Posted on 05/15/2014 7:24:11 PM PDT by SeekAndFind
Robert Krulwich/NPR
Poor Johannes Kepler. One of the greatest astronomers ever, the man who figured out the laws of planetary motion, a genius, scholar and mathematician — in 1611, he needed a wife. The previous Mrs. Kepler had died of Hungarian spotted fever, so, with kids to raise and a household to manage, he decided to line up some candidates — but it wasn't going very well.
Being an orderly man, he decided to interview 11 women. As Alex Bellos describes it in his new book The Grapes of Math, Kepler kept notes as he wooed. It's a catalog of small disappointments. The first candidate, he wrote, had "stinking breath."
Robert Krulwich/NPR
The second "had been brought up in luxury that was above her station" — she had expensive tastes. Not promising.
Robert Krulwich/NPR
The third was engaged to a man — definitely a problem. Plus, that man had sired a child with a prostitute. So ... complicated.
Robert Krulwich/NPR
The fourth woman was nice to look at — of "tall stature and athletic build" ...
Robert Krulwich/NPR
... but Kepler wanted to check out the next one (the fifth), who, he'd been told, was "modest, thrifty, diligent and [said] to love her stepchildren," so he hesitated. He hesitated so long, that both No. 4 and No. 5 got impatient and took themselves out of the running (bummer), leaving him with No. 6, who scared him. She was a grand lady, and he "feared the expense of a sumptuous wedding ... "
Robert Krulwich/NPR
The seventh was very fetching. He liked her. But he hadn't yet completed his list, so he kept her waiting, and she wasn't the waiting type. She rejected him.
Robert Krulwich/NPR
The eighth he didn't much care for, though he thought her mother "was a mostly worthy person ... "
Robert Krulwich/NPR
The ninth was sickly, the 10th had a shape not suitable "even for a man of simple tastes," and the last one, the 11th, was too young. What to do? Having run through all his candidates, totally wooed-out, he decided that maybe he'd done this all wrong.
"Was it Divine Providence or my own moral guilt," he wrote, "which, for two years or longer, tore me in so many different directions and made me consider the possibility of such different unions?"
Game On
What Kepler needed, Alex Bellos writes, was an optimal strategy — a way, not to guarantee success, but to maximize the likelihood of satisfaction. And, as it turns out, mathematicians think they have such a formula.
It works any time you have a list of potential wives, husbands, prom dates, job applicants, garage mechanics. The rules are simple: You start with a situation where you have a fixed number of options (if, say, you live in a small town and there aren't unlimited men to date, garages to go to), so you make a list — that's your final list — and you interview each candidate one by one. Again, what I'm about to describe doesn't always produce a happy result, but it does so more often than would occur randomly. For mathematicians, that's enough.
They even have a name for it. In the 1960s it was called (a la Kepler) "The Marriage Problem." Later, it was dubbed The Secretary Problem.
Robert Krulwich/NPR
How To Do It
Alex writes: "Imagine that you are interviewing 20 people to be your secretary [or your spouse or your garage mechanic] with the rule that you must decide at the end of each interview whether or not to give that applicant the job." If you offer the job to somebody, game's up. You can't go on and meet the others. "If you haven't chosen anyone by the time you see the last candidate, you must offer the job to her," Alex writes (not assuming that all secretaries are female — he's just adapting the attitudes of the early '60s).
So remember: At the end of each interview, you either make an offer or you move on.
If you don't make an offer, no going back. Once you make an offer, the game stops.
According to Martin Gardner, who in 1960 described the formula (partly worked out earlier by others), the best way to proceed is to interview (or date) the first 36.8 percent of the candidates. Don't hire (or marry) any of them, but as soon as you meet a candidate who's better than the best of that first group — that's the one you choose! Yes, the Very Best Candidate might show up in that first 36.8 percent — in which case you'll be stuck with second best, but still, if you like favorable odds, this is the best way to go.
Why 36.8 percent? The answer involves a number mathematicians call "e" – which, reduced to a fraction 1/e = 0.368 or 36.8 percent. For the specific details, check here, or Alex's book, but apparently this formula has proved itself over and over in all kinds of controlled situations. While it doesn't guarantee happiness or satisfaction, it does give you a 36.8 percent chance — which, in a field of 11 possible wives — is a pretty good success rate.
Try It, Johannes ...
What would have happened if Johannes Kepler had used this formula? Well, he would have interviewed but made no offers to the first 36.8 percent of his sample, which in a group of 11 ladies means he'd skip past the first four candidates. But the moment he'd met somebody (starting with lady No. 5) that he liked better than anyone in the first group, he'd have said, "Will you marry me?"
In real life, after a period of reflection, Johannes Kepler re-wooed and then married the fifth woman.
The way Alex figures it, if Kepler had known about this formula (which today is an example of what mathematicians call optimal stopping), he could have skipped the last batch of ladies — the sickly one, the unshapely one, the too-young one, the lung-disease one — and, all in all, "Kepler would have saved himself six bad dates."
Instead, he just followed his heart (which, of course, is another tolerable option, even for great mathematicians). His marriage to No. 5, by the way, turned out to be a very happy one.
Probably Kip Addotta. He’s a natural comic genius!
Need a woman with a bass boat - please send pic of boat ...
Women=Money*Time; but, since time IS Money
Women=Money2
As we all know, money is the root of all evil, therefore
Money=√Evil and so,
Money2 =(√Evil)2 or,
Money2=Evil and, as we have seen,
Women=Money2 Therefore,
Women=Evil
So, it's proof positive that Women ARE Evil! QED
Makes no sense! If you're holding out for one that's better than any in the first group, and there is none, you are stuck with the last one you interview, with expected rank of (N-1)/2, but which could be the worst one.
I suppose this 1/e stratagem maximizes the expected rank of your choice. But after all, you're only going to do it once!
The truth is, psychologically, men make money to get a woman. The man with the most money gets the pick of more women. It is true sex makes the world go round. If there were no women, men wouldn’t have the incentive to make money as there would be no pay off that important to them.
Tell us how you really feel Johnny heh.
You must have some war stories from hell.
put out frequently after marriage?
You described my wife, but her love for video games has waned, so of course mine has to too, but now she’s angry that I shoot my guns so much because I spend lots on ammo lol.
Haha, very good strategy, glad it’s working.
Actually, m’Lady, it depends on the age bracket under study. ... And in my case, how long since the last divorce.
How's that working out for you?
This made me think of those times in a parking lot, driving down a long corridor of cars toward the mall entrance, wondering about the optimal time to just grab an available space (do I take this one, or drive just a LITTLE farther hoping for better one).
Not equating women with parking spaces, mind you.... :-)
bookmark
Well, I quickly ( cough, cough ) wrote up a simulation for the suggested stratagem assuming 100 candidate interviews, ranked 1 through 100, and taken in random order. I used 36 for the cutoff of the “automatic refuse” sample, and then followed the strategy of taking the first one better than any of the sample of 36, or settling for the last interviewee.
1000 trials are well within trivial response time, and here are the results for several runs of 1000 trials:
358 142 81 28 21 12 7 7 6 11 7 7 4 3 4 2 4 3 2 5 3 3 3 6 5 2 3 3 4 5 6 4 4 2 2 1 4 6 3 6 4 1 6 0 4 3 4 3 5 4 2 5 4 1 6 7 3 3 2 2 2 5 4 3 7 1 5 5 4 2 4 0 2 4 3 5 3 1 1 3 4 5 5 5 4 4 4 3 2 4 2 7 1 7 8 4 0 4 4 1
405 153 62 30 28 15 10 3 7 4 5 1 6 2 0 5 3 4 5 5 1 4 2 5 4 4 4 6 5 2 4 8 8 4 2 2 4 3 5 2 3 0 2 0 5 4 1 3 4 4 3 2 0 3 3 0 3 1 5 3 2 6 3 1 3 3 0 2 0 2 7 4 2 5 5 2 6 3 4 1 4 2 4 2 2 1 1 0 2 4 5 8 4 6 4 1 0 2 3 3
371 157 67 23 16 12 5 5 8 6 2 3 3 1 5 2 2 4 3 2 1 1 5 9 6 2 6 4 2 6 2 4 5 5 5 6 2 4 0 2 3 4 3 1 1 4 3 3 3 4 0 1 1 3 6 5 4 8 6 1 2 7 1 3 4 1 4 3 2 5 3 4 6 6 3 6 3 2 4 1 1 6 6 4 4 4 4 7 4 1 6 5 2 4 3 5 4 6 10 6
... so it looks like a good strategy, in that it seems to optimize my chance of selecting a high ranking candidate. It gave me a top 10 candidate in 673, 717, and 670 out of 1000 trials in the three runs shown.
A store that sells new husbands has opened in New York City, where a woman may go to choose a husband. Among the instructions at the entrance is a description of how the store operates:
You may visit this store ONLY ONCE! There are six floors and the value of the products increase as the shopper ascends the flights. The shopper may choose any item from a particular floor, or may choose to go up to the next floor, but you cannot go back down except to exit the building!
So, a woman goes to the Husband Store to find a husband. On the first floor the sign on the door reads:
Floor 1 - These men Have Jobs.
She is intrigued, but continues to the second floor, where the sign reads:
Floor 2 - These men Have Jobs and Love Kids.
'That's nice,' she thinks, 'but I want more.'
So she continues upward. The third floor sign reads:
Floor 3 - These men Have Jobs, Love Kids, and are Extremely Good Looking.
'Wow,' she thinks, but feels compelled to keep going.
She goes to the fourth floor and the sign reads:
Floor 4 - These men Have Jobs, Love Kids, are Drop-dead Good Looking and Help With Housework.
'Oh, mercy me!' she exclaims, 'I can hardly stand it!'
Still, she goes to the fifth floor and the sign reads:
Floor 5 - These men Have Jobs, Love Kids, are Drop-dead Gorgeous, Help with Housework, and Have a Strong Romantic Streak.
She is so tempted to stay, but she goes to the sixth floor, where the sign reads:
Floor 6 - You are visitor 31,456,012 to this floor. There are no men on this floor. This floor exists solely as proof that women are impossible to please. Thank you for shopping at the Husband Store .
PLEASE NOTE:
To avoid gender bias charges, the store's owner opened a New Wives store just across the street.
The first floor has wives that love sex.
The second floor has wives that love sex and have money and like beer.
The third, fourth, fifth and sixth floors have never been visited.
Beer... and power tools. Those are incentives.
/johnny
See, I started off by making sure she liked to shoot. Then I checked for video games and the like. Now she just complains we live too far from a decent range.
I’m still ok, she likes to shoot, she just doesn’t realize how much .308 ammo can go through a semi automatic heh.
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