The mustard watch test for novel abstractions

A famous satire provides unexpectedly useful baseline criteria for new intellectual frameworks.

Jean-Yves Girard’s (pseudonymous) “Mustard Watches: An Integrated Approach to Time and Food” lampoons research papers that aim to justify low-utility formalisms or to introduce novel (but dubious) abstractions unifying apparently unrelated domains. The opening summary is a pretty good indication of what to expect in the rest of the paper:

The paper introduces the concept of mustard watch, a common generalisation of the concepts of watch and of mustard pot. The main property of mustard watches is that they can deliver mustard in any desired quantity (theorem 1) and still display time with a precision of 30 seconds (theorem 2). But the real superiority of mustard watches over classical ones is expressed by our theorem 3: a mustard watch with no mustard in it is at least as precise as an ordinary one.

While some of the delight of this paper is that it can be read in multiple layers, each satirizing a different aspect of superfluous (or actively counterproductive) intellectual exercises, it’s worth considering how one of the face-value claims of this paper points to useful criteria for new abstractions that were sincerely proposed:

1. does this strictly improve on all of the things it might replace?
2. if so, is it possible to demonstrate this improvement while taking advantage of the new generality?

Theorem 3 at least acknowledges the importance of the first criterion (i.e., a “degenerated” mustard watch, which contains no mustard, is at least as accurate as a classical watch). However, part of Girard’s satire is that the paper doesn’t bother to show that a mustard watch that actually contains mustard is also at least as suitable as a classical watch for timekeeping: therefore, there is no evidence that actually employing the new abstraction is feasible or useful.

More general abstractions can enable new practical systems that address formerly distinct capabilities in an elegant way, make deeper connections between other techniques more perspicuous, and expose novel implementation techniques or optimizations. However, many proposed abstractions don’t do these things, or convincingly argue that they are strictly more general than the abstractions they aim to replace, or demonstrate that they are actually useful in their full generality or in practical contexts.

Any new abstraction that isn’t at least as well-motivated as a mustard watch probably isn’t worth further consideration.