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Mathematics and Sex
The way one studies patterns mathematically is by building models for the behavior being modeled. This is why most of this book is about mathematical models for interpersonal behavior. Well, that together with some amusing anecdotes that make the book a fun read even if you know the literature very well. Still, before I go any further with this review I want to remind everyone that the key question to ask oneself when reading any book that does mathematical modeling of any topic is always the same: are the models built realistic?. Mathematicians can't answer this question: only research by scientists (i.e., experience) can. Einstein probably put it best when he said:
"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."
While we do study models for their applicability and their eventual predictive use by and for science, mathematicians can and do also study them for their intrinsic mathematics beauty, and some of the models Cresswell discusses in this book are certainly very pretty (in the mathematical sense of beauty--because the solutions are elegant, though the pun is intended.)
As an example of what this whole subject is like let me tell you about a long-studied model of interpersonal behavior that the author discusses in Chapter 3, a chapter titled "Road Testing the Bed"--I kid you not.
"You have to choose your life mate. The rules we adopt for this model are that you will be presented 100 choices one after another, you may date them, sleep with them, whatever. But, at the end, you must say yea or nay and if you say nay, you will never see them again."
What strategy should you adopt? Well, if you wait to the end, the odds are only 1/100 that the last person is the optimal choice; ditto if you choose the first person. The modeler then asks: what strategy should you adopt for optimum results? A little bit of mathematics involving infinite series gives the answer. You can prove mathematically that the best strategy is to look at (approximately) the first 36.787944117144235 people (rounding it to, say, 37 people) and then you should choose the first person from that point on that is 'better' then the previous 37 people. This increases the odds of your finding the best match from 1% to about 37%- roughly a 37 times improvement. (In the pre-politically correct literature this model was called "The Sultan's Dowry Problem," or "The Secretary Problem"; now, alas, it is usually called simply an example of an "Optimal Stopping Problem." )
Is this a good model for how we behave? Is this a strategy that one can realistically adopt? Certainly, 100 possibilities seems like a lot of choices to have if one is not the current day equivalent of a sultan -- a movie star or an athlete. But the model is intriguing, if not totally realistic and applicable.
Models that spring from modification of the rules of the Sultan problem have always been one of my favorites in this area. This makes Chapter 3 my favorite chapter: it is chock full of goodies with lots of interesting variations of the original problem, and thus even more interesting models. Some may be far more applicable. For example, if you get to play the cad and can keep potential mates 'stockpiled,' then, by stockpiling seven potential mates, there's a strategy that you can use to increase the odds of finding the best one to 96% or so! Or, in another variation of the model, whose solution she refers to as the "twelve bonk rule," there's a result that says that if you simply want to ensure that your choice is better than 90% of the other choices available, simply 'sample' the first 12 possibilities and pick the first person who is better after the first 12. This strategy gives you a 77% possibility of success.
I obviously can't go over all the models she builds, the interesting results she cites, or the interesting observations she makes in a review so let me simply give you some of the high points of the remaining chapters:
Chapter 1 is entitled "Love, sweeeet love" and mostly consists of showing you various differential equations that can model love's attraction and repulsion i.e. variations on standard "prey-predator models." For example, she mentions the following model of attraction:
"The more Romeo loves Juliet, the More Juliet wants to run away ... Romeo gets discouraged and backs off, Juliet finds him strangely attractive. Romeo tends to echo her..."This model gives rise to a standard and very simple first order differential equation. She then talks about more sophisticated versions of this model including one by Rinaldi that tries to model a famous love poem by Petrarch. (Personally, I think these models are only useful for learning differential equations but don't shed much light on the problem.)
Chapter 2 is called "Marriage and the Happily Ever After" and describes models for behavior in a relationship, including an analysis of how absurd the folk tale is that more sex occurs in the first year of marriage then in all subsequent years combined. Probably the most interesting work she talks about in this chapter are the models by Guttman et al. intended to analyze conversations between lovers to determine if the relationship is on the rocks. In this case the models they build are known to be highly accurate in predicting problems in the relationship.
Chapter 4 is entitled "Dating Services -- are you really being served?" and it has a fascinating analysis of the perils of questionnaires that try to match too many variables (i.e. why those questionnaires don't help that much). As she points out, this is called the "curse of dimensionality" in the literature. The problem is that if you are trying to determine whether two points are very close in n-dimensional space where n is large, you are unlikely to get a whole lot of difference between points and so closeness doesn't really matter much.
Chapter 5 is called "Pairing Up," and shows how Game Theory can (should?) enter into the problem of "choice" preferences. This chapter is a very nice gateway into models that are studied in the greatest depth in economics; there is an incredibly interesting literature on these issues. One should start with Arrow's paradox on voting (that most logical axiom systems for building choice models are actually inconsistent and can't simultaneously be satisfied) and then work up to real problems with how congressional seats are allocated in the United States. Wikipedia has good articles to start with on these models.
Chapter 6 is called "Action Reaction Attraction" and is about ways to model people's attractiveness. This means things like symmetry as a cross cultural model for beauty, and waist-to-hip ratio for females as a cross-cultural model for male choice. Whether these models are correct is an extremely active area of research in anthropology and evolutionary psychology. The jury seems to still be out, but the evidence for their truth is certainly growing.
Chapter 7 is called "Pick a Sex, Any Sex" and is a tantalizing hint of what the mathematics of evolution is all about. In particular this chapter includes a nice discussion of how sex itself can evolve. (It seems paradoxical that the question of how sex itself can evolve is not yet resolved. After all, in a naive "selfish gene" approach to evolution, it would seem seem that asexual methods of reproduction win hands down. But, as usual, the issues are more complex then naive models would predict. For example, who would have thought that parasites might be the reason sex arose? Again, for more details on the science behind the models the author discusses, you can start with a useful Wikipedia article. Ridley's popular science book called the Red Queen (or anything by Maynard Smith) is where to go next.
Chapter 8 is titled "How Ovaries Count and Balls Add Up," and is about models for feedback levels of hormone concentration and circadian rhythms and didn't particular interest me.
Finally, Chapter 9 is called "Orgasm" and I'm not going to summarize it, since that would be telling.
To sum up, is this book perfect? No. I think more mathematically literate people would like appendices which give some indication of the deeper math behind what she discusses. For example, the math that shows why the answer I gave above to the Sultan's choice problem really is approximately 36.787944117144235 - or more correctly n/e, where e is the base of natural logarithms and n is the number of choices one has to go through, is well within the reach of any 2nd year calculus student. The differential equations she introduces in other chapters can be understood by anyone with a good engineering or math background. The game theory and even a proof of Arrow's theorem should be accessible to any literate person etc. As is, though, anyone with even some knowledge of or interest in mathematics will find this book great fun.
You can purchase Mathematics and Sex from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.
The movie Beautiful Mind on the life of John Nash present a scene in a bar where he gets his novel idea (which led to a Nobel Prize).
A beautiful women with 3 of her (so-so) friends, 4 guys. If we all go for the cutie, her friends get no attention, go away and we all lose. If we each take one (a guy being luckier than the other), every girls feels she get attention we all 'win'.
Is this scene true or pure romanced fiction? In any way, a good representation of Math + Sex (if this is possible).
Eureka Science News - automatically updated
"You have to choose your life mate. The rules we adopt for this model are that you will be presented 100 choices one after another, you may date them, sleep with them, whatever. But, at the end, you must say yea or nay and if you say nay, you will never see them again."
What strategy should you adopt? Well, if you wait to the end, the odds are only 1/100 that the last person is the optimal choice; ditto if you choose the first person.
The 1/100 chance that the last person is the optimal choice assumes there exists one optimal choice in the original batch of 100 in the first place.
And what is sexual behavior but the most intriguing pattern of all?
Apparently he never saw Pi.
sig?
Come on, you know you were curious! Here's the author, Clio Cresswell.
http://www.betterhumans.com/News/news.aspx?article ID=2004-12-10-2
Finding supports anecdotal evidence and reinforces evolutionary theory of human mate selection
Betterhumans Staff
12/10/2004 3:20 PM
Men don't want to marry powerful women, shows a new study that supports anecdotal evidence and reinforces evolutionary theories of human mate selection.
The study highlights the importance of relational dominance in mate selection and discusses the evolutionary utility of male concerns about mating with dominant females.
"These findings provide empirical support for the widespread belief that powerful women are at a disadvantage in the marriage market because men may prefer to marry less accomplished women," says social psychologist and study lead author Stephanie Brown of the University of Michigan in Ann Arbor.
Subordinate attraction
With the help of a grant from the US National Institute of Mental Health, Brown and coauthor Brian Lewis from the University of California, Los Angeles tested 120 male and 208 female undergraduates by asking them to rate their attraction and desire to affiliate with a man and a woman they were said to know from work.
"Imagine that you have just taken a job and that Jennifer (or John) is your immediate supervisor (or your peer, or your assistant)," study participants were told as they were shown a photo of a male or a female.
After seeing the photo and hearing the description of the person's role at work in relation to their own, participants were asked to use a nine-point scale (in which one is not at all, and nine is very much) to rate the extent to which they would enjoy going to a party with Jennifer or John, exercising with the person, dating the person and marrying the person.
Brown and Lewis found that males, but not females, were most strongly attracted to subordinate partners for high-investment activities such as marriage and dating.
Cautious investors
"Our results demonstrate that male preference for subordinate women increases as the investment in the relationship increases," says Brown. "This pattern is consistent with the possibility that there were reproductive advantages for males who preferred to form long-term relationships with relatively subordinate partners.
"Given that female infidelity is a severe reproductive threat to males only when investment is high, a preference for subordinate partners may provide adaptive benefits to males in the context of only long-term, investing relationships--not one-night stands."
According to Brown, the findings are consistent with earlier research showing that expressions of vulnerability enhance female attractiveness. "Our results also provide further explanation for why males might attend to dominance-linked characteristics of women such as relative age or income, and why adult males typically prefer partners who are younger and make less money."
The research is reported in the journal Evolution and Human Behavior (read abstract).
Chapter 7 is called "Pick a Sex, Any Sex" and is a tantalizing hint of what the mathematics of evolution is all about. In particular this chapter includes a nice discussion of how sex itself can evolve. (It seems paradoxical that the question of how sex itself can evolve is not yet resolved. After all, in a naive "selfish gene" approach to evolution, it would seem seem that asexual methods of reproduction win hands down. But, as usual, the issues are more complex then naive models would predict. For example, who would have thought that parasites might be the reason sex arose?
What we have here is a pontificator, a purveyor of much BS, a master in the art of using many words to say nothing.
a tantalizing hint of what the mathematics of evolution is all about.
A tantalizing hint? Seems like a pretty crappy chapter if all it has to offer is a hint, doesn't it? Why not just tell us? Is it because the chapter has no idea? Is it because this whole sentence doesn't mean anything at all, and you're just saying there's a tantalizing hint because you have no clue what the chapter is about and we can't prove there's no hint in there? Even if there is a hint, what if the hint is TOTALLY BORING?
In particular this chapter includes a nice discussion of how sex itself can evolve. (It seems paradoxical that the question of how sex itself can evolve is not yet resolved.
There's no paradox here - having a discussion about something that may not yet be resolved is, well, normal. Seems the author just wanted to use the word "paradoxical".
After all, in a naive "selfish gene" approach to evolution, it would seem seem [sic] that asexual methods of reproduction win hands down.
What do you mean, "it would seem"? Does it, or doesn't it? Or is the author just covering his butt because he no idea whether it does or doesn't? And why is there an "After all" in there when this has absolutely NOTHING to do with the sentence before this one?
But, as usual, the issues are more complex then naive models would predict.
Maybe because that's the DEFINITION of naive? And what issues? The author hasn't even told us what issues he's talking about! I also think this summary would have been improved if the author had mentioned that the sky was blue and the earth is down. Of course, the author probably would have said something like "And as everyone knows, the sky is not royal blue, but paradoxically, more of a turquoise, and as usual, one would find the earth, unsurprisingly, located in a direction not above them, clearly showing that the issues are unresolved."
For example, who would have thought that parasites might be the reason sex arose?
An insectophiliac? What is this an example of anyway, other than how the author may have bored their professor into passing their thesis without reading past the first page?
If you've got nothing to say, don't just spew crap. It hurts my brain.
paintball
This was in sharp contrast to the Electrical Engineering department...
And the brethren went away edified.
This isn't the norm, but I've seen it more than once. Men really can marry above their level if they give it a little effort. In fact, now that I think about it, every Slashdotter married... had to marry above their level (self included).
Oh, absolutely. I agree 100%. I'm definitely nothing to look at, and I'm routinely amazed by the women that I get just because I *try*. Most guys just see a good lookin' chick, and assume they don't have a chance, but women don't think the same way. Many women could care less what the guy looks like (to a certain point).
I don't respond to AC's.
but if you want to use game theory to analyze sex, here's an article about faking orgasms.
Don't know where this comes from, but the best mathematical model is the one where the age that you find girls most attractive is half your age plus 7 years. So a 10 yo boy thinks 12 yo girls are hot (10/2 + 7) A 20yo thinks 17yo girls are good, 30yo goes for 22yo, 40 for 27 etc. It works out pretty accurate.
Probably developed by mathamatitions on a Saturday night "If I could get a date on a Saturday night, what age would I go for?"
You obviously didn't hear the Bush administration's recent report that high school students are uninterested in sex.
Unfortunately, the author of the review didn't actually offer much insight into the quality of the writing.
/. reader, but not for anyone who's made it past the adolescent humor phase.
Cresswell doesn't do a very goood job of integrating the actual math with the implications of the the theories. She'll say things like "Mathematicicans would use an equation that looks like this: [large integral here]", but then not explain the integral or math at all, and instead launch into a discussion of the social ramifications of the mentioned theory.
When it comes to the social aspects, she's not a very clear writer either. Her writing style can be ambiguous and make it difficult to follow her examples.
Her writing is also filled with cheap sexual puns and insinuation. Perhaps good for your average
Overall, the book had some interesting notions and some notable flaws. She didn't do anyone any favors by pointing out the scary math and then ignoring it. She could have conceptually addressed the math a little more without scaring off the math-phobic. It also could have benefited from a good editor.
(Apologies for the vague examples; I haven't got a copy of the book with me.)
Reading from the Kama Sutra, Chapter 1
This excerpt came up in an interview with this book's author which you can read here
What's the corresponding formula for ladies though?