One definition of a coincidence is that it is a remarkable concurrence of events or circumstances without apparent causal connection. And that gives away the answer to the question: rather than believe that such an extraordinary thing should have no cause it might appear to make more sense to believe that there is some underlying cause, of which we are just unaware.
That’s perfectly reasonable. After all, evolution has programmed us to seek causes for events. Animals survive if they learn that one event is likely to lead to another: that movement in the grass means a tiger is lurking nearby, or that a particular colour and shape of a fruit means it’s poisonous. Those animals which survive go on to produce the next generation.
In fact, people dramatically underestimate how often such coincidences, without any background cause, should be expected to occur during the normal course of life.
Furthermore, we are surrounded by things which do have a cause, but which seem almost magical: live pictures appearing on a cellphone, aspirins making a headache vanish, aircraft not plummetting from the sky.
So that’s why some people believe coincidences are meaningful: we expect events to have causes, and when something as startling as a coincidence occurs we may look for its cause.
However, the truth is that not all extraordinary coincidences do have hidden causes, or meaning of any other kind. Sometimes they are simply - coincidences. In fact, people dramatically underestimate how often such coincidences, without any background cause, should be expected to occur during the normal course of life. I explore this in my book, The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day. This describes five underlying laws of probability, which braid together to form a rope of explanation of improbable events, showing why, as Persi Diaconis put it, the really unusual day would be one where nothing unusual happens. One of these laws, the law of truly large numbers, shows that most of the coincidences we encounter in life will be just chance events.
Having said that, the fact that we should expect these things to happen, and that they have no hidden meaning, should not detract from the pleasure we feel when they do happen to us. I still get a tremendous kick out of the fact that the 104th president of the Royal Statistical Society served at the same time as the 104th president of the American Statistical Association, the first time such a coincidence had ever occurred since the founding of the two societies in the early nineteenth century (I was the Royal Statistical Society’s 104th president). And I was stunned when I was invited to talk about my book at a venue in the town of Bournemouth, a venue I’d walked past every day on my way to school between the ages of 7 and 11, and a town I’d not been back to in 40 years. But neither of these coincidences had any meaning.
The question also has a hidden depth. The answer - that some things just happen by chance - reflects the fact that the universe does not have any intrinsic meaning, and that there is no fundamental meaning to life. This can be an uncomfortable recognition - as I said, we have been programmed by evolution to seek causes, to find narratives explaining why things happened.
Because coincidences alert us to the mysterious hiding in plain sight. They suggest causal connections that current science may not accept. Meaningful coincidences can offer advice, spur psychological change, help with decisions, help find people, things and ideas we need like a romantic partner, a job and creative possibilities. They also can increase our spiritual awareness and alert us to potentials latent within us like telepathy and human GPS. See my book Connecting with Coincidence for further details.