Edge.org often posts intriguing questions. A pretty large cross-section of scientists and other thinkers then post their answers. The most recent question is: What scientific concept would most improve everyone’s scientific toolkit?
I’m not thrilled with the phrasing, but the answers are quite interesting. Three of my favorites were
Starting with the last one first, on the one hand, this is pretty obvious. On the other hand, I do think it is widely underappreciated! Part of the goal of the course I teach at Columbia, Frontiers of Science, is to equip our first-years with some of the most basic tools that scientists use all the time so that they can apply them broadly.
Now, duality is a great answer. It’s one of the most fascinating things nobody in the broader public really knows about. The earliest examples of duality—in the sense meant by Amanda Gefter—came from studying idealized physics models in two dimensions (one space, one time). These are rather near-and-dear to my heart since my PhD studies focused on these types of models. The key idea here is that two radically different physical theories can actually be descriptions of the same underlying system. Read the Edge.org page for a bit more…I actually think it’s about time I wrote something discussing duality myself. Hopefully I can do so in the near future.
Finally, the philosophical concept of “supervenience” is a great choice that more people should know about. It’s a rather rigorous way of formulating the intuition that “higher level” things rest on “lower level” foundations. For example, an object’s temperature is a higher level property that arises from the random jiggling motion of the atoms that make up the object. The key point is that the precise way that the jiggling happens doesn’t really matter since the temperature is a sort of averaging out. However, if the temperature of the object changes, this inevitably must be reflected at the level of the jiggling—in particular, if the object gets hotter, the jiggling gets more violent. We say that the temperature supervenes on the underlying motion of the atoms.
There seems to me to be a tension between the notions of duality and supervenience. To say something supervenes on something else implies that the something else is more fundamental—in fact, it could be taken as a definition of what it means to be more fundamental. However, one implication of duality is that fundamental entities in one description of the system actually become non-fundamental in the other. In other words, fundamentality is a property of how you describe the system. Now, there may be some systematic way of choosing which description is best in a given circumstance, but as far as I can tell, that doesn’t really get you around the problem. I haven’t seen anyone try to tackle this meaningfully…