try to insist that *all* relevant resources be quantified, and *all* known physics taken into account.  As we will see, these straightforward ground rules have been casually ignored in some of the literature on exotic computational models.

Throughout the article, I assume basic familiarity with complexity classes such as $\mathsf{P}$ and $\mathsf{NP}$ (although not much more than that).  Sometimes I do invoke elementary physics concepts, but the difficulty of the physics is limited by my own ignorance.

After reviewing the basics of $\mathsf{P}$ versus $\mathsf{NP}$ in Section \[BASICS\], I discuss soap bubbles and related proposals in Section \[SOAP\], and even report some original experimental work in this field.  Then Section \[QUANTUM\] summarizes what is known about solving $\mathsf{NP}$-complete problems on a garden-variety quantum computer; it includes discussions of black-box lower bounds, quantum advice, and the quantum adiabatic algorithm. Section \[VQM\] then considers *variations* on quantum mechanics that might lead to a more powerful model of computation; these include nonlinearities in the Schrödinger equation and certain assumptions about hidden variables.  Section \[REL\] moves on to consider analog computing, time dilation, and exotic spacetime geometries; this section is basically a plea to those who think about these matters, to take seriously such 