The Riddle of Existence

Section One


The Zero Ontology


What is the connection between:

1. One's a priori intuition that there's no conceivable reason, or even explanation-space, for why anything at all exists. [This powerfully felt preconception is hard to express in natural language without spuriously reifying ("turning into a thing") non-existence or Nothingness i.e. asking "Why isn't there Nothing rather than Something?" and thus running the risk of lapsing into Heideggerian obscurantism. But see below].

2. The quantum-mechanical wave-function of the Universe, the allegedly exhaustive formal description of the world, encodes how everything that physically can occur/exist does occur/exist with some density or other. Taken literally, this increasingly popular and deceptively "anything-goes"-sounding interpretation of the quantum formalism actually rules out all of the world's traditional cosmologies. This is because of their varying degrees of disguised internal inconsistency. Post-Everett "no collapse" interpretations of QM exclude a lot else besides. For Universal QM is far less permissive than it sounds in some ways. Yet tragically - at least to my negative utilitarian mind - its entailment of googolplexes of hell-branches means it is horrifically more prolific in others.

3. In the Universe as a whole, the conserved constants (electric charge, angular momentum, mass-energy) add up to/cancel out to exactly zero. There isn't any net electric charge or angular momentum. The world's positive mass-energy is exactly cancelled out by its negative gravitational potential energy. Provocatively, cryptically, elliptically, "nothing" exists. [What is so special about the conserved constants? Will everything internal to the universe, and analogously everything internal to black holes, turn out to be derivable from the conserved constants; and thus, in a sense to be explicated, be derivable from the properties of zero?]

4. Black holes:

  • have [possible complications aside] "no hair". From an external observer's perspective, they are simply and exhaustively characterised by the conserved constants (internally, on the other hand, they may possess all sorts of properties, e.g. Shakespeare-loving infalling astronauts; you and me?).

  • ultimately evaporate via Hawking radiation to 0, or something akin to 0(?).
5. The universe can itself be treated, contentiously, as a black/white hole (?? omega = 1, the critical value) Does the universe evaporate "hairlessly" backward/forward to 0???? ) [Notes: some non-standard physics: Are the Big Bang and Big Crunch not just type-identical(?), but token-identical?? Is the Big Bang a black hole evaporating??? If the expansion of the universe isn't really accelerating, does the universe have an event horizon in our distant future/past when the (cold) universe (omega=1) is at maximal volume, eventually decaying via Hawking radiation? Are all time-like and space-like paths closed, entailing that spooky EPR correlations aren't really non-local?? Does the Multiverse 'expand' symmetrically both "backward" and "forward" in time from/to its final/initial low entropy condition (?) - granted that the entropy of a (universal?) black hole is given by the logarithm of the number of microstates consistent with the area of its shrinking/expanding event horizon?]

6. Mathematically :

  • 0 can/must be construed as (a condition akin to our conception of?) a number.

  • The whole of mathematics can, in principle, be derived from the properties of the empty set, Ø. [Since Ø has no members, in the standard set-theoretic definition of natural numbers it can be identified with the number zero, 0. (this is still problematic; should 0 be regarded, not as the empty set, but as the number of items in the empty set? And what's the ontological status of the empty set?)] The number 1 can be defined as the set containing 0, i.e. simply the set {0} that contains only one member. Since 0 is defined to be the empty set, this means that the number 1 is the set that contains the empty set as a member {Ø}. The number 2 can be understood as the set, {0, 1}, which is just the set {Ø, {Ø}}. Carrying on, the number 3 is defined to be the set {0, 1, 2} which reduces to {Ø, {Ø}, {Ø, {Ø}}} Generalising, the number N can be defined as the set containing 0 and all the numbers smaller than N. Thus N = {0, 1, 2 ...N-1} is a set with N members. Assuming only the concept of the empty set Ø, each of the numbers in this set N can be replaced by its definition in terms of nested sets. Proceeding to derive the rest of maths from the properties of the natural numbers is more ambitious; but it's conceivable in principle. All that then remains to be done is to explain the empty set i.e. why (a condition analogous to our concept of) the empty set must be the case]

  • The existence of any number, in virtue of its properties, entails the existence of all the others i.e. a system of mathematics couldn't exist bereft only of the number, say, 42; and the existence of any number, in virtue of the full set of its properties/structural relationships, entails the existence of every other number. Thus there aren't any "atomic" facts in mathematics. Given further that mathematics [Gödelian complications aside] exhaustively and uncannily encodes the world (Wigner's "unreasonable effectiveness" of mathematics in the natural sciences), then perhaps there aren't any "atomic" facts about the world either. The properties of any one thing [0?] entail the properties of all the others.

  • Insofar as they are well-defined, the summed membership of the uncountably large set of positive and negative numbers, and every more fancy and elaborate pair of positive and negative real and imaginary etc terms, trivially and exactly cancels out to/adds up to 0. Alternatively: the sum of all infinities - starting at negative infinity and going to positive infinity - is zero. [actually, since there are powerful arguments that the subtraction of same-size infinite cardinals is not defined, any 'cancellation' isn't really trivial. Platonic abstracta are pathological beasts.] Immanent in 0 is their strict equivalence and consequent intersubstitutivity. (link to Everett?? Net energy etc of Multiverse = 0 = all possible outcomes) [Yet why not, say, 42, rather than 0? Well, if everything - impossibly, I'm guessing - added up/cancelled out instead to 42, then 42 would have to be accounted for. But if, in all, there is 0, i.e no (net) properties whatsoever, then there just isn't anything substantive which needs explaining.]
NEXT: Section 2