Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Do Infinite Worlds Believers Buy Lottery Tickets?
Some of the philosophic problems with infinite nature positions
Scientific American recently sent a special mailer about many worlds QM and infinite universe theories. While splashy and well laid out, and in some places reasonably interesting speculative stuff, it struck me that it would be more appropriate if it had come from a magazine called Metaphysical American. Which is certain to exist in the alternate world over that-away if you just go far enough. If you let “certain to exist” mean something other than what the words obviously say in ordinary English usage, anyway, as those theories do.
At one point in the reasoning, large-scale uniformity of (suitably coarse) structure of matter (or in this case, the lack thereof) is presented as evidence that the universe is infinite in all directions in ordinary space-time (a hardly novel position, incidentally, that dates at least to Epicurus). Sometimes in science we legitimately employ heroic induction, to extrapolate apparent laws to regions unknown. But in this context, this move struck me as more of a heroic non sequitor.
The universe might be finite but growing forever, twice its visible size and mostly uniform in all directions at sufficient scales. It might have had an intricate nested structure with characteristic scales and detailed patterns, that repeat infinitely in “tiles” across infinite reaches. (Whether that is consistent with observations depends on the scales posited). It might even be clumped into balls that look like island universes in empty space (as Kant thought, a forerunner of what we now know about galaxies), but then have these balls within cells that tile that space on a spatial scale millions of times larger again. As bare abstract possibilities, there is no connection between presence of spatial structure on observable scales, and infinite or finite extension. They are orthogonal questions, all four possibility boxes are occupied. Patterned locally or not, either is compatible with finite size or infinite size.
What is actually happening is a subtle instance of the straw man argument. A weak position for a particular finite universe theory is constructed, (strictly, finite positioning of matter within a universe that might or might not also be finite in space) and (weak, merely suggestive) evidence against it is then extrapolated into evidence against any finite universe theory. If we saw observable matter visibly peter out into rarified emptiness at large distance scales, that would be observational support of an island “universe” – without ruling out the abstract possibility of many separate islands far beyond the observable scale.
Notice that being consistent with hypothetical possibilities beyond the observable scale is not a requirement for any theory. We would say the data are consistent with an island universe. Can we say, because instead we see uniformity, that the data are not consistent with such a universe? No. We can only rule out a characteristic scale below some threshold.
An historical parallel might be of some interest. Aristarchos of Samos hit upon the correct hypothesis that the earth orbits the sun while also rotating, accounting thereby for the apparent motion of the heavens and the seasons. Aristotelians countered that if he were correct, there ought to be parallax in the apparent positions of the fixed stars, over the course of a year. In fact there is such parallax, but the stars are far enough away compared to the base line created by the earth’s orbit, that it is very small, so small it was only successfully measured in the 19th century.
Aristarchos noticed the possibility and countered the argument against him, but with a poor formulation of his case. He said there would be no parallax if the fixed stars were infinitely far away. He didn’t say, “very far”, he said “infinitely far”. Geometrically true, but physically nonsense. The Aristotelians said he was positing an “actual infinity” and dismissed the correct cosmology on the basis of that supposed no-no.
The Aristotelians had rafts of such dos and don’ts, which managed to constrain them to physical positions that were completely wrong. But they had arguments for each one, passed on to them by the prestigious codifier of logic. They easily convinced themselves anybody who differed on any one was just an incompetent reasoner, insufficiently up to speed on the “math” of the day. Scads of much more modern sounding positions were meanwhile found and formulated by looser speculators, sneered at by the cognoscenti – atoms, inertia, objective chance, the solar system, equivalence of earthly and celestial matter, an origin of the visible universe in time etc.
In fact the argument did deserve to be dismissed, but not for that reason. Aristarchos had reacted to a piece of observational data that did not fit his theory, by an extraneous additional hypothesis that taken literally rendered his theory untestable. Instead of boldly predicting there would be parallax or his theory was wrong, he immunized his theory against empirical falsification on a critical point, precisely where his opponents’ case was strongest.
The stronger argument and the truth do not necessarily coincide. Men do not always formulate their arguments in the best way possible, and even when they do, the critical evidence may simply be missing. Making an argument harder to refute in argument is not the same as improving it as a theory. It is harder to know the truth than it is to argue rationally. Rational argument does not of itself produce agreement with others possessing the same evidence, let alone agreement with the truth (a much higher standard – we know precious little). Rational men will disagree on hard questions.
One moral is that speculation cannot be outlawed from rational investigation. But another is that little is decided by shooting down a weak form of an argument contrary to one’s own position. It is the strong form that must be considered. Ideally, we want the strong forms of all the arguments before us as a spectrum of plausible positions.
There is another problem with the inference from uniform observed matter to a supposedly infinite universe, however, that leads to my labeling it a heroic non sequitor. Suppose the infinite universe theory is correct. Then there must be any number of regions in which the distribution of matter differs from the uniformity seen on visible scales, unless some additional positive law supposedly forces uniformity on those scales. In the latter case, observed large-scale uniformity is evidence for that law, not for what sort of universe it occurs within. Leaving that nuance aside, any observed distribution of matter is consistent with an infinite universe in which all physically possible distributions of matter over such scales, occur somewhere. X is not evidence for Y if the truth of Y does not imply the existence of X.
The reason the writer obviously thinks that it is such evidence, is he is invoking an unstated additional minor premise. He thinks his infinite universe would be uniform on large scales “mostly”, with the regions differing from uniformity rare, perhaps measure zero exceptions in a sea of uniformity. (He also implicitly assumes the bit of the universe we can observe is enough to qualify as “large”. In a strictly infinite background, this is arbitrary. It might take something a trillion times larger to qualify as more than miniscule, for whatever the relevant physical laws might be). He is appealing to the principle that what we can observe is not to be taken as special, but as indicative of whatever else we cannot see.
This is ordinarily a sound inductive principle, though not logically necessary (meaning, it can easily be wrong but it is OK as a first guess). But it has peculiar weaknesses in the hands of those stumping for an infinity of possibilities we even in principle cannot see. His overall position, after all, is not only that anything can happen but that everything does. To deduce from this as a supposedly necessary consequence, that (almost) everything we don’t see must look like what we can see, is simply inconsistent reasoning. “Anything we don’t see must still happen”, is a necessary consequence of the position he is arguing for.
It is philosophically possible that everything happens, we can consider it speculatively. What we can’t do is argue that because everything happens, things must happen exactly this way rather than that way. The principle of non-specialness has lost its moorings. The basis of that principle is a pragmatic belief that what we have already seen results from some internal necessity, which we consciously choose to expect to continue, until events teach us otherwise.
I don’t know whether those scientists enamored of such theories recognize the transfer of explanatory responsibilities they are engaged in. When physics decides to tell us that everything happens somewhere, it does not reduce what remains to be explained. It simply exports the explanatory problem. Rather than ask what the universe I live in will do in the next five minutes, one is instead left with the equal puzzle, what universe my consciousness will be experiencing five minutes from now. The answer “all of them” is falsifiable, and false.
A theory may deterministically deduce the branching trajectories of a billion possible universes per nanosecond, but if all it can tell me about which branch I will experience is “who knows?” then it simply is not explaining experience. It is instead explaining the temporal development of a hypothetical construct, with tiny projections onto experience, which makes contact with it on a set of measure zero. It is not explaining overworlds of possibility; it is simply failing to explain experience, leaving that to somebody else.
Note that denying that it is possible to explain any further is equivalent to leaving the explanation to somebody else; it has no further content, as a claim. The epistemic bar anyone else has to clear is unchanged. They need not even take notice of the previous theory. They can either explain experience or they can’t.
Here are two plausible alternate cosmologies, and my claim is that the infinite world types cannot point to a place where they make claims that are both falsifiable and distinguish their theory from either of these. They may make falsifiable claims that coincide with either. They may make claims that differ from either of these, without being falsifiable. But the challenge is to state claims that are consistent with infinite worlds, inconsistent with either of these, and observationally falsifiable.
Alternative one I call objective indeterminism. QM accurately describes the world, and there is nothing more basic underneath it. Indeterminacy in QM formalism reflects actual indeterminacy in the world, metaphysical chance. Some one thing happens, and which it is, is completely uncaused. The material universe is finite in space and to date in time, though it may be open ended in either extension in the future direction – consider that an empirical question and as yet unknown. It might even be objectively undetermined up to now (consistent with the basic outline of this view – i.e. it might depend on an uncaused future event), though I doubt that.
Alternative two I call non-local emergent determinism. There is some underlying non-local deterministic generator beneath QM (perhaps at quantum gravity scales, perhaps smaller still), and QM is an emergent coarse-grained property of that underlying system and its currently observable statistical regularities. The underlying system is objectively non-local in the emergent space-time that it generates - all the action at a distance you might want to get around Bell’s theorems. Things that happen here and now really depend on things that happened there and then, and you can’t isolate them in a small ball around either. The material universe is strictly finite, as are its underlying possible states. It is also irreducibly complex, limiting prior predictability of its details. The trajectories the universe would follow from slightly different underlying states might be as distinct as you please, which might result in limits on observational knowns, but one trajectory is the one the universe is actually on.
Each of these positions is clearly distinct from infinite worlds. They are also clearly distinct from each other. Each predicts we will find different things to be true within physics, beyond what we already know. Neither tells us that anything we could find will be consistent with it, and will only alter in tiny ways where we are to consider ourselves to be in some cosmic probability distribution that realizes everything, somewhere. To my mind, that means both are much more robust philosophically speaking. They are trying to say more about the world.
Scientists must be free to speculate. Speculation is valuable because guessing is essential to finding the truth, which can lie beyond men’s present imagination and beyond what their present evidence may make plausible. But if they wave their hands and say anything can happen and probably will, it is not the most impressive use of that freedom.
Philosophically, it is trying to avoid being wrong, when the point is instead to risk being wrong. Tell us which world you think we will live in, and if you are wrong about it, iterate on the guess. Don’t tell us instead that there are a lot of guesses and some of them are bound to be right, someplace. It is not important to avoid error. Error is good for you, and it is man’s natural state whether he likes it or not. It is important for your theories and your convictions to make contact with the world.
The American pragmatist Charles S. Peirce defined belief as the willingness to stake much upon a proposition. You can tell whether a man is giving you his honest opinion or “just jawing”, by whether he is willing to back his statements with his actions. Note that this is only a test of psychological honesty, not of truth.
Do those attracted to infinite worlds theories buy lottery tickets every chance they get, to enjoy their riches in those universes in which they win? Right, in some worlds they do and in others they do not. But that doesn’t answer the question, it just reformulates it. Which sort of world are we in, one where they’ll believe in Peirce’s sense in anything, or one in which they are covering lacunae within their theories by just jawing?
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