Natural logarithm is also called hyperbolic logarithm. Take the transcendental number [fc (] e =1+11! + 12! + 13! +… = 2 765 438+0828 … [fc]] is the logarithm of the base. Represented by the symbol "l n", there is a natural logarithm table to check. When x approaches positive infinity or negative infinity, the limit of [1+( 1/x)] X is equal to e, which is actually discovered through this limit. It is an infinite cyclic decimal. Its value is approximately equal to 2.7 1828 1828 ... It uses e to represent the logarithm based on e, which is usually used for ㏑, and e is also a transcendental number. E is widely used in science and technology. Generally, logarithm based on 10 is not used. Taking e as the base can simplify many formulas, and it is the most "natural", so it is called "natural logarithm" Vortex or spiral is a very common form of natural things, such as: a wisp of smoke curling up, ripples swaying gently on the blue lake, several snails slowly climbing the fence and countless stars dancing in the quiet night sky ... The aesthetic significance of spiral, especially logarithmic spiral, can be expressed in exponential form: φkρ=αe, where α and k are constants, φ is the polar angle and ρ is the polar diameter. For the convenience of discussion, we define e or the form composed of e as "natural law" Therefore, the core of "natural law" is E, and its value is 2.7 1828 ... This is an infinite cyclic number. The beauty of "natural law" "natural law" is the form of E and E after some transformation and recombination. E is the essence of "the law of nature", and it is a function mathematically: (1+ 1/x) x is the limit when it approaches infinity. People should study the power of (1+1/x) and the limit when x approaches infinity when studying some practical problems, such as the cooling of objects, the reproduction of cells and the decay of radioactive elements. It is this finiteness obtained from infinite change that develops from two opposite directions (when X tends to positive infinity, the limit of the above formula is equal to E = 2.7 1828 ..., and when X tends to negative infinity, the result of the above formula is also equal to E = 2.7 1828 ...), which fully embodies the formation of the universe. Modern cosmology shows that the universe originated from the Big Bang and is still expanding. This description is consistent with the entropy law, that is, the second law of thermodynamics, which is one of the two great discoveries in the second half of19th century. The law of entropy points out that the evolution of matter is always in the direction of destroying information and disintegrating order, and gradually degenerates from complex to simple and from high to low. The limit of degradation is disorderly balance, that is, the state of maximum entropy, a state of inaction and death. What is this process like? It is not difficult to understand just by looking at the photos of spiral galaxies in astrophotography. If we must find the motive force that Aristotle said, then we can regard the universe as a clockwork mechanism that is wound up in advance, or simply regard the whole universe as a huge clockwork. History is just the process of this clockwork constantly striving for freedom and releasing energy. The evolution of organisms has opposite characteristics, which is very different from the entropy described by the second law of thermodynamics. It enables organisms to avoid the decline of trends and environment. Any life is a dissipative structure system, and the reason why it can avoid the death state approaching the maximum entropy is because life can continuously absorb negative entropy from the environment through metabolic processes such as eating, drinking and breathing. The essence of metabolism is to let the organism successfully eliminate all the entropy it has to produce when it is alive. On the one hand, the "law of nature" embodies the collapse process of natural systems in the direction of chaos (such as the decay of elements), on the other hand, it shows the essence that life systems can maintain their stability and promote their development (such as cell reproduction) only through an orderly process. It is precisely because of this feature that order and disorder, life and death are in the same form, and "natural law" has important aesthetic value. If the barren desert is the entropy increasing state of "natural law" in disorder and death, then the vast and vibrant grassland is the dynamic and stable structure of "natural law" in order and prosperity. Therefore, the desert makes people feel solemn, boundless and thought-provoking, reminding people of all kinds of difficulties and bumps in the course of life; Grassland, on the other hand, makes people excited, happy and feel the joy and happiness of life. E = 2.7 1828 ... is a quantitative expression of "natural law". The image expression of "natural law" is a spiral. There are five mathematical expressions of spiral: (1) logarithmic spiral; (2) Archimedes spiral; (3) interlocking helix; (4) Hyperbolic spiral; (5) spiral. Logarithmic spiral is the most common spiral in nature, and other spirals are also related to logarithmic spiral, but at present we have not found the general formula of spiral. The logarithmic spiral was introduced by Descartes in 1638. Later, Swiss mathematician Jacob Bernoulli made a detailed study on it, and found that the involute and extension line of logarithmic spiral are still logarithmic spiral, and the tangent of each point and pole of logarithmic spiral is still logarithmic spiral, and so on. Bernoulli was surprised by these interesting properties and left a will on his tombstone to draw a logarithmic spiral. Willianm Hogarth, a famous British painter and art theorist, deeply felt that spirals or spirals gradually narrowed towards their centers, which were all beautiful shapes. In fact, we can easily find the spiral in the works of ancient and modern artists. Why can our feelings, our "spiritual" eyes, often be satisfied instinctively and intuitively from such a spiral form? Doesn't this mean that there is a more primitive isomorphic correspondence between our spirit, our "inner" world and the external world than history? As we know, protein, as the basic substance of life phenomenon, participates in all the work of life process in life, and its function is so complex, efficient and mysterious that it is closely related to its structure. Chemists found that protein's titanium chain is mainly spiral, and the nucleic acid structure that determines heredity is also spiral. The ancient Greeks had a musical instrument called Feng Qin Ming. When its strings vibrate in the wind, it can make a beautiful tone. This tone is called "vortex tail effect". It is thought-provoking that the inner ear structure, an auditory organ formed by human beings through long-term evolution, also has a vortex shape. Is this for the convenience of enjoying the ancient Greek wind chimes? And our fingerprints, hair clips, etc. The physiological structure of this aesthetic subject corresponds to the isomorphism of the external world and is the natural basis for the harmony between "inside" and "outside". Some people say that the beauty of mathematics is the brilliance of "one", which is invariant under the action of as many transformation groups as possible, that is, it is the expression of the universal law of nature and the unity of "many" and "one", so "natural law" also flashes the brilliance of "one". Who can say how much convenience and success E = 2.7 1828 ... have brought to mathematicians? People praise the rigidity, clarity and truthfulness of straight lines and appreciate the beauty, change and implication of curves, but they don't know that any straight line and curve can be composed of enough parts on the spiral. Some people say that beauty is the unity of subject and object, the unity of inner spiritual world and outer material world, so "natural law" also has this unity. Human understanding develops according to the law of negation of negation, and the history of society and nature also follows this dialectical development law. What gives this form a vivid expression? Spiral! Some people say that beauty lies in the rhythm of things, and the "laws of nature" also have this rhythm; Some people say that beauty is a dynamic balance and eternal change, so "natural law" is also a dynamic balance and eternal change; Some people say that beauty lies in the dynamic structure of things, so the "laws of nature" also have this structure-such as hairspring in watches, clockwork in machines and so on. "Natural law" is the unity of formal reasons and dynamic reasons, the image expression of things, and the same expression of concrete and abstract. Limited life is rooted in infinite nature, and the pulse of life consciously adjusts its movement and rhythm according to the melody of the universe ... organic and inorganic, internal and external, social and natural, and all things are one. Is this all the aesthetic mystery revealed by the "laws of nature"? Don't! "Natural law" always has endless aesthetic connotation, because it symbolizes the vast and profound nature. Because of this, it attracts people worthy of unremitting exploration, thus showing the essential power of human evolution. (originally published in the fourth issue of Science Spring, 1984, Original title: the laws of nature-the treasure of aesthetes and artists) Attachment: This is two digits after the decimal point: E =: 2.7182818284 59045 23536 02874 71352 66249 77572 47093 69995 95. 3 82 178 525 16 64274 27466 39 193 20030 5992 1 8 174 1 35966 29043 57290 03342 95260 59563 0738 1 32328 62794 34907 63233 82988 0753 1 9525 1 0 190 1 15738 34 187 93070 2 1540 89 1 49 93488 4 1675 09244 76 146 06680 82264 800 16 84774 1 1853 74234 54424 37 107 53907 77449 92069 55 / kloc-0/70 276 18 38606 26 133 1 3845 83000 75204 49338 26560 29760 6737 1 13200 70932 8709 1 27443 74704 72306 96977 2093 1 0 14 16 92836 8 1902 55 15 1 08657 46377 2 1 1 1 2 52389 78442 50569 53696 77078 54499 69967 94686 44549 05987 93 163 68892 30098 793 12 773 6 1 782 15 42499 92295 7635 / kloc-0/ 48220 82698 95 193 66803 3 1825 28869 39849 6465 1 05820 93923 98294 88793 32036 25094 4365 438+0 17 30 1 23 8 1970 684 16 14039 70 198 37679 32068 32823 76464 80429 53 1 18 02328 78250 98 1 94 55865 438+05 30 175 67 173 6 1332 0698 1 12509 96 18 1 88 159 304 16 9035 1 59888 85 193 45807 27386 67385 89422 87922 84998 92086 80582 57492 796 10 484 19 84443 63463 24496 84875 60233 62482 704 / kloc-0/9 78623 20900 2 1609 90235 30436 9 94 18 49 146 3 1409 343 17 38 143 64054 6253 1 52096 / kloc-0/8369 08887 070 16 76839 64243 78 140 5927 1 45 635 4906 1 303 10 72085 10383 7505 1 0 / kloc-0/ 157 47704 17 189 86 106 87396 96552 1267 1 54688 957 03 50354 02 123 40784 98 1 93 3432 1 068 17 0 12 10 05627 88023 5 1930 33224 7450 1 58539 04730 4 1995 7777 0 93503 6604 / kloc-0/ 69973 29725 08868 76966 40355 5707 1 62268 447 16 25607 98826 5 1787 134 19 5 1246 6520 1 03059 2 1236 677 19 43252 78675 39855 89448 96970 96409 75459 18569 56380 23637 0 162 1 1 2047 74272 28364 896 13 422565 438+0 64450 78 182 44235 29486 36372 14 174 02388 9344 1 24796 35743 70263 75529 44483 37998 0 16 12 54922 78509 25778 2 5620 92622 64832 62779 33386 56648 16277 25 164 0 / kloc-0/9 10 59004 9 1644 99828 93 150 56604 72580 27786 3 1864 15 5 19 56532 44258 69829 46959 3080 / kloc-0/ 9 1529 872 1 1 72556 34754 63964 479 10 14590 40905 86298 49679 12874 068 70 50489 58586 7 / kloc-0/747 98546 67757 57320 568 12 88459 2054 1 33405 39220 00 1 13 78630 09455 60688 16674 00 1 69 8420 5 58040 33637 95376 45203 04024 32256 6 1352 78369 5 1 177 88386 38744 39662 53224 98506 54995 88623 428 1 8 99707 73327 6 1765 438+07 83928 03494 650 14 34558 89707 19425 86398 77275 47 109 62953 74 152 1 / kloc-0/ 15 1 36835 06275 26023 26484 72870 39207 643 10 05958 4 1 166 12054 52970 30236 47254 92966 6938 / kloc-0/ 15 137 32275 36450 98889 03 136 02057 2 48 17 6585 1 18063 03644 28 123 1 4965 50704 75 102 54465 0 1 172 72 1 15 55 194 86685 08003 68 532 28 183 152 1 9 60037 35625 27944 95 158 284 18 82947 876 10 85263 98 139