16、黄金分割

黄金分割——绝美的比例。

Golden mean—perfect proportion

1996年我在坦桑尼亚首都达累斯萨拉姆海边的海市上发现了上百种贝壳,那些贝壳的造型堪称精美绝伦,简直难以想象,尤其是海螺,那种螺旋上升的造型令任何建筑师也望尘莫及,难道贝类生物的大脑比人类的大脑更发达?

In 1996, I discovered hundreds of species of conches in the marine products market by the seaside of Dares Salaam, the capital of Tanzania. Those shells were incomparably and unimaginably beautiful. The spiraling structure of the whelk, in particular, will dwarf the best works of any architect. Is the brain of a shell creature more advanced that that of a man?

后来我观察过向日葵的花盘,发现花盘中籽粒的排列不论是向左看还是向右看都成螺旋线型,不论某个花盘中结多少籽粒,籽粒之间毫不拥挤,我想,难道向日葵的祖先是大学毕业生,仰或获得过博士学位,否则,它的子孙怎能想象出那种绝美的排列顺序?

Later by observing the flower discs of sunflowers, I discovered that the arrays of seeds in the discs take spiral shapes whether they are seen leftward or rightward, and that the seeds are not crowded upon each other no matter how many seeds there are in the discs. I figured the ancestors of sunflowers must have had college education or have obtained doctoral degrees, otherwise how could their offspring have ever thought of so perfect a sequence of arrangement?

再后来我观察太阳系星体的排列,地球的大小与人体及植物的排列,植物生长时树枝的排列及树叶的排列,各种花瓣的排列,各种昆虫头部大小与躯干及爪子的排列,人体五官、四肢与主体的排列等等,等等,发现宇宙大自然中的一切都有一定的比例,而这个比例不是哪个生物体自身控制的,而是“天定”的,也就是说,宇宙中有一个“神秘的力量”在控制着物种个体的发展方向。

Then by observing the arrangement of the celestial bodies in the solar system, the size of the earth, and the arrangement of human body and plants, the arrays of branches and leaves of growing plants, the arrays of different petals, the sizes of various insects and the arrangement of their trunks and legs, and the arrangement of five sense organs, four limbs, and torso of human body, and so on, I discovered that everything in nature has a certain proportion, which is not controlled by an organism itself but predestined by heaven, namely, there is a mysterious power that controls the development direction of an individual organism.

比如人(请你伸开你的手掌观察),为什么手掌上只有5个手指头?为什么中指一定要比其他四指长?为什么拇指不与其它四指并排,为什么小拇指三个指节的长度恰好是无名指两个指节的长度?为什么除拇指外其余四指都有三个骨节,而拇指只有两个骨节?假如小指的长度比中指长,中指比食指短,或者中指再长出一个指节,比食指和无名指长出2厘米,会如何呢?

Take man for example (please open your hand). Why are there only five fingers on the palm? Why is the mid finger longer than the other four fingers? Why the thumb does not stand in line with other four fingers? Why is the total length of the three knuckles of the little finger rightly the total length of two knuckles of the ring finger? Why does the thumb have only two condyles while all other four fingers have three? What will happen if the little finger is longer than the middle finger, the middle finger is shorter than the index finger, or if the middle finger has one more knuckle and is two centimeters longer than the index finger and ring finger?

当然还可以提出万万亿个问题,如,为什么人体的高度几千年来始终保持在1.73米上下?为什么老鼠的眼睛那么小,而马的眼睛那么大?为什么草长不成参天大树?为什么男性的阳具大小与女性的阴道宽深相匹配?等等,等等。

We can raise thousands of trillions of questions. For example, why has the height of man remained at about 1.73 meters for thousands of years? Why are the eyes of mice so small and the eyes of horses so large? Why cannot grass grow up into towering trees? Why does the size of man’s penis match the depth and width of woman’s vagina? So on so forth.

只要我们抓住一个问题,一直追问到底,就不得不承认,一切现象的背后有一个“神秘的力量”,或是“神秘的法则”在支配着一切。

As long as we examine a question thoroughly, we will have to admit that behind every phenomenon there is a mysterious power or enigmatic principle governing everything.

各种事物之间,比如银河系、太阳系、地球、月球、人、狗、鸟、树、草、昆虫、细菌等等之间有一个和谐的比例;各种事物自身各部位之间,比如人体的大小与眼睛、头、嘴、手臂、腿、五脏六腑、血管等等之间有一个和谐的不可逾越的恰如其分的比例。

There is a harmonious proportion between everything, for example, the galaxy, solar system, the earth, the moon, man, dog, bird, tree, grass, insect, bacterium, and so on. There are harmonious, appropriate and insurmountable proportions between the different parts of everything. For example, the size of human body, and its proportions with eyes, head, mouth, arms, legs, five internal organs, and blood vessels.

比例就是上帝。就是说,各种比例是上帝的智慧安排。

Proportion is The Greatest Creator. That is to say, the various proportions are arranged by The Greatest Creator.

上帝的智慧是无穷的,就象圆周率Pi,永远是无穷无尽的,是神秘难测的,永远有无限的信息。

The wisdom of The Greatest Creator is boundless, just like the circumference ratio Pi, which is endless, enigmatic, and forever infinitely informative.

人类发现了圆周率,就认识到了上帝智慧的博大精深,就明白了物质世界有无穷无尽的奥秘,不得不对大自然的神奇奥妙而感到惊讶和震撼,对生命有一个无限的未来而感到心神激荡,对有一个美好的未来而心驰神往。

With the discovery of circumference ratio, man has realized The Greatest Creator’s extensive and profound wisdom, and the endless mystery of the material world. Man cannot but feel thrilled and enthralled by the wonder and profundity of Mother Nature, spellbound by the infinite future of life, and fascinated by the wonderful future.

人类的智慧也是无限的,人类又发现了一个秘密——虚数i,虚数就是-1的平方根。-1有平方根吗?乘法的符号规则是:正正得正,负负也得正,任何数的平方均为正数,那么,-1的平方根就根本不存在。

Man’s wisdom is also endless. Man has discovered another secret—imaginary number i, the square root of -1. Does -1 have a square root? The rule sign of multiplication is: two positives make a positive, and two negatives also make a positive, and the square of any number is a positive number. Then the square root of -1 does not exist at all.

既然根本不存在,为什么又要引出一个虚数概念呢?

Now that the square root of -1 does not exist, why is the concept of imaginable number introduced?

当科学发展到量子力学的时候,爱因斯坦都迷惑不解了,他认为宇宙是有序的,一切事物只要知道它的现状,就能了解它未来的发展和变化。而量子力学说:“测不准。”因为小粒子的位置测的越精确,它的速度就“测不准”,若小粒子的速度测准了,它的位置就“测不准”。是吗?

When science enters the period of quantum mechanics, even Einstein became puzzled, because he thought that the universe is orderly and that the future development and changes of anything are predictable as long as the current status is known. However, quantum mechanics put forward the theory that “accurate measurement is impossible”. The more accurate the measurement of the position of a small particle, the less accurate the measurement of its speed, and if the speed of a small particle is accurately measured, the measurement of its position will not be accurate. Is it so?

量子力学中的波函数如何表示?没有虚数的参与,就建立不起复平面,没有复平面,就不知道什么是复数,没有复数,波函数就无法表示。

What is the expression of wave function of quantum mechanics? Without imaginable numbers, there would be no complex plane; without complex plane, there would be no complex number; without complex number, wave function can not be expressed.

当我们深入到微观世界深层次的时候,就发现虚数这个看似“虚无缥缈”的东西是自然规律的一种反映,“虚无缥缈”的东西,人们认为不可能的东西实质上却起着至关重要的作用。

When we probe deeper into the microscopic world, we will see that the seemingly illusory imaginable number has actually reflected natural laws. The illusory thing, regarded as impossible by people, actually plays a critical role.

由此我们认识到,上帝这个“虚无缥缈”的力量,不是存在不存在的问题,而是决定着一切事物发展变化的决定性因素。

Hence we come to realize that, instead of a question of existence or not, the “illusory” power of The Greatest Creator is actually a decisive factor which determines the development and change of everything.

由此我们认识到,实数之外有虚数,物质世界之外还有一个反物质世界。

Hence we realize that there is imaginary number in addition to real number and that there is nonmaterial world apart from material world.

由此我们认识到,生命体除了肉体之外,还有一个灵体的存在。

Hence we come to understand that in addition to the flesh of life there is a spiritual entity.

由此我们认识到,时间不仅仅是纵向的,还有横向的时间,也就是说,对物质世界而言,时间是纵向的,但对“虚无缥缈”的反物质世界而言,时间却是横向的,具体到人,人的肉体的时间是纵向的,有过去,有现在,有未来,有生,有死,但人的灵体的时间是横向的,灵体在任何时间点上都可以离开肉体进入横向时间之内。

And we come to understand that time is not only longitudinal but also transverse. That is, for material world time is longitudinal but transverse for the “illusory” nonmaterial world. As far as man is concerned, the time of man’s flesh is longitudinal, with the past, the present, the future, the birth and the death. But the spiritual entity of man is transverse, and at any point of time the spiritual entity can leave the flesh and enter the transverse time.

物质世界中的正数和负数可以构成一个函数,在这个函数中有4个象限(区域),如果我们现在把虚数加进去,就构成了一个复函数,这个复函数却有16个象限(区域)。请问自己:“我的生命现在处在哪个象限中?”

The positive and negative numbers of the material world can form a function. Such a function has four quadrants (areas). If we include the imaginary numbers into the function, we will have a complex function. A complex function has 16 quadrants (areas). Ask yourself please, “Which quadrant is my life in at present?”

本节的主要目的是探讨自然界的比例,在所有的比例中,人们发现了一个特殊的比例,那就是黄金分割,黄金分割(Phi)是继圆周率Pi,虚数i之后的又一个自然奥秘。

The main purpose of this section is to explore the proportions in nature. Of all the proportions, people have found a special proportion—golden mean, another secret of nature after the circumference ratio Pi and the imaginary number i.

那么什么是黄金分割Phi呢?

Then what is the golden mean Phi?

以人体为例,若身长与脚底板到肚脐眼的长度比值等于脚底板到肚脐眼的长度与肚脐眼到头顶的长度比值,那么,这个比例就叫黄金分割。这个比值是多少呢?

Take human body for example. If the ratio of height and the length from sole to navel equals the ratio of sole to navel and from navel to top, then the proportion is golden mean. What’s the proportion?

黄金分割的比值是1.61803398874989484821……

The ratio of golden mean is 1.61803398874989484821……

再看一种数字排列,0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610……

Let’s look at another array of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610……

以上数字有一个特征,那就是某个数恰好是前两个数之和.

The above figures have a feature, that is, a number is just the sum of the previous two numbers.

这个数字排列中,每一个数被前一个数整除,就会得到以下数字:1,2,1.5,1.666,1.6,1.625,1.61538,,1.619,1.6176,1.61818…,1.61797…,1.61805…,1.61802…,1.61803…,1.61803…,1.61803…继续下去,其值趋向为1.61803398874989484821…..

If each number of this array is divided by the number before it, we can derive the following numbers: 1,2,1.5,1.666,1.6,1.625,1.61538,1.619,1.6176,1.61818…,1.61797…,1.61805…, .61802…,1.61803…,1.61803…,1.61803… If we continue the process, the value tends to be1.61803398874989484821…..

这个比值有什么意义吗?

What is the point of this value?

它有无限多的涵义。其中的一个含义是:美。

It contains unlimited meanings. One of them is: beauty.

本节开头谈到的贝壳,特别是海螺,它精美绝伦,为什么?因为它是按照黄金分割的比值发展的;鲜花为什么令人赏心悦目,因为它们是沿着黄金分割生长的; 植物的种子之间为什么不互相“打架”?因为它们是按照黄金分割排列的;有些人为什么看起来非常俊美?因为她们的身材处处体现着黄金分割;为什么乐器能奏出美妙的旋律,因为乐曲的弦和曲调接近黄金分割的比例;为什么有些建筑物很协调,令人舒畅,因为这些建筑物的布局是以黄金分割来设计建造的……

Why are the conches mentioned earlier in this section incomparably beautiful? It is because they have developed according to the ration of golden mean. Why are flowers so pleasing to the eyes? Because they have grown according to golden mean. Why don’t the seeds of plants “fight with each other”? Because they are arranged according to golden mean. Why do some people look so pretty? Because every part of their figures reflects golden mean. Why can musical instruments play melodious tunes? Because the chords of the instruments and the melodies approximate golden mean. Why do some architectures look so harmonious and comfortable? Because the layout of these buildings have been designed according to golden mean…

试想,一个人的脖子象长颈鹿的脖子,或一个人的眼睛象老鼠的眼睛,或两只胳膊比猿猴的胳膊还长,美吗?

Will you think it is beautiful if a person has the neck of a giraffe, the eyes of a mouse, or the arms longer even than those of an ape?

在四周围的房子都是8米高的地方,突然盖出一个80米高的楼房,或者在高楼林立的地方盖一个5米高的平房,会和谐吗?

Will it be harmonious if an eighty-meter building is built among the eight-meter houses or if a five-meter bungalow is built among clusters of high buildings?

在农村长大的人知道,若一个村庄所有村民的住房都是低矮的平房,假若有人突发奇想,建造出一座三层高的楼房,这家人必定要倒霉。美国世界贸易大厦被炸,表面上似乎是恐怖分子所为,实际上与它的高度有关。同理,在一个高楼林立的地区内,经常住在一个平房中,你将被受到压抑,你包括你的子女就别想有所发展。

People growing up in the countryside know that if all villagers live in low bungalows and someone builds a three-storey building on a whim, this person is sure to suffer bad luck. Why was America’s World Trade Center blasted off? Seemingly it was destroyed by terrorists, but actually the destruction has something to do with its height. Similarly, if you live in a bungalow in an area surrounded by high buildings, you will feel depressed, and you and your children will have little chances of development.

经常在电视中看到评委们给参选人打分,“去掉一个最高分,去掉一个最低分,真优美子的得分为…”

We often see judges give scores for contestants on television, “the final score for Zhen You Mei Zi is … after crossing out the highest point and the lowest score”

为什么要取掉最高分和最低分?因为这个最高分和最低分有问题,因为它不协调,因为它走到了极端。两极相通,物极必反。任何事物它必须要在一定的比例之内发展,它必须要与周围事物相协调,超过了这个比例范围,它就不美了,就不协调了,不和谐了。

Why should the highest and lowest scores be crossed out? It is because they are problematic, discordant and extreme. Things always reverse themselves after reaching an extreme. Everything must develop within a certain proportion, and must be agreeable with its surroundings. If the range of proportions is exceeded, it is no longer beautiful and harmonious.

什么叫和谐?恰如其分的比例叫和谐。

What is harmony? Appropriate proportion is harmony.

什么叫美?恰如其分的比例排列叫美。

What is beauty? Appropriate proportional array is beauty.

黄金分割是一切比例中最和谐、最美的比例。

Golden mean is the most harmonious and most beautiful of all proportions.

一切事物的发展都受比例的制约。美国要成为世界强国,它必须要救助贫穷的国家,不能强的太过头,否则,必然要受到自然规律的惩罚;一个贫穷落后的国家,必须要奋起前进,否则,就会必然走向灭亡。

The development of everything is controlled by proportion. America should help the poor countries if it wants to become the world power. It should not be overly powerful; otherwise it will be punished by natural laws. A poor and backward nation should strive forward, otherwise it will perish.

人类也一样,如果人口的数量增加到与其他动植物的数量比例不协调的时候,就象一棵树的某一个枝子急剧生长,那么,这个树枝到一定的时候不是自身折断,就是会把树拉倒,甚至要连根拔起来,当然,既然比例后面有一股“神秘的力量”,或叫“自然法则”在支配着比例的协调,那么,急剧膨胀的人口必然要受到发展限制,如果人类自身能控制,那是再好不过的,如果控制不了,那就要用自然的力量了,比如,战争、地震、水灾、火灾、瘟疫、饥谨、炎热等等办法降低人口数量。2003年突发的萨斯病毒难道不是大自然向人类敲响的警钟吗?

This is also the case with human being. If the population has increased to such an extent that it has lost harmony with the number of plants and other animals, there will be no way to sustain the continuous growth, just like a rapidly growing branch of a tree. If the branch does not break off, it will pull down or even uproot the tree. Since there is a mysterious power or law of nature to govern the harmony of proportions, the exploding population will certainly be controlled. If man can exercise the control by himself, so much the better. If population cannot be brought under control, then the power of nature will play its role. For example, wars, earthquakes, flood, fire, plague, famine, and torridity can all play their roles in reducing the population. Isn’t the outbreak of SARS in 2003 an alarm bell knocked by nature for mankind?

比例是自然界的一个神秘力量,比例控制着宇宙中一切事物的发展和变化。

Proportion is a mysterious power in nature that controls the development and changes of everything in the universe.

那么,这个比例是谁制订的?难道不是上帝吗!

Who but The Greatest Creator has formulated this proportion?

发布者:Jena Wang

I am Jena from China. I was a resident living in Chinese Largest Ecovillage —New Oasis for Life Community. I like ecovillages life mode. I am also interested in spiritual articles. Here I just share the Greatest Creator's love to me and my personal daily life. Hope you can enjoy my blog, thank you for reading.

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