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一本奇特的书：数学和性 (转载自小木虫)
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一本奇特的书：数学和性
任何事情只要用心去做都可以是精致美丽的，数学也一样可以是优雅的，从容不迫的，这是我的感受。
书的导言是这么写的：
大多数人看到数学和性同时出现在一个句子会大为疑惑，不管两者之间是否有深深的联系；还是让我们抛弃那些陈词滥调跳入数学的温床去吧。
这本书开创了一个新的领域——从来没有人把数学和日常生活之间的联系解释的这么深入浅出。作者Clio Cresswell 将带你进入一个迷人的、有趣的偶尔捎带欢闹的旅途，展示数学如何回答那些关于Love、Sex和约会、婚姻方面的令人不知所措的问题。
数学和性是一本激发年轻人智力的寓教于乐的书。
Clio Cresswell博士从事过许多不同的职业，当前她是一名南威尔士大学（澳大利亚）的讲师，同时也是一名作家，不久前被提名并当选为第25周最美的人！她在法国南部长大后移民到澳大利亚并开始研究数学。她在得到博士学位后不久获得了大学奖金。
Clio也有相当广的媒体经验，从电视——包括座谈、美女和野兽、温室栏目，到电台——三M和国家电台。她也是会议客座发言人，基金发起人等等。这是她第一本书。
让我们看看网上的评论：
(Gary Cornell)写到“唔，多么令人感兴趣的题目啊！当我获得数学博士学位的时候，性和数学是风马牛不相及的，我怀疑这个题目是否弄错了：应该是数学和性的缺乏吧。但是，时代不同了，作者甚至还获得了流行杂志上第25周全澳最美的人的称号，她引用Hardy的话说，‘数学是研究学习的一种方式：发现、交流、影响并且应用’，那么这方式是否也可以包括性行为方式呢？
数学的研究方式是根据事实来建立模型，通过研究模型来了解现实。这就是为什么本书通过讲述数学模型来解释行为方式。Well，即使你已经听过那些奇闻轶事，阅读本书仍然是一种享受。接下来，在我进一步评论之前我想提醒一下，阅读每个数学模型的关键在于问自己，这些数学模型是否有现实意义？数学家是不能回答这个问题的，只有通过研究（有时也需要一点点经验）。爱因斯坦说过：数学家说是的时候它们往往仍然是不确定的，当他们肯定的时候肯定不是在谈论实际。
当我们为了应用而用科学的观点来研究模型的时候，数学家往往注意到这些模型本身所具有的内在的美（数学上的，也是形式上的），Cresswell在书中讨论的模型从这个意义上讲当然也是漂亮的（尤其解的精巧——这个美是双关的含义）。
让我先给你举一个模型的例子，是关于人际模型的，在书中第三章提到的：道路测试床！
“你不得不选择生活伴侣，现在我们做个模型假设，你可以有100个选择，一个接一个，你能和他们（她们）约会，做爱，或者无论做什么（这个模型这点可真够疯狂的——kergee注）。但是最终你必须说是或不，一旦说不，你将永远见不到他们（她们）。”
现在问题是你该采取何种策略呢？Well，你在选择最优结果的时候，最后一个人和最初的一个机会都只有1/100。模型所要求的：你怎样才能得到你最有的选择呢。要得到答案，只需要一点点无穷级数的知识。数学上（逼近论）能证明最优的策略是先看第37个，你从这个开始，你的机会将从1%增长到了37%（当然是很粗略的）（这个模型也叫土耳其皇帝嫁妆问题或者秘书问题，通常呢叫做最优停止问题）（我想前面的36个说不定也有好的呢，这个例子只是说可能性的大小，而不是确切的，运气不好的煮熟的鸭子也会飞呢——kergee注）。
这是我们如何行动的好的指南吗？这个策略现实中我们能采用吗？当然，100个人的选择太多了，不是一般人所能做到的，除非你是皇帝——唔，现在没有皇帝了，那么是影星或者是运动员总可以吧。这个模型看起来蛮有趣的，但实际根本不能采用，没有现实意义。
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.
显然我不能在这里穷尽作者书中所举的例子，关于她书中有趣的例子和观察在下文中有一个简单的描述：
第一章 "爱、甜蜜的爱" 提出了大量的能引起喜爱和憎恶的问题，来源于 "捕食-被捕食模型." 例如，她提到了下列模型的起源：
“罗密欧越爱朱丽叶，朱丽叶越想逃跑……罗密欧失望了，打退堂鼓，朱丽叶发现他奇怪的吸引力，罗密欧回应她……”
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.)
第二章 "婚姻和幸福" and describes models for behavior in a relationship, including an analysis of how absurd the folk tale is that more ###### 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.
第四章 "约会服务—你真的被服务了吗?" 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.
第五章 "配对" 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.
第六章 "作用与反作用" 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.
第七章 "性" and is a tantalizing hint of what the mathematics of evolution is all about. In particular this chapter includes a nice discussion of how ###### itself can evolve. (It seems paradoxical that the question of how ###### 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 ###### 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.
第八章 "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.
最后一章 "高潮" 我不能用一句话概括
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.
读书荐书
https://wap.sciencenet.cn/blog-81613-40536.html
上一篇：美科学家称用数学方法可改变婚姻走向
下一篇：数学学科名称翻译
任何事情只要用心去做都可以是精致美丽的，数学也一样可以是优雅的，从容不迫的，这是我的感受。
书的导言是这么写的：
大多数人看到数学和性同时出现在一个句子会大为疑惑，不管两者之间是否有深深的联系；还是让我们抛弃那些陈词滥调跳入数学的温床去吧。
这本书开创了一个新的领域——从来没有人把数学和日常生活之间的联系解释的这么深入浅出。作者Clio Cresswell 将带你进入一个迷人的、有趣的偶尔捎带欢闹的旅途，展示数学如何回答那些关于Love、Sex和约会、婚姻方面的令人不知所措的问题。
数学和性是一本激发年轻人智力的寓教于乐的书。
Clio Cresswell博士从事过许多不同的职业，当前她是一名南威尔士大学（澳大利亚）的讲师，同时也是一名作家，不久前被提名并当选为第25周最美的人！她在法国南部长大后移民到澳大利亚并开始研究数学。她在得到博士学位后不久获得了大学奖金。
Clio也有相当广的媒体经验，从电视——包括座谈、美女和野兽、温室栏目，到电台——三M和国家电台。她也是会议客座发言人，基金发起人等等。这是她第一本书。
让我们看看网上的评论：
(Gary Cornell)写到“唔，多么令人感兴趣的题目啊！当我获得数学博士学位的时候，性和数学是风马牛不相及的，我怀疑这个题目是否弄错了：应该是数学和性的缺乏吧。但是，时代不同了，作者甚至还获得了流行杂志上第25周全澳最美的人的称号，她引用Hardy的话说，‘数学是研究学习的一种方式：发现、交流、影响并且应用’，那么这方式是否也可以包括性行为方式呢？
数学的研究方式是根据事实来建立模型，通过研究模型来了解现实。这就是为什么本书通过讲述数学模型来解释行为方式。Well，即使你已经听过那些奇闻轶事，阅读本书仍然是一种享受。接下来，在我进一步评论之前我想提醒一下，阅读每个数学模型的关键在于问自己，这些数学模型是否有现实意义？数学家是不能回答这个问题的，只有通过研究（有时也需要一点点经验）。爱因斯坦说过：数学家说是的时候它们往往仍然是不确定的，当他们肯定的时候肯定不是在谈论实际。
当我们为了应用而用科学的观点来研究模型的时候，数学家往往注意到这些模型本身所具有的内在的美（数学上的，也是形式上的），Cresswell在书中讨论的模型从这个意义上讲当然也是漂亮的（尤其解的精巧——这个美是双关的含义）。
让我先给你举一个模型的例子，是关于人际模型的，在书中第三章提到的：道路测试床！
“你不得不选择生活伴侣，现在我们做个模型假设，你可以有100个选择，一个接一个，你能和他们（她们）约会，做爱，或者无论做什么（这个模型这点可真够疯狂的——kergee注）。但是最终你必须说是或不，一旦说不，你将永远见不到他们（她们）。”
现在问题是你该采取何种策略呢？Well，你在选择最优结果的时候，最后一个人和最初的一个机会都只有1/100。模型所要求的：你怎样才能得到你最有的选择呢。要得到答案，只需要一点点无穷级数的知识。数学上（逼近论）能证明最优的策略是先看第37个，你从这个开始，你的机会将从1%增长到了37%（当然是很粗略的）（这个模型也叫土耳其皇帝嫁妆问题或者秘书问题，通常呢叫做最优停止问题）（我想前面的36个说不定也有好的呢，这个例子只是说可能性的大小，而不是确切的，运气不好的煮熟的鸭子也会飞呢——kergee注）。
这是我们如何行动的好的指南吗？这个策略现实中我们能采用吗？当然，100个人的选择太多了，不是一般人所能做到的，除非你是皇帝——唔，现在没有皇帝了，那么是影星或者是运动员总可以吧。这个模型看起来蛮有趣的，但实际根本不能采用，没有现实意义。
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.
显然我不能在这里穷尽作者书中所举的例子，关于她书中有趣的例子和观察在下文中有一个简单的描述：
第一章 "爱、甜蜜的爱" 提出了大量的能引起喜爱和憎恶的问题，来源于 "捕食-被捕食模型." 例如，她提到了下列模型的起源：
“罗密欧越爱朱丽叶，朱丽叶越想逃跑……罗密欧失望了，打退堂鼓，朱丽叶发现他奇怪的吸引力，罗密欧回应她……”
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.)
第二章 "婚姻和幸福" and describes models for behavior in a relationship, including an analysis of how absurd the folk tale is that more ###### 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.
第四章 "约会服务—你真的被服务了吗?" 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.
第五章 "配对" 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.
第六章 "作用与反作用" 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.
第七章 "性" and is a tantalizing hint of what the mathematics of evolution is all about. In particular this chapter includes a nice discussion of how ###### itself can evolve. (It seems paradoxical that the question of how ###### 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 ###### 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.
第八章 "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.
最后一章 "高潮" 我不能用一句话概括
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.
读书荐书
https://wap.sciencenet.cn/blog-81613-40536.html
上一篇：美科学家称用数学方法可改变婚姻走向
下一篇：数学学科名称翻译
