没在美国生活过的体育迷恐怕很难理解美式橄榄球野蛮表象背后的深刻，这个现象让我想起了玻尔关于量子理论的那句名言“Those who are not shocked when they first come across quantum theory cannot possibly have understood it”。兄弟在本文标题中所构建的类比是非常有内涵的，ETS应该可以考虑将其纳入2007年度GRE考试的逻辑题库，这样读过本文的考生就比没读过本文者有了点微不足道的优势。：-）

下面将这一类比略微展开论述，为节省时间尽量做到点到为止：

（1）我对美式橄榄球(American football，在北美简称football，其职业比赛联盟称为NFL)的起源历史没时间去做深入研究，只大致知道该运动项目与足球(soccer)和英式橄榄球(rugby)有深刻的渊源。今天的美式橄榄球在任何一个时刻的对阵双方人数都是11人，与足球完全一致。在我将美式橄榄球比作量子力学以及将足球比作经典力学的前提下，英式橄榄球扮演的角色就很像物理学中的Lagrangian和Hamiltonian力学。这个也许不够精确的比喻应该可以为完全不了解美式橄榄球的体育迷提供一个快速切入的概括。

（2）置疑美国人为何如此沉迷于“野蛮”而缺乏流畅性的橄榄球和在经典物理氛围中成长的物理学者从一开始就排斥量子假设的情形非常相似。美式橄榄球革命性地将离散(discrete)的概念引入大球项目，其基本单位"play"和普朗克的"quantum"完全对应。在美国电视上担任橄榄球评论的解说员至少有两个，其中一位就是像宋世雄老师那样的"play-by-play"评球员，另一位就是像张路那样的技术顾问。"play"概念的引入为球类的电视化和商业化铺平了道路，从而使得比赛的计时钟可以随时停下来，而我们知道足球比赛的一个重大缺陷就在于不能因为队员受伤而停钟，即便后来加入的伤停补时(stoppage time)也还是有很多主观性。在橄榄球比赛中每半场3次的暂停(NFL中外加一次公共暂停)是非常重要的，这能体现出主教练的clock management技巧，经常能够影响胜负。换言之，"play"概念的使用大大强化了球类比赛中运用时间的重要性。

（3）"play"概念也大力推进了体育统计学的深入发展。足球比赛中除了进球以外的统计数字少得可怜---像射门次数，角球次数，任意球次数等等需要好几分钟才能更新一次，而美式橄榄球的每一个play就能产生新的统计数字，这是美国文化的一个重要特点---instant gratification。在美式橄榄球中，在实现得分的大目标之前，必须脚踏实地争取完成那些小目标---不断获得向前推进的码数(yardage)，这实在是对人生的一种巧妙模拟。

（4）美式橄榄球队的构成比任何其它球类都要更接近于一个现实生活中的企业，其队员分工之细是无以伦比的。足篮排三大球比赛中的队员分工都是相对的，即便是足球比赛中的守门员在极端情况下也可冲入对方禁区得分。而美式橄榄球中只有极少数有特别才能的运动员可以胜任两个位置。因此橄榄球队的教练员和管理人员尤其需要具备企业家的素质，我们通过观看橄榄球的赛场内外可以悟出在其它球类比赛中无法体会的商战技巧。

（5）美式橄榄球对现代化高科技的运用也是首屈一指。通过无线通讯设备，教练员能够真正体验到在其它球类中无法相比的指挥统帅感觉。近十几年来引入的录像回放(instant replay)实在是球类运动史上的一个里程碑，成功地将裁判员肉眼实时观察所无法避免的误判最小化！而足球比赛中的红牌和点球制度一天不改革，黑哨现象就将是一个无法消除的”制度性毒瘤“ (柏杨在《白话资治通鉴》中对唐朝著名的”玄武门喋血“有类似的评论）。

可以不容置疑地说，美式橄榄球中教练现场指挥的水平和比赛胜负的相关度在所有球类项目中是最高的！如果双方攻防队员的综合实力大体相当，那么最后的赢家一定属于拥有更高智力水平教练的一方。例如新英格兰爱国者队的教练Bill Belichick就被誉为橄榄球场上的Bobby Fischer（美国著名国际象棋一代棋王）。很多情况下教练员在实战指挥中的智慧甚至可以弥补队员实力上的不足。这也是兄弟近年来在球类项目中最喜欢橄榄球的原因，我在电视机前只要看的是自己支持的球队（也就队每一个球员的特点都有所了解）的比赛，就能完全模拟主教练的角色在每一个进攻play之前给出自己的call，通常有以下几种方案：

A. 简单的地面跑动进攻 (straight running attack)
B. 简单的空中传球进攻 (straight passing offense)
C. 似跑实传 (play action pass)
D. 似传实跑 (draw play)
E. Bootleg pass (四分卫将球藏在身后向边线移动，让防守方以为是跑动进攻，自己的跑锋一定要将戏分演足。可以与方案C结合，也可以单独使用，在一个最佳时机发动空中传球进攻）
F. 跳蚤进攻 (flea flicker)

这里只列了比较常见的六种，实战中的变化还有很多。《孙子兵法》中的很多理论都能在美式橄榄球找到对应，尤其是”兵无常势，水无常形“，光是介绍橄榄球中各类攻防阵型大概就得用一篇综述论文的篇幅。研究过博弈论(game theory)的网友可以发现橄榄球中"跑"和"传"两种基本战略提供了一个简单使用的模型，可以用来印证von Neumann和Nash等人的经典理论。

（6）看懂美式橄榄球比赛需要的初期脑力投入远远高于任何其它球类。没有受过教育的人一般都能看懂足篮排三大球比赛，这就像没读过大学本科的学生也能基本了解经典力学。但对于非物理专业只学完普通物理的本科毕业生来讲，绝大多数人对量子物理的理解都处于夹生饭阶段。美式橄榄球的详细规则手册的厚度据说和同样开本的韦氏大词典差不多。CCTV据说在1980年代中期就播过美式橄榄球比赛，但NFL规则的复杂性对该运动在美国以外地区的普及很不利。我们同样很难想象在不久的将来，每一个平均水平的高中生都能基本了解量子力学。但我觉得每一个对自己智力水平非常自信的繁星网友不妨将在多短的时间内看懂美式橄榄球比赛作为一个测试指标，在美国以外的网友可以通过eMule下载一场完整的NFL比赛录像，同时以Wikipedia为工具了解NFL规则，应该能在寒暑假的一个星期内无师自通，呵呵。

多谢站长将本文收入繁星文集。今天下午兴之所致随手写了此文，略微修改后贴到了万维读者网的“竞技沙龙”，没想到反响奇好，居然上了万维首页的导读：

http://www.creaders.net/

国内网友估计进不了万维读者网，那里的众多回帖中有两个颇有见地，在此转一下并略加评论：

-------------------------------------------------------------------------------
复杂和量化并不一定代表更高的境界，即使在科学范畴。

送交者: 孙行土 2006年12月27日15:56:27 于 [竞技沙龙]
回 答: 橄榄球：足球 = 量子物理：经典物理 由 Omni 于 2006年12月27日14:54:24:

复杂和量化并不一定代表更高的境界，　即使在科学范畴。　
比如真正的大师往往可以将复杂的系统以简单明确的方式阐述出来。　切框框定得太紧了，就易少变化，　反而无味。　兵无常势，水无常形。　美式足球的一个大缺点就是分工过细，　相对容易PREDICTABLE，　而导致无味。
-------------------------------------------------------------------------------
送交者: dongcai 2006年12月27日16:05:21 于 [竞技沙龙]
回 答: 复杂和量化并不一定代表更高的境界，即使在科学范畴。

楼上文章有新意，有论据，有逻辑，但可惜忽略了西方文化的一个致命缺点就是分工
过于仔细。某种意义而言是优点，但这个优点迟早是致命伤
-------------------------------------------------------------------------------

我认为分工过细对个人发展而言是缺点，但对团队的运作而言则是优点。而个人的成功通常要依赖于团队的成功，因此个人利益必须服从团队利益。总体而言，分工明确是确保团队成功的“体”，但我们同样鼓励并培养那些在过细分工的前提下依然成为多面手的出色人才！一个经典的例子是NFL历史最伟大的角后卫Deion Sanders:

http://en.wikipedia.org/wiki/Deion_Sanders

他不仅在NFL中是个多面手，既是防守的中流砥柱，又能担任进攻时的接球手，还能客串特别行动队(special team)的回球手(punt and kickoff returner)。最令我叹为观止的是此人还是一个不错的MLB棒球手，这是飞人乔丹也没能进入的联盟！！不仅如此，Deion Sanders还参加过MLB的总决赛World Series，并在其中的一场击出过本垒打，可惜Sanders的球队没能最后赢得MLB的总冠军。他在“主业”NFL中夺得过两枚超级碗总冠军的戒指。我对Deion Sanders的佩服程度自然超过了我对乔丹的景仰。

因此，真正的“牛人”不会被社会分工束缚住手脚，美国社会的分工较细从总体而言是利大于弊。即便是非天才的普通人也可以通过不断改行来拓宽自己个人发展的余地，这就是人们常说的"think outside the box"。只有那些在某一个领域特别出众的人在选择职业上适合“从一而终”，因为他们在其它领域通常无法适应，例如Yau的能力分布曲线据说接近Delta函数，在数学领域取极大值。当然改行的可行性通常受制于养家糊口等种种客观需要，因此这类“求极值问题”也许难免要用到Lagrange Multipliers，呵呵。

【按】限于时间和篇幅，我在正文中没有对“跳蚤进攻”这一战术名词做深入解释。在此转贴一下Wikipedia的有关条目来弥补这个漏洞 ---

http://en.wikipedia.org/wiki/Flea_flicker_%28American_football%29

Flea flicker (American football)

A flea-flicker is an unorthodox play (often called a trick play) in American football. It is designed to fool the defensive team into thinking that a play is a run instead of a pass.

After the snap the quarterback hands off or laterals the football to a running back (or another player on his team), who then runs towards or parallel to the line of scrimmage. Before the running back crosses the line of scrimmage, he laterals the football back to the quarterback, who then looks for an eligible receiver down field to throw a pass to.

If the defensive players think it is just a normal running play, they will leave their defensive positions guarding against the pass to run upfield and cover the running back, leaving the quarterback free from any immediate pass rush, and leaving receivers potentially open to catch a pass.

The flea-flicker is an extremely high-risk play, and the result of it is almost always either a big gain, a turnover, or a big loss. One problem is that it takes a significant amount of time for the play to develop. During that time, the defense might get past the offensive line to tackle the running back before he can make the pitch to the quarterback, or sack the quarterback before he can throw the ball. Then there is also the risk that the running back could fumble if he is hit as he pitches the ball.

Because of these risks the play is rarely used in a game. However, with 32 teams in the NFL, there are usually several instances of the play each season.

Notable Examples

Some flea-flicker plays have been used in many key National Football League games, including the Super Bowl, leading to dramatic results.

* Super Bowl XVII, the Washington Redskins used a flea-flicker to try to fool the Miami Dolphins. However, the Dolphins were not fooled; Miami defensive back Lyle Blackwood intercepted the pass.

* Super Bowl XXI, the New York Giants successfully ran a flea-flicker play against the Denver Broncos: Quarterback Phil Simms passed the ball to receiver Phil McConkey who ran all the way to the Broncos 1-yard line before being tackled for a 44-yard gain. The Giants then scored a touchdown on the next play.

* During a 2005 playoff game against the Cincinnati Bengals, Pittsburgh wide receiver Antwaan Randle El ran the ball almost all the way to the right sideline before lateraling back across the field to quarterback Ben Roethlisberger, who then threw to receiver Cedrick Wilson for a touchdown. This was also a direct snap play.

Trivia

Joe Theismann of the Washington Redskins infamously had his career come to an end on a nationally televised Monday Night Football game at the hands of New York Giants linebacker Lawrence Taylor, after a failed attempt at a flea-flicker which didn’t fool the Giants’ defense. Upon tackling Theismann, Taylor’s entire weight came crashing down on Theismann, severely breaking his leg.

See also

* Football strategy
* Fumblerooski
* Statue of Liberty play

Category: American football plays

http://en.wikipedia.org/wiki/Category:American_football_plays

Let's see if I can get a party for your when you visit. maybe a karaoke contest, with some major local talents, xixi. I've digged up quite a few of your classmates too, including one at a Lhasa hotel.

The Music Tunnel has 5-9pm happy hours that's a real bargain. We'll know how J-town is next weekend.

Go Bills！

yippie，你来纽约的空头支票开了几年了，啥时候兑现啊？

Xixi, Happy Holidays!

My last 2 trips to the east coast were more than 15 hours long due to weather, including the Sept one. :( I am planning to spend much weekend skiing in Tahoe this winter. :) Maybe I'd have some chance in the summer?

Did you know that Chen Z had a major surgery a month or so ago? He had an accident in the summer. I will see Xu Q this weekend at the Karaoke place. Who'd thought he knew so much about pop music?

On the other hand, someone seems to have serious misgivings about the statistical methods Omni applied in his article. Xixi.

Really? Zhang had a surgery? We seldomly hear from him since he moved away from NY area. He will be in the city for the next 2 weeks, we will most likely get together this weekend.

I am not sure football is an improvement of soccer. When everything is so well designed, it takes the fun out of it. If there is no improvised performance, there is no fun. That why soccer is much more enjoyable.

And, football is way too specialized. The 350 pound nose gaurd whose sole purpose in life is to stop another 350 pound guy from another team can hardly be called as an example of athleticism. That's why soccer is a more natural sport. That's also why sometimes college football is more enjoyable than the NFL.

我好像对竞技体育都没什么兴趣，原因是无法参与（近视）。我一直不是很明白为什么很多人自己完全不玩球，却对球赛那么关心。这是不是一种精神寄托。就像是信教一样，不需要理由。

darn, the first back to back losing season since 85/86. congrats

guys! did you see the last play of BSU vs OU? whadagame!

the last trick play was Statue of Liberty! xixixi