Operationalism

Rereading "The Logic Of Modern Physics" by Percy W. Bridgman

I am back from New Orleans, where I attended NeurIPS 2023. I had gumbo, oysters, and fried catfish. I read and photographed a bunch of posters, more than I realistically can remember or use for my research. Meanwhile, at home, the second raccoon has finally been caught and the tree branches that were precariously hanging after being damaged by the first serious snow have been trimmed, restoring my backyard to safety. All is well.

Except for a little detail. On Friday I sat through the panel discussion at the workshop on Machine Learning for Physical Sciences. The discussion in general was not bad, but I felt mildly annoyed by a question that was asked to the panelists. Paraphrasing: How do you reconcile the fact that XAI tools may produce multiple alternative explanations with our belief, as scientists, that there is a single underlying truth?

Now the underdetermination of theory by data is a pretty well known limitation of science. In Bayesian inference nothing prevents your posterior from being -in general- multimodal. Those who work on creating AI-scientists know as much. It is for reasons presumably related to my mild feeling of annoyance at this question that I found myself rereading the book The Logic Of Modern Physics by P. W. Bridgman on the plane back.

Bridgman received his Nobel prize in 1946 for his work on high pressure physics. He developed a new kind of seal, allowing him to reach higher pressures than any experimentalist before him. Orders of magnitude higher. This must have made him acutely aware of the fact that the correspondence between our theoretical concepts and the series of concrete operations we put in place to relate them to the real world is extremely brittle and limited in scope. Whenever you think you are merely changing the way you are measuring something, you are instead -at least in principle- redefining the thing you are measuring. Pressure is the ratio of force to area, but how do you know you really reached a given pressure within an enclosed box? If you measure pressure through the changes in resistivity of a manganin gauge, you are in fact defining pressure that way. Whether the theory defining it as the ratio of force to area has anything to do with your measurements is an empirical question, and it does not matter much that some other way of measuring pressure -applicable to lower values of the quantity- seemed to work well with said theory.

Different ways of measuring length lead to different measurements. Who would have known? How do we reconcile this with our belief, as scientists, that there is a single underlying truth? Credits: Libretexts.

Let’s hear it directly from Percy:

We have already encountered new phenomena in going to high velocities, and in going to small scales of magnitude: we may similarly expect to find them, for example, in dealing with relations of cosmic magnitudes, or in dealing with the properties of matter of enormous densities, such as is supposed to exist in the stars. Implied in this recognition of the possibility of new experience beyond our present range, is the recognition that no element of a physical situation, no matter how apparently irrelevant or trivial, may be dismissed as without effect on the final result until proved to be without effect by actual experiment. The attitude of the physicist must therefore be one of pure empiricism. He recognises no a priori principles which determine or limit the possibilities of new experience. Experience is determined only by experience. This practically means that we must give up the demand that all nature be embraced in any formula, either simple or complicated. It may perhaps turn out eventually that as a matter of fact nature can be embraced in a formula, but we must so organise our thinking as not to demand it as a necessity. 

What a breath of fresh air from about a century ago, especially if compared to the arrogance of our times. Let’s hear some more of this music:

We may illustrate by considering the concept of length: what do we mean by the length of an object? We evidently know what we mean by length if we can tell what the length of any and every object is, and for the physicist nothing more is required. ‘To find the length of an object, we have to perform certain physical operations. The concept of length is therefore fixed when the operations by which length is measured are fixed: that is, the concept of length involves as much as and nothing more than the set of operations by which length is determined. In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations. 

What more can we say? QEF.