Coincidence

[chillzero]

Last year, I worked for one day at an office in a part of Birmingham City Centre called Five Ways. I've never worked there before, or since. That day, I was thinking about my friend Matt (who lives in London) as I had not spoken to him for a long while, and I had heard that morning that a Birmingham office of the radio station he worked for was going to be opened.

As I was only at the company for a day and had a lot to get done, I decided not to take a full lunch hour, but to pop over to the bakery and buy a sandwich to take back. Again, I had never been to this bakery before, (or since).

I walk into the bakery and there is my London friend Matt, buying a sandwich.

He was in Birmingham for one morning, for the opening of the new office, and was walking past the bakery on his way to the train station to go home. There was a window of perhaps two minutes for our paths to cross, as my office was in a different direction. We could only have met at that exact time in that exact place.

He was with a colleague, who was very bemused because it turns out that Matt had been talking about me at the exact moment I walked into the bakery.

Excellent coincidence

Well, you know, in Hollywooduniverse, this means that your destinies are tied toether, and only terrible misfortune can follow if you didn't both marry each other instantly, and live happily ever after.

I hope you are both very happy.

 

[Ersby]

I work in data entry and every record I process has a serial number, and I'm often surprised at the number of coincidences I go through in a single day, such as the same three figures cropping up in different records, or having a day in which a get several records ending with three figures the same.

I'm sure if I was numerologically minded I could use this to convince myself I'm special and that I know more than other people.

 

[Rodney]

I work in data entry and every record I process has a serial number, and I'm often surprised at the number of coincidences I go through in a single day, such as the same three figures cropping up in different records, or having a day in which a get several records ending with three figures the same.

I'm sure if I was numerologically minded I could use this to convince myself I'm special and that I know more than other people.

Why don't you try writing down seemingly coincidental events in a daily journal for a few weeks and then do an overall analysis of whether those coincidences actually are unlikely?

 

[MRC_Hans]

Coincidence is an excellent example of data mining, as several have already mentioned. We notice such strings of events, and remember them above the endless parade of equally unlikely, but non-spectacular strings that are constantly unfolding before us.

An example: Suppose I arrived at work at exactly 7:36:15 this morning. The train of events leading up to the exact time I arrive in the morning will start the previous evening and include me setting the alarm, and how late I went to bed. All kinds of events during the morning will come into play, the daily paper, how much dishes were left from last night to put into the dishwasher (I usually do that in the morning), the traffic enroute to work, etc. etc. Literally hundreds of events, which millions of people experience every day. All completely unremarkable and uninteresting, except if one day somebody happens to arrive at some time that spells out the birth date of his dad, who happens to die later that day, or something. Then, if he notices, he will dig through his memeory and construct some highly improbable chain of events. Which IS highly improbable, just like the one that nevertheless caused me to be in at 7:36:15 this morning.

Hans

 

[MRC_Hans]

Why don't you try writing down seemingly coincidental events in a daily journal for a few weeks and then do an overall analysis of whether those coincidences actually are unlikely?

That is exactly the problem: How can we calculate the probability? How do we know the number of opportunities for a coincidence to happen? Knowing the amount of numbers Ersby processes is probably not too hard, but how do we know the number of things they can potentially match?

Hans

 

[Rodney]

That is exactly the problem: How can we calculate the probability? How do we know the number of opportunities for a coincidence to happen? Knowing the amount of numbers Ersby processes is probably not too hard, but how do we know the number of things they can potentially match?

Hans

You're overcomplicating the situation. Ersby stated that he is often surprised at the number of coincidences he goes through in a single day, such as several records ending with three figures the same. Let's say that he processes 100 records a day. If the first time he checks each record, 5 of those 100 end in the same three digits (for example 1-2-3), would that not be highly unlikely? Now, if that situation arises only once in a period of several weeks, it wouldn't be that unlikely, but if it keeps happening, then it would be. I'm simply saying that, if someone here think (s)he is experiencing an unusual number of coincidences, that proposition can be tested to at least some extent by keeping daily records and then periodically analyzing those records. It's better than saying: "I seem to experience a lot of coincidences, but most folks on Randi's forum believe the universe is random, so there is no point in analyzing this phenomenon."

 

[opqdan]

Rodney,
Do the following examples help?
...
BillyJoe

That is a really, really cool post, and those examples are awesome. I think that I will have many opportunities to use that bridge one.

 

[Rasmus]

You're overcomplicating the situation. Ersby stated that he is often surprised at the number of coincidences he goes through in a single day, such as several records ending with three figures the same. Let's say that he processes 100 records a day.

He'd most likley be fired for slacking, if his data entry work is anything like what i used to do ...

If the first time he checks each record, 5 of those 100 end in the same three digits (for example 1-2-3), would that not be highly unlikely?

Why should it be?

What justifies the assumption that the numbers are fully random? My guess is that they will be anything *but* random.

Now, if that situation arises only once in a period of several weeks, it wouldn't be that unlikely, but if it keeps happening, then it would be.

And then what?

I'm simply saying that, if someone here think (s)he is experiencing an unusual number of coincidences, that proposition can be tested to at least some extent by keeping daily records and then periodically analyzing those records.

And it has been explained to you, several times, that it cannot be tested. OR at least: Not as easily.

What would you analyse those records for to begin with?

And, of course, the example of the bble code shows us that if you look long enough, you will find *something*. Only that doesn't suggest that you found anything special.

It's better than saying: "I seem to experience a lot of coincidences, but most folks on Randi's forum believe the universe is random, so there is no point in analyzing this phenomenon."

Nobody here said that.

 

[Cetecea]

I used to notice that when I drove around, a lot of streetlights would go off as I passed them. Yeah, I woooed a little, wondering, wow, maybe I am something special.

Of course, with a little logical kick in the head from a friend-- I started noticing all the lights that didn't go out...

I think there was even a challenge about this for the $1M.





Oh, and by the way... I am special...

 

[Hellbound]

Here's a good one:

Just today, after my lunch, I got onto the elevator to go to my office (on the 10th floor).

There were 9 other people on the elevator.

One person was going to each floor from 2 to 11.

What are the odds of that? 1 in 10 per floor, 10 floors, that's 1 in 10,000,000,000!!!

But it doesn't mean I'm psychic. It's just a coincidence.

And, oddly enough, the chances of one per floor are the same as the chances of everyone getting off at 10, or of 3 getting off at 2, 4 getting off at 6, and the rest at 10.

 

[Stellafane]

Here's a good one:

Just today, after my lunch, I got onto the elevator to go to my office (on the 10th floor).

There were 9 other people on the elevator.

One person was going to each floor from 2 to 11.

What are the odds of that? 1 in 10 per floor, 10 floors, that's 1 in 10,000,000,000!!!

But it doesn't mean I'm psychic. It's just a coincidence.

And, oddly enough, the chances of one per floor are the same as the chances of everyone getting off at 10, or of 3 getting off at 2, 4 getting off at 6, and the rest at 10.

This is bizarre -- usually something like this only happens when you absolutely have to get to your floor as fast as you possibly can, then the odds go up to 1 out of 1!

 

[BillyJoe]

opdan,

That is a really, really cool post, and those examples are awesome. I think that I will have many opportunities to use that bridge one.

I should hastily add that they are not original.

I have given them a fairly original slant but only because I can't remember the exact details of the original stories which I read a long long time ago, I think in the very early days of this forum. If you hang around long enough, you will find that some topics have a tendency to come up repeatedly.

BJ

 

[moopet]

A couple of years ago I pulled up at a set of traffic lights with my window open while I was trying to read directions of how to get to a friend's house. Being a man, I turned the CD player off so I could concentrate on reading my own handwriting, and what should I find, but that the car adjacent to mine is playing exactly the same song at the same point! I was wide-eyed and wowwed for a minute until, just as the car was pulling away, I heard it break into the jingle for the local radio station. I then entered a monastary for 14 years to hide my own personal embarrassment.

 

[Rodney]

Here's a good one:

Just today, after my lunch, I got onto the elevator to go to my office (on the 10th floor).

There were 9 other people on the elevator.

One person was going to each floor from 2 to 11.

What are the odds of that? 1 in 10 per floor, 10 floors, that's 1 in 10,000,000,000!!!

But it doesn't mean I'm psychic. It's just a coincidence.

And, oddly enough, the chances of one per floor are the same as the chances of everyone getting off at 10, or of 3 getting off at 2, 4 getting off at 6, and the rest at 10.

First, I agree, that's a good one; in fact, an excellent one. Second, I don't know that coincidences have anything to do with being psychic. Third, I don't think that you've calculated the odds correctly. Here is my take on the odds, assuming that you work in a building with 11 floors (or alternatively, work in a building with more than 11 floors, but the elevators that you take are restricted to Floors 1-11):

With 10 floors from which to choose, the odds that a given elevator rider will get off on Floor 2 is 10%. With nine riders (excluding you, who is getting off on Floor 10), the odds that exactly one rider will get off on Floor 2 is, according to the binomial distribution, 38.74%. Assuming that happens, there are now eight (other) riders left and -- because there now are only nine floors from which to choose -- the odds that a given rider will get off on Floor 3 is 11.1%. The odds that exactly one rider out of eight will get off on Floor 3 is, according to the binomial distribution, 38.97%.

Continuing this analysis for Floors 4-9 results in respective odds of one person getting off on each floor of 39.27%, 39.66%, 40.2%, 40.96%, 42.19%, and 44.42%. At that point (assuming that one rider does get off on each Floor, 2-9), only one rider (other than you) remains. The odds of that rider getting off on Floor 11, rather than your Floor 10, is 50%. Therefore, to calculate the joint probability of one rider getting off on each Floor, 2-11, the formula is (according to this analysis): 38.74% * 38.97% * 39.27% * 39.66% * 40.2% * 40.96% * 42.19% * 44.42% * 50% = 0.036%, or about one chance in 2,800.

 

[Hellbound]

First, I agree, that's a good one; in fact, an excellent one. Second, I don't know that coincidences have anything to do with being psychic. Third, I don't think that you've calculated the odds correctly. Here is my take on the odds, assuming that you work in a building with 11 floors (or alternatively, work in a building with more than 11 floors, but the elevators that you take are restricted to Floors 1-11):

With 10 floors from which to choose, the odds that a given elevator rider will get off on Floor 2 is 10%. With nine riders (excluding you, who is getting off on Floor 10), the odds that exactly one rider will get off on Floor 2 is, according to the binomial distribution, 38.74%. Assuming that happens, there are now eight (other) riders left and -- because there now are only nine floors from which to choose -- the odds that a given rider will get off on Floor 3 is 11.1%. The odds that exactly one rider out of eight will get off on Floor 3 is, according to the binomial distribution, 38.97%.

Continuing this analysis for Floors 4-9 results in respective odds of one person getting off on each floor of 39.27%, 39.66%, 40.2%, 40.96%, 42.19%, and 44.42%. At that point (assuming that one rider does get off on each Floor, 2-9), only one rider (other than you) remains. The odds of that rider getting off on Floor 11, rather than your Floor 10, is 50%. Therefore, to calculate the joint probability of one rider getting off on each Floor, 2-11, the formula is (according to this analysis): 38.74% * 38.97% * 39.27% * 39.66% * 40.2% * 40.96% * 42.19% * 44.42% * 50% = 0.036%, or about one chance in 2,800.

Which was pretty much my point. "Synchronicity", regarding as something beyond normal, is a result of misunderstandning of probabilities and post hoc signifigance applied to patterns that are noe more or less likely than any other.

 

[Rasmus]

And, oddly enough, the chances of one per floor are the same as the chances of everyone getting off at 10, or of 3 getting off at 2, 4 getting off at 6, and the rest at 10.

Excellent example.

Because, even though the same event was experienced by 10 people, only 2 had a chance to notice what was going on. Bummer for the guys getting of on the lower floors, they missed a good story right there.

Also, it is possible that this happens a lot and doesn't get noted at all: You just need more people entering the elevator at higher floors, and you would lose track of the original 10 people. (And they might all want to exit on the 1st floor on the way down or something, to not make it any less special.)

Rasmus.

 

[MRC_Hans]

You're overcomplicating the situation. Ersby stated that he is often surprised at the number of coincidences he goes through in a single day, such as several records ending with three figures the same. Let's say that he processes 100 records a day. If the first time he checks each record, 5 of those 100 end in the same three digits (for example 1-2-3), would that not be highly unlikely?

Depends on the distribution of the numbers. Those records are records of something, not random numbers. Perhaps some numbers are more common than others.

What you recommended was that he record the coincidences, but my point is that that is not enough. You need to find out what the chance is for coincidences to happen. And unless you know all possible sources for patterns in the records, you cannot know if there is something peculiar about them.

Hans

 

[MRC_Hans]

*snip*Continuing this analysis for Floors 4-9 results in respective odds of one person getting off on each floor of 39.27%, 39.66%, 40.2%, 40.96%, 42.19%, and 44.42%. At that point (assuming that one rider does get off on each Floor, 2-9), only one rider (other than you) remains. The odds of that rider getting off on Floor 11, rather than your Floor 10, is 50%. Therefore, to calculate the joint probability of one rider getting off on each Floor, 2-11, the formula is (according to this analysis): 38.74% * 38.97% * 39.27% * 39.66% * 40.2% * 40.96% * 42.19% * 44.42% * 50% = 0.036%, or about one chance in 2,800.

Again, that analysis assumes that all floors are equal. They may not be. People's reasons for being on the lift at that time may cause patterns.

Hans

 

[Rasmus]

What you recommended was that he record the coincidences,

Yes, the keyword here are the italics you used for "coincidences". Getting numbers 681, 465, and 715 is just as much a coincidence as getting 111, 112 and 113.

I have spend several years working with banking cards; the numbers are NOT random there. At most, certain blocks of digits are produced consecutively, other blocks are static for large batches of cards. (They encode regions or locations, etc.)

Then, the cards that one is dealing with are just a subset of all existing cards - these cards have something in common that may or may not be correspond to their serial number.

Also, if you spend your working hours hacking those numbers into your keyboards, you sometimes lose focus and see things that just aren't there. I had moments where suddenly the most random sequences seemed meaningful in and of themselves.

 

[MRC_Hans]

Yes, or look at this random list of numbers:

52250
17875
57750
123375
110000
35375
28250
35125
71750
124875
21125
125
6000
46375
6125
51250
86750
86000
119625
52500

....Obviously something weird going on here, right?

Hans

(edited for formatting .. How to make formatted lists?)