The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.—-William L. Bragg
There are different types of scientific writings.
Some report on inventions: a concrete problem without known previous solution is described, then a solution is proposed, then the merits of the solution beyond the initial problem statement are discussed.
Some report on optimizations: a concrete problem and known solutions are described, then an additional solution is described, then the new solution is compared with existing solutions.
Some report on discoveries: newly observed facts are described, optionally together with new models to link the new facts to existing knowlege.
My personal favorite is the kind that reveals “conceptual holes waiting to be filled”, such as the following examples:
- Mendeleev’s proposal for a periodic table was to provide a simpler understanding of the properties of elements that were already known at his time. However, once the merits of his table were recognized, the “holes” in the table created a sort of knowledge vacuum: the symmetry of the model was strongly suggesting that new elements were waiting to be discovered for the “holes” with the properties predicted by the table’s structure. This triggered the thorough investigation and subsequent discovery of the yet unknown elements germanium and gallium.
- Similarly, while the Standard Model of physics helped organize particles that had been known/theorized (electrons, protons), its model of 12 elementary particles also created a symmetric structure that left “empty” spaces, which lead to the subsequent discovery of the predicted elementary particles, for example the muon and tau neutrinos.
The criterion to recognize such knowledge vacuum is when the work suggests a conceptual model with a regular or symmetrical abstract pattern, but only has concrete instances (examples) for some special cases. For this reason, I call this type of scientific work frustrated elements of symmetry.
These categories are not exclusive, as some writing will contain aspects of all four.
I am looking for examples of academic publications which feature frustrated elements of symmetry. If you have any suggestion, please get in touch!