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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.
Looks like we've found a slightly confused answer right here.
No no no you've got it all wrong. First you start by hitting on the ugliest girl in the set. Then the next ugliest, then next ugliest. You have to get all the ugly chicks to be friends with you. That way when you start hitting on the hot chick they won't cock block like they normally would.
How appropriate that this follows up the previous story; an ask slashdot pondering what aspects of science would interest high school students.
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.
Offtopic but I have to say it.
I feel America's DARE program needs to be replaced by having kids watch Requiem for a Dream. They'll never do drugs.
sig?
is actually rather solvable, especially in this situation.
Most people decide to use Euclidean distance, or distance-squared. It's possible to do some statistical tests comparing it to Manhattan distance, or distance-added, and you end up with Manhattan distance often being a "better" indication. So why not exaggerate?
Take the general formula d=sum(abs(x_n^v),n=1..nmax)^(1/v). Euclidean distance is this formula with v=2, Manhattan distance with v=1. Lower v below 1 - 0.5, 0.3, or lower - and you get a distance metric that works quite well with high numbers of dimensions.
Meanwhile, back in reality, the meaning of this distance metric is something along the lines of "it's okay if there are a few major differences, as long as mostly we're a good match", as opposed to "avoid major differences at all costs" . . . so instead of getting someone who's marginally different from you in all ways, you get someone who's very similar to you except for one major difference.
Which can be interesting.
Sometimes, the kind of "interesting" that involves handcuffs . . . either in the good way or the bad way.
I don't know if any online dating sites do this or not. But they should.
(For the curious: On the surprising behavior of distance metrics in high dimensional space)
Breaking Into the Industry - A development log about starting a game studio.
Genetic diversity is the only saving grace for us non-alpha males
I don't care if it's 90,000 hectares. That lake was not my doing.
So in other words, if one Company were to own severaL differEnt rAdio stations, instead of each station being undeR separate ownership, the stations Collectively could tHen be more profitAble. In other words, someoNe could make a lot of moNEy by starting a company that buys out Lots of different radio stations (at prices based on profitability under single ownership) and then makes them (overall) more economically efficient than they were before.
I wonder how come no one's thought of this yet...
Remember the days when Republicans were the party of fiscal responsibility?
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
You are an idiot. The paragraph you quoted made perfect sense. You desperate attempts to pick it apart seem deranged, like the submitter is your lifelong enemy and you are desperate to show the world that you are smarter than him. I don't feel like going through all of your stupidity, so lets just take one example:
Submitter: 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.)
You: 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".
It is a paradox because sex is an essential element of reproduction, and hence darwinian selection, and so it seem obvious that our solid understanding of darwinian selection implies a good understanding of sexual evolution; yet we don't have a good understanding of sexual evolution.
You assertion that there is no paradox because it is normal to discuss unresolved issues is nonsensical. The submitter did not assert that it was a paradox because it was being discussed, and I don't know why you would think that.
Agreed... that great stuff.
But I'd have to disagree with him... he is *extremely* picky. He will only settle for the top 2% beautiful girls.
The top 2% is comparable to *the* ultimate babe in your highschool.
If he's not willing to accept girls who are not at least as beautiful as that girl everyone lusted for in highschool who is at the same time smarter than 85% of people out there, then you've got issues.
I've met one girl personally throughout all of my life that *might* qualify according to those criteria...
"I don't know that Atheists should be considered as citizens, nor should they be considered patriots." -George H.W. Bush
So, considering there are about 9,956,572 female australians, of which less than 50 are sexy enough for you, the chance of you getting laid is about 0.000005022, a rounding error from zero. And we haven't even started considering your own attractiveness from a woman's viewpoint.
More seriously, though: Those lists of 'most beatiful women' only take those who figure regularly in the media into consideration, and noone gets on television without a thick layer of make-up, and the lighting is always better than at a uni in a TV studio.