Golden mean—perfect proportion
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?
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?
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.
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?
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.
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.
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.
Proportion is The Greatest Creator. That is to say, the various proportions are arranged by The Greatest Creator.
The wisdom of The Greatest Creator is boundless, just like the circumference ratio Pi, which is endless, enigmatic, and forever infinitely informative.
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.
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.
Now that the square root of -1 does not exist, why is the concept of imaginable number introduced?
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?
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.
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.
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.
Hence we realize that there is imaginary number in addition to real number and that there is nonmaterial world apart from material world.
Hence we come to understand that in addition to the flesh of life there is a spiritual entity.
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.
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?”
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.
Then what is the golden mean Phi?
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?
The ratio of golden mean is 1.61803398874989484821……
Let’s look at another array of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610……
The above figures have a feature, that is, a number is just the sum of the previous two numbers.
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…..
What is the point of this value?
It contains unlimited meanings. One of them is: beauty.
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…
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?
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?
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.
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”
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.
What is harmony? Appropriate proportion is harmony.
What is beauty? Appropriate proportional array is beauty.
Golden mean is the most harmonious and most beautiful of all proportions.
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.
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?
Proportion is a mysterious power in nature that controls the development and changes of everything in the universe.
Who but The Greatest Creator has formulated this proportion?