I went to the pub last night with a couple of mates, one of whom is the founding member of the Tippling Philosophers. Because we are very cool people, we spent a large amount of time talking philosophy and theology. Strap yourselves in, this ain’t short.

My other friend talked about a couple of unexplained phenomena that he thought made him question whether there was some other force at play out there or not. He was talking about an Australian friend who was experiencing some personal issues in his life and (I am simplifying through my vague recollections here) was driving around one day and a white owl flew down and landed in the middle of the road. This had some significance to him. The other event was something like a postcard or picture around arriving on his doormats that was of his hometown and had some specified complexity attached to it in terms of the meaning that it invoked.

I’ve talked about this subject many times before and I repeated the essence of my posts to them both last night. My Tippling Philosopher friend was once a conservative Christian (though he now has experienced an evolution in his worldview to a point of some kind of universalist, deistic scenario) and he recounted a couple of incidences that had a great deal of specified complexity and to which he clearly attached a Christian meaning and these are events that still stick with him as being forceful and communicative, involving Bibles and prayers and whatnot. More on one of these claims later.

The argument goes that the level of complexity is so specific in these incidences – specified complexity – that this must point to some other (supernatural) agency.

Rauser’s Specified Complexity

I had this debate previously with evangelical Christian Randal Rauser and it essentially involves a proper appreciation of maths, probability and the sheer number of things that happen to people on a daily basis and the fact that there are some 7 billion people on the planet. This was Rauser’s account, from his book with John Loftus, God or Godless?, where one of his chapters recounted an anecdote involving prayer. In simple terms, this is it:

Pastor Kent Sparks, living in North Carolina with wife, were pursuing adoption with House of Ruth No luck in year and a half, so pursued private adoption in Georgia After adoption of daughter Emily went through, Kent called House of Ruth to leave message to suspend their file Staff were in meeting to discuss with a client who had chosen Sparks for a child Meeting ended, staff called Cheryl Sparks to tell her good news – another child for adoption Cheryl called a friend to ask her for prayer Kent returned from work and Cheryl asked him to conduct a devotion without telling him of the news Kent opened Bible and read Proverbs 3:27: “Do not withhold good from those to whom it is due, When it is in your power to do it.” Cheryl’s friend later phoned with a Bible verse, Proverbs 3:27 They adopted their second child, Cara

And this was the main evidence to support his argument that prayer works.

Kent and Cheryl’s case evinces these same hallmarks of contingency, complexity and specification. While these events are obviously contingent, they are also complex since they involved multiple factors timed together (e.g., Kent’s call concurrent with the adoption meeting), and they included specified information (e.g., two independently confirmed referenced to Proverbs 3:27). Consequently, Kent and Cheryl (and we) are fully justified in drawing the conclusion of divine action in confirmation of the adoption. (p. 142)

All events have the same probability

The root of the problem is that people have a tendency to attach meaning to things at certain times but ignore the fact that things with similar complexity happen all of the time but to which they attach no meaning. Indeed, every single event that ever happens has exactly the same probability – the probability of 1. Not only this, but everything that happens has exactly the same level of complexity.

If I look at, say, going to the pub with my two friends last night, one of whom was a last-minute text invite, the things that had to be in place for that to happen, involving partners, children, work patterns, dinner times, seemingly random events, and so on, mapping back through history (our parents meeting and having us as children, the evolution of man), last night’s meeting was astronomically imp[robable – in one sense – but had 100% probability – in another sense (it happened). But none of us attached that much meaning to last night’s encounter. This is key. I could have attached a whole bunch of meaning to the meeting and then reverse-engineered the probability of the meeting taking place, and concluded that God must exist because the meeting was effectively miraculous in its probability. It’s all about what yopur reference set of events is in terms of generating a calculation for specified complexity. I never find anything with specified complexity in my life because I am not looking for it and I have no use for it, but I could easily find it. It was a normal night at the pub. But the level of specified complexity was no different than Rauser’s or either of my friends’ accounts.

Prayer and asking for things to happen

Let me refer you to the chapter on prayer in my book from some years back, The Little Book of Unholy Questions (UK – on offer presently):

The subject of prayer provides several problems for the believer, if thorough critical questioning is followed through. Part of the issue of perceived success of prayer is down to religious people interpreting coincidence as divinely purposed, and this is very common. I am aware of this, and am constantly amazed at the amount of seemingly dauntingly huge coincidences that I go through on a daily basis. Most of these are so innocuous as not to even stick in the memory. Usually, this will entail reading a book, and a certain word that you haven’t heard for ages, and then hearing it five seconds later on the television in the background. Wow! Who would have believed it? The problem is, we see things as much bigger coincidences than they really are because we are unaware of the frequency involved in calculating the probability. For example, buying a lottery ticket might mean that the probability of winning the lottery is staggeringly small, say one in fourteen million. However, if you bought fifteen million tickets, then it becomes likely. Also, if you look at the frequency of tickets bought as a whole, then someone winning is a statistical certainty. To translate this across to the word scenario, then the number of words I read or use per year, and the amount of words I hear in the background per year, means that the occurrence of these weird coincidences actually becomes a statistical certainty too. Don’t just look at the incident in isolation, but in the greater context of everything around it. Now, as mentioned, these are innocuous cases. However, let’s look at something that happened to me the other day. I am the proud father of newly born twin boys. These two delights give us great joy, and yet they can also be a great challenge. When we introduced them to solids recently, they had a week of screaming the house down at night. This led my partner and me to have some degree of sleep deprivation, as they were waking every two hours to be breastfed. We sat down one Sunday afternoon and discussed this for about four hours. We had all the books out, and were scouring the internet for different routines, opinions and helpful tips. We were fairly stressed, and this was really important for us, especially as the boys were pretty stressed too. After all the talk and worry, we simply couldn’t conclude what to do – there were so many options. It was at this point that, had we been praying people, we would almost certainly have joined hands and prayed for strength and insight; for an answer. Giving up, I walked myself down to the local shop for some milk, as we had some surprise guests over for a cup of tea. Just walking out of my local shop as I got there, on a random Sunday afternoon, was a woman we knew from Twins Club. I had never seen her on this road before, or even outside of Twins Club. And there she was. I stood and talked to her for half an hour. She had had exactly the same problem with her twins, gave us a routine and some ideas, and hey presto, we were sorted and so much happier. What were the chances! Of course, had I prayed, this would have been bona fide proof that prayer works, that God listens to me, that my faith works. Imagine the joy in God’s works that I would have experienced, and imagine the evangelising I would have done at the church in telling my Christian friends of the ‘miracle’. I didn’t pray, and don’t hold that faith. What to a Christian in exactly the same sort of situation, and who has a real spiritual moment of transcendent evidence of prayer and faith, becomes just another funny coincidence to someone like me. For someone who prays frequently every day, the chances of a ‘successful prayer’ are very high. These coincidences happen all the time. But when they happen to a religious person, they take on a whole different religious meaning derived from the religious context. Prayer works for a lot of people who follow a lot of different religions. At least most of those gods don’t exist, so something must be up. “My God and my prayers work, but yours are just coincidences,” seems like special pleading to me. The chances are, in my opinion, that most (if not all) incidences of prayer working can be put down to coincidence. We do and say an awful lot of things every day, and we wish for an awful lot of things every day. Some of them are bound to actually happen. Besides, I’ve never seen an amputee grow back their limb after prayer. I have seen evidence of cancer naturally go into remission without prayer. Enough cancer patients get prayed for, for there to eventually be a correlation. Not, may I add, a causal relationship.

Littlewood’s Law

Let me now refer you to Littlewood’s Law:

Littlewood defines a miracle as an exceptional event of special significance occurring at a frequency of one in a million. He assumes that during the hours in which a human is awake and alert, a human will see or hear one “event” per second, which may be either exceptional or unexceptional. Additionally, Littlewood supposes that a human is alert for about eight hours per day. As a result a human will in 35 days have experienced under these suppositions about one million events. Accepting this definition of a miracle, one can expect to observe one miraculous event for every 35 days’ time, on average – and therefore, according to this reasoning, seemingly miraculous events are actually commonplace.

Ever since learning about Littlewood’s Law I have been cognisant of coincidences and ‘wow’ moments and I have to admit, I have bloody loads.

Archbishop of Canterbury William Temple once observed, “When I pray, coincidences happen, when I do not pray coincidences do not happen.” Many Christians can resonate with Temple’s wry reference to God’s providence. But atheists demur, charging that such experiences only evince a selection bias that counts the hits and ignores the misses.

And I would say that Randal’s example (and my friends’) simply does not represent a specified complexity that would prove God. Cheryl’s friend is likely to find some such relevant passage, and Kent would have such issues of the adoption at the forefront of his mind whilst choosing passages. As in my own case, things like this happen all of the time to people who don’t believe and don’t pray. They get forgotten, or not even seen as significant in any way.

Here is an excerpt which I posted on my previous blog to illustrate the point further:

A further nonreligious example

I have an analogy which I hope will illustrate why at least a lot of examples of alleged successful prayer or interventions of God take place.

Yesterday I was pumping up the tyres to my twins’ buggy. I have an old bicycle pump which I bought probably seven years ago. I bought it for £3 – peanuts. This pump has been very hard working – two bicycles and a buggy at regular intervals (the buggy particularly often needing pumping up). The pump has worked tirelessly (pun intended). For the first time ever, whilst pumping the tyres up to the buggy in the kitchen, I wanted to talk about this pump, and laud its efficiency, reliability and value for money to my partner. “This pump is brilliant. I’ve had it for seven years now, and it’s never let me down. I only paid three quid for it and it has been such a good bargain. Basically, it’s genius.” And, like a Greek tragedy, surprise, surprise. What amazed me was the timing. No sooner had I finished the ‘us’ of ‘genius’ than the mechanism of the pump twanged and it broke in my hands. The two of us burst out laughing at the sheer amazing coincidence of it. The first time, after very regular use for seven years, that I had ever even mentioned the pump, after singing its praises in my over-exuberant manner, it broke in my hands. Really, what were the chances!? It was like there was some supernatural force making that happen. It was like there was some supernatural force making that happen… And that made me think. Let me now change the analogy around – shift the paradigm. Let me now put myself in the position of being a praying Christian. I am said Christian. I am on my way to work, and am late for an important meeting for the first time. The level crossing that I cross very often is always down. As I approach, I fear it is down. But suddenly, I see it is UP! I race through it thanking God for doing that! Woo Hoo! Now imagine, just before I approach it, I give a little prayer. When it is up, and I race though, I think to myself, “God listened! I won’t be late for that crucial meeting! Thank you God!” Now imagine that same crossroad which is always down, is open after a little prayer with my critically ill partner on the way to the hospital. That small amount of time could be the difference between life and death. That same prayer has a massive consequence. Now God really is listening and I will remember that for the rest of my life. But let us return to the original event. The pump breaks after an amazingly coincidental exuberant display of affection for the pump. Hey-ho, I forget about it after a week. If I was a fervent believer, I would be praying multiple times a day, asking for things very often. The sheer volume of prayer means that many of them, by the laws of statistics, will be ‘successfully acted upon’. The sheer volume of things we do every day, every week and every year (considering we are often doing many thing simultaneously – driving to work whilst listening to the radio and thinking of my twins) means that, statistically, HUGE coincidences will happen remarkably often. If you attach a prayer prior to that, a remarkable event will seem to happen at the will of God in answering your prayer.

With regard to last night’s session in the pub talking of miracles, Colin (not his real name) claimed a miracle of answered prayer occurred whose specified complexity points towards it being a miracle. It went something like this (apologies if I misrepresent you here, Colin):

Colin had a specific problem which was affecting him badly with regards to a biblical passage. He was going away for the weekend to a Christian retreat/party. He, the next day or two, had an image in his mind of a golden sword. The next day he was in a book shop and the second or third book he pulled out had an image of a golden sword on the front. He opened it to a page in the book which answered all his worries. He claims this had such a specified complexity as to be best explained by it being a second-order miracle (one that does not violate natural laws).

I came back with some ‘incredible coincidence’ stories. The theistic claim is that these did not have the same level of specified complexity. I will now attempt to show you that this is wrong.

Remember my twins story. So what we have here is this:

We had a problem that was affecting us which we sought the answer to. Some surprise guests turned up unannounced We had run out of milk and I had, at that particular moment, to go to the shop to buy some. At the shop I met a mother of twins who I have never seen before or since on my road. She gave us all the answers we needed to our massive relief as she had been through EXACTLY the same issues.

Now let’s compare these two stories for probability. At the end of the day, miracles deal in probability and specified complexity is merely a reflection of probability.

But the specified bit is arguably arbitrary and reverse engineered. Even if I grant that the idea of specificity is entirely coherent (I don’t think it I because all events have the same level of specificity – the type theists like to think exists is post hoc attached). First of all, we have the problem. Colin is a Christian, there are many Christians and many have issues with passages in the bible. This problem we had involved not one, but four people, thus the probabilities that must exist to conspire to all of us being there to have that problem are higher. However, as an individual starting point, these probabilities are less relevant.

The catalyst: Colin had an image over a 2-3 day period which coincided with the cover of the book. We had a situation where we were discussing the problem at length and right afterwards some unannounced guests arrived. The actions of two other people must now be calculated such that the chances of them coming to our door, from living in London, are very low indeed. Suddenly they are there. AND THEN we had to have run out of milk in order for me to need to go to the shop. Just on the catalyst front, my story appears far more improbable, statistically.

Next, Colin is in a book shop and picks out a book which corresponds to his image. I walk to the shop and find not just anyone, but the EXACT person who had experienced THE EXACT SAME THING, there with her twins. I had and have never seen her there before. Had we prayed, she literally would have been the answer to our prayers. The probability of her being in that exact place at that exact time, of being a mother of twins with exactly the same problem (and for me to need to go to the shops at that time due to milk running out and unexpected guests) is astronomically more improbable that a book detailing information on a biblical passage being in a Christian bookshop full of other Christian books, when Colin would have been at least subconsciously searching for some answers.

As I was pointing out to Colin, I don’t think there is often an understanding of the massive improbability of coincidences like mine, and there is often a desire to make the calculations for probabilities which seem to involve purpose much lower due to intuitive belief that the events are purposes. At the end of the day, If Helen and I had held hands and prayed before my friends came to the door, that chain of events would have seemed more powerful, I posit, than Colin’s miracle claim. Heck, I would have been praising the Lord! And the more Christians pray, the more chance they have of having their prayers answered. But do they count all the times their prayers aren’t answered? No. Do we count all those billions of other coincidences that happen all the time? No, we simply aren’t aware of them.

Using Littlewood’s Law, of course, we know that highly improbable events take place with alarming regularity since the frequency of things we do and experience is phenomenal. Littlewood calculated you would experience a ‘miracle’ once a month.

Thus I hope to have shown that massive coincidences happen regularly and have just a low probability, and often lower (as in this case), than many religious miracle claims, and that’s if you don’t believe in a level playing field of probability anyway. Just because there is no perceived purpose does not mean the probability is any higher.

So, given these points, I think that Randal’s case is exceptionally weak, as are the cases of my friends. It certainly does not evidence God. Think of all the ways in which prayer could work that would leave one with no doubt. The complexity that Randal invokes is simply not strong enough or specified enough to do what he wants it to do. Only if you overload it with copious amounts of cognitive bias. Again, we could talk of growing back limbs and what have you – much more obvious signs of the supernatural (that never seem to happen…). What do we have instead? Events which look extraordinarily like coincidences, and coincidences that happen all of the time.

Move along now. Nothing to see here.

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