(Cross-Posted from PowerUp.)
Michael Shermer's latest column in Scientific American deals with artificial rankings of importance among the sciences from "hard" to "soft", and science writing from "technical" to "popular". I have to say I agree with the overall thesis that these rankings are rather artificial and not totally necessary. But that said, I don't agree with the way Shermer challenged the notion. When given the choice of how to do so, I can imagine two broad classes of options:
1. Make the modest, non-grandiose and largely accurate suggestion that the ranking system is flawed because all scientific knowledge is important and all disciplines deal with problems of varying complexity and difficulty; Or,
2. Propose a new ranking system that makes the extravagant, grandiose and gobsmackingly stupid claim to "precisely reverse" the order, making the social sciences the hard sciences and the physical sciences total weaksauce. (Giving lip-service to option #1 is also optional.)
Now to unveil Shermer's decision:
I have always thought that if there must be a rank order (which there mustn’t), the current one is precisely reversed. The physical sciences are hard, in the sense that calculating differential equations is difficult, for example. The variables within the causal net of the subject matter, however, are comparatively simple to constrain and test when contrasted with, say, computing the actions of organisms in an ecosystem or predicting the consequences of global climate change. Even the difficulty of constructing comprehensive models in the biological sciences pales in comparison to that of modeling the workings of human brains and societies. By these measures, the social sciences are the hard disciplines, because the subject matter is orders of magnitude more complex and multifaceted.
I'm sure that Blake and the rest of his physics friends will be glad to hear how “simple” constraining and testing a theory of quantum gravity is. But in the field of my pursuits, computer science, one would think it would be even easier. After all, physicists have to deal much more directly with the constraints of physical systems. We deal with abstract problems, abstract units of reduction and abstract models within which said problems are subordinated to feasible computations. Yet we still lack a rigorous proof that P != NP, that there exist one-way functions, or even that NP-complete problems would be approximately as hard for quantum computers as they are for classical computers. We don't even know how we would go about rigorously proving any of these assertions. Even the central principle of computer science, the Church-Turing thesis, lacks a rigorous axiomatization from which we could prove it, leaving it at least somewhat open to revision. A stronger version of the CT thesis, which posits that any Turing equivalent computing device generates the same problem classes as any other, is strongly called into question by the existence of polynomial-time quantum algorithms for factoring integers and solving various hidden subgroup problems (e.g., discrete logarithms).
“Simple”, indeed.
And not to nitpick, but Shermer's use of calculating differential equations as an example of a hard problem is in my mind exceedingly poor. You encounter differential equations by second semester calculus at the latest, so I would call them an intermediate topic. Or if I could have some wiggle-room, I'd call them a topic of varying difficulty. We still haven't proven the universality of Navier-Stokes in three dimensions, nor global regularity (e.g., no jumps of discontinuity) in the case that solutions in such dimensions always exist.
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