What is a coincidence?

By Arthur Kary.

The aim of this post is to get deep into coincidences, and try to figure out what exactly is going on. It would help if you thought of this as more of a hypothesis than any attempt at a theory, just me throwing out a few ideas to get everyone thinking about it. I’m going to argue that the dominant aspect of coincidences is the subjective attitudes we have towards the events, rather than the ontological nature of the events themselves.

Coincidences themselves do not exhibit the properties of ‘remarkable’ or ‘weird’. That an event is a coincidence is not like an object refracting particles of light, doing so whether someone is watching it or not. What makes coincidences so interesting to me is that they rely on an observer to recognise them. They need someone to add the remarkable to it through their perception of the event. A definition of coincidences I propose is ‘an unlikely and apparently uncaused relationship between objects or events, the observation of which causes in the perceiver a particular emotional response’. I will now talk about that particular emotional response, focusing on why we might feel it, and also bring to light the big role it plays in the overall coincidence phenomena.

Unlikely in that definition, taken simply, means you don’t come across it very often. But unlikely can also be looked at in a more abstract way. Given someone’s way of understanding the world, the possibilities and significance of any particular event occurring are apt to change.

The feeling of coming across a coincidence, I think, is the violation of one’s schema, or way of understanding the world, by an event that doesn’t fit in it, or is improbable according to it. Coming across someone who shares a birthday with you may seem an unlikely event in your schema, you may term it a coincidence, but as anyone who has attended a Phil Staines lecture knows, the probability of being in a room with someone who has the same birthday as you exceeds 50% with only 23 people in it. For the person who has that knowledge, that relationship does not have the same significance. Another important point is that despite each scenario ending up with different outcomes, either experiencing a coincidence or not, the physical events leading up to it are all the same. It is the interpretation on behalf of the individuals that changes the outcomes.

So to sum up my argument, I think coincidences are primarily the result of our expectations of the world compared to the world itself. Events and relationships in the universe do not have a significant quality or a weird quality as part of their constitutions. These properties are attributed by us, in our experience of those events. If we look at coincidences in this way, we are able to avoid attributing extra forces or phenomena to the universe, instead acknowledging how we may be shaping the world through our experience of it.


15 responses to “What is a coincidence?

  1. Interesting stuff!

    One thing I loved about the presentation was your distinction between types of coincidence. If I recall correctly, you distinguished between ‘small world’ and ‘speak of the devil’ coincidences.

    The difference being that a ‘speak of the devil’ coincidence involves some kind of immediacy, some direct connection – you’re thinking about person X and then you bump into them around the corner – whereas a ‘small world’ coincidence doesn’t (you’re thinking about person X and then you bump into their friend a little later).

    Correct me if I’ve misrepresented you there. I’d like to see if we can discriminate among types of coincidence even further.

    For example: what would you call the kind of coincidence that involves two very similar events following each other in quick succession? (A guy drops his apple in the gutter; you walk a few more steps and a lady drops her apple in the gutter). Is that still a ‘small world’ coincidence?

  2. What do we do, however, when there are objective similarities between two events that come together seemingly by chance? The most famous example of what Carl Jung called synchronicity was when a patient was telling him of a dream of receiving a golden scarab (in this case, a piece of jewelry), and then Jung heard a golden scarab beetle scratching at the window, trying to get in. It seems to me that this violates more than just our expectations, or rather, it violates our expectations for good reason. Often, of course, our expectations have a reasonable basis in long experience. We can even imagine a more extreme case of Jung’s story, in which, say, the patient’s dream included the scarab beetle jewelry being scraped against a window, making for an even more unlikely match with Jung’s beetle scratching at the window. So what do we do when there are objective similarities between events, similarities that experience has taught us really ought to be extremely unlikely?

  3. Thanks for dropping by, Robert!

    The word ‘objective’ is doing a lot of work for you there. What exactly do you mean by ‘objective similarity’? If you mean to claim that there is a world independent of our experience of it, then I would be tempted to agree. But if you mean to claim that our perception of a similarity is an ‘objective’ feature of the world, then I would disagree.

    Firstly, people disagree about the nature of coincidences. What for one person is incredibly coincidental is for another a mundane event.

    Secondly, consider whether or not it would be possible to program a machine to identify ‘objective’ similarities. Surely such a machine would only be as functional as its programming: it would work only inasmuch as it followed the schema, the way of looking at the world, that it had been programmed to follow.

    In the same way, our preconceived notions of what the world is and how it happens – our ‘expectations’, as you put it – are necessarily prior to the experience of a coincidence.

    So what do we do when confronted with events that we think are significantly similar? Well, we call them coincidences! 🙂

  4. Nick (assuming that’s your name),

    Call me old-fashioned, but I am just not ready to do away with the concept of objective similarities in the world. In practice, of course, no one is. Doing away with the concept of objective similarities on a practical level would leave someone non-functional. She would look at a coffee cup and see no similarity with anything else she had ever encountered before. As a result, she wouldn’t know whether to pick it up, lick it, or bat it away in fear. Without similarity, everything would be as brand new as it is to a one-day old infant, who, of course, is non-functional.

    I suspect we can agree that we are not ready to give up this concept on a practical level (we all, for instance, realize that the message we type into these little windows is extremely similar to the message that shows up above once we hit “submit”). The question then becomes, Are we willing to admit that our practical functioning is absolutely artificial, absolutely alien to or divorced from reality? If I understand you aright, that is what you are saying.

    But then, if we have a goal of trying to somehow be “in line” with reality, then we are put in a terrible bind. For the cost of fully mirroring reality equals becoming non-functional, and then presumably institutionalized. That’s a hell of a cost.

    Your thoughts?

  5. That’s a great point. For sure, understanding things in terms of similarity makes our lives a lot easier, and I don’t mean to argue that we should do away with the notion entirely. But I think it’s important to recognize that similarity and coincidence are not properties of things.

    I mean, this coffee cup will certainly share some ‘objective’ properties with this other coffee cup: they both reflect certain wavelengths of light, they are both composed of certain specific materials, they both displace certain volumes of water when placed in a sink, and so on.

    But the notion that they are similar is something that comes afterwards – we recognize that these two cups share certain properties, and we identify the relation between them as one of similarity.

    ‘Objective similarity’ implies to me that those cups have some additional property, say ‘cupness’, that identifies them as similar independent of our awareness as such. I think that’s a mistake. How would something like ‘cupness’ be manifested physically?

    This becomes even more problematic when we come to coincidences, where the objects between which we perceive some relation of similarity are often very different (a dream vs. a beetle).

    And I don’t think that an awareness of the way we apply concepts to the world leads necessarily to a detachment from reality. Believing that there is a reality is perfectly compatible with believing that we perceive it in different ways. Similarity is just one of the ways in which we perceive the world.

    (and yes, my name is actually Nick!) 🙂

  6. Nick,

    Thanks for your response. OK, maybe I’m beating this thing to death. But just in case we don’t have better things to do, let me try a new tack.

    Let me concede for the sake of argument that properties like “cupness” are not objective properties of a thing, but mere cultural forms applied to things by the human mind.

    Despite their subjective nature, the fact is that a great many of them are shared. You and I could both agree that a coffee cup does in fact have “cupness,” which is shown by the fact that we both call it a cup.

    Could it not still be significant if some unknown law or force or presence is drawing events together in such a way that different observers could agree are similar? Going back to the Jung story, I think any human observer would see the similarity between a golden scarab piece of jewelry and a living golden scarab beetle. Even if we say that “golden scarabness” is just a cultural idea rather than an objective quality, isn’t it interesting that something is bringing events together that share this particular cultural idea? Isn’t it perhaps worth investigating?

    I have experienced some truly remarkable coincidences, that in my opinion are even more striking than the Jung story, and whether we say that the similarities are objectively real or just cultural artifacts, it doesn’t blunt their impact.

  7. A nitpick here: the likelihood that /any two/ people out of 23 share a birthday exceeds 50%, because of the number of possible combinations of people present is large: 253, which is, less excitingly, the number of people necessary for the same likelihood of a match for any *specific* person. While you (Arthur) say that the significance of this kind of coincidence is diminished when you have that knowledge, I don’t think people ever really intuitively lose a sense of surprise at coincidences they know are statistically unremarkable.

    Humans are in some sense pattern-matching machines: we weigh occasions where there have been coincidences much more highly than those cases where there haven’t been. Which makes sense, because it’s hard to keep track of things not happening. But, when considering likelihood, those humdrum – and infinite – instances are just as statistically significant. Truly random series often feature repetition – rolling a 6 several times isn’t especially surprising – especially when order is drowned in a whole lot of disorder: 6 sixes, 7 sevens, and 8 eights (sadly not 9 nines) all appear within the first 200 million digits of pi, as testified to by this site ( http://www.angio.net/pi/piquery ). It’s plausible, but unproven, that as a transcendental number (one without a discernable pattern), pi, e and the like contain all possible strings of numbers within their infinite string of decimals. 300 5s? Why not! The complete binary code for Microsoft Word 2007? Sure! You get the idea 😛 Jung doesn’t tell us about the time when a patient recounted a dream about a devastating storm and then the postman came.

    Another facet of the same hit-registering, miss-discarding mechanism is that we’re *primed* to detect coincidence. Jung singles out the scarab jewelry detail from that particular dream and draws the connection with a particular event in reality. This comes back to the discussion of ‘cupness’ – to what extent is abstraction ‘real’, and when are we doing all the mental footwork two connect two dissimilar things into a lazy coincidence?
    Which brings up our remarkable powers of abstraction and analogy. That something in a dream can be mapped to reality and a piece of jewelry to a beetle may seem pretty unremarkable, but if you take it as a general rule that two jumps of abstraction are allowed before a coincidence becomes negligible then it doesn’t take much thinking to realise the sheer scope of things which could potentially be seen as coincidences if they happened together (a tautological sounding statement, but I’m using the original author’s definition of coincidence 😛 ). If we narrowed the criteria down – only cases involving dream jewelry and its window scraping living counterpart, perhaps – then we’d understandably see a drop-off in coincidence reporting!

    So when are coincidences ‘real’ and warranting attention? Well, there’s no hard and fast rule. What we normally do is find an explanation – “all those shops look the same because they’re part of the same franchise!”, “this stuff boils at the same temperature as that stuff because it’s the same substance at the same pressure following these natural laws!” etc. – or we don’t, and possibly write it off as a statistical inevitability.
    Perhaps tomorrow all existing explanations will be void, and nothing makes sense – perhaps shit just happens! The universe doesn’t have a contract with us. We explain what we can, as well as we can. Coincidences which seem to have something else behind them may well have, but until we have an objective view of everything – which is to say, never – we can’t know for sure.

    Perhaps that dipping too far into sophistry, but the basic concept holds: the only difference between significant coincidences and insignificant ones is that we explain some of them, and try to explain the ones that really bug us.

  8. @Robert: of course! Coincidences are still significant and they’re certainly worth investigating, regardless of how we choose to explain them 🙂

    Your suggestion of an unknown law or force is an interesting one. If Arthur’s around, I know he looked into philosophical explanations along those lines…I’ll give a holler out into the internet.

    @Al: thanks for commenting! So maybe Microsoft have been plagiarizing pi all this time? I smell an anti-trust suit.

    Human pattern seeking tendencies are fascinating. This recent article in the NYT, for example (http://www.nytimes.com/2009/10/06/health/06mind.html?em), comments on ‘the urge to find a coherent pattern’ – apparently we’re more likely to find patterns when we’re looking for them (sounds obvious, I suppose, but psychology is all news to me).

  9. I wonder if you can’t collapse the distinction between speak of the devil and small-world co-incidences. Dr Arthur takes a co-incidence to be an unlikely and apparently uncaused relationship between objects or events, the observation of which causes in the perceiver a particular emotional response. It seems to me that so long as we cash this out in terms of events then there is really very little to distinguish between small-world and speak of the devil co-incidences. The former holds between two external events whereas the latter holds between an external event and an internal event- say the expectation, anticipation or apprehension of an event. But when looked at like this- the distinction collapses. After all, it’s the experiencer’s experiencing of a believed connection between the two events (whether external/external or external/internal) that is the salient experience relevant to co-incidence.

    Having said all that, I think it’s best to take Dr Arthur’s definition as not excluding the possibility of objective similarities. In that sense it seems to me that what Robert says is largely on the mark; the point is that it’s not any objective similarity between two events that causes the experience of a co-incidence. Rather, it’s the experiencer’s belief that there is a similarity or connection between the two. The latter does not depend on the former in any strict sense. Two events may be objectively similar in Robert’s sense without that constituting a co-incidence. Similarly, two events may be experienced by an experiencer to be objectively similar without them actually being objectively similar and this may constitute a co-incidence.

    So to tie this back in to Dr Al King’s points, the above paragraph concerns what’s salient for the kind of similarity that’s required for the kind of experience which we take to be a co-incidence. The direct entailment therefore being that there are just no such things as insignificant co-incidences. One of the characteristics of the believed/perceived connection between two events is that it be one of significance. Otherwise it wouldn’t cause the experience of co-incidence in the first place…

  10. Let me drop an example in here, just to give us a real-life example to kick around. In July, I was talking to my 17-year-old daughter about her schooling here in Arizona. The context for this is that my second wife (not her mother) and I are planning on moving to England next year. Just a few days before this, I had told my 17-year-old about this, and that led us to talk then about how the schools in England are ranked higher than those in the US, and about how she heard that Arizona schools were ranked 50th in the US.

    The conversation in question was a continuation of that one. This time, I voiced my view that she has been taught shockingly little about subjects like history in her high school (she heartily agreed, saying her high school sucks). So I gave her a pop quiz, asking questions like “When was the Civil War?” and “Who was president during the Depression?” When she failed those, I jokingly asked her “Who was the first president?” She jokingly said, “Lincoln.” It was a bit sobering. Not being proud, my daughter had fun with it and took it all in stride.

    About two hours later, I received an e-mail from an e-mail news service. It was an article entitled “Dumb Americans Revealed.” It was about how Arizona high school students were asked to answer 10 questions from the US Citizenship and Immigration Services Exam. The Goldwater Institute said the results were “troubling” and said the students showed a “profound level of ignorance about American history, government, and geography.” Only 3% of the students passed it (got 6 right), while 92% of foreigners seeking citizenship pass it. It included questions about presidents, including “Who was the first president?”

    I made a list of all the things my conversation with my daughter had in common with the article. Here’s the list:

    1. Arizona high school students
    2. are shown to be shockingly poorly educated
    3. specifically, about US history
    4. This is revealed by a quiz they take about the US, which is focused on history and government
    5. At least some of the questions in the quiz are about presidents
    6. The quiz includes the question “Who was the first president?”
    7. This question is treated as something it would be embarrassing not to know (that was true in both cases)
    8. There is parental involvement in the quiz (I gave the quiz to my daughter; the article said, “How about we all just learn these basics and pass them along to our children?”)
    9. Arizona students or schools are compared unfavorably to foreigners or their schools
    10. Someone is emigrating to a new country (the reason for the conversation with my daughter was that I was planning to move to England; the quiz in the article was for people coming to the US)

    I don’t recall hearing anything about the quiz reported on in the article before I got the e-mail about it. Yet it was an uncanny mirror of the conversation I had just had with her–really uncanny. It didn’t just have one thing in common with the conversation, but rather ten, by my count.

    So, I just thought I would throw this out there to spark some discussion. What do we make of an experience like this?

  11. As I say, part of the issue is that we have a great ability to draw analogies and that we don’t take note of non-coincidences – another point is that, when it comes to human interaction, we’re neither constitutionally nor culturally unique, so the same issues and perspectives are often raised by different people.
    I’d say 4-9 really follow from the premise of the article, taken as the first 3, and 10 is a pretty wrenched comparison. The issue of educational quality in Arizona probably hasn’t come out of the blue entirely. Focussing on US history as a watermark of educational standards is a culturally influenced sort of thing – something considered locally important, as well as something that can be seen not to be merely inept not to know, but an affront to ideals etc. which is always a favourite line for articles to take and something parents feel is important.
    Other factors which would greatly mitigate any sense of ‘true’ coincidence would be if you found it on the internet, rather than being e-mailed it (being primed to notice – though as it stands, it was probably picked out from a number of articles, being something you were thinking about, and the news source may have been Arizona-centric) and it being found days or weeks later, relying more heavily on your ability to recall and relate events, but even as it stands it’s less remarkable than it appears first off. (I remember seeing an article like that, it was all over the ‘net – perhaps your daughter had already caught sight of it?)
    Of course, I’m not saying that you’re conspiring to find a coincidence where there is none – in the same situation, I’d have been surprised by the parallels as well. But after a bit of thought, the coincidence appears to be more “statistically negligible” than it first appears, and if also I can’t see an explanation for it, I write it off as “just a coincidence”.
    I *could* interpret coincidences as ‘signs’, but that doesn’t seem that as useful as taking advantage of explicable parallels.
    That said, detecting coincidences everywhere isn’t such a bad thing – when we talk about people “making their own luck”, it’s often related to their ability to recognise things relevant to them in unexpected contexts and taking advantage of them (look up Richard Wiseman for more on that).

  12. You guys know there’s a forum now? It’s http://www.socraticsociety.net/forum

    You can also discuss these issues here…I’ll put them up

  13. Hi, i just wanted to share something with you guys and hear your thoughts on it. So yesterday i happen to finish work early, a rarity in the silly season (retail) and whilst cycling home i bump into my sister, so it got me thinking, 3 seconds later/earlier and i would have missed her, the strange thing was i left out the back door to save time, i have only ever done this like twice in two years i wasn’t in a particular rush something were just telling me leave asap. Anyway this got me thinking was it a coincidence or was it something else, and i started thinking about all the memorable so called coincidences i have experienced in the past. Went home asked my other sister what her thoughts were on coincidences, and made a mental note to research it. OK, now this is where it gets interesting, we start talking about traveling the middle east, and how cool it would be to cycle in iran, and how i have only ever known one iranian guy, nice as pie, whom i used to work with 5 years ago.

    Long story short, im blasting down downhill on my way to work today, glance to the pavement and who do i see? my iranian colleague that i havent seen in FIVE years!! I was running late and going fast, i didnt stop to talk.

    So i have been rattling my brain around that one, and decided to give google a go, hope you guys can shed some light



  14. Hi all, I’ve always thought coincidences are just God’s way of getting our attention.

  15. Clapton Mbano CMb

    Going through your beautiful article 8 years down the line, I could not help but notice a mistake in your suggestion that “The probability of being in a room with someone who has the same birthday as you exceeds 50% with only 23 people in it.”

    In fact, 50% is the probability that “any 2 people in the group of 23 share a birthday.”

    As BetterExplained.com magnificently put it across, humans are a tad bit selfish.
    “In a room of 23, do you think of the 22 comparisons where your birthday is being compared against someone else’s? Probably.

    Do you think of the 231 comparisons where someone who is not you is being checked against someone else who is not you? Do you realize there are so many? Probably not.”

    “The fact that we neglect the 10 times as many comparisons that don’t include us helps us see why the “paradox” can happen.” (https://betterexplained.com/articles/understanding-the-birthday-paradox/).

    So, in short, in a room of 23 people, 50% is the probability that any two have a birthday match, not the probability that someone’s birthday matches any specific person’s. The difference is Vast.

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