Watch Out for Coincidences

It seems common for people to credit unlikely things to a divine source. I can think of plenty of “ridiculous” ones… Tim Tebow throwing for 316 yards (representing John 3:16), the appearance of the virgin Mary in grilled cheese, etc.

There are a few issues with crediting coincidences to the divine. First, plenty of very unlikely things happen whether it involves something spiritual or not. Second, You can always come up with a naturalistic explanation for certain things that happen.

However, does that mean we should be completely closed off to divine intervention? In other words, should we always assume that every unlikely event has a purely naturalistic explanation?

I think the answer to this question is no. We should not be set on this assumption if there is reason to believe that for a particular event, divine cause is more plausible than any naturalistic explanation.

What sort of criteria could lead us to think that an event had a divine cause? I can think of three things to look at (there may be more):

1. The event is overwhelmingly unlikely

2. The event (seemingly) has spiritual significance

3. There are few, if any, plausible naturalistic explanations

Looking at the two examples above, the Tim Tebow example could fail #3 because an obvious explanation is that Tebow simply had a good game and happened to throw that many yards. Plus it’s a stretch to make the spiritual connection in the first place. The grilled cheese example is questionable on #3 because a person could warp a very likely shape into something that looks like their image of Mary, like how you can warp the shape of a cloud to look like a bunny. Plus there’s little practical spiritual significance.

The three factors above can add weight to a divine explanation for an event. You can always come up with a natural explanation for an event. But the question should not just be “is there is a natural explanation?”, but instead should be “what is the most plausible explanation, no matter what the implications are?

With this question in mind, I now turn to a story that three years ago was sent to me, a questioning freshman, from a guy named Paul. You can choose to believe or not believe this story from his pastor. This is what Paul sent me:

I would like to share with you an additional event that the Pastor of my church recently shared with me that happened to him. He told me this after I told him some of the things that happened to me. He asked me if I thought that these kind of things only happen to me. I said YES!!!. I never heard any of these kinds of stores from people I knew and was never taught that they were readily available to be experienced, you just had to want to experience them

So here is what he told me,

His father once bought him a watch for good luck. The following day the watch stopped at exactly 2:15. He noticed that it stopped, then fiddled with it and set it to the right time and thought nothing further of it. The next day it again stopped at 2:15. So he thought it was simply broken and returned it to the store where it was bought. The clerk gave him the exact same replacement watch, same make-same model. The very next day the watch stopped again at 2:15, so he took the watch to the store and told the clerk. The clerk could not believe it and so started fiddling with it and set the watch for 2:14 and sure enough it stopped at 2:15 again in the store. So the clerk gave him an entirely different watch, different make/model. Sure enough the next day the watch stopped at 2:15 again. At this point, the pastor tells his wife to remember the time of 2:15 since God is telling him something about that time. The very next day, the watch doesn’t stop at 2:15 but keeps on going and never stops again. A week later at 2:15 PM he gets a call from a church that he interviewed at (one of many he had interviewed at and was considering) and they offer him the job. He knows it is the will of God that he take that position and does so on the spot….

Lets examine the watch event I described. The watch always stopped at 2:15 PM, never 2:15 AM. And that’s significant because there is no difference between the initial conditions of the watch at 2:15 PM versus 2:15 AM as it was an analog/mechanical watch and did not differentiate between AM and PM.

5 times the watch stopped at 2:15 exactly, plus the phone job offer came at 2:15 pm. That’s 6 events. Do you know what the probability of that event happening was?

Do you know much about statistics? Rather than dive into the theory, I will use a quick example.

The probability of flipping a coin and having it land heads 6 times is
0.5^6 = .015625 = 1.56%

The probability of having a 6 sided dice land on 1 six times is
(1/6)^6 = 2.14×10-5 = .0000214 = .00214%

What is the probability that the watch would stop at 2:15 PM 6 times has 2 answers depending on whether the watch stopped to the second at 2:15 PM or only to the minute. Since he is a pastor, he would not understand the mathematic implications of one versus the other. So he never took notice, except that it was at 2:15 and NOT 2:16 or 2:17… etc..

Lets calculate the odds of to the minute first. There are 60 minutes in an hour, 24 hours in a day. Recall that it never stopped at 2:15 AM, so that means we are dealing with a trade space of 24 hours. That means there are 24 x 60 = 1440 possible minutes.

Using the same math as before

(1/1440)^6 = =1.12e-19 = 0.000000000000000000112

If it were to the second, then it would be
24 hours X 60 minutes X 60 seconds = 86400 possible seconds

(1/86400)^6 = 2.4e-30 = .0000000000000000000000000000024

Do you know what the probability of winning the lottery is ?

1:22,957,480 = 4.36e-8=.0000000436

Odds of being struck by lightning in your lifetime (80 years)

1:5000 = .0002

Now consider the odds I mentioned about the watch in comparison to the other events. That’s why I call them “Miracles of incalculable odds”. People don’t understand 2.4e-30 terms. They understand 1:5000 as with lightning, but they can not grasp the other.

Let me make a better comparison for you. Found this write up on

So how many grains of sand are there in the world? You could start
off by trying to guess how many grains of sand there are in a spoon of
sand. Use a magnifying glass to count how many grains fit in a small
section. Then, count how many of those sections fit in your spoon.
Multiply the two numbers together to get an estimate.
“Using this same principle, plus some additional information,
mathematicians at the University of Hawaii tried to guess how many
grains of sand are on the world’s beaches. They came up with
7,500,000,000,000,000,000, or seven quintillion five quadrillion
grains of sand.”

That number is 7.5 x 10^18 or 7.5 billion billion.

How many stars, galaxies, clusters, QSO’s etc. in the Universe?

“To get the total stellar population in the Milky Way [that is, in our
galaxy alone], we must take the number of luminous stars that we can
see at large distances and assume that we know how many fainter stars
go along with them. Recent numbers give about 400,000,000,000 (400
billion) stars, but a 50% error either way is quite plausible.”

So in our galaxy alone, there might be between 2 x 10^11 and 6 x 10^11 stars

How many galaxies in the Universe?

“the Hubble telescope is capable of detecting about 80 billion
galaxies (although not all of these within the foreseeable future!).
In fact, there must be many more than this, even within the observable
Universe, since the most
common kind of galaxy in our own neighborhood is the faint dwarfs
which are difficult enough to see nearby, much less at large
cosmological distances. For example, in our own local group, there are
3 or 4 giant galaxies which would be detectable at a billion
light-years or more (Andromeda, the Milky Way, the Pinwheel in
Triangulum, and maybe the Large Magellanic Cloud). However, there are
at least another 20 faint members, which would be difficult to find at
100 million light-years, much less the billions of light years to
which the brightest galaxies can be seen.”

So the lower end estimate for the number of galaxies is 8 x 10^10

If we accept even the lower end of these Hubble figures, and if our
Milky Way has a typical number of stars in it, that puts the number of
stars in the universe to be at least
(2 x 10^11) x (8 x 10^10) = 16 x 10^ 21

So if we round the number of sand grains to, say, 10^20
and round the number of stars to, say 10^22
then there are at least 100 stars in the universe for every grain of sand on earth.

Using the same math as before

1.12e-19 = 0.000000000000000000112, for to the minute accuracy Watch

2.4e-30 = 0.0000000000000000000000000000024, for to the second accuracy Watch

7.5e18 = 7,500,000,000,000,000,000, for number of grains of sand in the world

16e21= 16,000,000,000,000,000,000,000 # stars in the universe

So the factual reality is that if I were to mark a G on a piece of sand anywhere in the world, you would be more likely to find that one piece with one pick, than for the watch event to have happened.

Actually they are very close 1.12e-19 versus 1.33e-19, if we round down they are the same. Interesting

If I use the model of accuracy to the second, then it isnt even close.

Lets examine the stars effect, if I were to ,metaphorically speaking, mark a G on a star anywhere in the universe, you would be more likely to find that hidden star with one pick, than for the watch event to have happened.

In fact you would be 26 million times more likely to find the hidden star than to repeat the watch example.

The interesting thing is that the Pastor only thought that it was maybe a 1/1000 event, and had only shared that story with a few people. These kinds of miracles happen all the time, but they remain hidden because most people dont know how special they are.

Now, after reading this story, I look back at the criteria:

1. The event is overwhelmingly unlikely

– That was one of the main points of this story. Check out the statistical figures given.

2. The event (seemingly) has spiritual significance

– This event affirmed this pastor’s decision to lead the church that called him at 2:15. This decision has significant implications; this pastor will likely be leading the people of this church for several years.

3. There are few, if any, plausible naturalistic explanations

– This is the key point I want to focus on. Of course, you could chalk this story (and others) up to coincidence. But if this event were to be explained in naturalistic terms, many pieces (rare in themselves)  would have to come together to fully explain how these events happened. Although possible, it would be very difficult to come up with plausible naturalistic explanation(s) that explain the entirety of this story. At this point, I think we need to be at the least open to the idea that there was divine involvement in this situation, especially in light of the spiritual implications involved.

However, I am only talking about one isolated situation here. As Paul hinted, there are a lot of stories involving miracle claims – extremely unlikely events with spiritual implications. If the total naturalistic viewpoint is held, ALL of these claims require a natural explanation, whether there is a plausible one or not. This view creates a nature-of-the-gaps scenario, where every event, no matter how unlikely or unexplainable, is credited to a natural explanation.

The opposite can occur as well (crediting only God when there is a clear natural explanation), so I am not saying that we should assume God is the explanation of all coincidences. I am saying that if a certain explanation of an event is the most reasonable one, we should consider it even if it involves bringing the divine into the discussion.

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2 Responses to Watch Out for Coincidences

  1. cquinnweb says:

    Hey, Jeremy, this is a cool post. I’m glad you’re incorporating probability into this, but your analysis is a bit of an oversimplification. (That being said, so will my counter argument because I’m not a statistics expert, but there are still a few issues with yours that even someone limited expertise like myself can notice)

    First, because your pastor did not record the time of the events in question down to the second, we cannot assume they are accurate to the second. Thus, we have to use the minute probability 1/1440.

    Second, the method you use to calculate the final probability of all the events occuring by multiplying their probabilities. There are two problems with this. One, this assumes the events are independent, and that each event was equally likely to happen at 2:15PM than they were to happen on any other minute in the day. I don’t believe we can assume that to be true. If I were to role a die 6 times and got a 6 every time, my first assumption would not be that I had gotten incredibly lucky, but rather that die was loaded. By the same merit, if a watch stops at 2:15 everyday, it could very well be that some mechanical defect in the watch makes it very likely for the watch to stop 2:15. And since the second watch is the exact same make and model, it could very well have the exact same defect. Without more data on the failure rate of those watches, there’s not really a good way of estimating exactly how likely it is that that specific model would fail at 2:15, (and the solution to that would probably involve probability distributions and calculus, which is above my pay-grade) but if there is some defect, that probability could very well be close to 1. Given that the clerk rewound the watch to 2:14 and it still stopped at 2:15, I think the existence of such a defect is highly likely.

    So really, you only have three events that I would be confident at saying are independent. Which is the first watch stopping, the third watching of a different make and model sstopping, and the phone call. That would give you 1/1440 ^ 3 which is 4.82e-7, which is less than the chance to win the lottery at 4.36e-8.

    Unfortunately, a more sophisticated analysis would require much more data, expertise, and time than I have. See, thing is we have to account for the fact that this could happen to anyone, and theoretically any time would work so long as the time kept repeating, and at any period in history in which watches exist. That would give this some similarities to the birthday problem, which reveals that it is surprisingly likely that 2 people will share the same birthday with a small group of people.

    We’d also need to estimate the rate at which the third watch fails.

    • linnjr02 says:

      Hey Colin, thanks for the comment – it’s a good one! It’s quite interesting to revisit this post since I wrote it six years ago.

      I think you provided a reasonable naturalistic explanation for the events, especially of the first watch. I would say there is a slight variation in that the watch only stopped in PM and not AM, and it would be unusual for that to happen with a watch defect. I’m unsure if we could add any more independent events in light of that variation.

      You are correct that much data and expertise would be needed to obtain a precise statistical figure for a circumstance like this. But getting to a correct statistical figure was not the point of the post.

      The story was an example that points to criteria we can use to determine if an event was a miracle or not. The story was quite helpful in that sense, whether one would say it’s a miracle or not.

      Another point was to say that even if this one scenario wasn’t a miracle, there is a wealth of miracle claims out in the world. Assuming that all these claims have naturalistic explanations without at least looking at the data shows that one has a strong bias towards naturalism. If even one of the thousands of miracle claims had a cause outside of the natural order, then that naturalistic assumption is broken down.

      Of course, you can say that we have good reason to make that assumption because of our every day experiences. But that leads to another long conversation about worldviews and where our assumptions begin 🙂

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