Image by Gerd Altmann from http://Pixabay.com

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.

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.

Eric Schwitzgebel

http://schwitzsplinters.blogspot.com/2020/05/your-infinite-counterparts.html