The goal of this article is to encourage the serious discussion of this question.  For concreteness, I will focus on a single sub-question: *can* $\mathsf{NP}$*-complete problems be solved in polynomial time using the resources of the physical universe?*

I will argue that studying this question can yield new insights, not just about computer science but about physics as well.  More controversially, I will also argue that a negative answer might eventually attain the same status as (say) the Second Law of Thermodynamics, or the impossibility of superluminal signalling.  In other words, while experiment will always be the last appeal, the presumed intractability of $\mathsf{NP}$-complete problems might be taken as a useful constraint in the search for new physical theories.  Of course, the basic concept will be old hat to computer scientists who live and die by the phrase, Assuming $\mathsf{P}\neq\mathsf{NP}$, …

To support my arguments, I will survey a wide range of unusual computing proposals, from soap bubbles and folding proteins to time travel, black holes, and quantum nonlinearities.  Some of the proposals are better known than others, but to my knowledge, even the folklore ones have never before been collected in one place.  In evaluating the proposals, I will 