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Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Do any of you have any noteworthy experiences where knowledge of math helped you in an unusual way?
https://en.wikipedia.org/wiki/Monty_Hall_problem
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Get Those Brain Cells Working: The Monty Hall Problem
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Two is not equal to three, even for large values of two.
(Score: 5, Insightful) by ledow on Friday July 29 2016, @11:05AM
I'm a mathematician, by education.
I just work in IT by trade.
I use the Monty Hall problem as a classic example of statistics, probability and human interpretation - why numbers "lie" to you all the time and so you can't just rely on the numbers alone without having the expertise to interpret them.
Monty Hall was the trigger behind thousands of mathematical academics telling the woman with the world's highest IQ that she was wrong. And she wasn't. It's an age-old problem, precisely because it's so simple and yet so unintuitive.
Even as a mathematician, the first time you see it you will be thinking "That can't be right" in your head until you do the maths to convince yourselves.
But it's a great demonstration of why that number in the news - even if completely accurate - shouldn't be the basis of your decision alone. Why you can't just guess at the best course based on instinct. And why you don't mess with statistics or probability unless you truly understand them (gamblers, please note).
The other ones that are great demos of why maths is self-consistent even when it appears not to be, why you don't mess with mathematicians at their own game, and why you shouldn't believe your eyes, is the "rearrange these pieces of a right-angled triangle, oh look we've made a bigger triangle" one. And then anything involving division by zero (those "look, we broke maths" equations that appear to work but contain a hidden division by zero).
Honestly, if people learned just a bit more statistics and probability, gambling revenues would plummet and shampoo ads would end up having to actually confess they are all really just Sodium Laureth Sulphate in varying different concentrations.
Remember, kids, 8 out of 10 cats prefer* it.
(Score: 2) by art guerrilla on Friday July 29 2016, @01:12PM
not buying it: if you euros are saying it is 'maths', when we 'murikans know it as mathematics, and THEN are saying you are 'mathematicians', not gonna allow it...
if you are saying 'maths', should be 'mathers'...
(Score: 2) by sjames on Friday July 29 2016, @06:54PM
Unless they are born in Germany, in which case they are called The Beaver.
(Score: 3, Informative) by JeanCroix on Friday July 29 2016, @01:15PM
(Score: 0) by Anonymous Coward on Friday July 29 2016, @03:54PM
I'm a mathematician, by education. ... Honestly, if people learned just a bit more statistics and probability, gambling revenues would plummet and shampoo ads would end up having to actually confess they are all really just Sodium Laureth Sulphate in varying different concentrations.
No they wouldn't. You are looking at this with a theoretical rational perspective, rather than a practical one. You are taking an psychological/marketing problem and trying to apply mathematics to it.
For the gambling one, there are numerous people who know the math and do it anyway. It's spending money to purchase enjoyment. Think of it this way. "I can spend $20 to see a movie for 2 hours of enjoyment, or I can spend $5 on some lottery tickets and fantasize for an hour over what I would do with millions of dollars." (The strictly rational person would eschew both of them as being irrational wastes of resources.) I suppose you only said revenue would plummet, though, so I guess that could be true as some people are "just that ignorant."
For the shampoo, people are buying an image and lifestyle fantasy. It's the same reason why the Mona Lisa is priceless but an copy is nearly worthless. In all practical ways they are identical, except they aren't. Likewise the Sodium Laureth Sulphate is all mostly identical (excepting that they have different levels of quality control, different amounts of add-ins to change how hair acts, etc), but convey a different feeling upon purchase and use.
Sure it's not rational. However, I'm reminded of the old quote that I heard in an economics class, "only two people act economically rationally: economists and sociopaths."
(I will add that your larger point that "even true numbers told in earnest can be deceiving" is very valid and insightful.")
(Score: 3, Interesting) by sjames on Friday July 29 2016, @07:10PM
On the other hand, I can take an hour walk and fantasize what I would do if I find a winning lottery ticket in the gutter.
I see your point in general, and have to wonder at economists that still cling to the idea of rational actors in a market. It makes the physicist's spherical cow in a vacuum seem perfectly reasonable in comparison.
What would really kill marketing as a profession would be an outbreak of high functioning autism.
(Score: 0) by Anonymous Coward on Friday July 29 2016, @08:57PM
> thousands of mathematical academics telling the woman with the world's highest IQ that she was wrong. And she wasn't.
Some of those probably got the problem second-hand. I know the formulation I got at first was not her full description and had a different conclusion (they hadn't specified he wouldn't open the door I had initially picked IIRC, and said he'd "randomly choose a door with a goat" which retains 50/50 if your door isn't opened and your choice between remainders is 50/50 if your door is opened - yes, really, it's a very different problem). Then their explanation of why it was so didn't make sense and I was left thinking this problem was a stupid fake for yeaaaars until I read the correct formulation, which is transparent to graph theory students. Which, thanks to Martin Gardner, I had unwittingly been since a pre-teen. And I was left SUPER frustrated at the person who presented it to me in the end, as the disinformation was mental muck that took some years to clear.
tl;dr - the monte hall problem is misdescribed sometimes too. :(