The Unbearable Slightness Of Being"For producing everything out of
nothing, one principle is enough"
The fundamental dichotomy between existence and non-existence, then, needs to be reformulated. The reformulated contrast lies between, on the one hand, something supposedly being the case that didn't cancel out - what might be named "free-standing" or substantive existence - and, on the other hand, something whose properties, in conjunction with everything else, do strictly cancel out/add up etc to (or are strictly equivalent to, and thus intersubstitutable with, etc.) 0. This is what it takes for 0 to be the case: an explication of what is entailed by the hypothesised logical impossibility of anything existing other than the universal manifestation of zero properties. The research program outlined here would be experimentally refuted if anything at all were found that didn't - in a sense still to be properly elucidated - sum to/cancel out etc to 0; and if the whole universe didn't itself subsist in a single pure 'entangled' state - an unimaginably vast superposition of alternative histories whose properties cancel out precisely to zero. On this conjecture, in the great majority of the quasi-classical branches of the Multiverse the properties of the world only approximately cancel to 0; but this mere approximate cancellation - as manifested by 'anomalous' microscopic quantum interference effects / 'spooky' EPR correlations - is a physical expression of the strict cancellation of properties to 0 in the Multiverse as a whole.
As it is sketched out so far, the zero ontology admittedly leaves scope for ad hoc manoeuvres, get-out clauses and dubious auxiliary assumptions. But it also places an immensely restrictive requirement on what can, and what can't, be properties of the world. This strategy amounts to pushing the mathematics as far as it can go. Yet it certainly doesn't stem from numerological dogmatism, mystical pi-in-the-sky Platonism, or a superstitious reverence for occult formalism for its own sake. It's simply that, so far at least, numerically encoding everything has seemed unfailingly to work. It thus presumably provides a clue - perhaps admittedly a deceptive clue - to the nature of Reality. Pursuing the strategy of bringing existence itself within the realm of mathematical science makes good sense in the absence of any better idea to the contrary. Time and again, progress in theoretical physics has been delayed in consequence of not taking the equations seriously enough. Admittedly, the cosmic(!) significance ascribed to the formalism here amounts - in seemingly ludicrous degree - to the secular apotheosis of mathematical literalism. Yet pushing a theory to its limits until it breaks down, in this case the meta-theory that mathematics can be used exhaustively to encode the world, has been an immensely fruitful strategy in science throughout its recent history. So it could well be worth pressing to its ultimate conclusion.
The mathematization of the world also offers a reassuring corrective to Hilary Putnam's pessimistic meta-induction about the whole scientific enterprise. Putman notes that by current lights (on purely descriptivist theories of reference, at least) previous putatively referring terms have failed to do so. Therefore [granting for our purposes here the epistemic legitimacy of induction] our own linguistic terms probably suffer reference-failure too. This sceptical meta-induction is most plausible when applied to successive, ground-level physical ontologies. (e.g. classical physics works/worked astonishingly well; but its fundamental ontology was just plain wrong). Happily, Putman's meta-induction is least tenable when (mis-)taken to embrace the extravagantly good incremental progress shown in deepening and unifying our mathematical description of the natural world - and the unbroken run of technological successes that this theoretical apparatus has allowed.
In fact, the potential for understanding the world that maths offers cuts both ways. A comprehension of the fundamental mystery would change our understanding of the nature of mathematics too, both substantively and in our emotional response to it. For if we understood specifically how mathematics precisely and non-arbitrarily numerically encodes our pleasures and pains, for instance, and every texture of our lives and loves, then mathematics as the universal scientific discipline would seem as emotionally absorbing as a good novel. This intimate relevance stands in contrast to how mathematics strikes all but the cognoscenti of mathematical aesthetes at present, namely as a sterile realm of timeless abstraction. But possibly only if we understood how mathematics encodes the precise texture of every experience, and its structural relationship to every other experience, could we really understand either mathematics or physics or consciousness. For if it is assumed that the values of what-it's-like-ness are exhaustively numerically encoded by (and could in principle be "read off" from) the quantum field etc -theoretic equations, then on the basis of the proposals mooted here, the values of what-it's-like-ness themselves express (in some presently unfathomable sense) the truths of mathematics. Precisely.
Perhaps the ubiquitous scale-invariant conservation of 0 even explains the "unreasonable effectiveness of mathematics" in the physical sciences (and also, if only we understood how to do it, everywhere else). For why is maths true?; or (in deference to the nominalist) why at least should the application of [a recast canonical part of] mathematics to the world yield predictive accuracy indistinguishable from precise truth? (This more cautious formulation reflects how, for instance, Darwin showed how Nature could simulate design with often uncanny verisimilitude by mere causal process. Mathematics apparently models the world more tightly than Nature mimics function - indeed one assumes that the mathematical formulation of a "Theory Of Everything" will attest it does so homomorphically - but this doesn't of itself show that abstracta must, or even can, be reified). Well, perhaps the answer to why maths is true is that if mathematics weren't applicable precisely and homomorphically to the world, then some substantive, free-standing and unneutralised existent or property could be the case. Maths has to hold good universally on pain of some 'uncancelled' object, event or property existing that needs to be explained - which would thereby open up an impossible explanatory regress. All the equations of mathematics, and 0 itself, on this surmise at least, are variant and derivative expressions of this same conceptually powerful principle, which is bound up with the very notion of an equation. Likewise, to ask a related question, why are symmetry principles the key to physics? Well, because if precisely 0 must ubiquitously obtain, then all changes can only be interconversions of 0. Anything other than 0 would leave the values of the fundamental constants of Nature as arbitrary inexplicables to be "put in by hand".