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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.
Ok, how many other people immediately did a google search to see how attractive she really was? The first link gives a decent picture of her. She's cute.
I believe that was a representation of the game theory.
http://cepa.newschool.edu/het/schools/game.htm
Actually its an economics problem. What Nash showed was that individuals maxamizing profit could lead to markets being heavily under utilized. A good example is radio stations:
Assume you have in a city you have
40k who like rock
30k who like news
12k who like country
9k who like classical
1 station: rock only
2 stations: rock + news
3 stations: 2 rock + 1 news the third station does better splitting the rock vote then going after country or classical (i.e you end up with 2 rock + 1 news).
4 stations: 2 rock + 2news
5 statations: 3 rock + 2 news
6 stations: 3 rock + 2 news + 1 country
it might even be worse if additional stations go after the rock and news markets trying to drive others out
_____
Under nash's ideas the stations can pool their earnings and:
1 station: rock
2 stations: rock + news
3 stations: rock + news + country
etc...
from "The Cyberiad" by Stanislaw Lem
Come, let us hasten to a higher plane
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n
Commingled in an endless Markov chain!
Come, every frustrum longs to be a cone
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.
In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.
I'll grant thee random access to my heart,
Thou'lt tell me all the constants of thy love;
And so we two shall all love's lemmas prove,
And in our bound partition never part.
For what did Cauchy know, or Christoffel,
Or Fourier, or any Bools or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?
Cancel me not - for what then shall remain?
Abscissas some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.
Ellipse of bliss, converge, O lips divine!
the product o four scalars is defines!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.
I see the eigenvalue in thine eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a^2 cos 2 phi!
There are many problems with mathematical modeling of human behaviour. Firstly, economic phenomena (and we can broadly characterize all phenomena as such) are not infinitesimal. They are discrete. Thus, various operations of calculus are completely invalid, as the reality of human action is not continuous, but discrete.
Secondly, human beings can choose. The reality of game theory is that it is a bunch of humbug which is often wrong, and when it's right, doesn't do any better than common sense would. In real-life situations, the only people who behave as game-theorists predict are actual game-theoreticians.
I suggest this article on John Nash and Game Theory. I also suggest this article by Prof. Murphy, and this excellent chapter on game theory by Ludwig von Mises.
social sciences can never use experience to verify their statemen
I love brainy chicks. Even if they aren't that pretty.
His search strategy is off.
Sure, a small proportion of the total population is actually eligible, but he can screen more than one candidate / day. Many will not meet his age requirements, attractiveness requirements, etc.
Apply some crypto-fu, take some shortcuts. Don't solve the problem the hardest way.
Of course, it's actually harder than he figures. I think the number of folks I could actually hang with lifetime are more than two standard deviations from norm...
Some chick I knew once wondered aloud "what's the difference between a cutie and a hottie?" Well...
The shape of a human jawbone is related to the amount of testosterone present during certain phases of development. Guys who have higher levels of testosterone turn out with square jaws and guys with lower levels turn out with rounder jaws.
Also, guys with higher testosterone levels are more likely to cheat on their sex partners, so from women's perspectives, over the course of evolutionary time natural selection taught women to view guys like this (unconsciously anyway) as better for short-term relationships (since they were unlikely to stay around), thus making them hotties.
On the other hand, guys with rounder jaws / lower testosterone were less likely to cheat on their partners, thus making them better-suited for long-term relationships, thus making them cuties.
Intelligent Design: because MATH is HARD.
Here's Clio's video. I'm late to the discussion, so I'm kind of surprised no karma whores got there before me!
But her parents are Australian.
Here is her picture http://www.saxton.com.au/saxton_db_data/images/Cre sswell_Clio.jpg
Moderators please ignore karma whoring.
This lady used to be my maths tutor in 1st year university... =)