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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.
69 :D
hey baby, I'll be your derivative so I can be tangent to all your curves.
+5, Truth
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
The Integral of e to the x equals f of u sub n,
which looks like
Sex = Fun.
Wow. Ascii sure takes the fun out of a high school math joke!
In the future, I would want to not be isolated from my friends in the Space Station.
In addition to "How 'bout you plus me subtract our clothes, you divide your legs and we multiply", I can use the less cheesy "Hey baby, I'm a mathamatician"
Oh, yeah.
-kwy
...especially the detailed, in-depth research into topics such as "fluid-damped, mutually exciting, pair-coupled oscillators."
Waddya know, Kevin Smith was onto something.
Christian Jones
Medicine. Mathematics. Mediocrity.
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).
What is so interesting about sex? This is nothing more than a thinly veiled attempt to use mathematics to sell a book on sex to the enourmous geek market. Shameless exploitation I tell you! Real geeks want Pi not Pie.
Some drink at the fountain of knowledge. Others just gargle.
I think you meant imaginary.
This rating is Unfair ( ) ( ) Fair (*) Funny
Sigh... If only. Modding would be so much more fun.
Yes it does.
"are the models built realistic?"
No model I've ever seen has been built realistic. They're always skinnier than hell and walk like they have a rotorooter up their ass....
"Is this Winkhorst a nova criminal?" "No just a technical sergeant wanted for interrogation."
Actually, they saying is more like 100. A friend of mine in college lived by this rule. We'd go out to bars, and he'd just go up to every woman he saw and ask until one said yes. He brought someone home every night, but, you can imagine the type of women that would be likely to say yes to that....
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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.
As the cowards have said, of course it's the optimal of that 100.
Given that, there are many different ways of measuring optimal, but I think that given the question "choose your life mate" the optimal has to be "person who you will be most happy with for the rest of your life".
Ok, we have a comparison function. Now I don't have a clue how you can tell which one is optimum - and besides you're only going to reach number 100 (assuming they're the best) if the second best was in the first 37.
I'm also assuming that no two people are exactly identical, and hence no two people are going to be exactly as "enjoy rest of life with" as each other. I think that's a fair assumption with humans.
This reminds me of this clever essay someone wrote, where he determines through demographics and statistical calculus why he will never have a girlfriend.
Hilariously geeky stuff.
SEO Copywriter. Just Say ON
Who cares? You just slept with a hundred people. :)
"The objective of securing the safety of Americans from crime and terror has been achieved." -- John Ashcroft
This was in sharp contrast to the Electrical Engineering department...
And the brethren went away edified.
She seemed fairly competent teacher although it was obvious she took the class at almost zero notice as a favour for someone and didn't know what the hell we were supposed to be learning. She struck me as someone more in to research than teaching, though that applies to most accedemics I guess.
I went onto IRC and for some reason, during the course of the conversation, I mentioned the fact that I just came back from a math tute which was taken by a youngish, blonde, female substitute. Since I was talking to males on IRC, someone asked the obvious question: "is she hot". My reply was something like: "she's ok I guess, nothing special... she might look better under different lighting".
Now I find out on slashdot that she was voted one of Australia's 50 most beautiful people. So now I am thinking, um, are my standards abnormally high or what? No wonder I can't get a date.
But it's funny that a woman can be standing less than two meters away from a guy for an entire hour but he won't know she's hot without slashdot. I'm not kidding either.
When Argumentum ad Hominem falls short, try Argumentum ad Matrem
Fellow geek guys, gather round. Let me tell you a vital secret:
Confidence. Is. Sexy.
Just like anything else, you have to work at it. Don't try to pick up the next "hot chick" you see, but do smile and nod, say "hello" as you pass by. Try that for a while, then move on to striking up a conversation with no intention of making a "pick-up". Practice this diligently and some day you'll be surprised as a beautiful woman is suddenly trying to pick you up.
I'm almost 35, certainly not better looking now than I was at say 22 and dateless. I'm certainly not rich (especially since I started downshifting and only work part-time now). But right now I'm almost getting more dates than I have time for. It's all attitude - by which I don't mean being an asshole, as some guys think is the ticket; just a quiet self-assurance goes a long way.
(Yes, I'm mid-thirties and still single, so if you want relationship advice go see someone else. I'm just talking about getting in the door here.)
Tom Swiss | the infamous tms | my blog
You cannot wash away blood with blood