Causal loops, infinite regresses, and information

On a reader’s recommendation, the wife and I took in the 2007 Spanish science fiction movie Timecrimes last weekend. Great flick. It’s a time travel story similar in structure to Heinlein’s “By His Bootstraps” (which I discussed in a recent post), though the plot is very different. Hector, the movie’s protagonist, spies through his binoculars a woman removing her shirt in the woods beyond his house. After going out to investigate, he comes upon the woman lying naked and motionless, and is then suddenly stabbed in the arm by an attacker whose head is wrapped in bloody bandages. (Since this is a family blog of sorts, I suppose I should alert the unwary viewer lest he be temporarily blinded by the rather bright pair of headlights that appears onscreen a couple of times, and I don’t mean the ones on Hector’s car. Good thing my wife was there to shield my eyes!)

If you haven’t seen the movie and don’t want it (partially) spoiled for you, don’t read any further. Fleeing through the woods in a panic, Hector stumbles upon a laboratory complex and makes his way inside one of the buildings to hide from his attacker. After bandaging his arm, he finds a walkie-talkie and makes contact with a scientist in another building on the grounds, who tells Hector that he can see his attacker approaching the building Hector is in and urges him to exit at the other side and make his way to where the scientist is. When he meets up with the scientist, the latter convinces Hector to hide inside a strange machine, which turns out to be a time machine. Hector is transported an hour or so into the past and – you guessed it – through a complex series of events it is revealed that the bandaged man who attacked him earlier was none other than Hector’s future self. And that’s just the beginning of the story’s Heinlein-style twists.

Now, one traditional objection to the possibility even in principle of time travel is that it would seem to entail that one might travel back in time and kill one’s younger self. This seems obviously impossible, for if one killed one’s younger self, then one would no longer be around at the point when one was supposed to be entering the time machine in order to go back and carry out the killing. In response, it is sometimes suggested that such paradoxes can be avoided by appealing to the “many-worlds” interpretation of quantum mechanics and construing the scenario in such a way that your killing of your younger self results, not in the annihilation of the version of you who goes back and does the killing, but rather in the branching off of an alternate universe in which another version of you does not live past the time in which your future self kills you (though of course you do live past that time in the universe from which this new one branched off, which is why you can travel back to do the killing).

This assumes, though, that we should be thinking of time travel as a way in which one might change the past. And of course, many time travel stories do make this assumption – Ray Bradbury’s short story “A Sound of Thunder” is one example, and the Back to the Future series of movies are another. But other time travel stories work on the assumption that the past is fixed, and that even if one travels back in time and tries to change the past, one will find that one’s circumstances do not allow one to do so – indeed, the time traveler will himself turn out to be the cause of certain past events, perhaps even the events he hoped to change. The Heinlein stories cited in my previous post on this subject work on this assumption, as do movies like 12 Monkeys and Timecrimes. In Timecrimes, Hector takes pains to ensure that certain past events happen exactly as he remembered them, and while trying to prevent certain other past events from occurring, he finds that he has inadvertently caused them to happen precisely in the attempt to change history. In 12 Monkeys, Bruce Willis’s time-traveling future self turns out to be the man he had, as a young boy, witnessed getting shot in an airport. The sex-changing time traveler in Heinlein’s “—All You Zombies—“ is his/her own father and mother. In “By His Bootstraps,” Heinlein’s protagonist is manipulated by his future self into becoming that future self.

Now, paradoxes of the sort represented by the suicidal time traveler are avoided on this sort of scenario. But other oddities replace them. For example, Hector makes his way into the woods, thereby setting out on his time-traveling adventure, only because he saw a woman there removing her shirt. But it turns out that she was removing it only because Hector’s future self forced her to, precisely so as to guarantee that his earlier self would see her. Jane in “—All You Zombies—“ is born because his earlier, female self was impregnated by his later, male self. But those later selves only existed in the first place because Jane was born. In “By His Bootstraps,” Bob Wilson learns a heretofore unknown language from a notebook that he takes from the future and later recopies after it wears out. But it turns out that the notebook he had taken was none other than a future, still unworn stage of the very copy he had made of it.

None of these cases involves the kind of contradiction seemingly entailed by the suicidal time traveler example. But they do involve a kind of circularity. Is it vicious? Some theorists of time travel seem to think not, or at least allow that such scenarios are in principle possible in a way the suicidal time travel scenario is not (short of the “many-worlds” interpretation, that is – though even then, it seems it is not really himself that the time traveler kills, but only an alternate version of himself). And yet there is obviously something very fishy about these scenarios. It is perhaps easiest to see what is wrong in the notebook example from “By His Bootstraps”: The earlier stage of the notebook came from the later stage, and the later from the earlier. But what about the information embodied in the notebook? Why did the notebook have just the content it did, rather than some other content or no content at all?

But something similar can be said about the other cases. Hector’s later self knew from memory that the woman would be visible to his earlier self from precisely such-and-such a spot in the woods, and therefore took steps to make sure that she would stand there. But his earlier self, because he had acquired the information about her location from observing where she was standing, was able to form those memories only because his later self had had the information in question. So why was it precisely that information about her location that got transmitted from the past to the future and then back to the past? Jane’s genetic information came from his/her “mother” and “father,” but they are really just later versions of her. So why was it exactly that genetic information that gave Jane his/her distinctive biological features? Why did Jane have that specific height and hair color, those specific behavioral predilections, and so forth – indeed, why was he/she a human being at all rather than a dog, or a blade of grass, or something inorganic? It is because we need an account of the informational content of these temporally looped events that merely noting that each event was generated by another is insufficiently explanatory.

Now, notice that exactly the same point applies, even if perhaps less obviously, when we consider an infinite regress of events into the past rather than a temporal loop. In “On the Ultimate Origination of Things,” Leibniz notes that if we were told that a certain geometry textbook had been copied from an earlier copy, that one from an earlier one still, that one from a yet earlier copy, and so on infinitely into the past, we would hardly have a sufficient explanation of the book we started out with. Moreover, why does the series of books as a whole exist, and with precisely the content they have rather than some other content? Tracing the series of causes backward forever into the past seems to leave the most important fact about the phenomenon to be explained untouched, no less than the time travel causal loop scenarios do.

Such time travel scenarios are philosophically significant, then, insofar as they illustrate how fatuous is Hume’s suggestion (made in the course of criticizing cosmological arguments) that identifying the immediate cause of each thing or event in some series of things or events suffices to explain the series itself. This is obviously insufficient in the time travel case, and there is no reason whatsoever to think it sufficient in the infinite temporal regress case. Even if time-travel-generated causal loops were possible in principle, we would still need to appeal to something outside them in order to account for the specific information content that is passed from link to link in the loop. And even if an infinite regress of causes into the past were possible in principle, we would still need to appeal to something outside of it in order to explain the specific information content that is passed from one link to another throughout the infinite series.

But is the example of Leibniz’s book misleading? Do series of causes in the natural order, where books and other artifacts are not in question, really involve transfers of information? Indeed they do. As the Aristotelian-Thomistic (A-T) metaphysician holds, each efficient cause inherently points beyond itself to its typical effect or range of effects, the generating of which is its final cause; and when this efficient causation involves the generation of a new substance, that substance will have causal powers of its own, and it will have inherited them from its causal ancestors. The “information” concerning the outcomes to which such causal powers point exists at each stage of the lifespan of each entity which has the powers, and it is transferred to each new substance which has the same powers. But you don’t need to be an A-T metaphysician or to use such Scholastic language to see that there are such transfers of information. It is evident also from the work of contemporary anti-Humean metaphysicians and philosophers of science like C. B. Martin, John Heil, George Molnar, Brian Ellis, and others, who advocate a metaphysics of causal powers which are “directed at” their manifestations (which is just what the Scholastics meant by final causality, whether all of these contemporary writers are aware of the parallels to Scholasticism or not). And it is evident from the “information” talk that contemporary physicists, biologists, and “naturalistic” philosophers are constantly helping themselves to – even though such talk is intelligible only if the natural world is not after all devoid of inherent “directedness” or finality, as the early moderns who overthrew Scholasticism are widely but falsely thought to have shown that it is.

(As my longtime readers know, this is not to deny that the early moderns made genuine scientific advances. The point is rather that their philosophical novelties were disastrously wrong, and the physicists, biologists, and anti-Humean metaphysicians and philosophers of science just alluded to are in effect reinventing the metaphysical wheel that Aristotelians and Scholastics had already perfected centuries ago. That more people don’t see this owes to (a) a failure to distinguish Aristotelian physics, which was refuted by the moderns, from Aristotelian metaphysics, which was not, (b) an uncritical acceptance of various anti-Scholastic clich├ęs and straw men, and a consequent failure to understand what Aristotelians and Scholastics really mean by “substantial form,” “final cause,” and the like, and (c) a vested interest in upholding the historical myth that Scholastic metaphysics – and, more to the point, the theological system it upheld – were somehow undermined by modern science. But that is a story I’ve told at length elsewhere, most notably in The Last Superstition.)

Of course, ID theorists have tried to make hay out of the idea that there is information in the natural order, but they muddy the metaphysical waters by talking about “probabilities,” “complexity,” “specified information,” and the like. The point has nothing to do with such hoo-hah, nor with either rejecting or accepting Darwinian accounts of this or that biological phenomenon. It is at once much simpler, much deeper, and more conclusive than all that. Nor is it some lame anthropomorphic “designer” or other that an explanation of the information embedded in nature requires. In fact it requires nothing less than the God of classical theism. That, at any rate, is what the Thomistic “argument from finality” represented by Aquinas’s Fifth Way aims to show. (The details can be found in Aquinas.) That argument holds that, apart from the sustaining action of God, there could be no finality in nature, no directedness of causal powers to their manifestations, no information content at all, not even for an instant – whether or not each instant is part of an infinite regress of instants, or for that matter part of a temporal loop of instants of the science-fiction sort illustrated by Timecrimes, Heinlein stories, and Stephen Hawking pop science books.
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