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REPRESENTATIONS FOR LOG2 | ||
Log2 | Symbol | Dimensional Representation |
(20=1) | Universal Creative: Great Absolute (taiyi) | Point |
(21=2) | Two Forms (liangyi: yin-yang) | Line |
(22=4) | Four Symbols: Digrams; Five Elements (sixiang; wuxing) | Plane: xy grid |
(23=8) | Eight Trigrams (bagua) | Cube or sphere: xyz grid |
(26=64) | Sixty-four Hexagrams | Space and Time |
Algebraically: (a = yang; b = yin); (see fig. )
2 = (a + b)
1) taiyi: (a + b)0 = 1
2) liangyi: (a + b)1 = a + b
3) sixiang: (a + b)2 = a2 ab + ba + b2
4) bagua: (a + b)3 = (a2 + ab + ba + b2) + (a + b) = (a3 + 3a2b + 3ab2 + b3)
= a3 + a2b + a2b + a2b + ab2 + ab2 + ab2 + b3
5) 64 hexagrams: (a + b)6 = a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6
Evolutionary Representations:
· Symbol (xiang): liangyi, sixiang, bagua
· Philosophy (li): accurate forecasting based on the hexagram images, judgments, and commentaries generated by its contributors
· Number (shu): binary; log 2
Yijing Schools:
· Nili jia (Han Dynasty): emphasized li
· Xiangshu jia (Song Dynasty): researched trigrams and hexagrams and found relationships between mathematical symbol and philosophy; emphasized xiang, shu, and li
· Daojia: used Yijing principles to explain and direct meditation (neidan)
· Chanpu jia: used Yijing principles for divination (predicting the future)
Timeless Hexagrams: Polar Opposite Hexagrams
Timeless hexagrams, or polar opposite hexagrams, establish an axis-grid that distinguishes each hexagram by quadrant. The cardinal hexagrams mimic the cardinal trigrams of the early heaven sequence. Thus, the quadrants established by the timeless hexagrams determine the each hexagram’s location according to the four phases of energy.
1) Heaven (S): Qian
2) Earth (N): Kun
29) The Abyss/Mastering Pitfalls (W):
30) Fire (E): Li
The place where a line is positioned within a symbol (ie. liangyi, sixiang, bagua) is a
Society | Human Body | Human Face | Space-Time | |
1 | Masses | Feet, lower leg | Chin | Length |
2 | Technicians, scientists, skilled workers | Thighs | Cheek | Width |
3 | Bureaucrats, politicians, administrators | Hips, lower abdomen | Nose | Height |
4 | Ministers, advisors | Upper abdomen | Ear | Past |
5 | Leader | Chest | Eye | Present |
6 | Sage, saint | Neck, head | Forehead | Future |
Yin and Yang Lines:
Quality:
· Continuous: yang
· Broken: yin
Number from bottom (inside):
· Odd numbered lines: yang
· Even numbered lines: yin
Most Favorable Lines:
· Lines 2 and 5 (rulers)
· Line 5 < 2 < 4 < 1 < 3 < 6
·
Line Actions:
· Occur from bottom to top
· Principle Action: lines 2, 3, 4 and 5
·
Ruling Line:
· Line 5
· Single yang or yin line amongst 5 lines of opposite polarity
Outside Lines:
· Line 1: considerations before the activity can commence
· Line 6: decline after the peak of activity
·
Line Correspondence:
· 1 ≫ 4 (minister)
· 2 ≫ 5 (ruler)
· 3 ≫ 6
· Favorable: if upper of two corresponding lines is yang and lower is yin; man leading woman
· Neutral: if corresponding lines have same polarity
· Unfavorable: upper line is yin while lower is yang
·
Trigram Lines:
· Lower: earth
· Middle: man
· Upper: heaven
·
Hexagram Lines:
· Lines 1 and 2: earth
· Lines 3 and 4: man
· Lines 5 and 6: heaven
·
·
Trigram Representations:
A hexagram consists of 2 primary and 2 nuclear trigrams that overlap.
Primary Trigrams:
· Upper: lines 4, 5, 6
· Lower: lines 1, 2, 3
·
Nuclear Trigrams:
· Upper: lines 3, 4, 5
· Lower: lines 2, 3, 4
Sources of Interpretation:
Sources of hexagram and line interpretations sprout from indigenous Confucian sociological ideology and Taoist natural philosophy and alchemical practicum.
Hexagram:
· C: Confucius: Humanity (man in the world of man); trigram imagery
· L: Liu Yiming, Translation: Ecology (man in the world of nature)
· E: Liu Yiming, Explantion (Thomas Cleary's paraphrase): Spiritual Alchemy (man in the world of heaven, Tao)
·
Lines:
· L: Liu Yiming Translation
· E: Explanation (my paraphrase of Thomas Cleary’s translation of Liu Yiming's explanation)
Hexagram Interpretations: 1-64
Odd hexagrams are heavenly following their source from Qian, while even hexagrams are earthly following their source from Kun.
Lotus Space ... 2005
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Modern Scientific Interpretation of Evolution & Cosmology

Fig 32: Comparison of the evolution of the universe from the big bang and the evolution of life on Earth shows that life has existed for a full third of the universes lifetime and is a long-term, stable feature of cosmic evolution. Astronomical events, such as asteroid and cometary impacts and nearby supernovae have always played amajor role in causing mass extinctions accompanied by volcanism possibly as a secondary consequence of the impacts themselves. However the advent of so-called human civilization is threatening in the next century to cause a mass extinction more serious than the cretaceous-tertiary event that wiped out the dinosaurs. Theprocess is caused both by direct impacts such as deforestation and habitat destruction and by genetically modifying the very species upon which we depend withoutconserving their naturally viable forms, so that our future becomes brittle and fragile, dependent on maintaining artificial growing environments and high-tech food distribution processes which would be disabled globally by the slightest of astronomical disturbances, leading directly towards human extinction. For a single species to cause a mass extinction of life's diversity, possibly lasting 10million years in one century is thus terminal folly. It is compounded by the ever increasing value biological resources have in the genetic epoch. There is thus a paramount need for us to rediscover our relationship with the cosmos and to take the responsibility to regenerate genetic and biological diversity to sustain our own future generations.

Links: Beyond Darwin - 1 2
Human Family Tree - 10 Adams, 18 Eves

Links:
http://www.nyior.com/acupuncturenewyork-www/Articles/Math_Iching.htm

The title “I Ching” implies three meanings:
1] Simplicity – the fundamental law underlying everything in the universe is plain and simple no matter how complex it may appear to be.
2] Transformation – everything in the universe is continually changing.
3] Persistence – a fundamental principle, a law that does not vary or change in space and time.
There is no documentation on the history of the I Ching. It is known that ancient Chinese scientists and scholars investigated the phenomena in the universe and discovered a commonality of laws and patterns governing all aspects of life. The origins of the I Ching was born from the desire to deduce the future based on knowledge of the natural operation of these laws and patterns which could be determined and predicted objectively.
These laws and patterns were recorded symbolically in a series of solid or broken lines. These solid and broken lines represent the primal energies of qi and the Yin/Yang. The broken line represents the Yin force and the solid represents the Yang force. The basic symbolic unit is a trigram, a combination of the three solid or broken lines. There are eight basic trigrams. By combining two trigrams the hexagram is formed, the total combinations possible is 64. These lines, trigrams, and hexagrams symbolize the forces of action and change and all the phenomena of the universe.
Tradition credits the inventor of the trigrams to Fu Xi, the first of Three Sovereigns who were said to be god-kings or demigods and used their magical powers to improve the lives of their people. It is said that he discovered these symbols carved on the back of a turtle. In ancient China, there was a huge flood. The people tried to offer some sacrifice to the river god of one of the flooding rivers, the Lo River, to calm his anger. Then, there emerged from the water a turtle with a curious figure/pattern on its shell; circular dots of numbers were arranged in a three by three nine-grid pattern such that the sum of the numbers in each row, column and diagonal was the same: 15. This 3x3 pattern later came to be known as a "magic square".
The combination of solid and broke lines forming the trigrams and hexagrams corresponds to the binary system of arithmetic, the same system used in computer programming. This mathematical interpretation was discovered by German philosopher Gottfried Wilhelm Leibnitz (1646-1716) who was the inventor of base-two, or binary arithmetic.
“Leibnitz believed that his mathematical system demonstrated God’s existence: All combinations arise from the Creator and nothing. In other words, God creates everything from nothing. Leibnitz was corresponding with a Jesuit missionary in China, Father Joachim Bouvet at the time. In1701, hoping to entice the Chinese to accept Christianity with his mystical calculations, Leibnitz sent Bouvet a copy of his published work on binary arithmetic. Bouvet recognized a connection between Leibnitz’s system and the I Ching’s symbols and sent him a circular arrangement of the hexagrams composed by Song dynasty philosopher Shao Yong. Remarkably, Yong’s arrangement was a mirror image of Liebnitz’s base-two system from 0 to 63.”[1]
Yin (broken line) = 0
Yang (solid line) = 1
Following the rules of binary arithmetic and reading the trigrams from the bottom line up:
yin/yin/yang = 001 or binary number one
yin/yang/yin = 010 or binary number 2
yin/yang/yang – 011 or binary number 3, etc...
Shao Yang believed “The Supreme Ultimate is a unity which does not move. It produces a duality, and this duality is spirituality. Spirituality produces numbers, the numbers produce emblems (symbols), and the emblems produce implements (things).” [1]
Scholars who have studied the I Ching have discovered similar laws in the science of the Mayan people [2] and in present day physics [3].
[1] The Complete Idiot’s Guide to Feng Shui, Elizabeth Moran and Val Biktashev, Alpha Books, Macmillan Co., NY, pg. 77.
[2] The Mayan Factor - Path Beyond Technology, Jose Arguelles, Bear & Company, Santa Fe, New Mexico.
[3] The Tao of Physics, Fritjof Capra, 3rd ed., Shambhala Publications Inc., Boston.
http://www.miyokographix.com/iching.html
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This is what modern mathematicians call the "octal numbers" and Yi Jing calls "Ba Gua." Both words, "octal" and "Ba", stand for 8.Finally, 8 times 8 equals 64. This requires either 6-digit binary numbers, or 2-digit octal numbers.As it turns out, 6 binary digit numbers are awkward to use. So we use two-digit octal numbers in Yi Jing (Ba Gua).Instead of writing a long list of 64 numbers, it is better to put the numbers in a square with 8 x 8 = 64 cells.The row number represents one octal number, and the column number represents one octal number.
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http://www.chinapage.com/classic/iching/binary.html
![]() | ![]() | ¹퇱 (I-Ching or Book of Changes) is an ancient scripture about natural phenomena and subsequently used for divination. It is now shrouded in mystery mainly because most people pay attention only to those part involving supernatural believe, which helps them to seek fortune and to avoid mis-fortune by randomly picking some sticks and attaching them to some meanings. The followings is an attempt to re-introduce the aspect on the philosophical thinking. It is a good example of the holistic approach to understand the nature and things - the opposition to reductionism so predominant in modern science. |
Figure 01 I-Ching, Authors [view large image] | Figure 02 The 64 Trigrams |
Similar to all academic endeavors, The content in I-Ching is the collective wisdom over many years by many individuals. It is usually only a few or just one of them who would organize all the knowledge into one whole piece. I-Ching is no different in this respect. There are three main contributors quoted up and down the Chinese history.
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Figure 03 I-Ching Patterns [view large image] |
| Event/System | Category | Pattern | High Level | Time Scale |
|---|---|---|---|---|
| Four Seasons | Nature | Regular cycles | Summer | 1 year cycle |
| Stock Exchange | Financial | Irregular cycles | Tops of bull market | Years |
| Global Climate | Geology | Irregular cycles | Warming periods | Millions of years |
| Stellar Evolution | Astronomy | 1 cycle | Main sequence phase | Billions of years |
| Life Span (Human) | Biology | 1 cycle | ~ 25 years old | Tens of years |
| Dynasty | History | 1 cycle | Zenith of prosperity | Hundreds of years |
| Scientific Theories | Physics | Almost constant, subjected to modification | N/A | Close to eternity |
| I-Ching | Philosophy | Near constant, subjected to interpretations | N/A | Eternity in some aspects |
| Pythagorean Theroem | Mathematics | Constant | N/A | Eternity |
![]() | ![]() | Table 01 shows that I-Ching covers a variety fields in a few patterns. While its applicability seems to be unlimited, it fails to provide further detail or insight into the events or systems. Modern holistic method uses non-linear equations to link together many parts such as in the world model (Figure 04), in which many causes (constructive as well as destructive) are considered together via the logistic equations to predict the state of world in the next 200 years. The picture derived from this way is still very general providing only a rough estimate. The methods of reductionism have to be employed to look into the components inside the crude perception in our daily experience. For example, the DNA sequence can be derived only by combining the knowledge from chemistry, biology, and physics (Figure 05). This elaborate way is very |
Figure 04 World Model[view large image] | Figure 05 DNA Sequencing [view large image] | different from the general view of I-Ching. It is not a matter of better or worse - it is just different ways of thinking in different circumstances. |
¶ Turn on the Traditional Chinese (Big 5) encoding in the browser to view the Chinese characters in this page.
http://universe-review.ca/R00-00-IChing.htm
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