This result says that, if John wants to maximize his probability of ending up with the best possible man, he should date 7 men and, then, marry the next man who is better than all of those men. Most on the dating market are not thinking this way — they want to maximize the probability that they end up with a pretty good spouse. Fear not, there’s a modification of the secretary problem that maximizes the probability of finding a high-value husband or wife.
I’m not going to cover the derivation for this flavor of the secretary problem in this post.
The layers that contain fossils and archeological clues can be dated by more than a dozen techniques that use the basic principles of physics, chemistry, and Earth sciences.
The cosmic microwave background (CMB) is light left over from the Big Bang.
It has revealed a wealth of information about our Universe and turned cosmology into a precision science. Some problems are so complex that, although we know how to solve them in theory, it would take billions of years to find a solution even on the fastest supercomputer.
In terms of the secretary problem, such a strategy would be: Scan through the first \( r \) integers and then choose the first option that is greater than any of the integers in \( [1,r] \). The above image is a prop to help understand the discussion that follows.
Assume that \(i\), the greatest integer, occurs at \(n 1\).
Still, I think I’d say something like, “My boy, evolution is a motherfucker and you need a new woman in your life.” He would probably protest that women were the problem and that he’s pretty sure the last thing he needs is another one. He’d like to settle down one day — maybe adopt a child with the right man. Examples of the secretary problem: As a general problem solving strategy, I often find it useful to first come up with a horrible solution to a problem and then iterate from there.
Then, I would let out the most condescending sigh imaginable, the sort of sigh that says I-have-unimaginable-wisdom-born-of-experience-and-am-from-the-future, and say, “Not that sort of woman. You need mathematics –” “Let me tell you about the secretary problem.” Consider the plight of John. He lives in Utah and likes country music, hunting, and four wheelers. He has a couple short-term relationships going on right now, but to Bruce or Sidney? I call this the dumbest-thing-that-could-work heuristic. In the case of the secretary problem, our horrible solution can be the lucky number seven rule: In an integer sequence, always choose the 7th item.Most people aren’t dating even four other people before marriage. At its core, the conflict implies that either the solution to the secretary problem does not apply or that humans are not gathering enough information before getting married.A number of experimental studies (here, here, here, and here) support the second view.Come on a trip through the world of complexity and meet the famous P versus NP problem.I learned a few things, though, like when you tell strangers that your long-term relationship has just been bulldozed as thoroughly as the Romans salted Carthage, they do this sorta Vulcan mind-meld and become super empathy machines. Valentine’s Day rolls around, and John finds himself, at the last minute, at Walmart, looking to pick up some chocolate and cheap Champagne, wondering, “Is this really what love feels like? Should he next Jim and take his chances on the dating market? John’s predicament is an example of the secretary problem — so named because we can imagine the same situation, except instead of a man searching for a husband, it’s a man interviewing potential secretaries. Let’s consider each man that John dates as an integer — the integer representing his “husbandness factor.” Thus, a sequence of lovers like \((Sidney, Bruce, Jim, Todd, Keith, Bruno, Terrence, Cecil, Nigel)\) would translate to the integer sequence \((1, 3, 7, 5, 8, 3, 1, 9, 4)\).Exciting scientific discoveries continually add to the broader and deeper public knowledge of human evolution.