Friday, May 01, 2020

Your Infinite Counterparts

The visible universe is tiny -- only about 93 billion light-years. The whole universe might be much larger, maybe even infinite. A trillion galaxies might be an infinitesimal fragment of a speck of the tiniest toenail of what there is. Think large!

If you think large enough, eventually you'll get recurrence. There are only finitely many ways a finite number of particles can arrange themselves, within some arbitrarily small error tolerance. Some of the same stuff, eventually, will repeat.

If we assume cosmic diversity in which we're not exceptional (for example, if we assume that it's not just flat vacuum apart from our one special region), then eventually among the things that will repeat is you. Not you you exactly. Your counterpart, let's say. Someone who, to some arbitrarily fine degree of precision, is just like you in locally measurable qualities. The more precision we want, and the more life history we want (the past five minutes? your whole life? the whole history of Earth?), the farther away in spacetime we should expect this counterpart to be. But if the universe truly is infinite, that counterpart will out be there, eventually, at some spatiotemporal distance. And then again somewhat farther, and again still farther, and again -- infinitely often.

If you don't want to be so self-focused, fine. Maybe you care more about your daughter. Eventually, there will be a counterpart of your daughter. Maybe you care about Socrates's conversations in Athens. Those will of course repeat, too -- in every possible variation.


My question is, what should our attitude be toward this repetition, if we assume it exists? Should you care that somewhere out there are infinitely many counterparts of you, your daughter, and Socrates in dialogue? Should the existence of such things have any effect on how you think about your own life or what's happening on Earth? Or is it all a big meh?

Nietzsche, for one, didn't think recurrence would be a meh.

What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: "This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy, and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence? -- even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again, and you with it, a speck of dust!"

Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: "You are a god and never have I heard anything more divine." If this thought gained possession of you, it would change you as you are or perhaps crush you. The question in each and every thing, "Do you desire this once more and innumerable times more?" would lie upon your actions as the greatest weight. Or how well disposed would you have to become to yourself and to life to crave nothing more fervently than this ultimate eternal confirmation and seal? (Gay Science 341, Kaufmann trans.).

Nietzsche's posthumous notes suggest that he might have been thinking of recurrence in something like the sense I've described, as a genuine physical conjecture (cf. Boltzmann and Poincaré), though that remains disputed.

We might challenge Nietzsche's implicit personal identity claim -- that if the hourglass of existence were turned over and everything was run again, it would be "you" doing all the same things, rather than merely a duplicate of you.


Straightaway, I can imagine two reasons to favor Team Meh. One concerns distance, the other causation.

On distance: These counterparts are, in all likelihood, very far from you, spatiotemporally. Maybe that distance matters. You probably care a lot about what's happening in your house, less about what's happening down the street, still less about what's happening on the other side of the planet, even less about what's happening in Andromeda, and basically not at all about something that's a googol lightyears distant. Distance breeds indifference.

On the other hand, there's something odd about thinking that distance per se is indifference-making. If someone kidnapped your daughter and took her around the world -- to New Zealand, say, if you're in the U.S. -- you wouldn't find yourself (I assume) growing more indifferent as she approached New Zealand and then, maybe, starting to care about her more after the kidnappers did a U-turn. More fancifully, if you knew that you'd be deep-frozen then revived after a trillion years in some other galaxy, you'd probably care about what your new home would be like even before you were frozen. The mere fact of its physical distance isn't enough to make it irrelevant to you.

Lack of causal interaction correlates with distance and maybe is a more justifiable basis for indifference. You normally have had and will have many more, and more important, causal interactions with your daughter than with a stranger in New Zealand, even if they are both in New Zealand right now. And in the deep-freeze case, you care about that future galaxy because it will be you there, carrying forward the effects of all your past choices and life events. You care about Earth Socrates more than counterpart-Earth counterpart-Socrates because Earth Socrates is the one who actually had the effects on your culture and philosophical tradition.

On the other hand, we can sometimes care about distant strangers, even when the causal threads are thin. And causation is cheap, if we're patient enough, echoing butterfly-like through the world, and maybe even scaling up infinitely over vast spans of time, so that eventually any action you do could have whatever arbitrarily specific effects you desire, on some far distant counterpart.

That last thought is so speculative that we might brush it aside. Fair enough (though read my post and book chapter on it, if you like). Lack of causal interaction, or lack of the right kind of causal interaction, might justify a "meh" reaction to those infinitely many far-distant counterparts, playing out all those versions of your life.

If "meh" is the reaction that you arrive at, or want to arrive at, you can probably justify it. But I invite you to consider whether, on reflection, you really do find the possibility of a universe with infinitely many duplicates and near-duplicates of whatever you care about to be meh, rather than worrying, intriguing, puzzling, or in some other way potentially of interest.


Suppose you are struck and killed by lightning. Somewhere out there in the infinite universe -- if standard physical theory is correct -- will be a suddenly congealed new version of you, in an arbitrarily large environment. Alongside the duplicate, if you are willing to look far enough, will be duplicates also of your home, your family, your country, your galaxy. (Sudden chance organization from disorganized chaos is, of course, extremely unlikely in any region of spacetime as minuscule as a few trillion light years. But literal infinitude is powerful.) This new entity and its friends will (presumably, but disputably) have seeming-memories, experiences, plans, attitudes, that are qualitatively identical to yours even if they have a radically different history. In some sense, no one will notice the gap. It will be as though you smoothly continued. (Compare Swampman. See also the story "Penelope's Guide to Defeating Time, Space, and Causation" in my recent book [free manuscript draft here].)

Sometimes, we treasure uniqueness. There's only one copy of the Michelangelo's statue of David. That makes it, maybe, uniquely valuable in a way that any one instance of Rodin's The Thinker, of which there are 28 castings, is not. Suppose that our galaxy were to happen only once. Suppose that the overall sum of awesomeness and value of our entire galactic history is n units. Now suppose a precisely similar version of it happens again, and again, and again. Is each version worth n more units? Or does repetition decrease the marginal value, so to speak? If you were God, choosing a universe, would you say -- well, we did that once, done, that's enough! Or would you say, replay, replay, replay, endlessly with no point of diminishing returns?

What Nietzsche seems to think most of us would find terrifying about repetition is that every decision we have would have infinite weight. We decide as it were, not only for ourselves, but for all our duplicates. (Though I wonder, on this perspective, if I'm not first in the chain, maybe I don't decide at all because an earlier version already decided for me?) Although what you choose wouldn't normally cause your distant duplicates to choose the same, it might at least signify that they would and will choose the same. In some sense, you speak for all of them. Maybe, if there's some chance in the process, or some divergence in the process due to small differences, you will make a different choice than some -- and so there will be near-duplicates of you playing out each possible choice, among which you either belong to the majority or you make an atypical choice. Do you follow the crowd of yourself? Is it too strange to find some small comfort in the idea that somewhere out there is a duplicate of you who made a better choice?

Just some things I find interesting to think about, if the universe is infinite.


If you enjoy my blog, check out my recent book: A Theory of Jerks and Other Philosophical Misadventures.

[image duplicated from here]


SelfAwarePatterns said...

Max Tegmark ran the numbers and claimed that there should be a duplicate of our observable universe 10^10^29 meters away. I'm not sure how he did that calculation.

My attitude is one of interest, but not any great concern. It's not like I'll ever have any way to interact with my doppelgangers. The situation seems similar to if the many worlds interpretation of quantum mechanics is true. In that case, while I've been typing this, there have been an uncountable copies of me generated, which unless someone figures out a way to cause interference between decohered branches of the wave function, means those copies are just as disconnected as the ones 10^10^29 meters away.

An infinite universe seems absurd. But a universe with any kind of boundary seems equally absurd. Even if space eventually curves back on itself, that just means it curves *within* something, where we're right back to the question of whether that outside realm is infinite, bounded, or curved inside something else.

Turtles all the way down.

Anonymous said...

I'm a huge fan. I'm also a theoretical physicist, and I have to confess that I take issue with this crucial statement that underlies your blog post: "If you think large enough, eventually you'll get recurrence. There are only finitely many ways a finite number of particles can arrange themselves, within some arbitrarily small error tolerance. Some of the same stuff, eventually, will repeat."

We do not know anything about the full sample space here. Yes, if the sample space is compact (closed and bounded), and, furthermore, if there is nothing special about our atomic configurations, then one could imagine that sufficiently distant regions of an infinitely large universe should feature near-repetitions of ourselves. This is a spatial counterpart of the Poincare recurrence theorem. (

But the full sample space could just as easily be non-compact, and right now we have no way to know for sure. The particles of the Standard Model may well not be all the kinds of particles that there can be. Other distant regions of an infinitely (or very large) universe might realize different menus of particle types, or something more exotic entirely. And in non-compact sample space, it is manifestly not true that anything has to repeat. Just consider a "random walk" in an unbounded 3D volume.

Arnold said...

Does an attitude towards presence defy time and descriptions...
...I would substitute change for repetition and eh for meh, thanks for the read...

"Knowledge was inherent in all things.The world was a library..."
...Chief Luther Standing Bear;

George Gantz said...

Eric - Interesting that your speculations on an infinite universe lead you to the question of "recurrence." In the realm of theoretical mathematics, the connections are to the formal notion of recursion, that is for an action on an object (sets, logic, numbers) to be able to act again on the output. Yes - turtles all the way down as your commenter notes. Recursion runs into some difficulties - thanks to Godel and Turing - namely, incompleteness and undecidability. Whether these are "meh" issues or not is the subject of the current FQXi Essay Contest ( ) A couple hundred minds are throwing their best stuff at the question. My take is that incompleteness, undecidability, complexity, infinity and their corollary limits to our understanding are features (not bugs) to the world, as they create the opportunity for autonomic consciousness and free will. (SEE: )
I have serious reservations about any speculations about infinite universes or infinite spaces. Max Tegmark's Mathematical Universe may be interesting but there is a simple counterexample that shows it is, and/or results in, cogitations that are meaningless. The infinite monkey theorem posits that a long enough random string will eventually produce all the works of Shakespeare. So if you happen to come across a manuscript that reproduces, word for word, the play Hamlet (say) - how do you know whether it is a work of genius or simply an unusual random string? One is a meaningful work of art and genius - the other is really just random gibberish. How can you tell the difference? Max thinks we are random beings in a random process and we just happen to be in the universe we are. But if you look at the physical characteristics of this place - the fine tuning constants, the predilection for life, the mystery of consciousness - it certainly looks like a masterful work of art and genius, at least to me.
Thanks! - George

Stephen Wysong said...

George Gantz: You wrote “The infinite monkey theorem posits that a long enough random string will eventually produce all the works of Shakespeare.”

It would seem that, if we scan the digits in any infinite non-repeating decimal as an infinite binary string—take Pi for example—we would find every written work, every visual creation in every digital format at every resolution and everything else that can be digitally represented, including all human knowledge. No art or genius required—infinity is inconceivably huge.

Stephen Wysong said...

A fascinating topic Eric! A PDF of Max Tegmark’s 2003 paper “Parallel Universes” can be downloaded from:

His Scientific American article of 2003 with the same title is derived from this paper I believe. As Anonymous (the theoretical physicist) points out, there are caveats—a few underlying assumptions—which are clearly identified by Tegmark. But if you can accept those, the notion is fascinating to consider.

Your question:

“... what should our attitude be toward this repetition, if we assume it exists? ... Should the existence of such things have any effect on how you think about your own life or what's happening on Earth?

When I was last considering this topic, I decided that the crucial issue regarding what to make of this comes down to how you define ‘you’. Are ‘you’ this one specific instance of yourself, as the phrase “your own life” implies? Or, perhaps you can understand ‘you’ to be a specific pattern of DNA at the instant of conception? In the first viewpoint there’s only one possible ‘you’—essentially ‘you’ are your very own worldtube at a specific range of 4-dimensional locations in spacetime. If you accept of the DNA idea then multiple “you’s” are possible, including the infinite series of ‘doppelgangers’ Tegmark writes about—“Is there another copy of you reading this article?” he asks.

If you can accept the expansive definition of ‘you’ as a DNA pattern, the infinity of ‘you’ comprises every possible variant of 'your' life, such that the collective You seems meaningful indeed. Distance and light cone causality are irrelevant. At a minimum, The Infinite You means that everything ‘you’ start will be completed by some instance of ‘you’, which I believe is the premise underlying Greg Egan’s Permutation City, in which a contribution of funds to the virtuality project means that it will be brought to completion in the world of at least one of your infinite incarnations. That’s all that’s required for all of the participants to achieve virtual immortality. With that consideration alone (and I’m sure there are more) I’m inclined to view The Infinite You as not-meh—it’s how I’ve come to conceive of myself. It is 'Me'.

Nietzsche’s Eternal Recurrence is distinguished from The Infinite You in that he conceived that the very same single lifetime is repeatedly instantiated and experienced. However, as I’ve written before, it seems unavoidable to conclude that we are all eternally re-experiencing (not ‘re-living’) our unchanging lives as encoded in spacetime in the Block Universe of relativity physics—lives that do not “happen” and have never “happened” but were wholly constructed to be repeatedly experienced. With the concept of The Infinite You added, then all of the infinite variations are repeatedly experienced. This reality is not a recurrence since nothing at all ‘occurs’ in the Block Universe so nothing 're-occurs' either.

Howie said...

If I remember correctly Cantor established different levels and kinds of infinity. That may play, plus not just the idea of something just like me, but something ""almost" like me, like me "but"

Howie said...

Plus I'm not sure whether we're talking of a a "physics" view of the universe where infinite variety means mere physical variation or an Aristotelian universe where people exist and people exist the way they are because of their peculiar histories and interactions with the environment

Eric Schwitzgebel said...

Thanks for all the comments, folks!

Anon May 1: You write: "But the full sample space could just as easily be non-compact, and right now we have no way to know for sure. The particles of the Standard Model may well not be all the kinds of particles that there can be. Other distant regions of an infinitely (or very large) universe might realize different menus of particle types, or something more exotic entirely." Thanks for the helpful qualification here. I agree that we need assume that this is false about the sample space in order to justify recurrence.

George and Stephen: These are interesting questions, and of course the answers will depend on what theories of consciousness, personal identity, meaning, etc., one accepts. I agree that Tegmark and Egan are terrific starting points here. I wouldn't be inclined to think of "you" in terms of DNA. One reason concerns identical twins right here on Earth. Something could arise by chance, rather than genius, but then carry forward meaning after it has arisen -- e.g., Swampman cases.

Stephen Wysong said...

Eric, your comment about identical twins motivated me to briefly research the issue of “selfhood” for the monozygotic, another very interesting topic. You wrote:

"I wouldn't be inclined to think of "you" in terms of DNA. One reason concerns identical twins right here on Earth.”

Since the concept of ‘You’ is inextricably bound with the concept of 'Self', I Google’d the topic “identical twins sense of self” and here’s a snapshot of what I found:


”However, identical (or monozygotic) twins come from a single egg that splits into two separate embryos by a still not well-understood mechanism, and have almost 100 per cent the same DNA.”

A minuscule technical point perhaps. Moving beyond that, however:


”The deep interconnection of psychological identity between twins is real. Unlike single-born infants and toddlers, shared identity is inevitable and normal. Some aspect of a twin’s sense of self is actually shared. ... From my personal and professional experiences, I know it is easier to corral wild horses than to set up ego boundaries for twins. ... Believing that you can actually dictate individuality in twins is short-sighted, futile, and grandiose. And clearly, some identity that is shared between twins is intractable and life-sustaining.”


”The prevailing view in current psychological research is that twins and relationships between twins are inherently abnormal and pathological. Notions of twins as being too close or too self-contained dominate. For example, the twin bond is characterized as a kind of psychopathological unit identity. A unit identity collapses individual identities into a single being ...”


”Results show that monozygotic twins have significantly higher scores than dizygotic twins for three factors: desire to remain undifferentiated, projection of the twin relationship, and enmeshment of self within the twin identity, showing that monozygotic twins have greater difficulties creating a unitary identity and have less of a desire to do so.”

Based on these findings, Eric, I think it’s fair to say that identical twins believe they are two separate instances of a ‘You’ even though no one uses that terminology. It seems reasonable to also conclude that identical twins know exactly what it feels like to be another person, which is a knowledge of another person's mind that we singletons cannot have. Perhaps the widely held singleton separateness notion of ‘You’ is unnecessarily restrictive.

My DNA-based ‘You’ viewpoint seems reinforced by what I’ve discovered and reported here, so I’ll continue to regard myself as an infinite cluster of organisms, which is undoubtedly the result of a lifetime of reading science fiction ... ;-)

Autumnal Harvest said...

I'm an ex-theoretical physicist, and mostly disagree with Anonymous. Yes, it's possible that the sample space is not compact, so I agree on a theoretical level. But I don't see the relevance of having particles other than those of the Standard Model. Assuming the set of particles is finite, it's hard to see why additional particles would matter. If the set of particles is inifinite, it's hard to see why we get such a restricted set in our region, unless there's some mechanism that causes certain types of particles to cluster in particular regions, in which case we likely (albeit not necessarily) end up with recurrence. I agree that at a theoretical level the sample space might be non-compact, but this is so difficult to imagine that it seems like a very minor clarification after the much larger assumption that the universe is infinite.

Arnold said...

Autumnal Harvest, infinite observation?, that theoretical observation may be independent, like theoretical infinity and theoretical physics, to our cosmos universe...meh?

Stephen Wysong said...

Autumnal Harvest: How did you come to be an extheoretical physicist? Can you “drop out”? ... ;-)

I agree with your remarks to Anonymous. I believe Tegmark’s first assumption for his Level 0 multiverse is “If the universe is infinite or sufficiently large ...” and the second assumption is that the composition and physics of our Hubble volume is representative of the universe beyond.

I’m curious about your causal connection comment. In Block Universe terms, as I understand it, there’s no causation at all—all events in the Block Universe are fixed and unchangeable. Causation is noted, or observed, only in the dynamic_view created by a flowing consciousness, but causality seems to me to be a statistical observation (very closely approaching a probability of 1) rather than an assured necessity. Of course, probability in an infinite field is a bit of a slippery concept.

In your comment that “If another part of the universe is completely causally disconnected, in some sense it doesn't even exist ...” the “in some sense” is a bit puzzling. The causal light cone in which we exist is but one of an infinite number of light cones external to our own, all of which are co-real. So why should that co-reality not factor into our thinking?

As to the universe being “finite in age” I believe that’s the dynamic_view interpretation—the Big Bang story. I can’t imagine the Block Universe as anything but eternal. It’s origin, if it had one, is certainly indeterminate. And if it were to cease existing at any point further along on the temporal axis, we wouldn’t be here ... would we?

I’m not, and have never been a physicist, but as an engaged onlooker, I’d appreciate your perspective on these points.

Eric Schwitzgebel said...

Thanks for the continuing comments, everyone!

Stephen: You write: "Based on these findings, Eric, I think it’s fair to say that identical twins believe they are two separate instances of a ‘You’ even though no one uses that terminology." I'm inclined to disagree. There's a strict sense of identity and then there's social identity and identification. Here's a test: If Ralph commits a crime is it fair to put his twin Robert in jail? If you owe money to Robert, is it fine to just pay Ralph instead (assuming they live in different cities with different bank accounts, etc.)?

Not sure about the block universe -- definitely don't want to commit on that; but I agree with you point about co-reality.

Autumnal: Thanks, that's very helpful!

Stephen Wysong said...

Eric, by “two separate instances” I meant two separate individuals, so Ralph goes to jail, not Robert. The identical twins’ “unit identity” comments I submitted earlier seem to me to say something, I’m not sure what, relevant to the philosophy/psychology of Self. I find it strange that “… the twin bond is characterized as a kind of psychopathological unit identity.” Psychopathological? Perhaps it’s a ‘normal’ development for monozygotic twins. I wonder how it develops—if two unrelated infants of the exact same age were raised together as identical twins, including dressing and treating them them alike, would they develop a unit identity? I suspect not. Perhaps the unit identity is biologically rooted—a brain functionality of some sort. I searched the topic with Google Scholar and found nothing at all, much to my surprise, since its a fascinating syndrome.

Regarding the block universe, I’m curious to learn why you’re “not sure.” With the proviso that certainty on any subject is not attainable, I’m “pretty sure.” Perhaps you might blog one of these days about your perspective.

Paul Davies wrote:

In their professional lives, most physicists accept without question the concept of the timescape [block universe], but away from work they act like everybody else, basing their thoughts and actions on the assumption of a moving present moment.

Most physicists subscribe to the timeless block universe because it’s an implication of relativity theory, for which the evidence seems overwhelming. Even physicist Lee Smolin must still believe while he continues his search for a replacement theory for relativity (I believe it’s called Shape Dynamics) in order to satisfy his recently developed desire for free will and an open future. Time Reborn is his book about that search and contains a lucid general audience description of the Relativity of Simultaneity that directly implies the block universe.

My belief in the reality of the block universe is grounded in the physics—as with other scientific issues, like climate change, I take my cue from the scientists. In my opinion, Philosophers of Time, who have endlessly sparred over Presentism vs. Eternalism are frequently driven by questionable arguments like, “Our perceptions tell us that flowing time exists.” And there’s endless wrangling over tensed statements and the like, as if grammatical/linguistic issues determine what is real. Like Smolin, many philosophers' thinking seems motivated by free will desires. I don’t believe Philosophy is a credible place to look for clues to the architecture of the universe.

In my few years of research, I was surprised to find that Einstein was alone in his consideration of the consequences for humanity of the block universe. In a very few quotations, he used the engaging phrase “the eternity of life” to refer to his conclusions. For the curious, my paper on the subject “The Consequences of Eternalism” (formerly “Einstein’s Breadcrumbs”) can be downloaded from:

Autumnal Harvest said...

Stephen: I mean that I used to get paid to do theoretical physics, and I no longer gain paid for it. :)

If something happens somewhere that has no causal connection to us, I'm not sure in what sense it's real - we have no way of testing anything about it. If a tree falls in a forest, and not only does no one hear it, but it's not possible for it's falling to affect us an any way, tenuous or not, in what sense can you say whether it's truly fallen or not? To me, if something can't have any causal connection to us, it seems not real, because nothing you hypothesize about it (tree has fallen, tree has not fallen, tree's atoms have spontaneously rearranged themselves to form an identical copy of Taylor Swift, etc. . .) can be tested in any way.