Tuesday, 29 July 2014

What were the chances of me being born?

What were the chance of any specific person being born? More specifically, what were the chances of me being born? If we accept the prevailing belief, then our self or identity is determined by a specific sperm fertilizing a specific egg. A specific sperm and egg are required since it is believed that each sperm and each egg are unique. Armed with this information the blogger Ali Binazir has attempted to give an estimation of this chance. (update 18/11/2019. The webpage no longer exists)

He concludes:

Probability of your existing at all: 1 in 102,685,000 

That is a one followed by 2,685,000 zeros! Undoubtedly we can quibble about this figure. But, even though it might be wildly wrong in underestimating the true probability, we can nevertheless safely conclude that the probability of me being born are effectively zero. Since though I have been born it seems to me we have to reject the original stipulation that my identity is determined by a specific sperm fertilizing a specific egg.

I've never encountered anyone who actually agrees with me here. The common response is that the fact we were born is not remotely surprising. Indeed, they often make the rather bizarre claim that the probability of me being born, or any specific person being born, is actually 1; that is it is certain I would be born! And when I say it's a common response, I mean it's an extremely common response. For example in the comments section of Ali Binazir's blog entry there are many who express precisely this position.

But what could it possibly mean to say that it is a probability of 1 that I would be born? If our identity is indeed tied down to a specific sperm fertilizing a specific egg, then it cannot possibly be 1! My parents might never have met for example.

The gist of their argument can be gleaned by something Richard Feynman is alleged to have once said (obtained from here): (update 18/11/2019. This webpage also no longer exists)
“... I had the most remarkable experience this evening. While coming in here, I saw license plate ANZ 912. Calculate for me, please, the odds that of all the license plates in the state of Washington I should happen to see ANZ 912. Well, it’s a ridiculous thing”.
Well, obviously the probability would be 1 divided by the total number of license plates in the state of Washington. However, we can see his point. The fact he saw this particular license plate cannot be deemed to be surprising since whatever license plate he might have happened to glance at he could have asked the same question.

Transferring this to the probability of me being born, the point is that someone will be born, and that someone, whoever he may be, can always wonder at his own existence and argue that it is so unlikely that he were born that his existence cannot possibly be due to a specific sperm fertilizing a specific egg. But yet someone will be born and so it is certain that someone will express such astonishment. But then it might seem his conclusion -- and indeed my conclusion -- that his identity cannot possibly be determined by a specific sperm fertilizing a specific egg, is simply in error.

So, as I see it, that seems to be their argument. And on the surface it sounds reasonable enough. However, I regard the argument to be flawed. Let us now see why.

Let's consider something like the UK National Lottery. There are 6 balls drawn (let's forget about the bonus ball) from a total of 49 balls. There are approximately 14 million combinations of numbers (the order in which they are drawn does not matter). Each of these combinations have equal likelihood of being drawn. Thus any arbitrary combination of balls has 1 chance in approximately 14 million in being drawn. A combination such as 1, 2, 3, 4, 5, 6 is no less likely than any arbitrary combination such as 7, 16, 23, 29, 35, 43. This being so, then according to these people, we ought not to be any more surprised if last night's lottery numbers were 1, 2, 3, 4, 5, 6 then if they had been a combination of numbers such as 7, 16, 23, 29, 35, 43.

But of course we would be surprised if last nights lottery numbers had have been 1, 2, 3, 4, 5, 6, and rightly so. To argue that we ought not to be surprised, or worse still to argue the probability is 1, is to fail to recognise that some combinations of numbers are special, and that 1, 2, 3, 4, 5, 6 is the most special combination of numbers of them all. 1, 2, 3, 4, 5, 6 is special in the sense that the numbers are not arbitrary but have a pattern which draws our attention. What we ought to be doing is not comparing the probability of this special combination of numbers with any arbitrary combination of balls -- which of course are the same -- but rather comparing the probability of this special combination of numbers with the total sum of all the probabilities of all non-special combinations of balls taken as a whole. Hence we are entirely justified in being very surprised if last nights drawn balls were 1, 2, 3, 4, 5, 6.

In order to drive this point home we can consider other scenarios where the prior probability of an event is somewhat less than 1 in 14 million. Let's consider a game of Whist or Bridge. Apparently the probability of each of the 4 players being dealt all 13 cards of each suit is 1 in 2,235,197,406,895,366,368,301,559,999. Despite such an event being alleged to have actually occurred, as for example in this news article, and indeed on other occasions such as here, I think it can be safely concluded that this wasn't just happenstance and infer that either somebody fixed the cards beforehand, or the deck of cards was inadequately shuffled, or they are simply not telling the truth.

The point being that if 4 people were dealt such hands, we would regard it as either miraculous, or some shenanigans or some other factor were at play biasing the distribution of cards. I assume the vast majority of us would not declare that such an event was not remotely surprising, least of all would we declare that the chance of it happening was 1.

Is the case of me being born different? To answer this question we have to consider whether me being born is special compared to anyone else who might have been born in my place. Now from my perspective I am justified in considering me being born is special since, if anyone else had been born in my place, then I would never have existed. It is true that from an objective perspective me being born is no more likely, or less likely, than any other person who might have been born in my place. True but irrelevant. It is also the case that last night's lottery draw of 7, 16, 23, 29, 35, 43 is objectively no more, or less likely, than 1, 2, 3, 4, 5, 6 being drawn, but it is the meaning we human beings bestow onto the latter sequence of balls which is all important. Likewise each and every one of us consider ourselves to be special compared to anyone else who might have been born in our place.

It might be argued by some people at this point that I'm omitting a crucial factor here. They might entirely agree with me that certain combinations of lottery balls and certain Whist hands ought to be considered extremely surprising, but argue that the scenario of being born differs in a crucial way. That is to say that in stark contrast to the examples of lottery balls and card hands, if I had never been born, then I would never have existed to wonder about it. I can only wonder about my existence if I had actually been born. Hence the fact I find myself in existence cannot be deemed to be remotely surprising.

Supplementing the argument in this way is, however, also flawed. This can best be seen by the use of another slightly different analogy, an analogy used by the philosopher of religion Richard Swinburne. He says:

"Suppose that a madman kidnaps a victim and shuts him in a room with a card-shuffling machine. The machine shuffles ten packs of cards simultaneously and then draws a card from each pack and exhibits simultaneously the ten cards. The kidnapper tells the victim that he will shortly set the machine to work and it will exhibit its first draw, but that unless the draw consists of an ace of hearts from each pack, the machine will simultaneously set off an explosion which will kill the victim, in consequence of which he will not see which cards the machine drew. The machine is then set to work, and to the amazement and relief of the victim the machine exhibits an ace of hearts drawn from each pack. The victim thinks that this extraordinary fact needs an explanation in terms of the machine having been rigged in some way. But the kidnapper, who now reappears, casts doubt on this suggestion. ‘It is hardly surprising’, he says, ‘that the machine draws only aces of hearts. You could not possibly see anything else. For you would not be here to see anything at all, if any other cards had been drawn.’ But of course the victim is right and the kidnapper is wrong. There is indeed something extraordinary in need of explanation in ten aces of hearts being drawn. The fact that this peculiar order is a necessary condition of the draw being perceived at all makes what is perceived no less extraordinary and in need of explanation". (Obtained from here) (update 18/11/2019. This webpage is yet another one that no longer exists)

Swinburne utilized this analogy to illustrate the fact that what has been labelled the anthropic principle does nothing to explain why the Universe is such an orderly place -- a point with which I am in full agreement even though I do not concur that this necessitates the existence of a traditional concept of God (see some musings of my own here). But it also equally applies to any anthropic principle type argument that attempts to render the fact I was born as something unsurprising. As Swinburne's argument illustrates, this simply isn't true. In fact, despite first appearances, it is no more effective than the original argument and Swinburne's analogy illustrates the fatuity of both.

In summary then, given that the chance of being born is 1 in 102,685,000, even if that is only a very rough ballpark figure, this chance is so incredibly small as to be effectively zero. Hence any position which holds that we are both selves and that our selves are determined by a specific sperm fertilizing a specific egg, cannot realistically be maintained. I do not believe this conclusion is obviously problematic for materialism, at least so long as the existence of a persisting self is denied (I discuss the issue of a persisting self here).


  1. Very interesting. Some thoughts:

    Surely the problem with all this, is that meaningfulness is separate from likeliness, and this indeed a matter of viewpoint? You touch on this a little.

    Our victim saved by card-shuffling has had an exceptionally meaningful experience from his perspective, and it is natural to seek an explanation that matches that level of meaning. However, to everyone else the tale requires no further explanation. He was simply very lucky, and the fact he is amazed = the fact that he still exists.

    Similarly with the lottery numbers. There is nothing special about '1,2,3,4,5,6' except to people familiar with arabic numerals. We are justified in being surprised only because it's a pre-existing pattern in our culture. To anyone else, it requires no special treatment or further explanation.

    Your existence is meaningful to you - and, hopefully, to a few other people! - but it is only meaningful to you because you do exist. All events which have already occurred have a probability of "1" of having occurred; we cannot wind back to the probability beforehand and be retroactively amazed!

    However, if we sit here now and work out the probability for a future event based on physical principles of the phenomenon in question, make a prediction, and then it shows up meaningfully, that's different.

    Which brings up a good side point: It is not at all clear that all possible births, or all possible planets, had equal weighting. When calculating the probabilities of events, readying ourselves to become 'amazed', we would need a clearer model of the processes involved in the chains of events. Otherwise we're doing something akin to saying: "Hey, isn't it amazing that I'm sat at these GPS co-ordinates right now! There are x-million possible co-ordinates! So the probability of this being the case is x-million to one!"

  2. The point about the GPS co-ordinates is the whole reason why I wrote this blog entry in the first place -- it was an attempt to show that such reasoning is transparently flawed. You're just saying the same type of things other people say and which I hoped I'd addressed.

    In the kidnapping case a bystander ought to be just as amazed as the intended victim. However if there are, say a quadrillion permutations, and a quadrillion people were kidnapped by a quadrillion kidnappers who carried out this procedure, then on average 999,999,999,999,999 victims would die. The 1 person who survived would be amazed, but we ought not to be.

    But a quadrillion people were not kidnapped, only one was.

    The point that the probability of an event that has already occurred is 1 is banal in the extreme. That is so almost by definition, unless we could travel back in time! If someone were continually dealt all the spades in each hand when playing bridge, then that person ought to know that he is not just receiving 13 cards randomly. Saying the probability is 1 in that sense after you received 100 such hands in a row is true, but of course is wholly irrelevant.

    I'm not sure where you're getting possible planets from. Richard Swinburne was talking about the order in the Universe.

    1. The Kidnapper

      Your extended kidnapping analogy doesn't change how amazed someone should be, surely? If there were a quadrillion cases taking place, but each case was unaware of the other cases - i.e. for them, equivalent to only one case taking place: theirs - would that change the amazement levels expected for the case where the victim survived? No, surely?

      It really does get back to meaningfulness. Meaningfulness doesn't make anything more or less likely - of course! For the hands of card, all hands of cards are equally probable or improbable. Just because some hands are more desirable, or some hands correspond to a pattern held special by the players (because they correspond to a sequence they recognise, or colours they recognise) doesn't make them more special or unusual from a likelihood point of view.

      The GPS Analogy

      The GPS example is an example of saying that a particular state is unlikely just because there are other possibilities, when in fact you would be able to say the same thing no matter which of the states you were in. Fair enough, of course.

      But if we add into the mix that one of the co-ordinates is your house and you find yourself there, we can extend the metaphor. Either:

      * If you are amazed to find that, in daily life, your GPS co-ordinates correspond to those of your house a lot of the time, then that is like the anthropic principle (it is no surprise, it is obviously going to be the case: you are home).

      * If what has happened is you've been transported using a "random co-ordinate teleported machine" and you end up in your house, it's like the kidnapper story (you are only in a position to be amazed because you are at that location).

      [By "all possible planets" I didn't mean that we could be born on Mars or something, I meant "Planet Earth as it is". I wasn't very clear on that! I just meant that the universe was ordered such that we were on a breathable planet in this location, that sort of thing.]

    2. Not sure what the purpose of your last reply was. Doesn't matter if each intended victim is aware of all other victims, if he is the one that survives then he will be amazed and justifiably conclude that not all is as it seems. And a bystander will not be at all amazed unless the victim is special compared to all possible others.

      I can't discern any disagreement with my original blog entry in your latest reply, so I'll just leave it at that.

  3. if inflation is true (and thats almost true), space is infinite, probability of you is 1. Read Max Tegmark's Our mathematical Universe

  4. I understand your issue because I made similar considerations for my own. At first, I realized that a Multiverse like the one that Max Tegmark proposes may allow all the possible conditions have their chance to happen, but still this let me unsatiflied. Then I realize that the real problem is not to find ourselves as winners in this game, but the more basic fact of finding ourselves as players in the life-game. I called it the "individual existential problem". I am trying to formalize the idea, and I would like to hear your opinion.


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