Which is to say, I think there is a big problem in teaching people (biologists, at least) to think up hypotheses. In that, the reasoner knows the final product must be of some non-trivial complexity, in the colloquial sense of the word, but that he isn’t really allowed to put forward anything too complicated, because it’s too easy to imagine a just-so story. (So now I will imagine myself a just-so story, because duh.)
One way to tinker with research is to think of your tools, whether material or mathematical, as part of the picture instead of the brush and paints that nobody displays at the exhibition. For example, people who compare methods for staining plants’ roots for fungi see that the results are different and wonder what that tells about the physiology of the root as a whole; the relationship of the dye and the cytoplasm may depend on pH, and there comes a point when one can swear the difference in pH must be the property of the cytoplasm and not of the procedure of staining. From this, one may assume that the acidity of the cells changes depending on the development of the mycelium inside the root (and the age of the root, and other things); but why, exactly?… And then, comparing modifications of the methods and knowing at least the chemical structure of the dye, one may build hypotheses about the underlying physiological processes.
It’s hard to view, for example, scanning electron microscopy (or something comparably multi-stage) as an “alien artefact in the world” rather than “a great big thing that by the good will of its operator lets me see the surface of very small things”, but I think that such approach might be fruitful for generating hypotheses, at least in some not-too-applied cases. There must be fascinating examples of mathematical tools so toyed with. I mean, almost (?) all that I have read about math that was interesting for a layman, was written from this angle. But in school and college, they go with the “great big things” approach.
(hash tag ramblingasalways)
Which is to say, I think there is a big problem in teaching people (biologists, at least) to think up hypotheses. In that, the reasoner knows the final product must be of some non-trivial complexity, in the colloquial sense of the word, but that he isn’t really allowed to put forward anything too complicated, because it’s too easy to imagine a just-so story. (So now I will imagine myself a just-so story, because duh.)
One way to tinker with research is to think of your tools, whether material or mathematical, as part of the picture instead of the brush and paints that nobody displays at the exhibition. For example, people who compare methods for staining plants’ roots for fungi see that the results are different and wonder what that tells about the physiology of the root as a whole; the relationship of the dye and the cytoplasm may depend on pH, and there comes a point when one can swear the difference in pH must be the property of the cytoplasm and not of the procedure of staining. From this, one may assume that the acidity of the cells changes depending on the development of the mycelium inside the root (and the age of the root, and other things); but why, exactly?… And then, comparing modifications of the methods and knowing at least the chemical structure of the dye, one may build hypotheses about the underlying physiological processes.
It’s hard to view, for example, scanning electron microscopy (or something comparably multi-stage) as an “alien artefact in the world” rather than “a great big thing that by the good will of its operator lets me see the surface of very small things”, but I think that such approach might be fruitful for generating hypotheses, at least in some not-too-applied cases. There must be fascinating examples of mathematical tools so toyed with. I mean, almost (?) all that I have read about math that was interesting for a layman, was written from this angle. But in school and college, they go with the “great big things” approach. (hash tag ramblingasalways)