is completely wrong in usual scientific experiments: learning that the correlation between two variables is zero (within the uncertainty) is as strong a result as saying that it is significant and positive. Of course, the first outcome is less likely to lead to a high-profile paper.

The assumptions

A basic assumption in physical sciences is that of "homogeneity": the outcome of an experiment should not depend on its location, time or the personality of the scientist. Mitchell does not address this point directly, but seems to imply that getting all the details right for precisely replicating an experiment is next to impossible. He then blames this on the replicators' lack of some sort of "core competence". This is a valid point: if Nature is the same everywhere but the experimentalists are sloppy, their results will of course differ. From this I would however draw two uncomfortable conclusions:

1. This sloppiness may just as well affect the initial experiment as the attempt to reproduce it.
2. It also undermines an entire field of study if there is no way of distinguishing careful scientists from the careless (or incompetent) ones.

In "tabletop" physics, replicating an experiment is relatively cheap¹. It is also crucial: our research builds on someone else's results, and very often the replication is a necessary step before being able to go further. Chemists sometime spend weeks or months in order to reproduce published protocols. Needless to say, this is not done to prove the original author wrong ! Neither of these points seems to apply in psychology, as presented by Mitchell.

Finally, I find quite strange Mitchell's attitude that replicating experiments is almost morally wrong: "One senses either a profound naiveté or a chilling mean-spiritedness at work." This goes beyond mere scientific debate and sounds more like responding to a personal offense.

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^{1. Even in large scale experiments, reproducing the results may be necessary, albeit very expensive. A good example is the search for the Higgs boson, with the two experiments, ATLAS and CMS, working side-by-side but without communicating (see for instance Jon Butterworth's "Smashing Physics".)↩}