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At what point do coincidences stop being coincidences?

Would anyone care to experimentally test the hypothesis?
More people are attacked by lions the night after the full moon than on any other day in the lunar month. This is a real and measurable effect; And it has a reasonable explanation. Can you guess why this should be the case?

My guess is that as the moon becomes full, most of the prey is hiding because it is too light out and too risky to be seen by lions. So, the day after the full moon, the lions haven’t eaten for several days and are very hungry and taking bigger risks to eat. And the humans are the only species stupid enough to be out in the bright moonlight.

The shortage of gold hunting opportunities as the Moon waxes may well contribute, but the main cause is that the day after a full moon, the moon doesn't rise until after the sun has set. So after a fortnight of light evenings, suddenly there's a period of darkness just before people close up for the night - and people have had at least a week of getting used to bright moonlight after the sun has set, so they're less wary of being benighted.
I dono why, whenever there is a full moon my beard grows faster and I want to get naked and howl at the moon. Touching silver coins makes me ill.
So, here's another weird coincidence...

A "Strong causal adjacency" if you will...

So the other day I found a crow's feather on the sidewalk. I decided to take it and make some kind of pretty thing with it, it being the first such time I had the prescience of mind to pick one up, and it was on the sidewalk just in front of my house.

Now, often it is said, though it does not necessarily mean anything, that a crow's feather is a rare portent of fortune and fate.

Certainly I don't see many around.

Anyway, the feather cleans up nicely despite looking gross and fucked up at first.

I ended up hanging it together with a ruby and a bit of gold I got from my husband for recovering the tiny diamonds and (different) ruby set in it.

It's been hanging there for all of a day or so, when I find a golden earring, also not far from where I live.

This configuration is roughly a "prosperity charm" mixing ideas of red/luck/prosperity, against fate/fortune, and gold.

And note, I still maintain that this is coincidental!
I "put no weight down" on such events.
What a coincedence, I was thinking of the thread and sure enough there was a new post.
For me, I ask if I can I come up with an "unifying theory" that ties the all the "coincidences" together. Does that unifying statement offer explanations, mechanisms, and make predictions. We then compare all the "hypothesis" side by side to see if they can be listed in an order of relative reliability.

"Full moon", we can see better so we can move around easier. The move we move around, the more trouble we tend to get into.
When the fourth event happens. Then you take your FAMAS and go after the happener,

Eldarion Lathria
Coincidences that are a million-to-one against are fairly common (cf. Littlewood's Law). Expect a billion-to-one coincidence once per lifetime or so. (I do NOT attempt to make definitions rigorous.)

Here's my birthday coincidence.

My birthday landed on Sunday one year as did my wedding anniversary, my parents' anniversary, and the birthdays of both my children, and of my wife, and of my father, and of both my grandfathers and three out of eight of my great grandparents. Thus the birthdays of ten of my closest relatives (twelve counting the wedding anniversaries) all landed on Sunday this year. In fact, all twelve land on the same day every year ... except that my wife is off by one in leap years.

So twelve out of 20 day slots are the same day. This strikes me as very unlikely if rather contrived. But the odds are only about 200,000-to-one against if my arithmetic is correct.

~ ~ ~ ~ ~ ~ ~ ~

I hear or read credible accounts of coincidences HUGELY odds against. These are mostly far more interesting and unbelievable than my own anecdote. But here goes:

My wife lost her mother shortly before I met her. Her old home was allegedly haunted by mother's ghost. People refused to sleep in that house, even migrant workers unaware of the ghost stories.) My wife and I bought an empty lot a few miles away and began erecting a house. The lot included an allegedly haunted orchard.

Let's not give credence to the haunting stories; but since they are essential to the anecdote we'll call the stories 50-to-1 against.

The orchard has some bee hives; a large beehive drops from its tree branch and breaks up once a month or less. The chance we'd pick that day to picnic in the orchard is 10-to-1 or more against. Or rather 100-to-1 since the beehive dropping is most likely on a day with high winds, a day we'd choose NOT to picnic. The orchard is large enough that it is 20-1 against us picnicking right next to the about-to-fall beehive.

So far we're up to 100,000-to-one against. That's nothing: coincidences like that happen every day.

It was a fine calm day for our picnic. Just to make conversation I asked my wife to talk about her mother's ghost and alleged hauntings. Before she could reply, a large crash and buzzing sounds alerted us to the beehive's fall and imminent danger to our newborn babe. My wife rushed the child to the corner of the orchard.

I've hardly spoken of her mother's ghost before or since. What are the chances that I'd mention the ghost on the day of the picnic? 10-to-1? The very same minute just before the hive fell? 500-to-1? The very SECOND before? 10,000-to-1.

If we accept these numbers, we're looking at a one-in-a-billion event. But even these are not particularly newsworthy.

But the story isn't over yet. The next step changes the odds from a ho-hum billion-to-one to many trillions-to-one, if you accept my account.

I returned to the picnic site to retrieve our stuff, then rejoined my wife. I said "Wow! That happened just EXACTLY at the time I asked about your mother's ghost ..." But before I could finish my sentence, the sky turned very dark. Very suddenly there were very strong winds blowing sandy dirt with great force. We huddled around baby and covered her to protect her eyes from the wind-blown dirt. We were immobilized — unable to return to our car — until the wind abated.

It was almost as though my mentions of mother's ghost provoked these ominous and dangerous events.

Although the day had started calm, the houses we passed on the drive home all had their storm shutters closed for this freak wind. I did realize that the hive's dropping was probably due to a gust of wind related to, but a few minutes before, the sudden gale. But it was the alignment to the very second of each of my two mentions of mother's ghost that struck me as very unlikely coincidence.
So twelve out of 20 day slots are the same day. This strikes me as very unlikely if rather contrived. But the odds are only about 200,000-to-one against if my arithmetic is correct.

I don't get it. Why aren't the odds one in seven?

If these people are all born seven days (or multiples of seven days) apart, then their birthdays will be on the same day of the week every year. In any given year, the odds of that day being Sunday are one in seven.
So twelve out of 20 day slots are the same day. This strikes me as very unlikely if rather contrived. But the odds are only about 200,000-to-one against if my arithmetic is correct.

I don't get it. Why aren't the odds one in seven?

If these people are all born seven days (or multiples of seven days) apart, then their birthdays will be on the same day of the week every year. In any given year, the odds of that day being Sunday are one in seven.

I explained poorly. The coincidence was that the people's birthdays were all the same, not that they all happened to be Sunday. Ignoring leap-year complications, if our birthdays all fall on Sunday this year, they'll all be Monday next year.

The chance that N people so coincide is 1 in 7N-1. One-in-seven when N=2; one-in-two billion when N= 12; one-in-eleven quadrillion when N=20.

The coincidence I detailed was less pure. When M < N, the odds that exactly N out of N+M people have the same birthday is
One in { 7^(n+m-1) / c(n+m,n) / 6^m }

N=12; M=0; One in 1977326743
N=12; M=1; One in 177452400
N=12; M=2; One in 29575400
N=12; M=3; One in 6900927
N=12; M=4; One in 2012770
N=12; M=5; One in 690656
N=12; M=6; One in 268589
N=12; M=7; One in 115446
N=12; M=8; One in 53875

Swammerdami said:
So twelve out of 20 day slots are the same day. This strikes me as very unlikely if rather contrived. But the odds are only about 200,000-to-one against if my arithmetic is correct.
So the arithmetic was NOT correct; the odds are one in about 54,000. This error is a matter of some dismay to me as the younger me was once rather good at such simple arithmetic. At least I caught the error myself before thorough humiliation.
A statistical correlation is not causation, but it can be a cause to look for an underlying connection.

I was standing in front of my building. A perjed car had ist blinkers on. A car pulled in behind it. The driver put on his blilers and the frqucy of the flashing matced exactly. Lights on both cars flashed at exactly the same time.

Random coincidence or caused by something? The odds of that happening are extremely low.

I would think te there is a distribution of birthdays. If so the odds of any coincidences can be calculated.

Learn something new everyday. The birthday paradox.

If N random people are in a room, the classical birthday problem provides the probability that at least two people share a birthday. The birthday problem does not consider how many birthdays are in common. However, a generalization (sometimes called the Multiple-Birthday Problem) examines the distribution of the number of shared birthdays. Specifically, among N people, what is the probability that exactly k birthdays are shared (k = 1, 2, 3, ..., floor(N/2))? The bar chart at the right shows the distribution for N=23. The heights of the bars indicate the probability of 0 shared birthdays, 1 shared birthday, and so on

An exponential distribution. A plot in the link.

In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox is that, counterintuitively, the probability of a shared birthday exceeds 50% in a group of only 23 people.

The birthday paradox is a veridical paradox: it appears wrong, but is in fact true. While it may seem surprising that only 23 individuals are required to reach a 50% probability of a shared birthday, this result is made more intuitive by considering that the comparisons of birthdays will be made between every possible pair of individuals. With 23 individuals, there are (23 × 22) / 2 = 253 pairs to consider, much more than half the number of days in a year.

Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population.

The problem is generally attributed to Harold Davenport in about 1927, though he did not publish it at the time. Davenport did not claim to be its discoverer "because he could not believe that it had not been stated earlier".[1][2] The first publication of a version of the birthday problem was by Richard von Mises in 1939.[3]
I haven't posted in ages, but my password still worked, so yeah! As a human, I imagine if you see things enough times so that you give it a name, because it is easier to use the name to express that given instance of the category events, then it is no longer a coincidence.
Is there an accepted method to determine when it is sound to think that coincidences aren't random? I'm talking in every day life, where things happen without lab conditions, and the mind makes connections between things in a free form way. We all know the mind loves to make connections, but is there a point where one can say, "aha! there is some unseen link?" because sometimes there is, isn't there?
As soon as one can accurately predict it.

That's pretty much what I was going to say. But being me, I feel the need to use a lot more words than Jimmy.

We've evolved to be pattern-finders. Not all patterns are real, most are illusory. But that tendency to find patterns is what has allowed us to develop science and technology.

Lots of things will seem like they're not random. Partly, this is because our brains really, really, really want to find patterns in everything, and they're constantly trying to subconsciously impose a pattern on pretty much everything we ever do. Partly, it's because we're incredibly bad at perceiving, acknowledging, and understanding randomness. I mean, we really suck at it. Tell a human to paint a picture with random spots on it, and you'll almost always end up with a painting that is nearly (but not quite) a uniform distribution of spots.

Something stops being coincidence when 1) a pattern can be identified and 2) the pattern allows for prediction.

It doesn't have to be 100% perfect prediction, but it does have to produce predictable outcomes. Not every infant grows at the exact same rate, nor do they all begin talking at the exact same age. But the pattern is real enough that we have observed developmental stages that a baby goes through as they age.
Probability can be a harsh mistress. Something associated can be just coincidental.

You only said that because it's a full moon.

Well, I heard a newscaster on one of the local stations a while back explain that of course the moon affects us. It causes the tides, she said, and we're 98% water. You can't argue with logic like that.
She is absolutely right, except that last 2% actually represents 85% of what controls us. So while the moon effects us because we are 98% water (despite the fact the moon is always running around the Earth, regardless of how much reflected light we see), it actually only counts for about 15% of our actions.
;) I'd say it's more like 25% if you happen to be a woman.
Man, I really hate it when I end up posting in a necromanced thread because I didn't notice the dates. Sorry folks!
Such is a demonstration of the difference between the conscious and the unconscious. When I count to three and snap my finger you will become perfectly conscious and forget what just happened.

Sigmund Bank
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