The Science of Coincidence

an old favorite. Yeah, this is our episode on the science of coincidence. It's it's one that we really enjoyed putting together. I think it's definitely an evergreen episode that tests us, you know, it stands the test of time. I think I recorded this one before I was actually a host on the show. I was doing a guest episode. This is one of the first ones I ever Did's right, that's right. Yeah, So it's it's a strong one and if you've heard it before, then I think it's a

perfect one to re experience. And if you are a newer listener to the show, then hey, listen to it for the first time. So without further ado, let's jump into the repeat. So I've got one for you. Tell me if you've heard this one before. Lincoln and Kennedy. Yes, you know this. I was first exposed to this in middle school when a teacher of mine get gave us a list of these like it was some kind of really important fact we needed to learn. But yeah, how

about this. Abraham Lincoln and John F. Kennedy, two American presidents. Both were elected to Congress in the year forty six, Lincoln in eighteen forty six, Kennedy in nineteen forty six. Both were elected president in the year sixty, Lincoln in eighteen sixty, Kennedy in nineteen sixty. Each of their last names both contains seven letters. Uh. And then there's this whole list of coincidences that keeps going. They were both shot in the head, they were both assassinated by Southerners.

They were both succeeded by Southerners. Their vice presidents were Southerners. Both vice presidents were named Johnson. What are the odds? Yeah, I remember this being rolled out, perhaps in a history class, and uh, you know that the list would start about these coincidences, and I would kind of tune out after

the first one or two. Um, And I guess that that kind of boils down to the type of people in the world, like they're there are people out there who just tune out after the first coincidence or two, and then there are those who obsess about it and see this as as something something really crucial and something really telling about these two men, about the history of this nation, et cetera. That might be the difference between us, Robert, because I did not tune out. I was my mind

was blown to uh, to borrow from a popular phrase. Yeah, I I sat there in my desk like, wow, what are the odds? You know, must to be some kind of ghost spirit controlling this. It just I was amazed that there are two twin souls are basically the same entity reincarnated and and and tracked hunted by the same extra dimensional force. Yeah. Or there there was some sort of like cosmic literature teacher trying to get me to

observe parallels between the meaning of these two men. Yeah, it's another one of course that comes to mind is the death of Thomas Jefferson and John Adams, two individuals who, of course very interconnected in the history of the United States as well. Sure, both instrumental drafting the Declaration of Independence, which was signed to July four, seventy six. Both men died on the same day, July four, eight twenty six, exactly fifty years to the day after the document was ratified.

So that that you know that that kind of hits you like. I like that one because that one's nice and succinct. You know, what were the chances? You don't need a list, it's right there. Yeah. I mean they were they were good friends, so maybe there was you could imagine some level of synchronicity about, you know, when you're giving up and sort of handing it over to the reaper. But but the dates are kind of compelling there.

It would be even crazier, though, if I found out now that you played John Adams in a production of seventeen seventy six. No, but I was in a production of Seven Times. Here you go. I played Thomas Jefferson in a been a production of seventeen seventy six. So we're tied into it too. There's no escaping the black hole of coincidence. Okay, I've got an even crazier coincidence. No, it's probably not. This is kind of dumb, but why do so many action heroes have the initials JB, James Bond,

Jason Bourne, Jack Bauer, Jack Burton my favorite? Well, I mean, what are the chances? Actually, we have no idea, do we? Yeah? I haven't read any I mean maybe there's some really deep statistical study on this out there, but uh yeah, maybe it is it that, on one hand, is just possibly pure luck. And we only pick up right on there there being a JB here, JB there, because we're also not taking into account all the other j B initials out there, like like does Jim being factor into this?

Probably not, and all of the action heroes that aren't j B s. Yeah, And then to what extent is it just completely almost subconscious? You know, because you have an action hero and and by extension of action hero, you think of mythological hero and the symbolic power of the hero and how it resonates through uh, through our culture and through through our our the way we view the world, and and perhaps that ends up informing it.

You You have James Bond in your mind, and then you end up creating Jason Bourne and Jack Bauer in the same way, and I'm just purely spitballing here. You could perhaps have the mythic hercules in your mind, and then when you need to create another, you know, mythically strong hero, perhaps you go with the Hulk. The same kind of consonants. Yeah, we associate sounds with with ideas, certainly. Yeah, now another crazy one. And I love this one in

part because it involves Edgar Allan Poe. Of course, Edgar Allan Poe only wrote one novel his entire career, you know, mostly known for his his excellent short stories. But the novel in question published an eighteen thirty eight the narrative of author Gordon Pym of Nantucket. I've never read it, never mean, I never read any there. But the fiction of this story is you have a crew of a ship called Grampus. They wind up adrift with no food

or water, and so first they catch a towrartoise. They eat it, but eventually they have to draw straws to see who winds up as a dinner and uh an individual named Richard Parker draws the short straw, so they stab him and then they eat him. And then they build a house on the boat so that they can bury him behind the wall. Yeah, I mean, you gotta play the greatest hits, right, here's where he gets crazy.

Years later, in eighteen eighty four, a yacht named the minion Net leaves England, is headed towards Sydney, Australia, and it sinks in a storm. Four men wind up adrift in a lifeboat. They catch a turtle. They eat it all right, But again you're probably thinking at this point, Okay, you know turtles, how hard are they to catch? There are lots of turtles in the world. They're all tasty. Yeah, And if you're four men in a boat in the middle of nowhere and you're hungry, you're gonna eat it.

No good deal. But then it turns to cannibalism, and this too you might think, well, what a four guys in the middle, in the middle of the ocean in a little boat. They're hungry, They've only had one turtle to eat. It's kind of inevitable, right, Well, this is this is crazy. But aboard this vessel you have a seventeen year old named Richard Parker, the same name as the individual they ate in pose novel. This guy falls overboard,

drinks a bunch of seawater to quench his thirst. Uh. And so he starts going, he starts deteriorating really quickly here and they side, well, he's he's about to die. We're gonna have to eat him, and they eat him. So you have these this fictional account of cannibalism seeming to inform this real life act of cannibalism years later, and in almost identical circumstances. Yeah, and it's so gruesome you can really doubt that they staged it to happen

on purpose because of the novel. Yeah, Like I can't imagine them being on the boat and someone saying, look, I read this book, and uh, there was a guy in the book named Richard Parker, and they ate him in your name is Richard Parker. So I'm not saying we have to eat you, but come on. Yeah, it's like the worst school play ever exactly. Alright. So in this we're talking about coincidence, and in this episode we're talking about coincidence and the science of coincidence, how we

perceive a coincidence. Uh, but let's let's get down to brass tacks. What exactly is a coincidence? Yeah, and specifically I think we should think about what's the difference between a coincidence and just an improbable event um So of standard Oxford dictionaries, definition is a remarkable concurrence of events

or circumstances without apparent causal connection. Okay, so that's sort of playing up on the like the two different things coinciding, like like the Pim right, like the Gordon Pim example, or like Jefferson and Adams, you know, dying on the same day. Another way of putting it is that it's a concurrence of events that is quote perceived as meaningfully related with no apparent causal connection. Um and and that quotes from a paper that we're gonna end up talking

about later in this episode. But I think that's something we should highlight, is that a coincidence has a perceptual element. It's something that seems to be important to us, like it has a psychic weight. But you know it, it kind of comes back to what we're talking about earlier about the two students in the classroom. One of them is just enthralled by the Kennedy Lincoln coincidence list and the other is, uh, it's just tunes out on it. Because that that kind of comes down to how we

can look at coincidence in life. You can either say was just pure dumblock. It is just a matter of statistics. And then there's the the the view that there's something else going on here, that there is some sort of connected, connective tissue that we were just not privy to. And we have seen some very you know, thoughtful and informed study on both sides of the issue. Right, there have been brilliant people throughout the years who paid way more

attention to coincidences than we might today. I mean, we all experience coincidences. I would be shocked if there was someone who would say, no, I've never experienced anything like a really weird concurrence. It happens every single day. It happened to us we were talking about while we were researching these podcasts, like just strange topics coming up and seemingly unrelated episodes. Yeah, I mean, of course, that kind of gets down to that, like the power of coincidence.

Coincidence can can kill you, Coincidence can can make you rich. Coincidence can just be this seemingly meaningless, little connective tissue between two things. Um, and it's trapped. It's so easy to fall into especially given how important causation and determination are in human culture. Right, And we'll get more into that later, but I mean you you almost can't fault an individual for for thinking about these coincidences in terms of some sort of connection. Now, and you see it

at every level. I mean, what is the meat cute and every romantic comedy. It's always some kind of coincidence that brings people together. And on the opposite end, you've got famous scientists who have tried to investigate, you know, what's the meaning of coincidences. I think one great example is the Austrian biologists Paul Camera. Uh you know, if if you ever have that feeling like wow, I think

everything's connected, he did too. So Paul Camera lived from eighteen eighty to nineteen twenty six and he was a proponent of Lamarckian evolution. Have you ever, I'm sure you're familiar with this. This is the the one that, just to give everyone a quick reminder, the idea that say, giraffes, their next grow long because they're reaching for those top those top leads, and so it's like one generation informing the next. Yeah. So normally, now what we believe is

min Dalian genetics. You know, you inherit, you inherit your genetic traits from your parents germ cells, and you pass those same genetic traits onto your kids. And unless you have a certain mutation, that can be basically random. But yeah, Lamarchian ideas where that you could, you know, maybe if you work out a lot or something, your kids will

be born with bigger muscles or something. You strain your neck trying to reach something in this life, and in the next life, your kids will have longer necks by virtue of your straining. Yeah. And so in one famous experiment, Camera claimed to have caused male specimens of a of an animal called the midwife toad to grow these black forearm pads that some species of male toads have, and

that they used them to hold onto females during mating. Unfortunately, some other scientists in the field examined camera specimens and found that the black pads on his toads had been injected with artificial inc and so Camera denied responsibility for that. And I guess nobody really knows whose fault that was, but the accusation here would be that he cheated, which is important because we'll come back to cheating, right. But

Camera wasn't only interested in toads and inheritance. He was also interested in coincidences, like he kept a diary of daily coincidences. And just one example against id it in a in a paper that we're going to bring up in a bit, his brother in law tells him that he attended a concert and held both the ticket for seat number nine and the coach check ticket numbered nine. WHOA, yeah, yeah.

But anyway, that itself doesn't seem all that interesting until you start making lists, which Camera did, and he added them up over time, and I have to admit, when you add it's it's kind of like the Lincoln Kennedy thing. The first one isn't all that interesting until you start adding them together, and then it really gets your attention. There's this cumulative effect of this like snowballing kind of attention, getting significance of coincidences that pile up on each other.

So Camera organized these thoughts into a hypothesis he called the law of seriality uh, and he posited basically this underlying force in reality that was a quote world mosaic or cosmic kaleidoscope that brings like objects and events together. So almost a kind of emergent order, uh in the Chaos show, which I can buy into. And we see in emergence as as a major topic in understanding and intelligence, evolution, etcetera.

So why not coincidence? Sure? But of course Camera wasn't the only scientist who has been interested in coincidences and who has attributed some significant role in the universe to them. Carl Young. Carl Young loved coincidences. Carl So, Carl Young was a Swiss psychiatrist. You probably heard of him as sort of like a he's one of the big names in psychology and psychiatry following Freud. It's like the Mantle. But Young was was very much into sort of interesting

borderline magical esoteric ideas. So he loved the paranormal. He was interested in meaningful connections and mystical truths, esp astrology, psychokinesis, all kinds of stuff like that. And so naturally he was really interested in coincidences. And so he wrote a book called Synchronicity and a Causal Connecting Principle. And this book was actually uh, it was I think extracted from a larger volume of his work and eventually published on

its own. But I read this book when I was in college, and I remember thinking at the time, yet again playing up on my I guess I'm susceptible to this kind of thing. I was like, I wonder if he's onto something here. It seemed really interesting. So what kind of coincidences did Young notice? Well, he gives one example. This is the one that's always cited. It's it's it's his favorite example. It's the Golden Scarub. So in a

ninety one I believe it was essay on synchronicity. Young told the story that he had been seeing a female patient for psychoanalysis, and Young believed basically that she was languishing because she was in sort of a prison of rationality. She was just too rational. She she wouldn't quote open up to the human side of life. For Young, I think this had a decidedly sort of supernatural tinge to it.

And um, he wanted to uh and this is from a particular translation quote sweeten her rationalism with a somewhat more human understanding. So one day she was in psychoanalysis telling him about a dream she had had where one gave her a golden scarrub. And Young claims at that very moment an insects started knocking against the window of the office where they were, and he opened the window and he caught the insect and it was a beatle.

It was a scarub type of beatle. And he said it was like a green color, but in the right light it reflected the light and looked gold. And then he presented it to her in this moment of you know, one of those there are more things in Heaven and Earth than I dreamt of in your philosophy kind of moments, and and he hoped that this helped shatter her rationalism. And so I don't know if that happened to me.

If I had just been talking about a beatle and then a beatle started knocking against the window, I'd probably think that was interesting. But I don't know if I had designed any meaning to it. Yeah, it doesn't really smack of just Heaven sent beetle sent to you, open up my mind and make me more, you know, in love with life because of just a lot of beetles flying around out there. Sure, but Young commented that when coincidences like these accumulate, it's what we were talking about earlier.

The more of them happen, the more we take note of them. Uh, and with good reason, because it's harder to explain them away by random chance. The more they accumulate, you fill up that entire diary with them, right, Yeah, it has way to it exactly. So Young came up with this term synchronicity to describe the a causal connecting principle that links meaningfully significant events that couldn't be connected

by physical causes. So he's not saying that there's like a there's like a you know, a ghost that put the beetle there, because that would be in some way causal. Instead, he's saying, there's another force in the universe other than causality. It sort of runs parallel to causality that connects events and and creates links of significance. But it's not physics.

Like I kind of in making sense of it in my own head, I thought of it in terms of this room or recording, in in which case we have wires that are running outside of the walls, then running across the floor and under the table, and then there are the wires within the wall that we cannot see. And so the wires that are running outside of the walls are are kind of like causality. We can we can see them. We're in causality. We our brain spends a lot of time making sense of cause and effect.

But then there's this idea that there might be some other force at work within the walls. We can't see it, we're not we're not privy to it. It's exact in an ins and outs, but it's it's making things interconnected. It's it's these connections are popping up throughout our life, throughout the Times game. Yeah, causality connects events in the physical realm, and according to Young, synchronicity would connect events

in sort of like the psychic meaningfulness realm. That it was this force it makes things have meaning and shows us meaning by bringing unlikely events together. Okay, so this would be kind of like an um. Have you seen Interstellar? Yes? Okay, so there's the whole bit in there about love. Is this uh, this connecting force like that seems to line up rather closely with this idea of synchronicity. Yeah, I think that makes sense. So coincidences obviously have this power

over us. They captivate us, they seem significance, They make us wonder if there is some kind of magical or super psychic force at work, and sometimes it can be hard to tell because we don't know how to analyze coincidences, you know, like there, when something happens, like you get a number nine from the coach check and then you're in seat number nine, there's really no reason to ask why something like that happened, but you can perhaps ask,

wait a minute, did anything significant actually happen. Indeed, now we've talked about the the sort of supernatural end of the pool, the idea that there is some sort of of intrinsic synchronicity connecting these these events, and now we're gonna we're gonna look at a more critical and more

skeptical side of the pool. Right, So, several times so far in this podcast we've referred ahead to a paper, and this is sort of a classic paper in statistics and mathematical analysis of coincidences, and it's called Methods for Studying Coincidences. It was published by the Journal of the American Statistical Association in December nineteen eighty nine. I think it had been given at a been given as a

presentation in eighty seven a couple of years before. But it's by Percy Diaconis and Frederick Moss Stellar, and they were I believe, Harvard mathematicians, and Diaconis and Moss Stellar offer four main categories of explanation for seeming examples of synchronicity. You know, they refer to camera, they refer to young, and they say, what what do we make of these events? And and how can we tell if something is actually going on that's worth noting. So the first of the

options is that there is an actual causal link. It's not a coincidence, because there's a cause that to seemingly disparate events happen together. The second one is psychology. It's something about the way our brains work, the fact that we're noticing what seemed to be coincidences, and will definitely have more on that later. Another point is what they call the multiplicity of end points, and this is going to be about how how we count something as a hit.

And then the last one that they cite is called the law of truly large numbers, and that's going to be about statistical context. So I think we should go back and look at causes first. So when something happens that's seemingly just a huge coincidence, you should always consider the fact that there might be a cause that's more

obvious than you realize. This would, of course be the birthday problem, right, which is a problem that that people will encounter just everywhere, right and in your workplace that's Google, etcetera. I mean we can encounter it right here in the podcast Chamber Joe Win your birthday July six, mind Sectober six? Whoa synchronicity? Are you serious? I'm serious? Were sixteen sixteen? Okay? What happened when you were sixteen? What city were you in? Oh, Paris, Tennessee.

I was in Tennessee too when I was sorry, I was in faith fal Tennessee. But still Tennessee, Tennessee. Man, some weirds going on? Yeah or but but worth noting here is notice how we're we're singling in on the hits. We totally missed the same day birthday by by many months, but we're counting as a hit because we both had sixteen. Yeah,

so here's the birthday problem. Let's say you're in a subway car and you're riding around with some random strangers, and because you are extremely rude, you start getting people's attention, getting them to take their headphones off, and you you asked the strangers in the car all of their birthdays. That's not rude, that's just good manners. I mean, it's a it's a nice breaker. Okay, Yeah, you might want to know if today's their birthday and you should for

them this cake that you found on the ground. Yeah, So how many people would you have to ask before it's more likely than not that you'd find two people with the same exact birthday. Well, let's see, three sixty five days in a year. Uh so you think, well, maybe I need a talk to three sixty five people, right, or maybe twice that. Yeah, I mean, I'm I'm not good at doing math like that immediately, but that's where

I would have gone the first place in my head. Okay, it's got to be like one in three sixty five times two or something like that. But no, the answer is twenty three. Okay, but we're not going to take the time to explain all the math. You can go look that up online. It is well documented. Uh, this is a classic problem. If you ask twenty three people in a room, in a train car, whatever, you have reached the fifty fifty odds that two of them will

have the same birthday. And one of the key points here is that you're not starting with the specified birthday. You're not saying how many people do I have ask before I find somebody with my birthday? You're trying to find one match, right, Yeah, in this group of if you ask twenty three people, odds are two of them will have the same birthday. What if you want to find three people with the same birthday, that's got to be astronomical, right, I would think, so, I mean you

think that would just multiply it. Yeah, No, Actually, if your train car can hold people, chances are in your favor you reach odds again if you ask a D eight. So that just shows that the statistical probability of in this case this is a birthday match occurring, he's actually, uh far greater than we we we may get a credit. Yeah. I think the point is that we are often surprised by events that are not statistically unlikely at all, Like they just don't match our intuitions. Basically, what we we

have exaggerated intuitions for how unlikely some things are. Especially it turns out particular types of things, for example, things that happened to us. This is a funny thing we're we're way more surprised about coincidences that happened to us than coincidences that happened to other people. Oh yeah, because we're all the center of our own stories, right, We're

gonna be We're more interesting, We're more invested in this one. Um. I mean, just to come back to back to the statistical possibilities, I mean, just thinking back to how we both were like whoa sixteen, whoa Tennessee. But when you really break it down, like the chances of us scoring the same day, I mean the same date within a month, that's what one and thirty one and thirty one chance

for the most part. And Tennessee, what we could say, Well, we're both living and working in Atlanta, so there's probably a reasonable chance that we would come from a southern state, of which there are I mean, but not that many. There's very many literature majors from Tennessee end up in Atlanta. That's not unusual. Yeah, um, but so hey, there could be another cause though. So that's just the apparent cause. The cause that's um readily available. You just haven't looked

at the math. There could also be a hidden cause. When something appears to be a coincidence, it's not actually a coincidence because there's an actual causal link that you don't know about. Um. The classic example of this would be cheating and gambling. Yes, this is where a person rolls a dice, right, Yeah, So so you roll a pair of dice, you know, a hundred times in a row, and let's say you you roll a seven nineties six

out of those hundred times. Yeah, like the more the more every time you roll and you get the same number he gets. That gets even more astronomical that have happened. How could that possibly have happened? Well, obviously if there's a hidden cause, which is the dice are loaded so that they will turn up a seven pretty much every time. So there you you you don't have to be a god to do it. You just have to be a cheater with a pair of loaded dice exactly. And another

example comes to mind. This was a going back to Carl Young. Carl Young was associated with the physicist Wolfgang Polly, and Polly was famous for coming up with the Polly exclusion principle, which is important in quantum mechanics. I don't remember exactly what it does right now, but that's right, but yeah, he um, so he was a known physicist

and it did really important work. But Polly, I think, was also sort of interested in the you know, strange synchronicity type ideas, and Polly, in addition to the Polly principle, which is an actual principle of science, wasn't known for the Polly effect, which is a more anecdotal effect. But the story goes like this, everywhere Wolfgang Polly went, machines broke. Ah.

This is the classic watch stopper scenario. Yeah, so he would show up in a lab somewhere to test out some equipment and what do you know, the equipment and working today. Can't figure it out, And then he'd leave the lab and suddenly it'd start working again. Uh. Don't know how many of these stories are actually true, but this is a popular anecdotal legend, and we'll just accept that it's true for the purpose of the conversation. That

everywhere he went it seemed like stuff wouldn't work. In fact, there was even one anecdote I read about where some people were working in a lab and their equipment stopped working and they joked, is you know Wolfgang here is as he come down the hall uh and then later they found out that he just happened to have been changing trains in that city on that day at the time that their equipment malfunction. He has some long reaching effects. So whether or not that's true, right, let's go ahead

and settle now. But but if it were true, you could perhaps look for actual hidden causes. It might not be a synchronistic coincidence that, you know that the universe, the the Unice Eunice Mundi is trying to tell Wolfgang Polly something about his relationship with miche Jeans or something. It could be perhaps that Polly had a habit of scuffing around his office carpet before heading into the lab, and that led him to discharge a lot of static

electricity which could break some really delicate instruments. Or Polly is just really clumsy. Yeah, and of course he's also not taken to account all of the machines that are not breaking in Polly's life, right, it's literally everything he touches. Does it just fall apart and rust, you know, before his very eyes? Or is it just oh, this thing broke? How could that happen? How could a machine and this little device made by human how could this possibly stop working?

You know, so you end up that you end up honing in on those instances where it doesn't work right. And it's also i think probably not communicating the reality about lab equipment, which is that it probably breaks all the time, and there's a lot of it. Any lab is going to have a lot of equipment, and all of it has a half life and and and a death point. Yeah. Um so, so yeah, that's the idea of the hidden cause. And then of course those are

just some hypothetical examples were offering. The true hidden cause would be the one we haven't even thought of, you know, the cause that's an actual physical causal link that's causing things to malfunction in Poulic's presence, but we can't even guess what it is. It might be there. Yeah, so I think we should move on to another one of the points that Diaconis and Mostell are making their paper, which is the quote multiplicity of end points or the

sort of like the cost of close point. Yeah, because if we have already illustrated close counts and coincidence, like when we're talking about birthdays, we were looking for the same day in the same month, but we settled for sixteen. You know, we were looking for the same Tennessee town and oh my god, we accidentally went to the same high school and didn't realize it. But we'll settle for

just the same state. And that's what we're doing. We're we're constantly looking for these these little coins as to line up, and we'll settle for something that's close. And if you settle for close, the statistical possibilities just blow up, such as of the birthday situation. Um, if you want to uh to, uh to, if you want to hit

a near birthday match with a group of people. So you're back on the train car, back on the train car, and you're willing to to settle for all right, let's see who on this train car has a birthday within a day of each other. You know, we'll settle for a close match. Then you only seven people are needed for that. So yeah, so so coming down from from a perfect match to a near match just opens it

up tremendously. And then, of course, when you think about the accumulation effect that we were talking about earlier, it makes it much easier. If you are accumulating close matches, you keep building up close matches, and over time they start to look significant because they just turned into hits in your memory. You know, you don't remember, well, that was kind of close. You remember, there's a hit, and

then another hit and then another hit. And some of these might be actual hits, of these might be close hits, but they all kind of blend together. Yeah, this brings to mind like cold readings and uh, you know the whole psychic game right where you throw out, oh, i'm i'm I think there's somebody named Joe in your life and you're like, well, I have an uncle Joseph. There you go, close becomes a perfect match and then in the blink of an eye, and then that is how

you reckon your memory. Okay. Then, also when studying coincidences, that this is another category of of Diaconis and Mustellar. There's the law of truly large numbers. And this is a point about context. So let's say somebody encounters of an event that is truly incredibly unlikely for a person to experience. So it's not one of those things with a hidden cause. It's not one of those things where the odds are actually, you know, much more probable than

you realize. It's truly unlikely, you still have to consider context. You have to consider this event against the vast number of uncounted dice rolls of human experience that it is nestled in. So here's an analogy. Let's say you're talking to a professional poker player and she tells you one time she was playing five card poker and she was dealt a royal flush on the opening bet of a hand. Then not to trade any cards, she just got a royal flush. Now, the odds of being dealt a royal

flush or about one in six fifty thousand. I think it's like sixty nine thousand or something like that, about one and six d fifty. But you wouldn't say to this poker player he must be lying or like you know, or you must have been cheating in this game, because you understand that the anecdote is in context. If she's a professional poker player, depending on how long she's playing, she might have been dealt hundreds of thousands of hands

in her life. And on top of that, she's one player out of many, and maybe not everybody has had that experience. So when considered in context, really improbable events start looking like, oh okay, well, Yeah, this is the one chance in however many. Yeah, this is kind of the it'll it's bound to happen eventually, right, Like enough people are trying a given thing, it's gonna line up. The monkeys are going to compose the complete works of

Shakespeare than enough time. Yeah, So there are improbable events, but there are just a lot of chances to achieve them. There are seven point three billion people on Earth today, and according to the Population Reference Bureau, there's an estimated a hundred and eight billion people who have ever lived.

So considering that, if there's an event that has a one in a million chance per year of occurring in somebody's life, let's say it's I don't know what the actual chance of this is, but having a baseball bat thrown over a wall and it hits you on the head or something, Uh, it should still happen to seventy three hundred people every year, just given the population of

the Earth, that that is the probability. If there's a one in ten billion chance of something ever occurring in a human's life, it should still have happened to at least ten people in human history. And it kind of comes back around to the idea of think nicity the union idea, because even though we're we're talking about about real numbers and uh, and just our sort of our inability to really make statistical sense of the actual odds of things. Uh, those actual odds, the computation of those odds,

they kind of exist within the wall. They kind of exist outside of our perception and our understanding of life in the small sense, in the individual sense. So in a way, uh, the synchronicity lines up well with with it with the statistical likelihood of things happening. We just we're just not privy to it. Yeah. I think that connects back to the fact that there is a personal significance for us even if there is not a statistical significance. Again,

it's not surprising that somebody won the lottery. It would be really surprising if you won the lottery. That's not actually objectively surprising, it's just surprising to you, which of course brings us to psychology. Yeah, and we save this for last because I think this might be the most significant of all of these factors. And this is the fact that sometimes it's not even the numbers. Sometimes it's not even the data. It's just that we are wired

to bow at the altar of coincidence. It's how our brains work, indeed, I mean, that's just how we survive. That's how we make sense of the stimuli and our environment. That's how we form our memories, and that's how we plan for the future. Yeah, So let's look at some psychological phenomenon that that are sort of related to our tendency to take note of coincidences and maybe attribute to them more magical significance than they might actually have. Uh,

how about even heard of the batter main Hoff phenomenon. Yeah, this is the frequency illusion. This is I guess the famous example of this would be you just learn a new word, you know, you either encounter in a book and you're like, WHOA, I don't know that when you look it up, and your rather taken with it, and then it seems to pop up everywhere you just learned it,

and it's all around you. So it's like discovering a flower exists for the first time you've never seen before, and then suddenly it seems to be growing in every pot across town. Yeah. Yeah, And so the weird name actually comes from a West German terrorist organization doesn't have

anything to do with them. Really. I I read that the origin of this was that the phenomenon supposedly got its name because a message board user somewhere online told the story of encountering information about the batter Mine Hoff Gang and then just suddenly seeing that again within like twenty four hours. Um, and I'm sure this has happened to you. It's happened to me all the time. This actually happened to me while I was researching these podcasts

were recording today. So in the other podcast we're recording today, Uh, there's a mention of Prince Chipi island off of the west coast of Africa, and I had when I when I got to them in the research, I realized I had just been reading about that island for the first time, like less than twenty four hours before, for completely unrelated read.

I'm not related to astronomy or anything, but see. Yeah, you see those kind of weird littal coincidences pop up all the time, and uh, I've often found that to be the case to seemingly unrelated episodes, but there'll be some little thread that connects them. Um. You know. Another example the frequency illusion that I often see is I'll I'll come across like a new concept or a concept I wasn't that familiar with, and I'll do a deep dive in in it for a podcast podcast such as

super Normal Stimuli. It was a big one, and after I researched it, I was just I was just seeing it everywhere like it. It kind of a topic like that of you know, sufficient depth. It kind of changes the way you look at the world and then you see reflections of it just all around you. And uh and and so it can be something as simple as

a as a word. It can be something that's you know, a particular place, a particular you know, a particular band, a particular work of a literature, or it can be uh, you know, a philosophical mindset suddenly because you're aware of it, you're hyper aware of it, you're excited about it, You're going to see it in the rest of the world. Yeah, um yeah. And there there could be lots of reasons.

One could be that hidden causal connection. You know, there are actually reasons that you're investigating similar stories around the same time, are reading similar material that might use a new and unfamiliar word around the same time, because you have interests and drives that are sort of unified by time. Uh. Also, the authors of the paper we were talking about earlier have that they have their own sort of mathematical analysis

of this, don't they. And they sort of explain how it's not that unusual that you should, you know, at a certain point, after acquiring a word for the first time, see it again. Yeah, that's just sort of expected to happen. Yeah, they're just there. There's a finite number of words that you're going to see them again. Um. And of course this plays into apothenia. Uh. This is uh, this is

a term comes to us from German science. Is Claus Konrad who coined api finia from the Greek appo away and uh uh and finea to show in nine and he was studying acute schizophrenia, during which connections and meanings seem to web together around unrelated details. So this is the basic idea here is we're always looking for patterns and signals from our environment. I mean, that's how we think, that's how we live, that's how we survive, particularly when

it comes to assessing threats. Okay um, And so we have we often have this tendency to perceive patterns and connections in random or meaningless data. Um. For instance. Uh. One example that comes to mind here is you have some sort of silly police drama on right, They're looking at a map of the city, and they have little pins showing where the crimes are at. And then what

do they see. They see like a pentagram, Right, there's some sort of order, And of course in the show it always makes sense, right, like the the Satanic killer actually is trying to kill people so that his crimes look like a pentagram in a map. But you can see that pentagram without any planning at all, or some other or symbol. Yeah, if you want to see that pentagram in the planning, you can see that pentagram in

the planning of just about anything. Um. But what this basically breaks down to is a false positive in statistics, a type one error in cognition. And this is something that plays into religion, gambling, conspiracy theory, and just are and also our need to see faces everywhere. Right. It's the reason we see uh, figures in the constellations in the sky, right. I mean it's a very few people these days actually think that the stars were arranged to

look like a figure from Greek myth. Yeah, because you think whoever was doing it would do a better job, right, I mean, yeah, it's it's not very good. It's kind of a crappy portrait. But you know people saw it. Yeah, yeah, they saw the pattern and we just can't help. But see, patterns were pattern recognition engines, as we've mentioned before here.

And there's the thing is there's an evolutionary advantage for us pattern recognition apes in making that type one error because essentially you have you have a you have a type one air or any other type two right, false positive, false negative. And the classic example is that of you know, rustling in the bushes on the on the prehistoric savannah, right, because there's a possibility that a big cat is about to spring out of those rustling bushes and kill us,

or it could be the statistical noise of wind. Exactly. A false positive just gets you hot and bothered over nothing and maybe a good laugh. I thought it was a tiger and it was just wind. But a false negative that gets you killed. Yeah, so obvious, there's obviously

a selection pressure to favor false positives. Yeah, exactly. So I mean so that just plays into how we think and how we behave as humans and are overwhelming tendency to see the pattern when there isn't one, to see the connective tissue between events in this case, when there isn't any right, So, yeah, and so in that way a coincidence can represent a pattern to us, we start thinking what does it mean? I mean, and there's likely

a connection between apophenia and creativity. This is a theory that was put put forth by Swiss neurologist Peter Bruger Uh in a two thousand one book, Hauntings and Poulter Guy's Multidisiplinary Perspectives. And he was studying Apophanian patients suffering from psychotic episodes UH that were beginning to find spontaneous

meaning and random aspects of their life. And his research revealed that high levels of dopamine H disposes his patients to find meetings, patterns, significance where there was there was none. So creativity apophenia, Uh, you know, it's what is creativity. But ultimately, you know, finding new patterns, new connections, new ways to arrange existing ideas and motifs uh into something new, right, of course, Yeah, I mean we often see that as

sort of the core of the creative principle. It's you know, understanding like, oh, this is connected to this other thing. And very often the connections you see between events or objects or ideas and say a literature class or something like that, are they are still psychic phenomenon. It's something that we are putting together out of our need defined meaning. That's right, and a lot of times that meaning that

we need to find. You know, we we already have our our minds made up about what that meaning is. This brings us to confirmation bias, which of course is always a big one. This, of course is the idea that we have a tendency to search for or interpret information in a way that confirms your preconceptions about life, about about basically anything, which leads to statistical errors that

cloud your decision and problem decision making, a problem solving ability. Yeah, so this would come into play if say you are already looking for a pattern of coincidences, say you've had to like to sort of synchronous strange events happen in one day, You're looking for a third and that's going to bias the way that you sample data. It's probably going to make you look for things that are sort of a close hit something you might have ignored otherwise

to confirm your pattern. Hypoth assists that there's gonna be something in line with this second thing. You know, it's the same like people dye in threes. I was just thinking of that. Yeah, like you, if you're lucky, you'll get like to a list celebrities dying at the same time. But then often like the third one has to be like a radio star for the whole days. You know, it's something that doesn't really match up, but you'll take it.

It's totally fleets the prophecy exactly right. It's confirmation by us. You're you're bringing it in because you've got to make

it fit the pattern. Yeah, it's kind of like when you listen to an episode of This American Life and like that they have the theme for the show, and like the intro hits the theme, the second segment really hits the theme, the third segment, the second third segment, you know they mostly hit this theme, and that last one you're kind of like, I don't know, close enough, close enough to close out the show, but you're really

kind of strayed from the overall theme. Um. But then that's pretty much how we approach life in general, whether you're talking about belief in UFOs, ancient Egyptians and alien tech, bigfoot, or or office conspiracies, well, whatever it happens to be. If you're looking for something to be true, uh, you

can find it. So if it plays into scientific analysis, you have a you know, a theory you want and you want to see it proven out, and you subconsciously scow your the results of the experimentation in your favor. You want to love that new movie that just hit the theaters, so you wind up looking for reasons to love it and focusing more on that and and being

perhaps a little less critical than you normally will. And then, of course there's a racial aspect too, right you You, if you happen to distrust members of another racial group, you wind up focusing on the evidence that supports your existing distrust rather than evidence that challenges it. Oh yeah, people are definitely likely to oversample stuff that confirms their

bigotry or biases. So if yeah, if if you have a preconceived stereotype, you're looking to make things fit evidence that doesn't fit it, you just kind of like that's noise, It doesn't matter. Yeah, I mean, for the most part, you're kind of maintaining the castle of you know, fortress sanity and fortress worldview and uh and and so you want to to focus as much on the stuff that

keeps the walls up as possible. Yeah, of course this all works perfectly because post addiction is largely a result of the brain's task of continually integrating sensory stimuli and reconciling conflicting information into a unified vision of reality, a unified story again in which we are the central character. Yeah, I mean, that's just simply how our memory. Yeah, I mean, you you always see the pattern of clue is left by the mystery writer once you've had the ending revealed.

You might not notice it while you're going through the novel to the first time. All right, So there you have it, the science of coincidence. Hope you enjoyed the rerun or the first run if you had not heard the previous one. Yeah, So I hope you will take something away from this that you can apply to your everyday life when you think about all those strange coincidences you encounter day in and day out, and do they

really mean something. Indeed, now, in the meantime, if you want to explore more episodes of Stuff to Blow your Mind, head on over to stuff to Blow your Mind dot com. After you will find all the podcast episodes. You'll find videos, you'll find blog posts, you'll find link out to our social media accounts such as Facebook and Twitter. We'll blow the mind on both of those who also find us

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