Genuinely interesting stuff you learned at school/university/work

Ha! No way! Great thread though MrsHathaway. I might have to add a less brain hurting contribution now!

I agree - the MH problem is often written out badly (hi, Curious Incident in the Night Time), and omits the crucial info about whether it is always a goat that is made visible, ie whether MH knows what he is doing.

If it was on purpose that DOND left someone with a choice of two boxes, one with a big prize and one without, then there would be an improved chance by switching, but because all the boxes were removed at random, it makes no difference because it boils down to the same 50:50.

My brain hurts

I agree, NotDavidTennant.

If DOND only involved 3 boxes, we can think through how it differs from MH. If we call the prizes A, B, C, (A the smallest, C the biggest) then there are six equiprobable possibilities:

1. Contestant holds A, and chooses to open the box with prize B, leaving C still in play.
2. Contestant holds A, and chooses... C. B is in play.
3. Contestant holds B, and chooses ... A. C is in play.
4. Contestant holds B, chooses ... C. A is in play.
5. Contestant holds C, chooses ... A. B is in play.
6. Contestant holds C, chooses ... B. A is in play.

Which cases result in a gain on switching? 1, 2, 3 - that's 50%

If MH was doing the choosing, in cases 2 and 4 he would (secretly) stop himself from opening C, because he wants to leave the winning prize unopened. That means 1,2,3 and 4 all now are beneficial on switching.

Incidentally, I think this is why people find the problem paradoxical, because it seems like Monty Hall is eliminating a door at random and therefore it should have no effect on the outcome, but in fact he is not.

Gertrude, I think what you're not quite getting is that in MH the door that is opened must contain a goat. MH is not allowed to open the door containing the car.

If in MH a door is opened at random with no regard to whether it contains a car or a goat then there is no advantage to switching. It is only because MH is constrained in which door he is allowed to open (and therefore is not making a purely random choice) that it offers an advantage to switch.

In DOND the boxes are opened at random so it matches the case where a door is opened at random, not the original MH where the door is not opened randomly.

Also an interesting language one I've come across is how often the same proverbs crop up in different languages and cultures. I taught a class a while ago where the only instructions were to pair up with someone who speaks a different language to you, teach them a proverb from your language, what it means in English and how to say it in your language.

Most students found that they had really similar proverbs despite being, say, Chinese and German, or Syrian and Brazilian. We discovered that humans aren't as creative as we give ourselves credit for

The winner that day though, was a Turkish student who found his language had a completely unique proverb. He came to the front of the class and proudly told us,

"If you shit with conviction, you can shit through steel!"

It's still my favourite proverb and I guess it counts as I learned it in a classroom

Um, but in MH you start with 1/3 chance of having picked the car. A door is then opened knocking out a goat, thus by your logic increasing your chance of having picked the car to 1/2, which goes against the whole MH argument.

Having said that, I did convince myself in the middle of the night that using Bayes Theorem on DOND leads to a 50:50 outcome, but by morning I had a renewed state of being unconvinced.

Another language based one, about a handful of languages which use geographic coordinates rather than egocentric coordinates.
This is Guy Deutscher explaining it far better than I could:

The area where the most striking evidence for the influence of language on thought has come to light is the language of space — how we describe the orientation of the world around us. Suppose you want to give someone directions for getting to your house. You might say: “After the traffic lights, take the first left, then the second right, and then you’ll see a white house in front of you. Our door is on the right.” But in theory, you could also say: “After the traffic lights, drive north, and then on the second crossing drive east, and you’ll see a white house directly to the east. Ours is the southern door.” These two sets of directions may describe the same route, but they rely on different systems of coordinates. The first uses egocentric coordinates, which depend on our own bodies: a left-right axis and a front-back axis orthogonal to it. The second system uses fixed geographic directions, which do not rotate with us wherever we turn.

We find it useful to use geographic directions when hiking in the open countryside, for example, but the egocentric coordinates completely dominate our speech when we describe small-scale spaces. We don’t say: “When you get out of the elevator, walk south, and then take the second door to the east.” The reason the egocentric system is so dominant in our language is that it feels so much easier and more natural. After all, we always know where “behind” or “in front of” us is. We don’t need a map or a compass to work it out, we just feel it, because the egocentric coordinates are based directly on our own bodies and our immediate visual fields.

But then a remote Australian aboriginal tongue, Guugu Yimithirr, from north Queensland, turned up, and with it came the astounding realization that not all languages conform to what we have always taken as simply “natural.” In fact, Guugu Yimithirr doesn’t make any use of egocentric coordinates at all. The anthropologist John Haviland and later the linguist Stephen Levinson have shown that Guugu Yimithirr does not use words like “left” or “right,” “in front of” or “behind,” to describe the position of objects. Whenever we would use the egocentric system, the Guugu Yimithirr rely on cardinal directions. If they want you to move over on the car seat to make room, they’ll say “move a bit to the east.” To tell you where exactly they left something in your house, they’ll say, “I left it on the southern edge of the western table.” Or they would warn you to “look out for that big ant just north of your foot.” Even when shown a film on television, they gave descriptions of it based on the orientation of the screen. If the television was facing north, and a man on the screen was approaching, they said that he was “coming northward.”

More information here: www.nytimes.com/2010/08/29/magazine/29language-t.html?_r=0

We used this piece from Guy Deutscher, plus others, to show that, when teaching English as a foreign language, you can never assume that languages all work from the same rule book. This is an extreme example of course, but more commonly met ones are the use of gender in language, languages like Turkish and Japanese which look grammatically "back to front" and so on. I could ramble on for hours

RJnomore - I think your reasoning on the DOND boxes is flawed.

I believe there are actually 22 boxes, but that's a technicality and doesn't affect the argument.

At the start, there is 1/22 chance that you hold the largest prize in your box.

A box is opened. That knocks one prize out, so now there is a 1/21 chance that your box holds the largest unrevealed prize. (If the opening revealed the largest prize, then obviously we reset our definition of the largest unrevealed prize, but that doesn't change the argument).

Another box is opened. Now there is a 1/20 chance that your box holds the largest unrevealed prize.

After 20 openings, there is a 1/2 chance that your box holds the largest unrevealed prize. There is a 1/2 chance that the other unopened box holds the largest unrevealed prize. So swapping is a 50:50 chance of getting the largest unrevealed prize.

Here's another one. Humans are pretty much the only animals to have whites in our eyes. The cooperative eye hypothesis suggests that this was an evolutionary advantage that let our early ancestors communicate silently by eye movement when out hunting.

In other animals, the shape of the pupil tells you whether they are predator or prey. A vertical slit pupil is likely to belong to a small predator like a fox that ambushes its prey, enabling it to judge pouncing distance accurately. Round pupils belong to large predators like tigers that chase down their prey, while prey animals like goats have horizontal pupils and eyes on the side of their head to see danger approaching. Their eyes rotate like gyroscopes when they are eating to maintain the parallel with the horizon.

I was told by a friend whose partner is a shepherd, that they can make sheep have multiple births (twins) by what they feed them/where they graze. Twins in sheep are more economically beneficial, so it's useful to be able to have as many sets as possible every year

DS used to watch Mr Tumble with great interest, though he was a great talker and we had never used any kind of signing. He started making up his own signs. I seem to recall twirling round and touching the floor meant "biscuit"

And on twins again, the Yoruba of Nigeria (and elsewhere in West Africa) have a massively higher rate of twin conceptions than anywhere else because their staple foodstuff is yams that does something to women's hormones.

I was once at a loose end in Carmarthen for some hours. I know no Welsh but having heard that it was similar to French and knowing w is a vowel, I managed to decode lots of signs and street names. Eglwys - eglise - church.

I'm fascinated by my children acquiring language - ds age 2 could sign as much as he could speak, but that being roughly the limit of my sign, he stopped using it much as he learnt more and more English, but even 5 years later he will still use a sign for emphasis. And he can code-switch beautifully, from pure Sarf Lahndan Innit with his mates (but all role-playing uses Generic American Tough Guy accent! ), to much more standard English at home and, without my pushing it, Extra Nice Voice with lots of please and thank you when with my parents! Dd is still at the stage of regularising every verb and wants to logicify English.

I learned that hearing voices is remarkably common, though people usually don't admit to it - the main problem with schizophrenia and other illnesses where that's a symptom is that the sufferer feels compelled to listen to them.

Eggs in mammals have two poles, and the sperm always enters around the equator, thus defining front and back of the new organism. It's only after about 5 divisions that the ball of cells starts to specialise so some cells are different types from others, though - until that point you can still divide the ball of cells to create identical twins or more and somehow each cell knows where to put top/bottom and front/back axes.

On the subject of twins, the Romans believed twins were one soul with two bodies, so gave them names like Loquax and Anti-Loquax.

I was once sitting in a café in Brittany which had tablecloths printed with Breton words and their French and English translations. All the really old basic words, like fire and house, were exactly the same as in Welsh.

Love the idea of speaking German in England!

We noticed that DS codeswitches (in a very minor way) and has done from very young. Y family is from the NE of England, DH is a born and bred cockney. DS swaps between accents and slang depending on which family he is talking to. From being about 2 he would talk to me about baath time, but DH ran a barth apparently. It happens before anyone else speaks so it isn't just mimicking what he hears. I am quietly fascinated by it!

Thank you for the thoughts on colours and how we see them- I'm glad other people find this as interesting as I do!

Fair enough! Uni is definitely wasted on the young. All my best, most motivated classes have been mature students. I have an entire manifesto based on developing life-long learning over uni at eighteen for the day when I get the call from number ten to take over education

I learned that culture and religion plays a massive impact on the way people experience psychosis.

Selective seretonin reuptake inhibitors (antidepressants) aren't very selective, apart from citalopram, which is why citalopram is very hard to stop taking and the others have horrible side effects.

A sign of sepsis can be either a high or low temperature.

A high temperature can be a sign that someone is detoxing from benzodiazepines too quickly and is at risk of having a withdrawal seizure.

Something else I learned about addiction is that almost everything we think we know about addiction is wrong

Psychosis is not always bad, schizophrenia is sometimes better left untreated

Dolls are really useful for reducing stress in those with dementia

Service users find my working environment really traumatic

Also on the Consonant shift re the Portuguese, They use 'R' where other languages use 'l', eg. praca, praia, prata, branco instead of place, playa,plate, blanca, blanche from English, Spanish, French etc.