Saturday, November 3, 2012

One possible meaning of "learning something"

- Gautham

Sometimes I come away after reading a paper or going to a talk and I say to myself "That was nice. I feel I learned something." Opinions no doubt disagree about what is the most desirable meaning of the word to "learn" in the context of scientific research. One possible sense, that I think I like, is that to have learned something is:

to reduce the problem of explaining a phenomenon to that of explaining one that is more basic, simpler or general.

In biology we can think of a few instances where science has proceeded in the "reduction" learning method. The theory that Darwin is famous for was incredible because it reduced the problem of accounting for the immense variety of species (the "mystery of mysteries") to the problem of explaining phenotype variation and its inheritance. Consider the problem of bacterial chemotaxis. E. coli move towards regions where the concentration of a desirable chemical is higher. It constitutes learning something to reduce the problem of how they do this to the problem of how they remember whether they just "ran" from an area of high or low attractant. In our lab's work, the problem of explaining incomplete penetrance of certain skn-1 mutants in C. elegans was reduced to the problem of explaining the variability in gene expression of end-1 in those mutants.

In this sense, the ultimate in learning about a phenomenon is to reduce it to pieces that are not deemed to need further reduction or to plug it into phenomena that are extremely general such as physical law. For example, reducing the phenomenon of conventional superconductivity to the electron-phonon interaction, and thus reducing it to the basic rules of quantum mechanics and electrodynamics, means that in some sense everything about it has been learned. When one gets to the point of a proof where one can write "It therefore suffices to prove that quantum mechanics is correct," one can be sure that a kind of progress has been made.

Reductions can be proved correct, and therefore guaranteed to have been a learning of something, by several methods.
- Reconstitution in biology. In molecular biology, different parts of a putative explanation can be identified with objects such as proteins that can be physically purified and put back together to reconstitute a process. Combined with experiments that delete components from a natural environment, both necessity and sufficiency can be proved.
- Conceptual reconstitution. This standard from physics is a form of reconstitution that works when the system is simple enough to think about but its reduction is impossible to physically separate into parts. You cannot, in the lab, delete an axiom or turn off Maxwell's equations and redo the experiment. Conceptual reconstitution usually involves mathematical derivation or computation. Biology is such a low-symmetry problem that we are used to entertaining the possibility of modifying or extracting one thing without changing anything else. With a few exceptions like isotope exchange experiments, physics and chemistry are relative strangers to that approach.

Some efforts do not, on their own, imply that something has been learned if using reduction as a strict requirement. To make an observation that does not distinguish between competing reductions (theories) of a phenomenon does not on its own reduce. However it may suggest to someone a new reduction. That seems to be the hope underlying many high-throughput experiments these days. Also, an observation can lead to a new phenomenon, to a question we did not even know, and that may lead to new learning. So it is unwise to always deride pure observation as a kind of shooting in the dark or fishing for questions. Superconductivity needed to be observed before it needed to be reduced. And as to what Leeuwenhoek did with his microscope, where would we be without that?

On the other hand, some might argue that observation of a new fact, not reduction, may be the loftiest goal. It does not seem right to put some explanation at a higher rank than Romer's discovery that light travels at a finite speed. Surely, this discovery was critical to the later explanation of the origin of light by Maxwell, its value appears to be partially independent of its later utility.

Feynman warns when talking about the character of physical law that: "Now such a topic has a tendency to become too philosophical because it becomes so general, and a person talks in such generalities, that everybody can understand him. It is then considered to be some deep philosophy." But it is probably a good thing for each scientist to have their own idea of what they can hope to learn by their research.

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