Wednesday, June 01, 2022

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.


[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.

[image source]


Arnold said...

let's try probability-measurement for a "sustaining infinity"...

The way I read a cosmology like 'sustaining infinity' then is...
...nothing is measurable beyond it's infinite self; any measuring are probable's inside infinity...

Probable infinite motion would be a fundamental force for other fundamental forces like knowing-understanding-being; always related in motion...

Are causes/ripples more than push pull, before after, active passive... moton as, push pull balance, before after present, active passive neutral...

Howard said...

Why not feel fatalistic? A drop in an ocean of infinity that drowns us out?
Everything has happened and will happen no matter what our actions.

Howard said...

Can there be events or things so unique they appear once even in an infinite series, and complexity waters down causality, doesn't it, especially when hard to tease out from other events?

Howard said...

I mean the Christians claim Jesus is a singular and unique event- would you posit there is some other planet where a Jesus pops up as a Messiah and is crucified in Jerusalem by the Romans?
Very Star Trekky

Anonymous said...

Part of me wonders whether biological organisms serve as a kind of causal dampening mechanism.

Alex Popescu said...

Hey Eric,

Interesting piece.

"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"

The problem with this line of reasoning is that it doesn't appear to be arguing against the age of the universe being a low number, but rather against there being any possible origin to the universe at all. That's because there is no finite age to the universe which would not have been an inherently surprising time to have been born in. Even if the universe were 10^5561! years old, it would still be impossible (or at least maximally improbable) to have been born in that "young" age.

I think this simply shows that the argument breaks down with infinities, and not that we should reason against the big bang theory. Consider that cosmologists approach the measurement problem not by throwing up their hands and concluding that we are Boltzmann brains, but by tackling the infinites with regularization/renormalization etc...

Eric Schwitzgebel said...

Alex: Right, it's an argument that if it's infinite in one temporal direction, then it's probably infinite in both directions. I don't think the arguments necessarily break down with infinitudes, though I do agree that infinitude needs to be handled carefully because lots of unintuitive things are true about it (e.g., the equal cardinality of the counting numbers and the squares of the counting numbers, sensitivity of results to the manner of counting).

Alex Popescu said...

Hey Eric,

I understand, thanks. I think I would say two things in response:

The first is that this argument cuts both ways. If (infinite future entails infinite past) then (not infinite past entails not infinite future). Thus, we should only reach the conclusion that there is probably an infinite past iff our prior for an infinite future is higher than our prior for a finite past. But this seems unconvincing to me. Granted, there's not much strong evidence for either, but our evidence for the future history of the universe seems weaker because it relies on everything that the observation of the big bang singularity relies on (the reliability of our cosmological model) plus some assumptions about the future behavior of dark energy (that it functions like a cosmological constant) which we are really not so sure about. So, it seems like our prior for a finite past is at least as high, if not higher, than our prior probability for an infinite future.

Secondly, when I say the argument breaks down with infinities, I mean that we should rethink the naive anthropic reasoning that led us to the conclusion in question, and not that we should abandon reasoning about infinities of course. Specifically, we should either rethink the SSA assumption, or modify the reasoning by introducing some parameter to negate the effects of infinity. Regarding the former, consider two scenarios:

1. We have two possible universes, universe 1 has a finite past & future with finite observers. Universe 2 has a finite past but infinite future with an infinite number of observers. On SSA, we should reason that our posterior for universe 2 is basically zero, so we are most likely to be in universe 1. This is true even if our prior for universe 1 was super small, so long as it was not infinitely or maximally small.

On SIA however, the improbability of our birth rank in universe 2 exactly cancels out with the maximal probability of our being born in universe 2 to begin with. So, our likelihood of being born in either universe just reduces to our initial priors.

The point is that our anthropic probabilities under SSA have gone haywire, and they don't seem to track reasonable probabilities. It certainly seems reasonable to suppose that we could have ended up in a universe with a finite past and infinite future (or backwards) in the sense that it is physically possible, but SSA would basically make this impossible. If physicists had super strong evidence in favor of such a thesis, SIA would allow us to seriously entertain the hypothesis, and so it seems superior.

If that doesn't convince you, consider a second scenario.

2. There are three possible universes: The same two as the ones above, and third with an infinite past but infinite future plus a conjunction of super silly hypotheses (e.g. I am actually God, you are actually a deluded rabbit who thinks he's a human etc...). Because of the conjunction of silly auxiliary hypotheses, our prior for universe 3 will be very low, but crucially it would never reach zero (unless it is logically impossible). This means that our posterior for universe 3 will still be infinitely more likely than universe 2. This clearly seems absurd.

It seems like the only way around this is to either give up SSA or to implement some regularization scheme to handle the infinities (by introducing some probabilistic "cutoff" at some finite threshold).

Eric Schwitzgebel said...

Thanks, Alex! Super interesting and helpful.

You write:

"If (infinite future entails infinite past) then (not infinite past entails not infinite future). Thus, we should only reach the conclusion that there is probably an infinite past iff our prior for an infinite future is higher than our prior for a finite past."

On this point, I simply agree. It does cut both ways, and which way it cuts depends on your priors.

On 1 and 2: Generally, I'm sympathetic with SIA rather than SSA for Sleeping Beauty, so I'm not clear on why you seem to be assuming that my position is committed to SSA rather than SIA. One way to wiggle out of the consequence that we should assign zero or infinitesimal probability to there between finitely many past and infinitely many future observers is to allow reasonable doubt about how much weight to put on principles such as SIA or SSA in thinking about the shape of the universe. I think it's reasonable to have less than 100% credence in philosophical principles about how to assign credences! Finite thresholds might do it too, but that kind of seems like cheating and much might turn on the seemingly arbitrary choice of how high a threshold to use.

Alex Popescu said...


I just assumed you were partial to SSA because of your infinite predecessors post which utilized doomsday style reasoning, apologies for misrepresenting your position. Now that I think about the matter more clearly however, I would say that some kind of methodology for treating infinities is inevitable, regardless of whether one adopts SIA or SSA. It is true that SIA allows you to make sense of probabilities in finite-infinite asymmetric time situations, but it still runs into its own difficulties with infinites. For example, we can imagine two infinite universes (with infinite observers), but where one universe has the absurd auxiliary hypotheses attached in conjunction. It seems like under SIA, our posterior will be the same (maximally likely) regardless, and so we would still need some means for making sense of infinities in order to differentiate the two cases. On the other hand, an infinite symmetric time universe is still far more (maximally) probable than an infinite asymmetric time universe on SIA.

To sum up, I would say that on naive anthropic reasoning (without a methodology for handling infinites) we quickly run into trouble with infinite time asymmetric situations on SSA, and with symmetric time situations assuming SIA. Thus, whether we adopt SIA or SSA will merely change the character or nature of the particular absurdities regarding infinity but won't actually do away with the problem itself. It seems then that your meta-reasoning regarding reasonable doubt about SIA or SSA won't solve the ultimate issue (unless I'm misunderstanding it).

In regards to a fixed threshold being "cheating", I would say that there are alternative methodologies for handling infinities. For example, we might imagine some continuous cutoff, where the probabilities gradually decrease as the number of observers get larger and larger. As long as the sum of our individual probabilities approach the limit of some finite threshold, we are still set. In this way, we can still rationally conceive of two different universes with different amounts of vast observers yielding different probabilities. We don't have to 'reject' thinking about such matters because the amount of total observers in both happened to be beyond some fixed probabilistic cutoff. Additionally, we can similarly adopt mixed credences regarding what the actual continuous decrease in value should be.

That's just one example. The point is that it seems like we are forced to adopt some methodology, and whatever that methodology is might undermine your reasoning (because we can posit that our birth rank is not special once we adjust for our "cutoff").

Howie said...

Might we say a universe having no beginning or end would violate the Copernican principle: all times would be in the middle of history equally?

Eric Schwitzgebel said...

Thanks for these helpful and thoughtful comments, Alex -- and sorry about the slow reply! I've been distracted with traveling.

I do think that infinitudes often lead to strange results and need to be handled carefully on any view, though some of the points you raise would also arise for large but finite numbers like a googolplex. With finite numbers, one might also want a cutoff or some discounting procedure, though it's hard to see how to make those non-arbitrary. I do think that meta-level uncertainty can pick up some of the slack here -- that is, uncertainty about whether approaches of this sort (SIA, SSA, or other formal alternatives) are the right way to go about thinking of this at all.

Alex Popescu said...

Hey Eric,

No worries for the slow reply! After thinking about this some more, I still feel somewhat uneasy about this entire line of reasoning. One exotic consequence of it, for example, would be to argue towards fractal cosmology (or at least a universe with symmetric infinite scale). That's because if the universe is asymmetrically infinite in scale, then it would be maximally improbable for us to have been born at any given level of scale (assuming the universe is atomic), if we can construct conscious observers at different levels of scale, or at least for higher levels. But our best theories of the universe (e.g. standard particle physics, string theory) depict the universe as being atomic. I think strings are supposed to be something like 10^-35 meters in diameter.

So we would either have to reject this picture as being an ultimate description of reality, or reject those theories of consciousness which don't localize consciousness to a specific level of scale (like standard computationalism/functionalism or IIT theory etc...)

On the other hand, this could all be ironed out by measuring probabilities across infinities. So, for example, the infinite number of observers at the lowest level of scale (presumably ours) would relatively outnumber the infinite observers at higher levels of scale. If we buy into this reasoning (and accept that we exist at the lowest possible level of scale) then the problem is solved. Unfortunately, the same treatment of a similar problem in multiverse cosmology leads to the youngness paradox. Oh well! It is indeed hard to wrap one's head around infinities, but it's fun to think about.

Eric Schwitzgebel said...

Interesting extension, Alex! I talk about scaling up in this post:
But I don’t connect it with Doomsday-style reasoning.

I agree that it’s fun and weird and should be taken with a grain of salt. That’s not to say that it’s just messing around with no real merit! But some substantial meta-level doubt is appropriate.