[barmar]

daveharty, on 2012-July-02, 09:51, said:

It probably does skew the probabilities to have identical twins in the class, but not as absolutely as it might seem. I once met a pair of identical twins that not only had different birthdays, but were born in different months.

Spoiler

They were twins, but not of each other.

[ArtK78]

Funny thing about the birthday problem.

In one of the first days of my college course in statistics and probability, we were asked to solve the birthday problem. The question is: How large a group of people (selected at random) do you have to have before there is a 50% or more probability that two or more of them will have the same birthday? The answer is 23.

[daveharty]

barmar, on 2012-July-03, 08:18, said:

They were twins, but not of each other.

Actually it was pretty straightforward, twin #1 was born at 11:15 p.m. on May 31, his reluctant brother made his first appearance 90 minutes later. Their family chose to preserve the distinction.

[kenberg]

Preserving the distinction of course makes sense. For one thing, as a legal matter they have different birthdays and there is no reason to confuse matters by acting otherwise.

But of course I submitted the story as an example of how a mindset (wanting to present a mathematics problem) can blind a person to obvious conditions making the problem as stated, taken literally, quite different.


There was an interesting, and tragic, story on NPR sometime back about a psychological experiment and a possible application. The experiment documented how people, when assigned a task, can be very oblivious to things going on around them. The subjects were to run behind someone, always keeping at the same pace (or some such assignment). Fights were staged not far off the path, in full view. Many of the subjects were totally unaware of the fights.
The real life application: Cops were trying to apprehend a suspect in a large park (maybe Central Park). He was described as African-American. One cop thought he saw him and was chasing him. Unfortunately some other cops spotted another suspect, call him suspect 2.. The real criminal had shot a cop and suspect 2 was beaten by the police. In fact, suspect 2 was an off-duty cop who had joined in trying to help. Now the first cop admitted to being on the very path where, off to the side, the guy was being beaten. He said that yes, he was on that path but had not noticed the beating. He was not believed he lost his job, I think he went to jail, and in general his life was ruined.

Other cops, some quite possibly in sight of the beating, said they were never in the vicinity. No way to prove otherwise, so they got off. The guy who acknowledged being on the path but not noticing because he was in pursuit of a different possible suspect had his life ruined.


Of course we don't know what actually happened, but reasoning that a guy who planned on lying would lie and say he was not there rather than say he was there but didn't see anything strikes me as pretty plausible. It may seem impossible, apparently many thought so, that he did not notice the beating. The psychology experiment suggests we rethink what is possible.

[barmar]

Inattentional blindness has been documented numerous times. One of the best examples is the "invisible gorilla test", described on the wikipedia page (the fight test as also described there).

[gwnn]

In unrelated news, Y U NO COUNT TO 13?

[Vampyr]

barmar, on 2012-July-04, 11:41, said:

Inattentional blindness has been documented numerous times. One of the best examples is the "invisible gorilla test",

I did this one once, but is it really possible that people fail to see the gorilla? I have doubts.

[RMB1]

Vampyr, on 2012-July-04, 16:50, said:

I did this one once, but is it really possible that people fail to see the gorilla? I have doubts.

Yes

I saw several videos of such experiments while touring London psychology departments last autumn.

[Mbodell]

Vampyr, on 2012-July-04, 16:50, said:

I did this one once, but is it really possible that people fail to see the gorilla? I have doubts.

It was shown without explanation to my psych class in University. Only about 20% of the class noticed the Gorilla (I was in the minority that noticed it). Note that you are asked to count the number of times the team in white passes the ball, so it isn't just some video, but one where you have a task.

And there are lots of example videos where people switch on people when they are doing something like looking at a map, or getting directions, or signing in at a desk. As in the stranger who started with them becomes a different person. Sometimes even changing height, hair color, and gender. Many, many people don't notice.

[Vampyr]

Mbodell, on 2012-July-04, 17:07, said:

Note that you are asked to count the number of times the team in white passes the ball, so it isn't just some video, but one where you have a task.

Yes, and the gorilla gets in the way and makes it harder to follow the motion of the ball and of course obscures some of the players, so while I guess I accept that some people miss it I just don't undrestand.

[Cthulhu D]

Vampyr, on 2012-July-04, 17:34, said:

Yes, and the gorilla gets in the way and makes it harder to follow the motion of the ball and of course obscures some of the players, so while I guess I accept that some people miss it I just don't undrestand.

I've seen pros who are watching a fairly simple scene for the purposes of an observation test fail to notice that two people standing in front of the camera blatantly and without any concealment pass a large package to each other (a cube with each face the size of a vinyl record).

It's actually amazing how bad people are at seeing things imho.

[blackshoe]

I met a guy once, in a bar, who'd made a hobby out of observing people. We had an interesting conversation for an hour or so. He saw — and remembered — things most people, including me, missed. The other side of the coin, perhaps.

[psyck]

Regarding the Twin puzzle, if the mother crosses the international date line after the 1st child is born, you can have the younger twin 1 day older than the elder twin, or even two days older at times if you arrange all this at Feb end.

[Zelandakh]

psyck, on 2012-July-05, 08:55, said:

Regarding the Twin puzzle, if the mother crosses the international date line after the 1st child is born, you can have the younger twin 1 day older than the elder twin, or even two days older at times if you arrange all this at Feb end.

No need for that, if you have the first child delivered just before midnight on Dec 31 1999 you can have them born in different millennia.

[gwnn]

The biggest difference I know of is 5 days. It goes something like:
Two people are talking. At some point one of them says "the day after tomorrow it is my birthday". A bit later she says "the day before yesterday it was my twin sister's birthday!".

I don't remember the specifics but I think it's something like:

1 day: because of a lost day at the end of February.
1 day: because the mother was travelling on an airplane/ship crossing the date line
1 day: because the speakers were also travelling on an airplane/ship crossing the date line
1 day: because there was a little time between the two moments

The mother was travelling on a ship on the evening of 28 February in a non-leap year. She had a baby at 23:55. The second baby was born on 2 March (15 minutes later). The speakers were travelling on a ship on the evening of 29 February in a leap year. "The day after tomorrow" was March 2, however after a few minutes the date was actually March 2 and the day before yesterday was February 29. Hmmm I confused myself again.

Anyway, one could envision the speakers and/or the mother living on a spaceship travelling near the speed of light, in that case the possibilities are endless.