Infinite Puppetry

About a year ago, I argued in a blog post that "Everything You Do Causes Almost Everything". If the universe is temporally infinite (as suggested by the current default theories in cosmology) and supports random fluctuations post-heat-death (as also suggested by the current default theories in cosmology), then every action you take will perturb some particles, which will perturb more particles, which will perturb more particles, in an infinite causal chain (a "ripple"), eventually perturbing some post-heat-death system in a way that results in any type of non-unique, non-zero-probability event that you care to specify. Wave your hand, and you will trigger a ripple of perturbances through the cosmos that will eventually cause a far-distant-future duplicate of Shakespeare to decide that Hamlet needs a happy ending.

Philosopher of physics Jacob Barandes and I have collaborated on a draft chapter developing the idea in more detail, for my forthcoming book with Princeton, The Weirdness of the World. I think you'll agree that the idea fits nicely with the book title!

The draft chapter more carefully articulates the physical assumptions required for the almost-everything-causes-almost-everything idea to work -- and then it adds some new thoughts, specifically the infinite puppetry idea.

Below I share the three final sections of the draft chapter, on infinite puppetry. (For more on almost-everything-causes-almost-everything see last year's blog post or the full chapter draft.) Thoughts and comments welcome as always!

Signaling Across the Vastness

The following will also almost certainly occur, given our assumptions so far: On some far distant post-heat-death counterpart of Earth will exist a counterpart of you – let’s call that person you-prime – with the following properties: You-prime will think “right hand” after the ripple from the act of your raising your right hand arrives at their world, and you-prime will not have thought “right hand” had that ripple not arrived at their world. Maybe the ripple initiates a process that affects the weather which causes a slightly different growing season for grapes, which causes small nutritional differences in you-prime’s diet, which causes one set of neurons to fire rather than another at some particular moment when you-prime happens to be thinking about their hands. Likewise, there’s a future you-prime who would have thought “A” if you, here on our Earth, had held up a sheet with that letter and not otherwise. Indeed, infinitely many future counterparts of you have that property. You can specify the message as precisely as you wish, within the bounds of what a counterpart of you could possibly think. Some you-prime will think, “Whoa! Infinite causation!” as a result of your having raised your hand and would not have done so otherwise.

These message recipients will mostly not believe that they have been signaled to. However, we can dispel their disbelief by choosing the fraction who, for whatever reason, are such that they believe they are receiving a signal if and only if they do in fact receive a signal. We can stipulate that we’re interested in you-primes who share the property that when your signal arrives they think not only the content of the signal but also “Ah, finally that signal I’ve been waiting for from my earlier counterpart.”[1]

There’s a question of whether one of your future counterparts could rationally think such a thought. But maybe they could, if they had the right network of surrounding beliefs, and if those beliefs were themselves reasonably arrived at. We’ll consider one such set of beliefs in the final section of this chapter.

Infinite Puppetry

You needn’t limit yourself to ordinary communicative signals. You can also control your future counterparts’ actions. Consider future counterparts with the following property: They will raise their right hand if you raise your right hand, and they will not raise their right hand if you do not. Exactly which counterparts have this feature will depend on exactly when you raise your hand and how, since that will affect which particles follow which trajectories when they are disturbed by your hand. But no matter. Whenever and however you raise your hand, such future counterparts exist.

Your counterparts’ actions can be arbitrarily complex. There is a future you-prime who will, if you raise your hand, write an essay word-for-word identical with the chapter you are now reading and who will otherwise write nothing at all. Maybe that you-prime is considering whether to write some fanciful philosophy of cosmology, as their last hurrah in a failing career as a philosopher. They’re leaning against. However, the arriving particle triggers a series of events that causes an internet outage that prevents them from pursuing an alternate plan, so they do write the essay after all. (A much greater proportion[2] of such future counterparts, of course, will write very different essays from this one, but we can focus on the tiny fraction of them who create word-for-word duplicates of this essay.)

Let’s call someone a puppet if they perform action A as a consequence of your having performed an action (such as raising your hand) with the intention of eventually causing a future person to perform action A. (Admittedly, you might need to agree with the assumptions of this chapter to be able to successfully form such an intention.) You can now wave your hand around with any of a variety of intentions for your future counterparts’ actions, and an infinite number of these future counterparts will act accordingly – puppets, in the just-defined sense.

We recommend that you intend for good things to happen. This might seem silly, since if the assumptions of this chapter are correct, almost every type of finitely probable, non-unique future event occurs, regardless of your benevolent or malevolent intent right now. Still, there is a type of good event that can occur as a result of your good intentions, which could not otherwise occur. That’s the event of a good thing happening in the far distant future as a consequence of your raising your hand with the intention of causing that future good event. So let’s choose benevolence, letting good future events be intentionally caused while bad future events are merely foreseen side effects.

A deeper kind of puppet mastery would involve influencing a person’s actions through a sequence of moves over time and with some robustness to variations in the details of execution. This might not be possible on the current set of assumptions. Raising your right hand, you can trigger arbitrarily long sequences of actions in some future you-prime. But if you then raise your left hand, there’s no guarantee that a ripple of particles from your left hand will also hit the same you-prime. Maybe all the ripples from your right hand head off toward regions A, B, and C of the future universe and all the ripples from your left hand head off toward regions D, E, and F. Similarly, if you raise your right hand like this, the ripples might head toward regions A, B, and C, and if you raise it instead like that, they head toward regions G, H, and I. So there might be no future counterparts of you who do what you intend if you raise your right hand now and then do what you intend when you raise your left hand later; and there might be no future counterparts who will do what you intend if you raise your right hand now, insensitively to the particular manner in which you raise it. In this way, there might be no sequencing and no implementational robustness to your puppetry.

Sequential and robust puppetry might only be reliably possible if we change one of the assumptions in this chapter. Suppose that although the universe endures infinitely in time, spatially it repeats – that is, it has a closed topology in the sense we described in Section 1 – so that any particle that travels far enough in one direction eventually returns to the spatial region from which it originated, as if traveling on the surface of a sphere. Suppose, further, that in this finite space, every ripple eventually intersects every other ripple infinitely often. Over the course of infinite time each ripple eventually traverses the whole of space infinitely many times; none get permanently stuck in regions or rhythms that prevent them from all repeatedly meeting each other. (If a few do get stuck, we can deal with them using the n^m strategy of Section 4. Also the rate of ripple stoppage would presumably increase with so much intersection, but hopefully again in a way that’s manageable with the n^m strategy.) When you raise your right hand, the ripples initially head toward regions A, B, and C; when you raise your left hand, they initially head toward regions D, E, and F; but eventually those ripples meet.

With these changed assumptions, we can now find future counterparts who raise their right hands as a result of your raising your right hand and who then afterward raise their left hand as a result of your afterward raising your left hand. We simply look at the infinite series of systems that are perturbed by both ripples. Eventually some will contain counterparts of you who raise their right hands, then their left, as a result of that joint perturbation. In a similar way, we can find implementationally robust puppets: counterparts living in systems that are perturbed by your actual raising of your right hand (via the ripple that initially traversed regions A, B, and C) and which are also such that they would have been perturbed had you, counterfactually, raised your hand in a somewhat different way (via the ripple that would have initially traversed regions G, H, and I). Multiplying the minuscule-but-finite upon the miniscule-but-finite, we can now find puppets whose behavioral matching to yours is long and implementationally robust, within reasonable error tolerances.

We Might All Be Puppets

So far, we have not assumed that anything existed before the Big Bang. But if the universe is infinite in duration, with infinitely many future sibling galaxies, it would be in a sense surprising if the Big Bang were the beginning. It would be surprising because it would make us amazingly special, in violation of the Copernican Principle of cosmology, which holds that our position in the cosmos is not special or unusual. We would be special in being so close to the beginning of the infinite cosmos. Within the first 14 billion years, out of infinity! It’s as though you had a lotto jar with infinitely many balls numbered 1, 2, 3… and you somehow managed to pull out a ball with the low, low number of 14 billion. If you don’t like a strictly infinite lotto, consider instead a Vast one. The odds of pulling a number as low as 14 billion in a fair lottery from one to a Vastness are far less than one in a googolplex.[3]

Cosmologists don’t ordinarily deny that there might have been something before the Big Bang. Plenty of theories posit that the Big Bang originated from something prior, though there’s no consensus on these theories.[4] If we assume that somehow the Big Bang was brought into existence by a prior process, and that process in turn had something prior to it, and so on, then the Copernican lottery problem disappears. We’re in the middle of a series, not at the beginning of one. Maybe Big Bangs can be seeded in one way or another. Heck, maybe the whole observable universe is a simulation nested in a whole different spatial reality (Chapters 4 and 5) or is itself a very large fluctuation from a prior heat-death state.

Suppose, then, that we are in the middle of an infinite series rather than at the beginning of one, the consqeuence of accepting both Copernican mediocrity and an infinite future. If so, and if we can trace chains of causation or contingency infinitely backward up the line, and if a few other assumptions hold, then eventually we ought to find our puppeteers – entities who act with the intention of causing people to do what we are now doing and whose intentions are effective in the sense that had they not performed those actions, we would not be here doing those things. Suppose you are knitting your brow right now. Somewhere in the infinite past, there is a near-duplicate counterpart of you with the following properties: They are knitting their brow. They are doing so with the intention of initiating ripples that cause later counterparts of them to knit their brows. And you are just such a later counterpart, because among the events that led up to your knitting your brow, absent which you wouldn’t have knit your brow, was a ripple from that past counterpart.

We the authors of this chapter – Eric and Jacob – can work ourselves into the mood of finding this probable. An infinite cosmos is simpler, more elegant, and more consistent with standard cosmological theory; if it’s infinite, it’s probably infinite in all directions; and if it’s truly infinite in all directions, there will be bizarre consequences of that infinitude. Puppetry is one such consequence. We would not be so special as to be only puppeteers and never puppet. It seems only fair to our future puppets to acknowledge this.

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[1] Compare this procedure with Sinhababu’s 2008 procedure for writing love letters between possible worlds. One advantage of our method over Sinhababu’s is that there actually is a causal connection.

[2] Here and throughout we bracket quibbles about ratios of infinitude by considering the limit of the ratio of counterparts with property A to counterparts with property B as the region of spacetime defined by your forward lightcone goes to infinity.

[3] Our reasoning here resembles the reasoning in the “Doomsday argument”, e.g., Gott 1993, according to which it’s highly unlikely that we’re very near the beginning of a huge run of cosmological observers. For a bit more detail, see Schwitzgebel 2022b. For another related perspective, see Huemer 2021.

[4] See notes 12 and 13 (in the full draft) for references. A note on terminology: “Prior” sounds kind of like “earlier” but is also more general in that there’s a sense in which one thing can be ontologically prior to another, or ground it, or give rise to it, even if they one doesn’t temporally precede the other (e.g., an object is prior to its features, or noumena are prior to phenomena [see Chapter 5 of the book draft]). Possibly, temporal priority is a relationship that only holds among events within our post-Big Bang universe while whatever gave rise to the Big Bang stands in some broader priority relationship to us.

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