• Try praying?


    I’ve been working in the UK for the last month (which partly explains my reduction in rate of writing), and I was fortunate to see Derren Brown perform live in Glasgow the other night.  The show was great – a fantastic mix of his amazing skills, stories about his personal life (including coming out as a gay man, and how he was unpopular at school), and some good solid advice on scepticism and rationalism.

    One of my favourite aspects of the show was the way he was able to explain how improbable events happen all the time, given enough opportunities.  At one point, he asked everyone to stand up.  Straight away, he asked all the men to sit down.  Next, he told all the women not in the 25-35 age group to sit down.  After a couple more such reductions, the people left standing were women aged between 25 and 35 who had a dog (or dogs) and at least two tattoos.  If you were a 30 year old, female, dog owner with several tattoos, you might feel a little spooked at this point – like Derren personally selected you from the crowd.  At this point, however, the lights came on, and everyone was amazed at how many people were still standing (well, everyone except the mathematicians).

    But the lesson is simple.  If there is a 1/100 chance that a typical person off the street is a woman aged 25-35 with a dog and a few tattoos, and if you have 2000 randomly selected people in a room, you’d expect around 20 of them to fit all the criteria (the audience was about 1700 strong, and there were a few dozen people left standing).  But if you were one of those people, and you hadn’t thought about the numbers, you’d be feeling pretty special.

    A while ago, I heard of another case that illustrates the same phenomenon, perhaps even better.  Suppose you’re looking through your email inbox, and you come across a message from a self-described sports tipping expert.  She tells you Team A will beat Team B in a match on the weekend.  You promptly go to the next email and forget about it.  Next week, you get an email from the same person saying that, this weekend, Team C will tie with Team D.  You think back to the previous email and look up the scores and, sure enough, Team A did beat Team B as the expert predicted.  So this time you watch the game between Team C and Team D, and it does indeed end in a draw.  This same pattern happens for another three weeks – you receive a prediction before the game, and the expert’s tips always turn out to be right – five correct predictions in a row.  By this time, you’re impressed.  The next email you receive from the expert says:

    “You’ll no doubt have noticed that I’ve now correctly predicted the outcomes of five matches in a row.  I didn’t just pick the favourites, though – some of these results were big upsets, so you can see I am highly skilled in the art of sport prediction.  If you had bet $100 on each of the matches, you would have made a profit of $1,000.  I can continue to send you my predictions for the remainder of the season, but you will have to pay for my advice from now on.  You can keep receiving my tips for a modest up-front fee of $200, payable to…”

    So you send off your $200, and now you’re really excited about the money you’ll make.  How lucky you are to have discovered, quite by accident, such a useful source of reliable information!  So, you make a few bets, following the expert’s predictions for the next few matches.  But suddenly, the predictions are not so great.  You find you’re winning some and losing some, and not really doing any better than you would if you relied on your own (far from expert) judgement.  So, what happened?

    Here is what happened…

    When you received your original email, another 1,000,000 people received exactly the same one.  Another 1,000,000 received an email identical to yours except predicting that Team B would beat Team A.  A further 1,000,000 were told that there would be a draw between Team A and Team B.  After the match (in which Team A beat Team B), the second and third groups of 1,000,000 never heard from the “expert” again.  Then, the first group of 1,000,000 were split into three groups.  The first group were told that Team C would beat Team D, the second that D would beat C, and the third that the game would end in a draw.  Since the game did end in a draw, the first and second groups never heard from the “expert” again.  The same pattern was followed for five weeks.  At the end of the first week, the original target of 3,000,000 was cut down to 1,000,000 who had received the first correct “prediction”.  At the end of the second week, approximately 333,000 people had received two correct predictions in a row.  After three weeks, 111,000 had received three correct predictions, then 37,000 after four weeks.  Finally, after five weeks, more than 12,000 people had received five correct “predictions” in a row.  And imagine now if just 1% of these people signed up and paid their $200.  The “expert” would pocket about $25,000.  And all with absolutely no skill whatsoever.

    The moral of both stories should be clear.  If some outcome has a 1 in X chance of happening, and a group far bigger than X has the opportunity to achieve the outcome, you can expect the outcome to occur several times.  People win lotteries, and people recover from “incurable” illnesses.  “Almost certainly not” does not mean “certainly not”.  A one-in-a-billion day happens to around 7 people every single day.

    Well, I was thinking about this as I was on the bus to the airport this afternoon, about to head back home.  And as we drove past a church, I noticed a big sign saying Try Praying.  The idea is obvious.  If you’re a skeptic, why not just try praying?  You’ve really got nothing to lose, right?  If there really is no god, then obviously nothing will happen, and you’ll have lost nothing – just a few seconds wasted, praying to an imaginary deity.  But if there really is a god, your prayer might result in something amazing – you might get that promotion you’ve always wanted, your mother might recover from her illness, you might restore your relationship with your estranged family – the possibilities are endless.  (And then I suppose you’d start attending that church.)

    But think about it.  Imagine if every resident of Edinburgh prayed a very specific prayer.  Suppose they all prayed for some event to occur, an event with, say, a 1% chance of happening.  Well, the population of Edinburgh is about 500,000.  So you’d expect a total of 5,000 unlikely events occurring (seemingly) as a direct result of prayer.  That’s a lot of “unexplainable coincidences”!  And if everyone prayed for several 1% events, then the list of “answered prayers” would be very long, indeed.

    But nothing would have been proved about prayer at all.  If the Edinburghians prayed to Zeus instead of (presumably) the Christian god, the same number of desired outcomes would have been achieved (still by chance).  Same with Allah, or the Flying Spaghetti Monster.  You can even pray to me if you want – tell me what happens!

    But, to the person whose son learnt to walk again, despite being given a 1% chance of ever getting the use of his legs back, it can seem like something truly special has happened.  Such people will most likely end up in the pews of the local church, telling their amazing story for the rest of their lives, and providing others with a great “reason” to believe in God.  In the meantime, for every such lucky family, another 99 sons are still in the wheelchair.  The trick didn’t work for you – you weren’t selected, and you can sit down, now.

    So, next time something unlikely happens to you, don’t assume it must be for a reason – it probably wasn’t.  Just remember that if enough people try and achieve something unlikely, someone will achieve it.  It has to be someone, and it just happens to have been your turn this time.


    Category: AtheismDerren BrownFeaturedMathematicsPrayer

    Article by: Reasonably Faithless

    Mathematician and former Christian
    • David Hill

      Isn’t it a matter of causality not statistical (im) probability?

      In the case of the clever sports tipster they are not predicting anything other than that a game will happen and someone will win – and cleverly deceiving 1000s of others in the process. (Incidentally, I think Derren Brown has featured this idea in a TV programme) But in the case of the person whose son starts to walk again, against all odds, we would do well to investigate why he recovered rather than simply saying 99 others didn’t, so he was just lucky.

      In the case of any reported answer to prayer, miracle, spiritual experience, people in Edinburgh who have answers to prayer, etc., we would want to ask what caused it (wouldn’t you?) and investigate the evidence around it. We may not be able to dismiss it by saying they were lucky. Perhaps there’s a cause. We investigate evidence for things that happen not evidence for things that don’t happen.

      If the door bell rings I look to see who is there. If the doorbell doesn’t ring I do nothing. Being lucky or unlucky isn’t the issue. Someone at the door is.

      • I guess I’m more thinking of things like where a doctor assesses that there is a 1% that you will regain the use of your leg (due to whatever causes they think are possible) – these things either happen or they don’t. For every 100 such patients, you’d expect 1 to get the use of their leg back. For every 100,000 such patients, you’d expect about 1,000 to walk again. Those patients will of course feel very special, but there is also just the statistical fact that, assuming the 1/100 chance is accurate, 1000 *will* walk again – it’s just a matter of who the lucky ones are. Of course, it might just be possible that God would look at a particular person and decide to heal their leg – but, unless there was something statistically significant, i can’t see how you could actually deduce that. This is why it would be great if something completely remarkable happened – like the classic “why doesn’t God heal amputees?” question – claimed miracles usually involve something with a small chance of happening (but which, by definition, *has to happen* to someone). Or if 50% of the people with injured legs were healed instead of 1%, and it just so happened that these 50% were precisely the Christians, that would be compelling, too. But a single person saying “look, I was given a 1% chance, then I prayed, then I was healed” – that just falls squarely within the realms of statistics – it is making an unjustified conclusion.

        • David Hill

          Thanks for doing a reply. I wasn’t really expecting it having only taken a ‘punt’ when I wrote in. So that’s kind of you. However I do need to come back to you after what you wrote.

          The causality issue is still not addressed. If the person with 1% chance of recovery does walk again we would all ask why. What happened to him? In this cause and effect universe, the basis of scientific investigation, we look for reasons! To say he was just lucky, it was bound to happen to someone sometime, avoids the issue about which we want to know the answer. Did the doctors do something unusual, did he do something unusual, was there some mischievous Christian praying, etc.?

          My point is that things don’t happen by chance. They have causes.

          There are plenty of so called miracles that are nothing more fortunate turns of events with an obvious cause. There’s nothing very unusual in such -except the gullibility of those who are congenitally religious. Conversely there are many, many experiences that have little chance of being described in such terms except by the most committed sceptic: deaf people hearing, blind people seeing, etc. My frustration is that it doesn’t happen quite so predictably as we might wish! There are plenty of un-answers to prayer as well. But the frequency and the nature of such healings and answers to prayer does baffle those who don’t like the idea of a God who does things.

          Back to your thesis of chance events. We could say that of all the billions of people who have died it is highly likely that one person would be raised to life again. The statistical probability would be high (albeit scientifically/medically impossible) given the numbers of people who have died. Somebody somewhere is bound to get lucky! But then we would be being neither curious nor scientific if we didn’t ask how it happened. If it has ever happened we would want to know if there was a cause rather than simply dismissing it.

          Kindest regards.

          • Hi David,

            Nice to hear from you again. You’re very welcome – I always try and respond to my readers – I appreciate it when someone shares their ideas.

            I somewhat agree about causes, but not entirely. Take something less controversial like a lottery – everyone might have a one in a million chance of winning, but *someone* is going to win. OK, you could say that something causes that particular combination of numbers, but I think this falls more into the “laws of physics” department than anything else – do you agree? And as for my example of a leg being healed, I’m thinking of a case when, for example, there is nerve damage and the body will just have to try and repair the nerves (as it tries to repair damage all the time) – it will be unlikely the repair will be successful, maybe 1/100 and depending on all kinds of chance factors, but we know it is just down to whether the individual is lucky. In this case, we know the “cause” – the human body just tries to fix itself, same as it did with all the 99/100 non-successful cases – but the actual success was due to luck, even though it might feel different to the 1/100 person who might have actually prayed.

            In general, sure, of course we should (and do) look for causes – if a person survives a really deadly virus, of course the medical researchers will try and work out if her body has something special that can be adapted for a treatment. But if such a cause is not easily identified, calling it a miracle is not warranted. I think that a miracle is only really a completely valid deduction if it is known that the event really could/should not have occurred by normal chances (no matter how unlikely) – eg, an amputee spontaneously regrows a leg, or a person burnt to a crisp in a fire comes back to life. I could list plenty of things that would convince me of a miracle.

            As for your comments about resurrections, I completely disagree. Your statement is easily modified to any number of statements like: with all the billions of people that have lived, it is highly likely that one person would be capable of teleporting to a distant galaxy. In such cases, the sheer number of people is unimportant – most important of all is the likelihood of the event in consideration. If we knew there was, say, a one in a billion chance of a person being able to teleport (or rise from the dead), then I would be happy to grant the statement(s). But without such knowledge, I wouldn’t accept it. Everything we know about physics (and human biology) says that people do not in general teleport (or rise from the dead – say, after 3 days of death – I assume you’re not talking about resuscitations on an operating table, for example). For this reason, if such an event could be demonstrated to have occurred, this would certainly qualify as a miracle (and yes, such an event should/would arouse much curiosity and investigation). But you can’t just say “there have been lots of people so it’s highly likely that [XYZ] has happened to at least one of them”.

            Just one more thing about the last paragraph. If you’re talking about “natural” resurrection, then I think your statement that this is “scientifically/medically impossible” leads to the original statement being false. But if you’re allowed to assume there is a God who can do any miraculous thing like perform resurrections, then I don’t see how questions concerning probabilities can be reasonably answered. What is the probability that such a God will cause any given person to teleport to a distant galaxy? Should we conclude that, since there have been billions of humans, *everything* logically possible is likely to have happened to at least one of them?