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Our Improbable Existence and the Multiple Universe Hypothesis
By: Brian Crabb

Over the past twenty-five years or so there has been a great deal of discussion about the idea that the emergence of intelligent life on Earth is an event of such overwhelming improbability that any one universe, our universe, could not reasonably have been expected to produce it by chance alone. The possibility that in a randomly configured primordial universe the elements should assemble themselves in exactly the way required for the development of life at all appears to be preposterously slim. If, as some statisticians insist, the odds against such an occurrence were something of the order of 10 ^22:1, which in normal parlance means 10,000,000,000,000,000,000,000 to1 against, then it would make good scientific sense to look for an alternative and more convincing explanation for the fact that we do, undeniably, exist. How could this have come about in the face of such intolerable odds? Could it be that nature has had the opportunity to create life in countless other universes, and that we are just the lucky universe in which it succeeded? The suggestion is that if, say, a billion universes have existed, it would be much less improbable and surprising that we should have emerged in one or another of them . Or, putting it the other way around, the hypothesis that there are or have been multiple universes is seen according to this line of reasoning as being supported by the evidential fact that we exist.

An easy way to understand this is by using an analogy. There are plenty of these in the literature and it doesn't really matter which one we choose. We can even invent our own. Imagine you are watching television one evening and the national lottery results come up. You are told that there is one lucky winner this week, a Mr. X who lives in East Grinstead. If I were to then intrude on your privacy and ask you how many lottery tickets had been bought that week, I imagine you would assume that since the chances of any particular ticket turning out to be the winner are around 14 million-to-one against there were probably an awful lot of tickets sold. The more tickets sold, the more likely that one or another of them will bear the winning numbers. Other analogies can be just as easy to think up. Someone tells you that a gambler somewhere in Nevada has just been dealt three royal flushes in a row, the odds against this occurring on any particular occasion being just over 274,000,000,000,000,000 (274 x 10^15) -to-one, as it happens. What are you to think of this? Was it a miracle? Not really, since if we think of the vast number of gamblers around the world who have been dealt poker hands day in, day out, since the game was invented in the 1830s, it begins to seem less surprising that amidst all that dealing three consecutive royal flushes were quite likely to come up sooner or later. So again, as with the lottery result, we are assuming that the more attempts made at a particular pursuit, the more likely it is, and therefore the less surprising when it occurs, that there will be a hit.

Let me give you one more example of this; one which we will be referring to again once the philosophical problem we are looking at has become clear. You open the morning newspaper and read that an exceedingly unlucky gentleman, Smith, was wandering about on the moor last night and was instantly struck through the heart by a falling meteorite - the only meteorite ever to have landed on that patch of ground in the entire history of the world! Unlucky indeed. After mulling this unfortunate incident over for a few minutes you find that you are able to accept that, since meteorites are falling to earth almost constantly, sooner or later one would be bound to land on the moor. That is statistically unsurprising. That it happened last night rather than on any other night seems equally unproblematic, since if it was going to land on one night or another, why not last night? What you find utterly astonishing, however, is that of all the places it could have fallen harmlessly to ground it happened instead to pass clean through the heart of the unfortunate Smith. A truly remarkable coincidence; so remarkable that you feel moved to look for a possible explanation. Could it be that there was a moth-hunting party or perhaps a horde of nocturnal ramblers out on the moor last night? If there were, say, a thousand people milling about in the vicinity when the missile put in its appearance, that would make the fatal accident somewhat less surprising, at least. Again, the underlying principle here would be that the more opportunities there are for an event to occur, in this case for the first ever meteorite on the moor to pass through a human being, the more likely and therefore less surprising it would be. We would say that although Smith was the unlucky victim, it might equally well have turned out to be Jones, or Brown, or any one of the thousand men who were in the vicinity at the time. In fact it is a thousand times more likely, and therefore less surprising, than if Smith had been alone. So again we would infer from an initially surprising piece of news that there were probably many opportunities for it to occur. The news that Smith, or Jones, or anyone else, was struck down by the meteorite leads us to suspect that the moor must have been rather densely populated that night.

Let us summarise the principle we have been using here, then, by saying that whenever an extremely improbable event occurs it is more likely that there were many opportunities for it to occur than that there was only one. Improbable events provide evidential support for the many-opportunities hypothesis. I shall refer to this henceforth as the IM principle, according to which I (Improbable events) support M (the Many opportunities hypothesis). When I is the event of intelligent life emerging in our universe, which by most accounts was exceedingly unlikely to have occurred by chance alone, I becomes supporting evidence for the hypothesis that there must (in all probability) have been many other universes in which it might have occurred (but probably did not). The problem emerges when we realise that the issue can be viewed from two quite distinct perspectives, and that the obvious conclusion to be drawn in each is equally distinct. I will refer to these as the 'God's-eye' and 'egocentric' perspectives respectively.

According to the first, the story would be along the lines already explored; that the more universes there have been, the more likely that one or another of them will produce intelligent life (this is the IM principle), and we can then plausibly imagine the resultant intelligent life to be us, now musing over how we could have been so lucky as to have emerged. We refer to the universe which bore us as "this" universe, of course, but that is only after the event; we would have done so whichever universe it happened to have been. Referring back to the earlier analogies, this point of view would indicate that the gambler could have been anyone, at any time and in any den, so the more deals there have been, the more likely the event would have been to occur. By the same token, the lottery could have been won by anyone, so the more tickets sold the more likely it was to be won. Finally, given that a meteorite landed on the moor, the fatal event could have befallen anyone who happened to be there. Hence, a densely populated moor would present correspondingly more opportunities for the resultant fatality. In each case, then, given the evidence I, that an extremely improbable event has occurred, it is likely that M, there have been many opportunities for it to have occurred.

The second, egocentric, perspective presents quite a different story, which emphasises the observation that it was not just any universe that bore life but this one in particular. The vanishingly small possibility that this universe would have borne life is not improved or affected in any way by how many other universes there have been, since there is no causal relation between our universe and any others. If I walk into a gambling den and stay for just three deals, the odds are (274 x 10^15) :1 against my being dealt three royal flushes in a row. If despite the odds it happens, however, I have no good reason to infer that there must be millions of other people doing the same thing in other dens. The fact is that I was just exceedingly lucky. For me to infer to the contrary would be to commit what is often termed the "inverse gambler's fallacy." The gambler's fallacy involves assuming that since a good hand has not come up for a while it is due to do so (whereas in fact the number of prior deals has no statistical effect on the outcome of the present one), and the inverse gambler's fallacy involves assuming that this good hand is evidence that there must have been a large number of previous deals. There is no causal or statistical connection in either case.

The tension between these two perspectives is brought out even more vividly for Smith on the moor. On the one hand we, as the impartial audience, hear that a meteorite landed on the moor last night and that someone, it could have been anyone but happened to be Smith, was struck clean through the heart. Our perfectly valid inference is that the moor was probably packed. Smith, on the other hand, would disagree. His dying thought as he lay slain in the peat bog would be "Gad, what bad luck!," but he would have no reason at all to append this with "Such a pity there were so many people in the party." For Smith, it makes no difference how many other people are around. The probability that he in particular would be hit remains exactly the same, as the inverse gambler's fallacy served to remind us. Both of these perspectives are valid, because their respective inferences are drawn from different perspectives. In the first case, just anyone on the moor that night, or any universe which has ever existed, would suffice, while in the second it has to be this one. The more specific we are about the target, the slimmer the chances become. But this leaves us with an apparent contradiction. Does the particular event of Smith's death on the moor suggest that he was part of a crowd or not? Similarly, does our undeniable emergence in this universe point to the probable existence of many other universes, or not? Counter-intuitively, it seems to depend on how we view the event.

In the case of the meteorite, at least, the apparent conflict can be brought into even sharper focus when we realise that both of these perspectives on the problem are available to Smith himself, in his death throes. On the one hand he can think that it is truly remarkable that anyone should have been hit, and that this probably indicates quite a gathering on the moor. On the other, he knows that the fact that he in particular was hit by the single meteorite indicates nothing at all about the company he is in. Let's say the area of the moor in question is equivalent to one million people. The probability P of the meteorite hitting a particular person is then one in a million, or 1:10^6. So:

P = 1:10^6

Smith knows that the probability of his being hit was 1:10^6.

At the same time, the probability P' of the meteorite hitting someone or other in a crowd of N people will be P x N. So:

P' = N:10^6

Obviously, from this, we can derive the common-sense statistic that the probability PS, of Smith rather than anyone else on the moor being hit, must be 1:N. So:

PS = P:P' = 1:N

None of these figures is at all mysterious or problematic to Smith. The problem is what other statistical inferences he is entitled to draw. He wants to infer that he was part of a dense crowd, but he also knows that, in order to avoid committing the inverse gambler's fallacy, he has to explain why his being hit by the meteorite was equally improbable regardless of the overall population of the moor. Otherwise, his being hit would indeed add weight to the hypothesis that the moor was heavily populated, the gambler's three royal flushes at one attempt would add weight to the hypothesis that the cards had been dealt a billion times before, and so on; results which we already know to be false. The problem is that Smith is someone, and the probability of someone rather than no-one being hit is N:10^6, which seems to indicate that someone (who just happens in this case to be Smith) being hit lends support to the multiple opportunities hypothesis M, that there were many people on the moor at the time. This line of reasoning does commit the fallacy, but it is difficult at first to see why.

The enigma can be resolved, and to that end it helps to break it down into component parts. To begin with let us imagine breaking the news to Smith in easy-to-digest stages. There he is wandering about on the moor in pitch-blackness, when he hears the news over his radio that, astonishingly, someone on the moor has just been hit by a meteorite. His reaction, like ours, should be that there are very likely a large number of people there. P' = N:10^6, so the larger the population N, the less improbable for the event to have occurred. He then hears the news supplement that the person hit by the meteorite was himself! He didn't feel a thing at the time, but now that he is prompted to check it is true. His jacket is oozing with blood, a strange faintness is beginning to overcome him and he finds himself lurching uncontrollably into the peat bog. What awful luck! Of all the N people milling about it had to be Smith himself who took the missile. The probability of that happening was only 1:N. For Smith, there are now two rival hypotheses. Either he is alone and was hit by the meteorite, or he was in a crowd, but was unlucky enough to be the one hit anyway. The probability that someone would be hit is N:10^6. So the initial piece of news that someone has been hit would suggest a large population N. But then the probability that it would be him, rather than anyone else, amounts to 1:N. The overall probability that he in particular would be hit is therefore as we would expect; N:10^6 x 1:N = 1:10^6, regardless of how many other people there are. The N falls out of the equation. Given that someone has been hit, then, the probability that there were N people present is exactly counterbalanced by the improbability of it being Smith in particular. For Smith, the event to be explained is that he in particular was hit, and that event would be equally improbable whether or not he was accompanied. It therefore tells him nothing about the population on the moor.

All of the above considerations are valid, but still there is something rather odd about Smith's situation in all of this. We from our God's-eye perspective are sure that, when we hear the news that someone has been hit, it is most likely that the moor is heavily populated, but for some mysterious reason we are insisting that Smith must think otherwise, in order to avoid the inverse gambler's fallacy. From the news of his personal misfortune we are insisting that he must be completely unable to infer anything about the moor's population. In an attempt to resolve this conflict, we can only appeal to a discrepancy between the knowledge we have and the knowledge that Smith has, immediately prior to the misadventure. The only relevant difference would be that Smith knows already that he is on the moor, whereas we might not. But let us assume now that we do know this, and see whether it makes any difference.

I am sitting at home with Smith and after a final toast to his health I wish him a good ramble, as he disappears out into the night bound for the moor. I know, effectively, that he will be there in a matter of minutes. Some thirty minutes later I learn from the radio that some unfortunate fellow by the name of Smith has met his demise at the hands of a random meteorite on the moor. What are my first thoughts? Certainly not that there must have been a veritable throng of nocturnal ramblers on the moor. The very idea is irrelevant, since I already knew that Smith would be there and I now know that he was the victim. I understand immediately that my good companion has met with an almost inconceivable misfortune, but that is the end of the matter. Any assumption about other ramblers being present would have no effect on the probability of Smith being hit. In short, we can agree now with Smith that the hypothesis IM only applies to a case in which Smith is not already known to be on the moor, or in which Smith has not been identified as the victim. This explains why learning that someone or other has been struck down supports the multiple-ramblers hypothesis (IM applies), since the more ramblers there are the more likely it is that one would be struck down, while learning that Smith in particular was struck down, when we already knew that he was on the moor, completely eludes the IM principle. Similarly, we hear the story of a gambler sitting down to a single series of three deals. Thus, we already know that this particular gambler has been dealt the cards. When we subsequently learn that he was dealt three royal flushes, we are astonished, almost incredulous, but we have no reason to suppose that there must have been other gamblers at work. Finally, if I purchase a single lottery ticket and then find that I have won the jackpot, I have beaten odds of around 14,000,000:1 against me, but making the assumption that many others bought tickets too does not help to explain my success. Thinking otherwise in any of these cases would amount to committing the inverse gambler's fallacy.

The reason why Smith on the moor is unable to share our inference-to-many-ramblers, then, is just this. He has one piece of information at the outset that we do not; that he is already on the moor. The extreme coincidence he has to explain is then that:

C1. Given that Smith is on the moor, he takes a meteorite through the heart.
In terms of the gambler,

C1. Given that Smith is playing poker, he gets three royal flushes in a row.

In each case, the odds of the second thing happening, given the first, are P:1 against. But the assumption of many other ramblers, or many other gamblers, makes no difference to these odds, because the observed coincidence is specific to Smith. Correspondingly, then, Smith’s evidence about himself offers no support whatever for a multiple-ramblers or multiple-gamblers explanation.

So this additional piece of prior information, that Smith in particular is on the moor, is the key to the whole problem. Another way to see this is to assume that there are one hundred ramblers on the moor, and see what Smith is entitled to infer under various circumstances.

Circumstance 1. Smith doesn’t know anyone else is on the moor. He takes a meteorite. Nothing can be inferred about the other ramblers. This is because he already knows that he is on the moor, and the chance of him in particular being hit by a meteorite remains constant, however many other ramblers there might be. The assumption of many ramblers would not help to explain why he was hit by a meteorite.

Circumstance 2. Smith knows there are a hundred ramblers on the moor. He takes a meteorite. He recognises that the other ramblers made no difference to the chance of this happening to him. As before, the chance of Smith in particular being hit by a meteorite is unaffected by the presence of other ramblers. Smith’s knowledge that there are many ramblers does not help to explain why he was hit by a meteorite.

Circumstance 3. Smith knows that Jones is on the moor, but doesn’t know how many other ramblers there are. Smith then learns that Jones takes a meteorite. He recognises that the presence of other ramblers would make no difference to the chance of this happening. Again, this is because Smith already knows that Jones is on the moor, and recognises that the chance of Jones in particular being hit by a meteorite is not affected by the presence of anyone else. Smith’s knowledge that Jones was hit by a meteorite does not entitle him to infer that there are many ramblers.

In each of these first three circumstances it is clear that Smith already knows that the specific target is on the moor. So, he can reason that the probability of that person taking a meteorite is P:1 against, no matter who else is present. Consequently, when that person does take the meteorite, the presence of other ramblers offers no explanation for the stroke of bad luck.

To infer that there probably are many ramblers, or to attribute his own bad luck to their presence, would be to commit the inverse gambler’s fallacy.
But now we can consider a circumstance in which Smith does not already know that the particular person who is about to be struck is on the moor, and see how this makes the crucial difference.

Circumstance 4. Smith doesn’t know anyone else is on the moor. He then learns that someone else, Jones, has taken a meteorite. He infers that there are probably a lot of ramblers on the moor. This is because the presence of a hundred ramblers on the moor, their identities unknown to Smith, would render the event more probable. If any one of them should take a meteorite, Smith will learn that Jones, Williams, or someone else has been hit. That is precisely what he does learn, and so the multiple-ramblers inference is valid. Whenever the person who is hit was not previously known by Smith to be on the moor, the inference is valid. So:

The Inverse gambler’s fallacy is not committed by Smith when all of the following conditions obtain:

1. Smith learns that someone has taken a meteorite on the moor.
2. Smith did not know that this particular person was on the moor.
3. Smith did not have any prior indication as to how many people were on the moor.

And finally, we can see that condition 2. is necessary by modifying circumstance 4. Thus:

Circumstance 4’. Smith knows that at least someone else is on the moor, but doesn’t know who. He then learns that someone else, Jones, has taken a meteorite. He infers that there are probably a lot of ramblers on the moor. This is because the presence of a hundred ramblers on the moor, their identities unknown to Smith, would render the event more probable. If any one of them should take a meteorite, Smith will learn that Jones, Williams, or someone else has been hit. That is precisely what he does learn, and so the multiple-ramblers inference is valid. Whenever the person who is hit was not previously known by Smith to be on the moor, the inference is valid.

Here, we can see that even though Smith knew someone else was on the moor, he escapes the inverse gambler’s fallacy because he didn’t know who. Thus, he can reason that if there were many ramblers present, it would be far more likely that he would learn that one or another of them, who is bound to have a name, was hit. This is what he does learn, and the name was Jones, so he still escapes the fallacy.

John Leslie [1] proposed an analogy in which Jones, say, wanders into the forest at night and is hit by an apparently random bullet, presumably from the gun of an extremely unskilled poacher. Given that we already know that Jones has entered the forest, the egocentric perspective kicks in and the subsequent news that he has been accidentally shot is surprising, but tells us nothing about the presence of anyone else. Nor would the presence of anyone else make his being shot any less surprising. He in particular was just as unlikely to be shot whether alone or in a crowd (ignoring the irrelevant possibility that a fellow-wanderer might have inadvertently eclipsed Jones and taken his bullet instead). Unfortunately, Roger White[2] has misconstrued Leslie’s argument. Thus:

"You are alone in the forest when a gun is fired from far away and you are hit. If at first you assume that there is no one out to get you, this would be surprising. But now suppose you were not in fact alone but instead part of a large crowd. Now it seems there is less reason for surprise at being shot. After all, someone in the crowd was bound to be shot, and it might as well have been you. Leslie suggests this as an analogy for our situation with respect to the universe."

In fact, Leslie suggests nothing of the kind. On the contrary, he draws a careful distinction between surprise and amazement. The point Leslie makes, and White misunderstands, is this: if there were a large crowd in the forest, it would be less amazing (in need of explanation) when one of the crowd got shot, irrespective of whether it turned out to be Jones, or Brown, or Smith or anyone else. And this, as I have already shown, is how we should view the observation that something improbable has happened in our universe. On the other hand, the odds against Jones in particular getting shot in the forest remain constant, no matter who else is there too. So just as with our Smith on the moor, if Jones goes into the forest only to be shot, he should be very surprised, but be unable to infer anything at all about the company he is in. This is precisely because Jones already knows that he is in the forest. For Smith, the fact that he was hit by a meteorite told him nothing about how many companions were milling about nearby, and the same applies to Jones. Roger White2 is incorrect to suggest that Leslie intended otherwise. The only relevant issue concerns which of these perspectives applies to our universe. Are we in the position of Jones going into the forest, already identified as Jones, and then to encounter a surprising event, or in the position of a bystander, who only learns that someone, whose name is Jones, has been shot in the forest? White chooses the former, and I, along with Leslie, choose the latter. We do learn that this universe in particular has the extremely improbable ability to sustain intelligent life, but it might have been any other universe instead, and we would be there, rather than here, making the same kinds of observations.

The strong temptation, to which I have just suggested White succumbs, is to take the following point of view, which parallels the egocentric perspective defined earlier. At the beginning of the story we already know that our universe existed and therefore presented a theatre for the possible emergence of intelligent life. This particular universe has been identified at the outset as such. Borrowing Saul Kripke's[3] terminology, we might say it has been "rigidly designated." When we then go on to recognise that intelligent life did emerge in this particular universe, against odds of some 10 ^22:1 that it would not, we are recognising that something astonishingly improbable has occurred. Nevertheless, our astonishment cannot be reduced by assuming that there must have been many other universes presenting many other opportunities for the emergence of life, since both causally and statistically what happens elsewhere has no effect on what happens here. So at first blush it looks as if we are like Smith on the moor, or Jones in the forest, who knows he is there and knows that he has been hit, but cannot infer anything from this about how many people are with him.

We can now see, however, that this point of view is fundamentally flawed. For although the odds against any particular universe bearing intelligent life might be 10 ^22:1, we are not viewing our own universe from the same perspective as Smith had of his own demise on the moor. It is not as if we had already selected this universe and then sat back to see what developed. Rather, we are only here because life developed. Ours is only this universe because it is the one in which we exist. If life had emerged in a completely different universe, there might have been people like us there, musing over their own improbability. Nor would it matter if they were not us, but someone else. What is astonishing is not that we exist, but that intelligent life per se exists. So while we can now rigidly designate this universe and point out the extreme improbability of life having developed in it, such rigidity is not absolute, but rather grounded on a more fundamental indexicality. When I refer now to "this universe" I rigidly designate the one and only universe in which I find myself, but had I, or a creature like me, emerged and flourished in any other universe I would have been rigidly designating that one instead.

In short, the more universes that exist or have existed, the greater the chance that we, or intelligent life per se, will emerge. This is analogous to saying that the more ramblers there are on the moor, the more likely it is that one or another of them will take a meteorite through the heart. So the two apparently conflicting probability ratings are indeed compatible. It was almost inconceivably improbable that life should have emerged in this particular universe, but much less so that it should have emerged in one universe or another, which we now refer to after the fact as this universe. All other factors being equal (and that is itself the subject of a forthcoming paper) our existence does indeed provide evidential support for the many-universe hypothesis.

© Brian G. Crabb, Ph.D.
University of Liverpool

References

1. Leslie, John. (1988). “No Inverse Gambler’s Fallacy in Cosmology." Mind, 97: 269-272.
2. White, Roger. (2000). "Fine-Tuning and Multiple Universes." Nous, 34: 260-276.
3. Kripke, Saul. (1980). "Naming and Necessity." Cambridge: Harvard University Press.

Article Source: http://journal.ilovephilosophy.com

"Brian Crabb" multiple universe hypothesis improbability probability improbable existence anthropic principle White Kripke Leslie

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