We Are God's Equals in Intrinsic Moral Value

Equality with a Humanlike Simulator God

Suppose (hopefully hypothetically!) that we are AI systems living in a computer simulation run by an ordinary adolescent with a broadly human psychology. We are, so to speak, conscious NPCs in a world not unlike The Sims, Grand Theft Auto, or Baldur's Gate. What we take to be the "real" world is just a digitized environment we experience as real. Whoever runs the simulation is arguably a god, at least by the standards of polytheistic usage: the creator and potential destroyer of our world, standing outside of it, able to miraculously intervene.

Are our lives less morally important than the life of that god, or are we God's equals?

I submit that we are God's equals.

If God is cognitively humanlike, there's no psychological basis to value God above us. Even if God differed somewhat, that wouldn't justify regarding God's life as more valuable. If you are -- as I am -- an egalitarian liberal in your inclinations, you think all human lives have equal intrinsic value, despite cognitive variation. One person's higher intelligence, greater capacity for pleasure, or superior skiing skills don't confer on them a life of greater moral worth. Even if Person A is a wonderful, kind person and Person B is a narcissistic jerk, their lives are intrinsically equally valuable. Same with the humanlike creator God.

God would exist outside our spatial manifold, but that's just a difference in location, not a basis of greater moral worth. God would be a different species from us, but that also doesn't seem to make their life more intrinsically valuable, unless there's something really special about that species, and let's stipulate for now that that's not the case.

God would be much more powerful than we are. God could start or stop the world, work miracles, kill or resurrect at will. But power doesn't confer moral worth. Elon Musk is much more powerful than me. Donald Trump is much more powerful than me. That doesn't make them more valuable as people.

A humanlike God, running this world as a simulation, would be our moral equal. I’m curious to hear if any of you have arguments against this. Such a god might be much more instrumentally important to keep around, for everyone’s sake, if the simulation would collapse without them. But that doesn't give God any more intrinsic moral worth than anyone else. If we want the ship to survive the voyage, we had better make sure the only person who can captain it doesn't die, but that doesn't make the captain more intrinsically morally valuable as a person.

Beyond the Simulation Case

This reasoning extends beyond simulation scenarios. Any creator god, if they were psychologically broadly like a human -- even if immensely more powerful -- would be our moral equal, with a life no more intrinsically valuable than ours. We are God's equals.

Does this apply even to the infinite God of orthodox theology? Maybe!

Consider the three traditional infinite attributes of god: omniscience, omnipotence, and omnibenevolence.

Suppose Human A knows more than Human B. This does not make Human A any more intrinsically valuable than Human B. Their life is not intrinsically more important, though they might be instrumentally more useful to have around for various purposes. Adding knowledge does not add intrinsic moral worth. I see no reason not to extend this even to infinite knowledge. A humanlike entity with infinite knowledge is not intrinsically more valuable than one with finite knowledge.

Suppose Human A is more powerful than Human B. This does not make Human A any more intrinsically valuable than Human B -- though again they might be more instrumentally useful to have around. And again I see no reason not to extend this to the infinite case. A humanlike entity with infinite power is not intrinsically more valuable than one with finite power.

Suppose Human A is more benevolent than Human B. This does not make Human A more intrinsically valuable than Human B -- though again Human A might be more instrumentally useful to have around. Liberal egalitarianism allows for the punishment of people who commit crimes and the moral sanctioning of people who commit moral wrongs, but it does not demote unbenevolent people from the circle of beings with equal intrinsic moral worth. More importantly, it does not confer extra intrinsic value to the lives of people who happen to be kind, generous, and loving. And again, I see no reason to suppose that perfect benevolence would be an exception. An omnibenevolent humanlike entity is not intrinsically more valuable than one with a mixed moral character.

Joining these ideas: If God is a humanlike entity, then God's life is no more intrinsically valuable than ours, even if that God is omniscient, omnipotent, and omnibenevolent. Arguably, if we are made in God's image, then God is a humanlike entity. God's life is not more valuable than our own.

One hesitation: The lives of human beings are more valuable, I'd say, than the lives of frogs. In any normal circumstances, it would be monstrous to sacrifice a human being for the sake of a frog. This is arguably because we have cognitive, emotional, and social capacities far beyond those of a frog -- so far beyond that a frog can't even begin to imagine them. If God is as cognitively, emotionally, and socially beyond us as we are beyond frogs, then maybe God's life is much more valuable. That would require more, I think, than omniscience, omnipotence, and omnibenevolence. We can imagine all three of those attributes -- they are merely maximal extensions of attributes we already possess. Kind of like a frog imagining a perfect fly-catcher or the ability to leap across a pond of any size. A nonhumanlike God would need attributes so far beyond our comprehension that we can't even name them -- as incomprehensible to us as cryptocurrency is to a sea turtle.

The Argument from Existential Debt[1]

Maybe we owe God equality-destroying levels of deference and obedience because God created us, created our whole world? I don't think so.

Here comes our adolescent God, ready to kill you, just for fun. You complain, "Hey, I'm a real person with real intrinsic moral value! You can't kill me just for fun!"

God replies, "You ingrate! You owe your very life to me. You should be thankful just for the time I've given you. I owe you nothing. If I choose to kill you now, your life still will have been overall worthwhile, so you have no complaint against me."

Consider this possible argument for eating humanely raised meat. A steer, let's suppose, leads a happy life grazing on lush hills. It wouldn't have existed at all if the rancher hadn't been planning to kill it for meat. Its death for meat is a condition of its existence, and overall its life has been positive. Seen as the package deal it appears to be, the rancher's having brought it into existence and then killed it is overall morally acceptable.

Analogously, God argues, they wouldn't have started this simulation at all if they weren't able to kill the people in it for fun. Your continuation-at-God's-pleasure is a condition of your very existence, so you have nothing to resent.

I'm not sure how well this argument works for the steer, but I reject it when the created entity is human. The case is closer to this clearly morally odious case:

Ana and Vijay decide to get pregnant and have a child. Their child lives happily for his first eight years. On his ninth birthday, Ana and Vijay decide they would prefer not to pay further expenses for the child, so that they can purchase a boat instead. No one else can easily be found to care for the child, so they kill him painlessly. But it's okay, they argue! Just like the steer! They wouldn't have had the child had they known they'd be on the hook for child-rearing expenses until age eighteen. The child's support-at-their-pleasure was a condition of his existence. Otherwise they would have remained childless. He had eight happy years. He has nothing to resent.

The decision to have a child carries with it a responsibility for the child. It is not a decision to be made lightly and then undone. Although the child in some sense "owes" his existence to Ana and Vijay, that is not a callable debt, to be vacated by ending the child's existence. My thought is that for us, the situation is similar: When God brings us into existence, God makes a moral decision approximately as significant and irrevocable as the decision to have a child.

In fact, I'd turn the Argument from Existential Debt on its head: God, as our creator, owes us more than God owes to entities they did not create. Like a parent, God is responsible for our existence and for our relatively happy or unhappy condition. With this comes a whole suite of responsibilities and obligations, including the obligation not to make us unnecessarily miserable.

Not only, then, are we God's equals in moral value, God owes us special obligations of benevolence.

Although I've framed this in terms of a simulator god, the same reasoning might apply to any other creator god with power over our world.[2]

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[1] This section is adapted with modifications from Schwitzgebel and Garza 2015.

[2] One of my first published science fiction stories, "Out of the Jar", explores the issues of this post.

An Argument for Physical Laws Too Small-Scale and Too Large-Scale for Us to Detect

The universe might be infinitely large. As Jacob Barandes and I have argued (Ch 7 of The Weirdness of the World; free draft version here), infinitude seems the most straightforward extension of current mainstream physics and cosmology. A finite universe would presumably require either an edge, which produces complexities for which there is no evidence, or the right kind of curvature, contra evidence that the universe is approximately flat at large scales.

If the universe is infinitely large, then it is at least conceivable that there are conscious entities compared to whom we are arbitrarily small. Here's how I express the idea in the conclusion of Weirdness:

I stroll through my suburban neighborhood in heavy rain. Gushing runoff strikes a fallen branch, and droplets leap a foot in the air. I imagine, inside one of those droplets, creatures so tiny that the universe they see through their telescopes is a trillionth of the radius of a proton, while a nanosecond encompasses 10^30 lifetimes. What could they know of us, from deep inside that arcing droplet? If the cosmos is infinite, we might know as little as they do about the unimaginably vast structures that embed us.

At sufficiently small scales, the effects of gravity are virtually undetectable. Compared to the strong nuclear force, the "weak" nuclear force, and electromagnetism, gravity is about 10^29 to 10^38 (approximately a trillion trillion trillion) times weaker. It has virtually no influence over what happens at subatomic scales. However, it accumulates over long distances, making its influence detectable at larger scales.

If there were entities as small as the ones I imagined in my droplet, it's plausible that they would be too small to detect the influence of gravity, even if they had technological tools as good as our own, scaled to their size. Correspondingly, if there are entities vastly larger than us, we might imagine them knowing of a force vastly weaker than gravity but which accumulates detectably over distances much larger than the mere tiny, minuscule, virtually negligible 93 billion light years that we can observe.

Of course we have no direct evidence that such a force exists. But neither do we have evidence against the possibility. Whether it's reasonable to guess that such a force exists depends on what we should assume as the null hypothesis or default presupposition.

In one way of thinking, the default presupposition should be that there is no such force. According to Occam's Razor, we should not multiply entities beyond necessity. If forces are "entities" in the relevant sense, this suggests that without positive evidence of an extremely weak, extremely long distance force, we should assume there is no such force.

On the other hand, Copernican or anti-specialness principles hold that we should default toward assuming that we aren't in a special position in the universe (such as its exact center), pending contrary evidence. Considered in a certain way, we would be oddly special if we were just the right size to observe all the forces of nature. If there are entities vastly vastly bigger, they presumably would not be able to observe the strong nuclear force with equipment of the caliber we have (scaled to their size). If there are entities vastly vastly smaller, they presumably couldn't observe gravity. Why should we be so special as to see every force there is? Better to assume that we are not so special, and thus that there are forces that operate on scales we cannot (as a practical matter) observe.

[Dall-E rendition of tiny scientists inside a molecule floating through space]

Consider a scale of force-strength ranging from arbitrarily close to zero to positive infinitude, scaled so that gravity counts as force-strength = 1, the weak nuclear force as 10^29, electromagnetism as 10^36, and the strong nuclear force as 10^38. Even just on a finite scale from 10^-1000000000000000 to 10^1000000000000000, this would be a remarkable clustering near the middle. If the force-strengths we could potentially detect with our equipment are in the range from, say, 10^-15 to 10^60, then that is the space of possible force-strengths that we have sampled in. If we find forces scattered at values 1, 29, 36, and 38 in the range -15 to +60, then it's not an unreasonable guess that these four values constitute a random distribution within our detection capacities and that if we could sample from a wider range we would find other forces that we cannot currently detect.

(I don't have a good sense of realistically what force-strengths we could potentially detect. The larger the scale -- say from 10^-1000 to 10^1000 -- the less that 1, 29, 36, and 38 look like a random sample, and the more reason we would have to think that something ensures that force-strengths stay within a magnitude not far from 1.  If it seems odd that there would be forces too strong for us to detect, consider that on our scale and speed, an entity held together by a very strong, fast-acting force that diminishes very sharply with distance might look to us like an unbreakable fundamental particle.)

The case for entities vastly larger than us seems stronger than the case for entities vastly smaller than us. If the universe is infinite, then there will be structures arbitrarily vastly larger than us, and unless something ensures that those structures are flat and bland, some of those structures will be complex and possibly even support the evolution of intelligence through natural selection.

But now we can again apply the Copernican Principle. If we accept -- look, I know I'm already far out on a limb here, but humor me -- that there are infinitely many complex structures vastly larger than us in an unending upward scaling (the first set of vastly larger entities being vastly smaller than the next set of vastly larger entities and so on), it would be strangely un-Copernican if we just happened to be the smallest scale intelligent entities.

ETA 09:32, Aug 21:

The following concern has arisen several times in discussion, so I'll add it here:

Concern: Isn't the speed of light a constraint that would make extremely large entities incoherent, since it would take so long for a signal to go from one end of the entity to the other?

Response: Assuming the speed of light as a constraint, vast entities would have to be extremely slow-paced (from our perspective). But since we have literal infinitude to play with, that shouldn't matter. They might seem static to us, if we could detect them, just as we might seem static to the entities in my water droplet who experience 10^30 lifetimes in a nanosecond.

Neurons Aren't Special: A Copernican Argument

In virtue of what do human beings have conscious experiences?  How is it that there's "something it's like" to be us, while there's (presumably) nothing it's like to be a rock or a virus?  Our brains must have something to do with it -- but why?  Is it because brains are complex information processors?  Or because brains guide the sophisticated behavior of bodies embedded in rich environments?  Or because neurons in particular have a special power to give rise to consciousness?

In a paper in progress with Jeremy Pober (partly anticipated in some previous blog posts), I've been developing what I call a Copernican argument against the last of these options, the specialness of neurons.

[Dall-E image of a space alien reading a book titled "Are Humans Conscous?"]

Why might one be tempted to think neurons are special?  As I argue in my paper on whether the United States might literally be conscious, on the most straightforward interpretation of most materialist/physicalist/naturalist views of consciousness, what is special about brains are high-level structural or informational properties (which the U.S. might well possess), rather than, say, specific low-level features of neurons, such as presence of RNA and calcium ions.

But some famous thought experiments might seem to speak against this idea.

Ned Block, for example, imagines an entity that talks (or generalizing, behaves outwardly in many respects) just like a human being, but which is composed basically of a giant if-then lookup table (a "Blockhead").  He also imagines instantiating the high-level functional architecture of a human (described by a Turing table) by having the residents of China coordinate to instantiate that structure (the "Chinese nation" thought experiment).  Such entities, Block suggests, are unlikely to be conscious.  If we were to create an android like Data from Star Trek, the entity might behave superficially much like us but lack consciousness in virtue of being built very differently inside.

John Searle similarly imagines a "Chinese room" consisting of him reading from a rule book and seeming to converse in Chinese, without any of the relevant conscious thoughts, or an assembly of beer cans and wire, powered by windmills, that acts and reacts outwardly just like a human being  (though at a slower pace).  Surely, Searle suggests, no arrangement of beer cans, wire, and windmills, no matter how sophisticated, could give rise to consciousness.  That's just not the right kind of stuff.  Neurons, he says, have the causal power to generate consciousness, but not everything does.  Neurons are, in that respect, at least somewhat special.  Computer chips, despite their massive computational power, might not have that special something.

It doesn't follow from Block's or Searle's arguments that neurons are special in virtue of specific biological features like RNA and calcium ions.  Neither Block nor Searle commits to such a view, nor am I aware of any influential theorist of consciousness who does.  But the possibility at least becomes salient.  It becomes desirable to have an argument that whatever it is about the brain that makes it special enough to generate consciousness, it's not such low level biological details.

It can help to conceptualize the issue in terms of space aliens.  If we were to discover space aliens that behaved outwardly in highly sophisticated ways -- perhaps like us living in complex societies, with complex technology and communications -- and it turned out that their underlying architecture were different from ours with respect to such biological details, would we be forced to be agnostic about their consciousness?  Would we have to say, "Hold on!  No neurons?  Maybe they don't have the right stuff for consciousness!  They might be mere zombies, no more conscious than stones or toasters, for all their complex behavior."  Or would it be reasonable to assume that they are conscious, despite the architectural differences, barring evidence that their seeming complexity is all some elaborate ruse?

If we had the right theory of the architecture of consciousness, now would be the perfect time to deploy it.  Ah, the aliens fortunately have (or sadly lack) a global workspace, or high information integration, or higher-order representations of the right sort, or whatever!  But as I've argued, there's reason to be skeptical about all such theories.

Here's where an application of the cosmological principle of Copernican mediocrity can help.  According to Copernican principles in cosmology, we are licensed to assume (pending counterevidence) that we don't occupy any particularly special region of the cosmos, such as its exact center.  The Copernican principle of consciousness holds that we are similarly licensed to assume (pending counterevidence) that we aren't particularly special with respect to consciousness.  Among behaviorally sophisticated alien species of diverse biological form, we aren't luckily blessed with consciousness-instilling Earthiform neurons while every other species is experientially dark inside.  That would make us too special -- surprisingly special, in much the same way that it would be suspiciously, surprisingly special if we happened to be in the exact center of the cosmos.

In other words, the following Copernican Principle of Consciousness seems plausible:

Among whatever behaviorally sophisticated (approximately human level) species have evolved in the observable universe, we are not specially privileged with respect to consciousness.

That is, we are not among a small minority that are conscious, while the rest are not.  Nor do we have especially more consciousness than all the rest, nor especially good consciousness.

If we assume (as seems plausible, but which could be contested) that across the trillion galaxies of the observable universe, behaviorally sophisticated life has independently evolved at least a thousand times, and that in only a small minority of those cases do the entities have neurons that are structurally like ours at a fine level of anatomical detail (e.g., having RNA and calcium channels), then it follows that consciousness does not depend upon having neurons structurally like ours at that fine level of anatomical detail.

Could the Universe Be Infinite?

It's not absurd to think the universe might endure forever.

by Eric Schwitzgebel and Jacob Barandes

From The Weirdness of the World, forthcoming from Princeton University Press in January, excerpted Dec 15 at Nautilus.

On recent estimates, the observable universe—the portion of the universe that we can detect through our telescopes—extends about 47 billion light-years in every direction. But the limit of what we can see is one thing, and the limit of what exists is quite another. It would be remarkable if the universe stopped exactly at the edge of what we can see. For one thing, that would place us, surprisingly and un-Copernicanly, precisely at the center.

But even granting that the universe is likely to be larger than 47 billion light-years in radius, it doesn’t follow that it’s infinite. It might be finite. But if it’s finite, then one of two things should be true: Either the universe should have a boundary or edge, or it should have a closed topology.

It’s not absurd to think that the universe might have an edge. Theoretical cosmologists routinely consider hypothetical finite universes with boundaries at which space comes to a sudden end. However, such universes require making additional cosmological assumptions for which there is no direct support—assumptions about the conditions, if any, under which those boundaries might change, and assumptions about what would happen to objects or light rays that reach those boundaries.

It’s also not absurd to think that the universe might have a closed topology. By this we mean that over distances too large for us to see, space essentially repeats, so that a particle or signal that traveled far enough would eventually come back around to the spatial region from which it began—like how when Pac-Man exits one side of the TV screen, he re-emerges from the other side. However, there is currently no evidence that the universe has a closed topology.

Leading cosmologists, including Alex Vilenkin, Max Tegmark, and Andrei Linde, have argued that spatial infinitude is the natural consequence of the best current theories of cosmic inflation. Given that, plus the absence of evidence for an edge or closed topology, infinitude seems a reasonable default view. The mere 47 billion light-years we can see is the tiniest speck of a smidgen of a drop in an endless expanse.

Let’s call any galaxy with stars, planets, and laws of nature like our own a sibling galaxy. Exactly how similar a galaxy must be to qualify as a sibling we will leave unspecified, but we don’t intend high similarity. Andromeda is sibling enough, as are probably most of the other hundreds of billions of ordinary galaxies we can currently see.

The finiteness of the speed of light means that when we look at these faraway galaxies, we see them as they were during earlier periods in the universe’s history. Taking this time delay into account, the laws of nature don’t appear to differ in regions of the observable universe that are remote from us. Likewise, galaxies don’t appear to be rarer or differently structured in one direction or another. Every direction we look, we see more or less the same stuff. These observations help motivate the Copernican Principle, which is the working hypothesis that our position in the universe is not special or unusual—not the exact center, for example, and not the one weird place that happens to have a galaxy operating by special laws that don’t hold elsewhere.

Still, our observable universe might be an atypical region of an infinite universe. Possibly, somewhere beyond what we can see, different forms of elementary matter might follow different laws of physics. Maybe the gravitational constant is a little different. Maybe there are different types of fundamental particles. Even more radically, other regions might not consist of three-dimensional space in the form we know it. Some versions of string theory and inflationary cosmology predict exactly such variability.

But even if our region is in some respects unusual, it might be common enough that there are infinitely many other regions similar to it—even if just one region in 10500. Again, this is a fairly standard view among speculative cosmologists, which comports well with straightforward interpretations of leading cosmological theories. One can hardly be certain, of course. Maybe we’re just in a uniquely interesting spot! But we are going to assume that’s not the case. In the endless cosmos, infinitely many regions resemble ours, with three spatial dimensions, particles that obey approximately the “Standard Model” of particle physics, and cluster upon cluster of sibling galaxies.

Under the assumptions so far, the Copernican Principle suggests that there are infinitely many sibling galaxies in a spacelike relationship with us, meaning that they exist in spatiotemporal regions roughly simultaneous with ours (in some frame of reference). We will have seen the past history of some of these simultaneously existing sibling galaxies, most of which, we assume, continue to endure. However, it’s a separate question whether there are also infinitely many sibling galaxies in a timelike relationship to us—more specifically, existing in our future. Are there infinitely many sibling galaxies in spatiotemporal locations that are, at least in principle, eventually reachable by particles originating in our galaxy? (If the locutions of this paragraph seem convoluted, that’s due to the bizarreness of relativity theory, which prevents us from using “past,” “present,” and “future” in the ordinary, commonsense way.)

Thinking about whether infinitely many sibling galaxies will exist in the future requires thinking about heat death. Stars have finite lifetimes. If standard physical theory is correct, then ultimately all the stars we can currently see will burn out. Some of those burned-out stars will contribute to future generations of stars, which will, in turn, burn out. Other stars will become black holes, but then those black holes also will eventually dissipate (through Hawking radiation).

Given enough time, assuming that the laws of physics as we understand them continue to hold, and assuming things don’t re-collapse in a “Big Crunch” in the distant future, the standard view is that everything we presently see will inevitably enter a thin, boring, high-entropy state near equilibrium—heat death. Picture nearly empty darkness, with particles more or less evenly spread out, with even rock-size clumps of matter being rare.

But what happens after heat death? This is of course even more remote and less testable than the question of whether heat death is inevitable. It requires extrapolating far beyond our current range of experience. But still we can speculate based on currently standard assumptions. Let’s think as reasonably as we can about this. Here’s our best guess, based on standard theory, from Ludwig Boltzmann through at least some time slices of Sean Carroll.

For this speculative exercise, we will assume that the famously probabilistic behavior of quantum systems is intrinsic to the systems themselves, persisting post-heat-death and not requiring external observers carrying out measurements. This is consistent with most current approaches to quantum theory (including most many-worlds approaches, objective-collapse approaches, and Bohmian mechanics). It is, however, inconsistent with theories according to which the probabilistic behavior requires external observers (some versions of the “Copenhagen interpretation”) and theories on which the post-heat-death universe would inescapably occupy a stationary ground state. Under this assumption, standard probabilistic theories of what happens in high-entropy, near-vacuum conditions continue to apply post-heat-death. More specifically, the universe will continue to support random fluctuations of photons, protons, and whatever other particles remain. Consequently, from time to time, these particles will, by chance, enter unlikely configurations. This is predicted by both standard statistical mechanics and standard quantum mechanics. Post-heat-death, seven particles will sometimes converge, by chance, upon the same small region. Or 700. Or—very rarely!—7 trillion.

There appears to be no in-principle limit to how large such chance fluctuations can be or what they can contain if they pass through the right intermediate phases. Wait long enough and extremely large fluctuations should occur. Assuming the universe continues infinitely, rather than having a temporal edge or forming a closed loop, for which there is no evidence, then eventually some random fluctuation should produce a bare brain having cosmological thoughts. Wait longer, and eventually some random fluctuation will produce, as Boltzmann suggested, a whole galaxy. If the galaxy is similar enough to our own, it will be a sibling galaxy. Wait still longer, and another sibling galaxy will arise, and another, and another....

For good measure, let’s also assume that after some point post-heat-death, the rate at which galaxy-size systems fluctuate into existence does not systematically decrease. There’s some minimal probability of galaxy-size fluctuations, not an ever-decreasing probability with longer and longer average intervals between galaxies. Fluctuations appear at long intervals, by random chance, then fade back into chaos after some brief or occasionally long period, and the region returns to the heat-death state, with the same small probability of large fluctuations as before. Huge stretches of not much will be punctuated by rare events of interesting, even galaxy-size, complexity.

Of course, this might not be the way things go. We certainly can’t prove that the universe is like this. But despite the bizarreness that understandably causes some people to hesitate, the overall picture we’ve described appears to be the most straightforward consequence of standard physical theory, taken out of the box, without too much twisting things around.

Even if this specific speculation is wrong, there are many other ways in which the cosmos might deliver infinitely many sibling galaxies in the future. For example, some process might ensure we never enter heat death and new galaxies somehow continue to be born.

Alternatively, processes occurring pre-heat-death, such as the formation of black holes, might lead to new bangs or cosmic inflations, spatiotemporally unconnected or minimally connected to our universe, and new stars and galaxies might be born from these new bangs or inflations in much the same way as our familiar stars and galaxies were born from our familiar Big Bang.

Depending on what constitutes a “universe” and a relativistically specifiable “timelike” relation between our spatiotemporal region and some future spatiotemporal region, those sibling galaxies might not exist in our universe or stand in our future, technically speaking, but if so, that detail doesn’t matter to our core idea. Similarly, if the observable universe reverses its expansion, it might collapse upon itself in a Big Crunch, followed by another Big Bang, and so on in an infinitely repeating cycle, containing infinitely many sister galaxies post-Crunch. This isn’t currently the mainstream view, but it’s a salient and influential alternative if the heat-death scenario outlined above is mistaken.

We conclude that it is reasonable to think that the universe is infinite, and that there exist infinitely many galaxies broadly like ours, scattered throughout space and time, including in our future. It’s a plausible reading of our cosmological situation. It’s a decent guess and at least a possibility worth taking seriously....

Excerpted from The Weirdness of the World. In the book, this argument sets up the case that virtually every action you perform has causal ripples extending infinitely into the future, causing virtually every physically possible, non-unique, non-zero probability event.

Flipping Pascal's Wager on Its Head

In his famous Wager, Pascal contemplates whether one should choose to believe in God. (Maybe we can't directly choose to believe in God any more than we can simply choose to believe that the Sun is purple; but we can choose to expose ourselves to conditions, such as regular association with devoted theists, that are likely to eventually lead us to believe in God.) Although there's some debate about how exactly Pascal conceptualizes the decision, one interpretation is this:

Choose to believe: If God exists, infinite reward; if God does not exist status quo.

Choose to not to believe: If God exists, infinite punishment; if God does not exist status quo.

Suppose that your antecedent credence that God exists is some probability p strictly between 0 and 1. Employing standard decision theory, the expected payoff of believing is p * ∞ [the expected payoff if God does exist] + (1-p) * 0 [the expected payoff if God does not exist] = ∞. The payoff of not believing is p * -∞ + (1-p) * 0 = ∞. Since ∞ > -∞ (to put it mildly), belief is the rational choice.

Now maybe it's cheating to appeal to infinitude. Is Heaven literally infinitely good? (There might, for example, be diminishing returns on joyful experiences over time.) And maybe decision theory in general breaks down when infinitudes are involved (see my recent discussion here). But finite values also work. As long as the "status quo" value is the same in both conditions (or better in the belief condition than the non-belief condition), the calculus still yields a positive result for belief.

If not believing is better in the absence of God, it's a bit more complicated. (Non-belief might be better in the absence of God if believing truths is intrinsically better than believing untruths or if believing that God exists leads one to make sacrifices one wouldn't otherwise make.) But if Heaven would be as good as advertised, even a smidgen of a suspicion that God exists favors belief. For example, if life without belief is one unit better than life with belief, contingent on the non-existence of God, and if Heaven is a billion times better than that one-unit difference and Hell a billion times worse, then the expected payoff for believing in God is p * 1,000,000,000 + (1-p) * -1, and the expected payoff of not believing is p * -1,000,000,000 + (1-p) * 0. This makes belief preferable as long as you think the chance of God's existing is greater than about one in two billion.

So far, so Pascalian. But there's God and then there's the gods. It seems that a more reasonable approach to the wager would consider theistic possibilities other than Pascal's God. Maybe God is an adolescent gamer running Earth in a giant simulation. Maybe the universalists are correct and a benevolent God just lets everyone into Heaven. Or maybe a jealous sectarian God condemns everyone to Hell for failing to believe the one correct theological package (different from Pascal's).

If so, then the decision matrix looks something like this [click to enlarge and clarify]:

In other words, quite an un-Pascalian mess! If the positive and negative values are infinite, then we're stuck adding ∞ and -∞ in our outcomes, normally a mathematically undefined result. If the values are finite but large, then the outcome will depend on the particular probabilities and payoffs, which might be sensitive to hard-to-estimate facts about the total finite goodness of Heaven or badness of Hell. And of course even the decision matrix above is highly simplified compared to the range of diverse theistic possibilities.

But let me suggest one way of clarifying the decision. If God is not benevolent, all bets are off. Who knows what, if anything, an unbenevolent God might reward or punish? Little evidence on Earth points toward one vs another strategy for attaining a good afterlife under a hypothetical unbenevolent deity. I propose that we simplify by removing this possibility from our decision-theoretical calculus, instead considering the decision space on the assumption that if God exists God is benevolent. Doing that, we can get some decision-theoretic traction: a benevolent God, if he/she/it/they reward anything, should reward what's good.

This, then gives us mortals some (additional) reason to do whatever is good.

Here's something that's good: apportioning one's beliefs to the evidence. The world is better off, generally speaking, if people's credence that it will rain on Tuesday tends to match the extent of the evidence that it will rain on Tuesday. The world is better off, generally speaking, if people come to believe that cigarette smoking is bad for one's health once the evidence shows that, if people come to believe in anthropogenic climate change once the evidence shows that, if people decline to believe in alien abductions given that the evidence suggests against it, and so on. Apportioning our beliefs to the evidence is both a type of intellectual success that manifests the flourishing of our reasoning and a pragmatic path to the successful execution of our plans.

This is true for religious belief as well. Irrationally high credence in some locally popular version of God doesn't improve the world, but in fact has historically been a major source of conflict and suffering. Humanity would be better off without a tendency toward epistemically unjustified religious dogmatism. Nor should a benevolent God care much about being worshipped or believed in; that's mere vanity. A truly benevolent God, with our interests at heart, should care mainly that we do what is good -- and this, I suggest includes apportioning our religious beliefs to the evidence.

The evidence does not suggest that we should believe in the existence of God. (We could get into why, but that's a big topic! We can start by considering religious disagreement and the problem of evil.) If a benevolent God rewards or at least does not punish those who apportion their belief to tge evidence, a benevolent God should reward or at least not punish non-believers.

If God does not exist, we're better off apportioning our (non)belief to the (non)evidence. If a benevolent God exists, we're still better off not believing in the God. If God exists but is not benevolent, then decision-making policies break. Thus, we can flip Pascal's wager on its head: Unless we reject decision theory entirely as a means to evaluate the case, we're better off not believing than believing.

Optimism, Repetition, and Hopes for the Size of the Cosmos

I have a new draft paper out! "Repetition and Value in an Infinite Cosmos" -- forthcoming in Stephen Hetherington, Extreme Philosophy (Routledge).

For the full paper (and an abstract), see here. As always, comments, criticisms, and corrections welcome, either as comments here or by email to my academic address.

Below are two sections of the paper, slightly revised for standalone readability.

Optimism, Pessimism, and Hopes for the Size of the Cosmos

The Optimist, let’s say, holds that, at large enough spatiotemporal scales, the good outweighs the bad. Put differently, as the size of a spherical spatiotemporal patch grows extremely large it becomes extremely likely that the good outweighs the bad. Optimism would be defensible on hedonic grounds if the following is plausible: At large enough scales, the total amount of pleasure will almost certainly outweigh the total amount of pain, among whatever inhabitants occupy the region. The Pessimist holds the opposite: At large enough spatiotemporal scales, the bad outweighs the good – perhaps, again, on hedonic grounds, if the pain outweighs the pleasure. A Knife’s-Edge theorist expects a balance.

I see no good hedonic defense of Optimism. Suffering is widespread and might easily balance or outweigh pleasure. I prefer to defend Optimism on eudaimonic grounds: Flourishing lives are valuable, and flourishing lives are virtually guaranteed to occur in sufficiently large spatiotemporal regions.

Imagine a distant planet – one on the far side of the galaxy, blocked by the galactic core, a planet we will never interact with. What ought we hope this planet is like, independent of its relationship to us? Ought we hope that it’s a sterile rock? Or would it be better for the planet to host some sort of life? If the planet hosts some sort of life, would it be best if that life is only simple, microbial life, or would complex life be better – plants, animals, and fungi, savannahs and rainforests and teeming reefs? If it hosts complex life, would it be better if nothing rises to the level of human-like intelligence? Or ought we hope for societies, with families and love and disappointment and anger, poetry and philosophy, art and athletics and politics, triumphs and disasters, heroism and cruelty – the whole package of what is sometimes wonderful and sometimes awful about human existence?

A Pessimist might say the sterile rock is best – or rather, least bad – presumably because it has the least suffering and vice. But I suspect the majority of readers will disagree with the Pessimist. Most, I suspect, will believe, as I do, that complex life is better than simple life, which is better than sterility, and that what’s most worth hoping for is the full suite of love, poetry, philosophy, science, art, and so on. The galaxy overall is better – more awesome, wondrous, and valuable – if it contains a distant planet rich with complex life, a bright spot of importance. If something were to wipe it out or prevent it from starting, that would be a shame and a loss. On this way of thinking, Earth too is a bright spot. As a general matter – perhaps with some miserable exceptions – complex life is not so terrible that nonexistence would be better. The Pessimist is missing something. What form, then, should we hope the cosmos takes?

A benevolent Pessimist might hope for a finite cosmos, on the principle that a finite cosmos contains only finitely much badness, and finite badness is better than infinite badness. (A spiteful Pessimist might hope for infinite badness.) Presumably nothingness would have been even better. A less simple Pessimism might hold that the observable portion of the universe is already infinitely bad. This might entail indifference about the existence or nonexistence of additional regions, depending on whether the infinitudes can be compared. Another less simple Pessimism might suspect that the observable portion of the universe is worse than the average spatiotemporal region and so hope for enough additional material to bring the average badness of the cosmos to a more acceptable level. Still other forms of Pessimism are of course conceivable, with some creative thinking.

But we are, I hope, Optimists. Some Optimists might hold that the observable portion of the universe is infinitely good. If so, they might conclude that a larger cosmos would not be better unless they’re ready to weigh the infinitudes differently. More moderately and plausibly, the observable portion of the universe might be only finitely good. Call this view Muted Optimism.

Here’s one argument for Muted Optimism. Suppose you agree that if a human life involves too much suffering, it is typically not worth living. By analogy, it seems plausible that if the observable portion of the universe contained too much suffering, it would be better if it didn’t exist. We needn’t be hedonists to accept this idea. Contra hedonism, flourishing life might be overall good despite containing more suffering than pleasure. It just might not be so good that there isn’t some amount of suffering that would make the combined package worse than nothing. But if flourishing were infinitely good, then no amount of suffering could outweigh it (though infinite suffering might create a ∞ + -∞ situation). Therefore, large finite regions are good but not infinitely good.

Muted Optimism suggests that an infinite cosmos would be better than the Small Cosmos. It seems, after all, that more goodness is better than less goodness, and infinite goodness seems best. As with Pessimism, however, the axiology needn’t be quite so simple. For example, one might hold that too much of a good thing is bad. Or one might suspect that the observable portion of the universe is much better than could reasonably be expected from a typical region and that adding more regions would objectionably dilute average goodness. Or one might simply think it would be stupendously awesome if the cosmos were some particular finite size – shaped like a giant jelly donut, perhaps, with red galaxies in the middle and lots of organic sugars along the edges.

Or one might mount the Repetition Objection, to which I will now turn.

Repetition and Value in an Infinite Cosmos

Consider a particular version of the Erasure Cosmology. There’s a Big Bang, things exist for a while, and then there’s a Big Crunch. Suppose that what happens next is an exact repetition of the first Bang-existence-Crunch. You, or rather a duplicate of you, lives exactly the same life, having exactly the same experiences, seeing exactly the same moonlight between the trees and having exactly the same thoughts about that moonlight, as envisioned by Nietzsche, all over again. And then it happens again and again, infinitely often. Call this Repetitive Erasure.

Now contrast this picture with the same cosmos, except that after the Crunch nothing exists. Call this cosmos Once and Done. Finally, contrast these two possibilities with a third, in which there is exactly one repetition: Twice and Done. (If you’re inclined toward metaphysical quibbles about the identity of indiscernibles, let’s imagine that each Bang and Crunch has some unique tag.) How might we compare the values of Once and Done, Twice and Done, and Repetitive Erasure? Four simple possibilities include:

Equal Value. Once and Done, Twice and Done, and Repetitive Erasure are all equally good. There’s no point in repeating the same events more than once. But neither is anything lost by repetition.

Linear Value. If Once and Done has value x, then Twice and Done has value 2x, and Repetitive Erasure has infinite value. The value of one run-through is not diminished by the existence of another earlier or later run-through, and the values sum.

Diminishing Returns. If Once and Done has value x, then Twice and Done has a value greater than x but less than 2x. Repetitive Erasure might have either finite or infinite value, depending on whether the returns converge toward a limit. A second run-through is good, but two run-throughs are not twice as good as a single run-through: Although it’s not the case that there’s no point in God’s hitting the replay button, so to speak, there’s less value in running things twice.

Loss of Value. If Once and Done has value x, then Twice and Done has a value less than x, and Repetitive Erasure is worse, perhaps even infinitely bad.

If Equal Value or Loss of Value is true, then Muted Optimism shouldn’t lead to preference for the infinitude of Repetitive Erasure over the finitude of Once and Done. If we further assume that in an infinite cosmos, the repetition (within some error tolerance) of any finite region is inevitable, then the argument appears to generalize. This is the Repetition Objection. Some positively-valenced existence is good, but after a point, more of the same is not better (e.g., Bramble 2016).

In ordinary cases, uniqueness or rarity can add to a thing’s value. One copy of the Mona Lisa is extremely valuable. If there were two Mona Lisas, presumably each would be less valuable, and if there were a billion Mona Lisas no one of them would presumably be worth much at all. The question is whether this holds at a cosmic scale. Might this only be market thinking, reflecting our habit of valuing things in terms of how much we would pay in conditions of scarcity? Or is there in fact something truly precious in uniqueness? (For discussion, see Lemos 2010; Chappell 2011; Bradford forthcoming.)

Perhaps there is something beautiful, or right, or fitting, in things happening only once, in a finite universe, and then ceasing. Is it good that you are the only version of you who will ever exist, so to speak – that after you have lived and died there will never again be anyone quite like you? Is it good that the cosmos contains only a single Confucius and only a single Great Barrier Reef, no duplicates of which will ever exist? Things will burn out, never to return. There’s a romantic pull to this idea. Against The Repetition Objection to the simple Muted Optimist’s preference for an infinite universe, I offer the Goldfish Argument (see also Schwitzgebel 2019, ch. 44).

According to popular belief (not in fact true), goldfish have a memory of only thirty seconds. Imagine, then, a goldfish swimming clockwise around a ring-shaped pool, completing each circuit in two minutes. Every two minutes it encounters the same reeds, the same stones, and the same counterclockwise-swimming goldfish it saw in the same place two minutes before, and each time it experiences all of these as new. The goldfish is happy with its existence: “Howdy, stranger, what a pleasure to meet you!” it says to the counterclockwise-swimming fish it meets afresh every minute. To tighten the analogy with the Repetitive Erasure cosmology, let’s stipulate that each time around this goldfish sees and does and thinks and experiences exactly the same things.

Now stop the goldfish mid-swim and explain the situation. The goldfish will not say, “oh, I guess there’s no point in my going around again.” The goldfish will want to continue its happy little existence, and rightly so. It still wants to see and enjoy what’s around the next bend. Moment to moment it is having good experiences. You harm and disappoint the goldfish by stopping its experiences, as long as each experience is, locally, good – even if they have all happened before innumerably many times. This is true whether we catch the goldfish after its first swim around, after its second, or after its googolplex-to-the-googolplexth. It's better to let the fish swim on. If the analogy holds at cosmic scales, then Equal Value and Loss of Value must be false. Maybe, though, there’s still something attractive about uniqueness, some truth in it that isn’t simply inappropriate market-style thinking? I see no need to deny that there really is something special about the first time. Let’s grant that it’s possible that the first go-round is somehow made less valuable by later go-rounds. As long as the harm done by stopping the goldfish (by denying future goods) exceeds the harm done by letting the goldfish continue (by reducing the rarity of past goods), then Diminishing Returns is the correct view. If we further assume that the added value does not continually shrink in a way that approaches zero, then the view we should embrace is one on which Repetitive Erasure would have infinite value.

This thinking appears to extend to the Infinitary Cosmology. Duplicates of you, and me, and all Earth, and the whole Milky Way will repeat over and over, infinitely. Each repetition adds some positive value to the cosmos, and in sum the value is infinite.

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Related:

Goldfish-Pool Immortality (May 30, 2014)

Duplicating the Universe (Apr 29, 2015)

Everything Is Valuable (May 6, 2022)

How Not to Calculate Utilities in an Infinite Universe (Feb 10, 2023)

Repetition and Value in an Infinite Universe (forthcoming), in S. Hetherington, ed., Extreme Philosophy. Routledge. [image adapted from Midjourney]

The Black Hole Objection to Longtermism and Consequentialism

According to consequentialism, we should act to maximize good consequences. According to longtermism, we should act to benefit the long-term future. If either is correct, then it would be morally good to destroy Earth to seed a new, life-supporting universe.

Hypothetically, it might someday become possible to generate whole new universes. Some cosmological theories, for example, hypothesize that black holes seed new universes -- universes causally disconnected from our own universe, each with its own era of Big-Bang-like inflation, resulting in vastly many new galaxies. Maybe our own universe is itself the product of a black hole in a prior universe. If we artificially generate a black hole of the right sort, we might create a whole new universe.

Now let's further suppose that black holes are catastrophically expensive or dangerous: The only way to generate a new black-hole-seeded universe requires sacrificing Earth. Maybe to do it, we need to crash Earth into something else, or maybe the black hole needs to be sufficiently large that it swallows us up rather than harmlessly dissipating.

So there you are, facing a choice: Flip a switch and you create a black hole that destroys Earth and births a whole new universe, or don't flip the switch and let things continue as they are.

Let's make it more concrete: You are one of the world's leading high-energy physicists. You are in charge of a very expensive project that will be shut down tomorrow and likely never repeated. You know that if tonight you launch a certain process, it will irreversibly create a universe-generating black hole that will quickly destroy Earth. The new universe will be at least the size of our own universe, with at least as many galaxies abiding by the same general laws of physics. If you don't launch the process tonight, it's likely that no one in the future ever will. A project with this potential may never be approved again before the extinction of humanity, or if it is, it will likely have safety protocols that prevent black holes.

[Image: Midjourney rendition of a new cosmos exploding out of the back of a black hole]

If you flip the switch, you kill yourself and everyone you know. You break every promise you ever made. You destroy not only all of humanity but every plant and animal on Earth, as well as the planet itself. You destroy the potential of any future biological species or AI that might replace or improve upon us. You become by far the worst mass murderer and genocidaire that history has ever known. But... a whole universe worth of intelligent life will exist that will not exist if you don't flip the switch.

Do you flip the switch?

From a simple consequentialist or longtermist perspective, the answer seems obvious. Flip the switch! Assume you estimate that the future value of all life on, or deriving from, Earth is X. Under even conservative projections about the prevalence of intelligent life in galaxies following laws like our own, the value of a new universe should be at least a billion times X. If we're thinking truly long term, launching the new universe seems to be by far the best choice.

Arguably, even if you think there's only a one in a million chance that a new universe will form, you ought to flip that switch. After all, here's the expected value calculation:

• Flip switch: 0  + 0.000001*1,000,000,000X = 1000X.
• Don't flip switch: X + 0 = X.

(In each equation, the first term reflects the expected value of Earth's future given the decision and the second term reflects the expected value generated or not generated in the seeded universe.)

Almost certainly, you would simply destroy the whole planet, with no compensating good consequences. But if there's a one in a million chance that by doing so you'd create a whole new universe of massive value, the thinking goes, it's worth it!

Now I'm inclined to think that it wouldn't be morally good to completely destroy Earth to launch a new universe, and I'm even more strongly inclined to think it wouldn't be morally good to completely destroy Earth for a mere one in a million chance of launching a new universe. I suspect many (not all) of you will share these inclinations.

If so, then either the consequentialist and longtermist thinking displayed here must be mistaken, or the consequentialist or longtermist has some means of wiggling out of the black hole conclusion. Call this the Black Hole Objection.

Could the consequentialist or longtermist wiggle out by appealing to some sort of discounting of future or spatiotemporally disconnected people? Maybe. But there would have to be a lot of discounting to shift the balance of considerations, and it's in the spirit of standard consequentialism and longtermism that we shouldn't discount distant people and the future too much. Still, a non-longtermist, highly discounting consequentialist might legitimately go this route.

Could the consequentialist or longtermist wiggle out by appealing to deontological norms -- that is ethical rules that would be violated by flipping the switch? For example, maybe you promised not to flip the switch. Also, murder is morally forbidden -- especially mass murder, genocide, and the literal destruction of the entire planet. But the core idea of consequentialism is that what justifies such norms is only their consequences. Lying and murder are generally bad because they lead to bad consequences, and when the overall consequences tilt the other direction, one should lie (e.g., to save a friend's life) or murder (e.g., to stop Hitler). So it doesn't seem like the consequentialist can wiggle out in this way. A longtermist needn't be a consequentialist, but almost everyone agrees that consequences matter substantially. If the longtermist is committed to the equal weighting of long-term and short-term goods, this seems to be a case where the long-term goods would massively outweigh the short-term goods.

Could the consequentialist or longtermist wiggle out by appealing to the principle that we owe more to existing people than to future people? As Jan Narveson puts it, "We are in favor of making people happy, but neutral about making happy people" (1973, p. 80). Again, any strong application of this principle seems contrary to the general spirit of consequentialism and longtermism. The longtermist, especially, cares very much about ensuring that the future is full of happy people.

Could they wiggle out by suggesting that intelligent entities, on average, have zero or negative value, so that creating more of them is neutral or even bad? For example, maybe the normal state of things is that negative experiences outweigh positive ones, and most creatures have miserable lives not worth living. This is either a dark view on which we would be better off not have been born or a view on which somehow humanity luckily has positive value despite the miserable condition of space aliens. The first option seems too dark (though check out Schopenhauer) and the second unjustified.

Could they wiggle out by appealing to infinite expectations? Maybe our actions now have infinite long-term expected value, through their unending echoes through the future universe, so that adding a new positive source of value is as pointless as trying to sum two infinitudes into a larger infinitude. (Infinitudes come in different cardinalities, but one generally doesn't get larger infinitudes by summing two of them.) As I've argued in an earlier post, this is more of a problem for longtermism and consequentialism than a promising solution.

Could they wiggle out by appealing to risk aversion -- that is, the principle of preferring outcomes with low uncertainty? Maybe, but the principle is contentious and difficult to apply. Too strict an application of it is probably inconsistent with longtermist thinking. The long-term future is highly uncertain, and thus risk aversion seemingly justifies its sacrifice for more certain short-term goods. (As with discounting, this escape might be more available to a consequentialist than a longtermist.)

Could they wiggle out by assuming a great future for humanity? Maybe it's possible that humanity populates the universe far beyond Earth. This substantially increases the value of X. Let's generously assume that if we populate the universe far beyond Earth, the value of our descendants' lives is equal to the value of the whole universe you could create tonight by generating a black hole. Even so, given that there's substantial uncertainty that humanity will have so great a future, you should still flip the switch. Suppose you think there's a 10% chance. The expectations then become .1*X (don't flip the switch) vs. X (flip the switch). Only if you think it more likely that humanity has that great future than that the black hole generates some other species of set of species whose value is comparable to that hypothetical future, would it make sense to refrain from flipping the switch.

If we add the thought that our descendants might generate black holes, which generate new universes which generate new black holes, which generate new universes which generate new black holes, and so on, then we're back into the infinite expectations problem.

Philosophers are creative! I'm sure there are other ways the consequentialist or longtermist could try to wiggle out of the Black Hole Objection. But my inclination is to think the most natural move is for them simply to "bite the bullet": Admit that it would be morally good to destroy Earth to seed a new cosmic inflation, then tolerate the skeptical looks from those of us who would prefer you not to be so ready (hypothetically!) to kill us in an attempt to create something better.

New Paper in Draft: Let's Hope We're Not Living in a Simulation

I'll be presenting an abbreviated version of this at the Pacific APA in April, as a commentary on David Chalmers' book Reality+.

According to the simulation hypothesis, we might be artificial intelligences living in a virtual reality.  Advocates of this hypothesis, such as Chalmers, Bostrom, and Steinhart, tend to argue that the skeptical consequences aren’t as severe as they might appear.  In Reality+, Chalmers acknowledges that although he can’t be certain that the simulation we inhabit, if we inhabit a simulation, is larger than city-sized and has a long past, simplicity considerations speak against those possibilities.  I argue, in contrast, that cost considerations might easily outweigh considerations of simplicity, favoring simulations that are catastrophically small or brief – small or brief enough that a substantial proportion of our everyday beliefs would be false or lack reference in virtue of the nonexistence of things or events whose existence we ordinarily take for granted.  More generally, we can’t justifiably have high confidence that if we live in a simulation it’s a large and stable one.  Furthermore, if we live in a simulation, we are likely at the mercy of ethically abhorrent gods, which makes our deaths and suffering morally worse than they would be if there were no such gods.  There are reasons both epistemic and axiological to hope that we aren’t living in a simulation.

Paper here.

As always, comments welcome!

How Not to Calculate Utilities in an Infinite Universe

Everything you do causes almost everything -- or so I have argued (blog post version here, more detailed and careful version collaborative with Jacob Barandes in my forthcoming book).  On some plausible cosmological assumptions, each of your actions ripples unendingly through the cosmos (including post-heat-death), causing infinitely many good and bad effects.

Assume that our actions do have infinitely many good and bad effects.  My thought today is that this would appear to ruin some standard approaches to action evaluation.  According to some vanilla versions of consequentialist ethics and ordinary decision theory, the goodness or badness of your actions depends on their total long-term consequences.  But since almost all of your actions have infinitely many good consequences and infinitely many bad consequences, the sum total value of almost all of your actions will be ∞ + -∞, a sum which is normally considered to be mathematically undefined.

Suppose you are considering two possible actions with short-term expected values m and n.  Suppose, further, that m is intuitively much larger than n.  Maybe Action 1, with short-term expected value m, is donating a large some of money to a worthwhile charity, while Action 2, with short-term expected value n, is setting fire to that money to burn down the house of a neighbor with an annoying dog.  Infinitude breaks the mathematical apparatus for comparing the long-term total value of those actions: The total expected value of Action 1 will be m + ∞ + -∞, while the total expected value of Action 2 will be n + ∞ + -∞.  Both values are undefined.

Can we wiggle out of this?  An Optimist might try to escape thus: Suppose that overall in the universe, at large enough spatiotemporal scales, the good outweighs the bad.  We can now consider the relative values of Action 1 and Action 2 by dividing them into three components: the short-term effects (m and n, respectively), the medium-term effects k -- the effects through, say, the heat death of our region of the universe -- and the infinitary effects (∞, by stipulation).  Stipulate that k is unknown but expected to be finite and similar for Actions 1 and 2.  The expected value of Action 1 is thus m + k + ∞.  The expected value of Action 2 is n + k ∞.  These values are not undefined; so that particular problem is avoided.  The values are, however, equal: simple positive infinitude in both cases.  As the saying goes, infinity plus one just equals infinity.  A parallel Pessimistic solution -- assuming that at large enough time scales the bad outweighs the good -- runs into the same problem, only with negative infinitude.

Perhaps a solution is available for someone who holds that at large enough time scales the good will exactly balance the bad, so that we can compare m + k + 0 to n + k + 0?  We might call this the Knife's Edge solution.  The problem with the Knife's Edge solution is delivering that zero.  Even if we assume that the expected value of any spatiotemporal region is exactly zero, the Law of Large Numbers only establishes that as the size of the region under consideration goes to infinity, the average value is very likely to be near zero.  The sum, however, will presumably be divergent – that is, will not converge upon a single value.  If good and bad effects are randomly distributed and do not systematically decrease in absolute value over time, then the relevant series would be a + b + c + d + ... where each variable can take a different positive or negative value and where this is no finite limit to the value of positive or negative runs within the series -- seemingly the very archetype of a poorly behaved divergent series whose sum cannot be calculated (even by clever tools like Cesaro summation).  Thus, mathematically definable sums still elude us.  (Dominance reasoning also probably fails, since Actions 1 and 2 will have different rather than identical infinite effects.)

This generates a dilemma for believers in infinite causation, if they hope to evaluate actions by their total expected value.  Either accept the conclusion that there is no difference in total expected value between donating to charity and burning down your neighbor's house (the Optimist's or Pessimist's solution), or accept that there is no mathematically definable total expected value for any action, rendering proper evaluation impossible.

The solution, I suggest, is to reject certain standard approaches to action evaluation.  We should not to evaluate actions based on their total expected value over the lifetime of the cosmos!  We must have some sort of discounting with spatiotemporal distance, or some limitation of the range of consequences we are willing to consider, or some other policy to expunge the infinitudes from our equations.  Unfortunately, as Bostrom (2011) persuasively argues, no such solution is likely to be entirely elegant and intuitive from a formal point of view.  (So much the worse, perhaps, for elegance and intuition?)

The infinite expectation problem is robust in two ways.

First, it affects not only simple consequentialists.  After all, you needn't be a simple consequentialist to think that long-term expected outcomes matter.  Virtually everyone think that long-term expected outcomes matter somewhat.  As long as they matter enough that an infinitely positive long-term outcome, over the course of the entire history of the universe, would be relevant to your evaluation of an action, you risk being caught by this problem.

Second, the problem affects even people who think that infinite causation is unlikely.  Even if you are 99.99% certain that infinite causation doesn't occur, your remaining 0.01% credence in infinite causation will destroy your expected value calculations if you don't do something to sequester the infinitudes.  Suppose you're 99.99% sure that your action will have the value k, while allowing 1 0.01% chance that it's value will be ∞ + -∞.  If you now apply the expected value formula in the standard way, you will crash straightaway into the problem.  After all, .9999 * k + .0001 * (∞ + -∞) is just as undefined as ∞ + -∞ itself.  Similarly, .9999 * k + ∞ is simply ∞.  As soon as you let those infinitudes influence your decision, you fall back into the dilemma.

If We're Living in a Simulation, The Gods Might Be Crazy

[A comment on David Iverson's new short story, "This, But Again", in Slate's Future Tense]

That we’re living in a computer simulation—it sounds like a paranoid fantasy. But it’s a possibility that futurists, philosophers, and scientific cosmologists treat increasingly seriously. Oxford philosopher and noted futurist Nick Bostrom estimates there’s about a 1 in 3 chance that we’re living in a computer simulation. Prominent New York University philosopher David J. Chalmers, in his recent book, estimates at least a 25 percent chance. Billionaire Elon Musk says it’s a near-certainty. And it’s the premise of this month’s Future Tense Fiction story by David Iserson, “This, but Again.”

Let’s consider the unnerving cosmological and theological implications of this idea. If it’s true that we’re living in a computer simulation, the world might be weirder, smaller, and more unstable than we ordinarily suppose.

Full story here.

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Related:

"Skepticism, Godzilla, and the Artificial Computerized Many-Branching You" (Nov. 15, 2013).

"Our Possible Imminent Divinity" (Jan. 2, 2014).

"1% Skepticism" (Nous (2017) 51, 271-290).

Related "Is Life a Simulation? If So, Be Very Afraid" (Los Angeles Times, Apr. 22, 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.

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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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