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MATHEMATICS AND SEX
by Clio Cresswell (Allen &
Unwin)
Review by Gary Cornell
Wow, what an intriguing title! When I was getting my Ph.D in math, the
words ’sex’ and ‘mathematics’ were not juxtaposed all that often, and I suspect
we would have been more likely to expect a book titled ‘Mathematics and the
(lack of) Sex.’ But, hey, times change and the author, who is not only a
mathematician but also someone who was voted one of Australia’s 25 most beautiful people
in their equivalent of People magazine — and remember this is the land of Nicole
Kidman — has a point. As she says, echoing G.H. Hardy’s famous comment in ‘A
Mathematician’s Apology: ‘Mathematics is the study of patterns: their
discovery, their interconnections and their implications.’ And what is sexual
behavior but the most intriguing pattern of all?”
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 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 mathematicians do generally 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.
Read the rest of the review.
Also, read Corrie Pikul's review of this book.
Do you have a review of your own? If so, send it to Bill Cherowitzo.
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