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我不可能做到别人要求我做每一件事,我只有足够时间去做我该去做的事情。如果我无法把每件事情都作到尽善尽美,这便意味着我想做的事情已经超过了我该去做。认清了自己的人生坐标,我的生活变得更为简单了,作息安排也更为合理。 魅力由它而生,它是苦难的根源,也是塑造坚强现在的原因。愿意相信别人,能够承担别人的信任,相信别人却是极其艰难的决定。心底的秘密存在于过去,找到那个能接受过去的人,就能有勇气焚毁所有的担心,融化冰封的城堡,让世界大地回春。

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Geek不可不知的9个方程式  

2011-11-06 18:26:44|  分类: message |  标签: |举报 |字号 订阅

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Geek不可不知的9个方程式 - die rose - die rose的博客

身为一个(伪)Geek,只会讲科学家段子怎么行!好好记住这九个公式,让你立刻成为高端Geek。

这世上有那么些方程式会让人感到目眩神迷,哪怕于我们这些绞尽脑汁才能侥幸通过高中代数的人亦是如此。世界的复杂性和不确定性被抽象、升华在秩序井然的数字中。靠着那一把字符,我们就能够把握宇宙自身。

Geek不可不知的9个方程式 - die rose - die rose的博客
For your enjoyment, the Wired Science team has gathered nine of our favorite equations. Some represent the universe; others, the nature of life. One represents the limit of equations.

为了让您也能体会到这种美妙,《连线科学》团队收集了九个我们最爱的方程式。他们中有些为宇宙代言;有的揭露了生命的奥妙;还有一个则为这些方程式定下了边界。
We do advise, however, against getting any of these equations tattooed on your body, much less branded. An equation t-shirt would do just fine.

不管怎样,我们郑重地告诫诸位,千万不要把这些方程式纹到自己身体上,更不要说用火烙了。一件印有方程式的T恤就足够亮骚。

Geek不可不知的9个方程式 - die rose - die rose的博客
Above:
The Beautiful Equation: Euler’s Identity

上图:美丽的欧拉等式
Also called Euler’s relation, or the Euler equation of complex analysis, this bit of mathematics enjoys accolades across geeky disciplines.

欧拉等式,又称欧拉公式,或者是复分析中的欧拉公式。它受到了所有古怪(极客什么的,最古怪了!)学科的崇敬。

Geek不可不知的9个方程式 - die rose - die rose的博客
Swiss mathematician Leonhard Euler first wrote the equality, which links together geometry, algebra, and five of the most essential symbols in math -- 0, 1, i, pi and e -- that are essential tools in scientific work.

瑞士数学家莱昂哈德·欧拉最先写下了这个等式。它将几何和代数,以及五个数学中最为根本的符号——0,1,i,pi和e——联系了起来。在当今的科学工作中,这五个符号是必不可少的工具。
Theoretical physicist Richard Feynman was a huge fan and called it a "jewel" and a “remarkable” formula. Fans today refer to it as “the most beautiful equation."

理论物理学家理查德·费曼是欧拉公式的狂热粉丝。他称欧拉公式为“珠宝”、“精彩绝伦”的公式。今天的粉丝们则称之为“最美的等式”。
The Entire Universe in Figures: Friedmann Equations

纳入了整个宇宙的弗里德曼方程

Geek不可不知的9个方程式 - die rose - die rose的博客
Derived from Einstein’s theory of General Relativity, the two Friedmann equations describe the life of the entire universe, from fiery Big Bang birth to chilly accelerated expansion death.

弗里德曼方程派生自爱因斯坦的广义相对论。这两个方程式描述了整个宇宙的生命历程——由宇宙大爆炸时的暴烈到不断加速膨胀后的死寂。

Geek不可不知的9个方程式 - die rose - die rose的博客
The formulas contain an odd term known as the cosmological constant (the triangle thing with no bottom), initially inserted by Einstein to counteract gravity and keep the universe eternally unchanging. When observations showed that the cosmos was actually expanding, Einstein called this insertion his biggest mistake. Recent experiments have vindicated Einstein, showing that there is a great and mysterious force known as dark energy accelerating the expansion of the universe. Its discovery was the subject of the most recent Nobel Prize in physics, though understanding how it works has thus far eluded scientists.

这组方程式包含了一个奇怪的项,被称为宇宙学常数(符号为没有底边的三角形Λ)。这个常数最早由爱因斯坦引入,用来抵消引力,使得宇宙能保持永远的静态(译者注:这段的意思应该是,爱因斯坦将这个常数添加到了爱因斯坦方程式中,以使方程式有静态宇宙的解)。当有观察显示宇宙实际上是在不断膨胀后,爱因斯坦称之为一生中最大的错误。不过新进的实验表明,在一种强大且神秘的力量——暗能量——的驱动下,宇宙膨胀的速度不断加快,这证明了爱因斯坦的清白。这一发现恰是最近颁发的诺贝尔物理学奖的主题——尽管科学家们对于它的机制依然毫无头绪。

Boltzmann’s Entropy Formula

玻尔兹曼熵方程式

Geek不可不知的9个方程式 - die rose - die rose的博客
Nature loves chaos when it pushes systems toward equilibrium, and geeks call this universal property entropy.

大自然热爱混乱,这让它将一个个系统推向平衡状态。极客们称这一宇宙属性为熵。

Geek不可不知的9个方程式 - die rose - die rose的博客
Austrian physicist Ludwig Boltzmann laid entropy’s statistical foundations; his work was so important that the great physicist Max Planck suggested that his version of Boltzmann’s formula* be engraved on Boltzmann’s tombstone in Vienna (above).

奥地利物理学家路德维希·波尔兹曼为熵奠定了统计学基础。他的成果是如此的重要,以至于伟大的物理学家马克斯·普朗克建议将这个方程式刻在波尔兹曼位于维也纳的墓石上(如图)。
The equation describes the tight relationship between entropy (S), and the myriad ways particles in a system can be arranged (k log W). The last part is tricky. k is Boltzmann's constant and W is the number of microscopic elements of a system (e.g. the momentum and position of individual atoms of gas) in a macroscopic system in a state of balance (e.g., gas sealed in a bottle).

粒子们在系统中可以被无数种方式组织起来(k log W),波尔兹曼的方程式描述了熵(S)与之的紧密联系。这有点难以理解。k是波尔兹曼常量,W指的是,在一个处在平衡状态的宏观系统中(例如,被密封在瓶子中的气体),微观系统的数量(例如,气体中原子的动量和位置)。
Note: Not to be confused with the other Boltzmann equation, which describes how gases or fluids move energy around.

提示:不要跟另一个波尔兹曼方程式弄混淆了。那个描述的是气体或液体如何移动周围的能量。

Electricity and Magnetism: Maxwell’s Equations

电与磁:麦克斯韦方程组

Geek不可不知的9个方程式 - die rose - die rose的博客

图片:The Z machine, 最大的X射线发生器。

Without these four equations, every lolcat on the Internet couldn’t exist. First put together by James Clerk Maxwell in 1861, the formulas describe all known behaviors of electricity and magnetism and show the relationship between the two forces. They state that a moving electric charge will generate a magnetic field while a shifting magnetic field similarly creates an electric field.

没有这四个方程,如今风靡互联网的各种萌图都不会存在。1861年,詹姆斯·克拉克·麦克斯韦将这四个方程放到了一起,解释了电与磁在当时已知的所有行为,并揭示了两者间的联系。它们表明,变化的电荷会产生磁场,变化的磁场同样能够产生电场。

Geek不可不知的9个方程式 - die rose - die rose的博客
The second equation, Gauss’ law for magnetism, also demonstrates a profound difference between electricity and magnetism. While electricity exists as separate charges, like the plus and minus of a battery, magnets always come in a joined pair; you can never break the ‘north’ part of a magnet from the ‘south’ side. Some recent physical models posit that north- or south-less magnets (known as magnetic monopoles) might actually be present in small numbers in the universe, and several experiments are busy searching for their existence.

第二个方程,高斯定理,同样展示了电与磁之间的深刻区别。电可以作为分开的电荷存在,比如说电池的正极与负极,而磁则总是要成双成对地出现。你永远无法将磁“北”极与磁“南”极分开。不过新近的一些物理模型断定宇宙中应当会有少数的磁单极,目前有数个实验正在积极地寻找它们。
Image: The Z machine, largest x-ray generator in the world.

Certain Uncertainty: Schr?dinger Equation

确定的不确定性:薛定谔方程

Geek不可不知的9个方程式 - die rose - die rose的博客

图片:亚原子粒子在氢气泡室中的“鬼”迹。

Erwin Schr?dinger’s famous equation reigns supreme over the smallest objects in the universe. It illustrates how subatomic particles change with time when under the influence of a force. Any particular atom or molecule is described by its wavefunction, the probability of where and when the particle appears, represented by the Greek letter psi.

埃尔文·薛定谔的著名方程统治着这个宇宙中最微小的物体。它解释了亚原子例子如何在某个力的作用下随时间变化。任何具体的原子或分子都可以被它的波动方程描述,它在何处、何时出现的概率,用希腊字母psi表示。

Geek不可不知的9个方程式 - die rose - die rose的博客
Unfortunately, since the early days of quantum mechanics, physicists have been at odds as to how exactly to interpret Schr?dinger’s equation. Some favor the idea that the wavefunction is merely a useful calculation tool but doesn't correspond to anything real. Others say it puts a limit on the amount we can know about the universe, since we only know what state a particle is in once it is measured.

很不幸,在量子力学的早期,物理学家们不知道如何准确地理解薛定谔的方程式。有些人倾向于认为波动方程不过是个有用的计算工具,但并不能与现实有任何对应。另一些人则认为,它为我们对宇宙的认识定下了界限,因为一个例子只有被测量了,我们才能准确知道它的状态。
Schr?dinger himself argued that the wavefunction represented a real, physical object. He disagreed with the a-particle-only-collapses-when-measured interpretation, and his famous cat experiment was actually intended to demonstrate that interpretation's shortcomings.

薛定谔自己则声称,波动方程代表了真实的物理对象。他也不同意那种“只要被测量,粒子就会坍缩”的论调。他著名的薛定谔的猫就是为了展示这种看法的缺陷所在。
Image: The ghostly tracks of subatomic particles in a hydrogen bubble chamber.

All Life Is an Island: Island Biogeography

所有的生命都是孤岛:岛屿生物地理学

Geek不可不知的9个方程式 - die rose - die rose的博客

图片:有报告称,在位于阿肯色州的Cache River野生生物保护区,于一片孤立的沼泽中发现了已经灭绝的象牙喙啄木鸟。

Though physicists can describe the universe's expansion in a few lines, the basic properties of life on Earth are far harder to quantify. During the latter half of the 20th century, biologists arrived at the theory of island biogeography, which described the dynamics of animal populations on islands. At left in this equation is the number of species a given island can support; at right, animal abundances, available areas, and rates of immigration and emigration. The theory has expanded beyond oceanic islands to include many types of ecologies, especially those isolated by human activity. Outside the polar regions, almost all nature now exists in human-defined islands -- and the biggest island of all, of course, is Earth.

物理学家们描述宇宙膨胀只需寥寥数语,但量化地球上的生命的一些基本属性则困难得多。在20世纪的下半叶,生物学家们发展出了一种理论,能够描述岛屿上动物数量的动态——岛屿生物地理学。这个理论还得到了拓展,不单是大洋中的岛屿,各种生态环境——尤其是因人类活动而被孤立的——也被纳入研究范围。除了极地,基本上所有的生物都生存在由人类“定义”的岛屿上——其中最大的,自然就是地球了。

Geek不可不知的9个方程式 - die rose - die rose的博客
Image: The Cache River wildlife preserve in Arksansas, an isolated patch of bottomwoods swamp where the extinct Ivory-Billed Woodpecker was reportedly seen.
The Essence of Evolution: Nowak's Evolvability

进化的本质:诺瓦克的进化性

Geek不可不知的9个方程式 - die rose - die rose的博客

图片:加利福利亚的Mono Lake上的日出。科学家们认为这个高温、缺氧、富含砷的湖与早期地球的环境很像。

At its most basic level, life is what replicates itself -- but how did it begin? It's the ultimate chicken-and-egg problem, and one that scientists studying what's called pre-life try to answer. On the left side of this equation, proposed by Harvard University mathematical biologist Martin Nowak, is a symbol representing all possible strings of molecules; at right are the speed of chemical reactions, the tendency of shorter strings to be more common than longer strings, selection pressures and fitness ratings. As Nowak has shown, all that's necessary for life to emerge are molecules subject to forces of selection and mutation. If those conditions are met, self-replication will emerge with the inexorability of gravity.

在生命的最初级阶段,它不过是在自我复制——但这是如何开始的?这是个终极版本的“鸡生蛋还是蛋生鸡”问题,同时也是一些科学家们研究被称之为“前生命”的东西,所要尝试回答的问题。方程式左边,是一个代表所有可能的分子字符串的符号,它由哈佛大学数学生物学家马丁·诺瓦克提出。方程式右边,是化学反应速度、短字符串比长字符串普遍的趋势、选择的压力和适应等级。如同诺瓦克所阐述的,生命的出现,只需要分子服从选择和变异的力量。如果这些条件满足了,自我复制就会如同苹果会落到地面般不可避免。

Geek不可不知的9个方程式 - die rose - die rose的博客
Image: Sunrise over California's Mono Lake, a hot, oxygen-deprived, arsenic-rich lake that scientists think mimics conditions on early Earth.
The Razor's Edge of Outbreak: R-Nought

雷泽的爆发边际:R0

Geek不可不知的9个方程式 - die rose - die rose的博客

图片:2009猪流感中在墨西哥城搭地铁的人。

Brought to mainstream attention by the thriller Contagion, R0, pronounced R-nought, is a very simple figure: It refers to the average number of people an individual infected with a pathogen will go on to infect. If it's less than one, the disease will burn itself out; if greater than one, it will spread. In a world where a flu virus from Mexico can infect millions of people around the world in a matter of months, this equation is as symbolic as it is straightforward.

R0,读作R-nought,因涉及到可怕的疾病传染性,获得了主流的注意力。R0是个非常简单的数字,它表示某个传染病患者,将疾病传染给其他人的平均数。如果它小于1,这个传染病就会自己消亡;如果它大于1,它就会传播开来。如今一个来自墨西哥的流感病毒在几个月内就能够感染数百万人,这个等式直接了当,具有标志性。

Geek不可不知的9个方程式 - die rose - die rose的博客
Image: Subway riders in Mexico City during the 2009 swine flu outbreak.
Hot or Not: The (Limited) Mathematics of Beauty

性感与否:“美”与数学

Geek不可不知的9个方程式 - die rose - die rose的博客
Not everything can be quantified, especially when it comes to matters of the human heart and mind. For decades, psychologists and biologists have tried to represent physical beauty in formula form; but even if some tendencies emerge when hundreds of individual preferences are measured, what any one individual considers beautiful is impossible to predict.

并非所有事物都能够被量化,特别是当它与人们的心性有关的时候。几十年以来,心理学家和生物学家们都在努力以数学公式来呈现外表的美貌;不过虽然在测量了几百个人的偏好之后,我们能找到一些趋势,但我们依然无法预测,具体的某个人将会对美貌有何高见。

Geek不可不知的9个方程式 - die rose - die rose的博客
At right is an equation from an unpublished attempt by Israeli computer scientists to design a program capable of quantifying the attractiveness of a face. "Y" is the empirical beauty score; at right, various measurements of how different features in a face compared to a baseline face. The program was brilliantly coded, but it didn't work very well.

这个公式来自于一帮以色列计算机科学家设计的程序,它能够将人脸的吸引力量化。“Y”是经验主义的美貌分数;右边,是不同的测量手段得到的该面孔与标准面孔的差异。这个程序乃天才之作,但似乎并不怎么好用。

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