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Wind and water: Feng Shui as complexity science

December 2018

Project: A Future State of Medicine: Tao, Big Data, and Chinese Medicine

Authors:

Long Island University

Preprints and early-stage research may not have been peer reviewed yet.

This paper explores the underlying information system of Chinese Feng Shui, translated literally as "wind and water," and compares and contrasts it with theories of complexity science, quantum mechanics, and systems science.

Yin and Yang Expressed as the Tai Chi symbol.

…

Yin and Yang Expressed as a daily cycle (Aarons, 2004).

…

Figures - uploaded by David Mainenti

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Content uploaded by David Mainenti

Content may be subject to copyright.

INFORMATION STUDIES │ INFORMATION SYSTEMS

Windandwater:fengshuiascomplexityscience

By DAVID MAINENTI DEC 21, 2018 DIS815

1. INTRODUCTION

As a new era of big data leads us towards Jim

Gray’s Fourth Paradigm1 of science, away from

computing and towards exploratory techniques

where theory ends and the scientific method

possibly becomes obsolete (Kitchin, 2014),

ancient systems of natural living hold the

potential to minimize and/or eradicate

difficulties and problems around the globe for

generations to come. For over 5,000 years, the

classical Chinese arts of acupuncture, herbal

medicine, qi gong, tui na, astrology, chiromancy,

and feng shui have been practiced as forms of

“medicine” in that they seek to channel or alter

natural processes for the purposes of curing

illness and achieving overall well-being (Seaman,

1992). Amazingly, these classical protocols all lie

above a singular, albeit complex, information

system based on Chinese cosmological theories

(Porkert, 1974) that were put into place well

before the invention of the written record. Until

recently, these cosmological medical practices

have been debated by scientists because they

share the troublesome characteristic that the

physiological structures at the root of the cures

are not always visible to Western techniques of

scientific observation (Lu & Needham, 1980).

Further complicating matters, the underlying

system is based on the fact that the fate of

individuals is derived from a human nature

linked to an all-encompassing, astrobiological

conceptualization of life (Wheatley, 1971). Yet,



1Jim Grey, a database software pioneer and Microsoft

researcher, sketched out an argument in 2007 that

computing was fundamentally transforming the practice

of science. The first three paradigms were experimental,

theoretical, and, more recently, computational science.

The fourth paradigm of discovery is based on data-

intensive science using databases, workflow management,

visualization, and cloud computing technologies.

like the Dewey Decimal System2 representing the

ordering of the books, rather than the bound

physical specimens themselves, this classical

Chinese medical system that includes feng shui at

its core was cleverly designed to evolve

holistically over time, a complexity science used

to assist humankind in understanding changes in

nature and how they affect our bodies, relatives,

friends, co-workers, and dwelling spaces. Can

such a seemingly powerful system be integrated

with artificial intelligence and big data analytics

to usher in a future state of existence?

2. BACKGROUND

At some point during the 1st millennium BC,

ancient Chinese sages developed, or adopted

from other civilizations, an intricate system of

innovative ideas pertaining to disease: the

concept that evil forces played a decisive role in

the prevalence of illness (Unschuld, 1980). In

response to this, a medicine of systematic

correspondence was created out of two related,

yet sometimes paradoxical, concepts: the yin yang

and five phases doctrines (Unschuld, 1986).

Ultimately, both concepts merged into a singular

structure, based on commonalities established in

the most classic of all Chinese scholarship works

from antiquity: the Yi Jing or Book of Changes. By

medieval times, Chinese scholars had forged a

comprehensive worldview based on the macro-

micro view that man mirrored in himself the

whole, believing physiological and pathological

2The Dewey Decimal Classification System is a library

classification system introduced by Melvil Dewey in 1876;

it introduces the concepts of relative location and relative

index, which allows for books to be catalogued in a

library, in their appropriate location, based on subject.

2

practices were greatly influenced by cyclic

astronomical, meteorological, climatic and

epidemiological factors (Lu & Needham, 1980).

Similar to acupuncture, and traditional Chinese

medicine as a whole, feng shui’s foundation lies

within this macro-micro doctrine. The premise

of feng shui is that rhythms and structures of the

earth parallel those of the human body, and

alterations of the earth bring about repercussions

upon individual human beings and the natural

environment (Feuchtwang, 1974).

Early skepticism of the system from the West

(Dukes, 1885; de Groot, 1897; Sarton, 1927)

arose from the belief that geomancy, as a whole,

was to blame for difficulties in promoting, in

China, Christianity, capitalism, and the natural

sciences (March, 1968). Yet others view it as a

beautiful astronomical, astrological, geomantic,

and horoscopic divinatory system, a type of

primitive classification, with a history going back

to the most distant times, governing all details of

life among the most immense population that

humanity has ever known; a system itself

composed of a number of intermingled systems,

dividing space, things, events, and time,

connecting everything together in the process

(Durkheim & Mauss, 1963). Jung (1950) even

stated “the ancient Chinese contemplate the

cosmos in a way comparable to that of the

modern physicist, who cannot deny that this

model of the world is decided by psycho-physical

structure.”

Most agree that feng shui has its place in the

classical literature of anthropology; however,

there is still much skepticism with how the

Chinese view a building, a grave site, or their own

bodies as intervening with the universe, bonded

to their physical environment, “working good or

ill upon it and being done good or ill by it”

(Freedman, 1968). For some, feng shui embodies

the image of a magical and personified nature; a

practice that rivals environmental determinism in

the West. In many ways, this was the basis of

Chinese objection to Western intrusion and

technology, along with the Westernization of

Chinese landscape, for, as they saw it,

Westerners, having no knowledge of feng shui,

destroyed the vulnerable geomantic harmony of

their land (Yoon, 1980). Feng shui functions as a

quasi-scientific and quasi-religious Chinese art

based on the concept that humans can only

benefit from nature when they are in harmony

with it, and the boundary between humans and

nature is left purposely unclear to allow for active

participation in the realization of latent man-

nature relationships (Yoon, 1982).

Many modern scholars remain perplexed as to

how a magical system of living in harmony with

environmental elements based on the flow of a

supernatural electricity called qi can still be

readily practiced by millions of people in

concrete, capitalistic modern cities across the

globe (Emmons, 1992), and yet feng shui has been

studied in relation to numerous modern

industries, including, but not limited to,

accounting (Gao & Handley-Schachler, 2003),

tourism (Buzinde et al., 2012), real estate

(Bourassa & Peng, 1999; Salleh et al., 2015),

historical geography (Lai, 1974), hospitality

(Ogilvie, 2018), urban planning (Madeddu &

Zhang, 2017), cultural studies (Marafa, 2003),

communications (Chen, 2007), health care

(Blum, 2004), computer science (Sridharan et al.,

2013) and architecture (Mak & Ng, 2005). Even

still, most view feng shui as a narrow, ritualistic

practice for either buying homes or selecting

burial sites, seemingly having returned to life,

along with the proliferation of new religions, in

reaction to modern nihilism (Hwangbo, 1999).

Langdon (1991) poses possibly the best bridge

into complexity science and big data analytics,

calling feng shui a cross between art and science,

or a pseudoscience, because, although it employs

meticulously gathered facts from nature, it does

not analyze them with modern scientific

procedures.

Complex adaptive systems are collections of

individual agents with freedom to act in ways that

are not always totally predictable, and whose

actions are interconnected in such a way that one

3

agent's actions may or may not affect the

experience of other agents (Plsek & Greenhalgh,

2001). Oftentimes within unclear boundaries,

agents respond to their environments by using a

set of internalized rules that drive action – rules

that need not be shared, explicit, or even logical

when viewed by another agent (Stich, 1990).

Because the agents can change, a complex system

can, and most often will, adapt its behavior over

time, for better or worse, depending on whose

point of view is being considered (Holland,

1995). Complex systems are commonly

embedded in other systems that are a part of a

larger system and, as they evolve, such related

systems are influenced, meaning that one cannot

fully understand any of the agents or systems

without referencing the others (Hurst &

Zimmerman, 1994). This interaction often leads

to tensions and paradoxes; while conventional

reductionist scientific thinking assumes

everything can eventually be figured out,

complexity science is comfortable and

sometimes holds in high regard such differences

(Axelrod, 1997).

Complex behavior within the arena of quantum-

mechanical laws of physics emerges from this

interaction among influential agents; for

example, the physical evolution of the universe,

operating in accordance with laws, has produced,

scattered through the cosmos, particular objects

such as the planet earth which, through processes

like biological evolution, has yielded other

objects such as a jaguar, which is capable of

adaption and learning, and eventually even other

particular objects, such as human beings, capable

of language and civilization and of discovering

such fundamental physical laws themselves

(Gell-Mann, 1995). This clearly portrays a

shortcoming in reductionist thinking: the

inability to account for surprise, creativity,

change, and emergent phenomena. Furthermore,

certain nonlinear phenomena, like complex

adaptive systems, have parts that, when

assembled, create unexpected emergent

properties that could not have been identified by

observing the system’s components; such results

have profound effects across many domains,

such as economies, wealth, politics, wellness, and

medicine, to name just a few (Rihani & De Soto,

2002). Thus, since all elements are changeable,

relationships are nonlinear, and behavior is

emergent and sensitive to small changes, the

entirety of a complex system is fundamentally

unpredictable over time, which means the only

way to understand it is to observe it in all its glory

(Lorenz, 1993). And yet, amazingly, upon

observing such complex systems over long

periods of time, inherent patterns emerge, and

very true and useful statements can be made to

explain its behavior (Briggs, 1992), leading to

attractor patterns that provide a comparatively

simple understanding of what first appears as

complex behavior, resulting, oftentimes, in

order, innovation, and progress.

Klir (2001) defines systems science using the

basic equation [S = (T, R)] whereby S denotes a

system, T a set of things distinguished within the

system, and R a relation or set of relations

defined on the set of things. Similarly, from a

modeling perspective, feng shui can be perceived

as an explanatory device, functioning as an

analog theoretical model that allows for the

widest variety of content known to humankind

and a gigantic scope of interpretation (Bruun,

2003). Beer (1985) states that a model of any

variable system is neither true nor false; instead,

it is more or less useful, and contains checks and

balances within it and in relation to its operating

environment, similar to the underlying systems

that have governed feng shui, unchanged, for

thousands of years. As noted by Forrester (1998),

human beings are reluctant to believe physical

and human systems are of the same kind, and

that social systems belong to the same class of

high-order, nonlinear, feedback systems; as a

result of human evolution, all social systems

appear to have already been designed. General

systems pioneer Boulding (1956) argued against

developing any sort of theory of everything

because such a system would inherently sacrifice

content. However, in this new era of big data,

such limitations may no longer exist, and the

4

complexities of nature as outlined by the

geomantic system, feng shui, could unearth a

skeleton similar to a massive system of systems

that analyzes the seemingly infinite interactions

of individuals within our natural environment,

evolving into a futuristic wellness program that

promotes health and well-being by identifying

patterns of disharmony at the earliest stages

possible. It is well worth our time and effort to

research such possibilities in order to discover if

a future state of natural living can exist based on

this complex, ancient system.

3. METHODS

The purpose of this research is to compare and

contrast historical concepts in system science,

systems thinking, and complexity science with

those found in the underlying system of feng shui

to determine if, in this new era of big data

analytics, a complete system of systems could

theoretically be constructed, powered by artificial

intelligence, to harmonize humankind with

nature, containing the potential to improve the

quality of life for many individuals around the

globe. This paper examines characteristics of the

information system existing beneath the

substrate of feng shui, namely yin/yang and five

phases theories, and compare their constructs to

published research in the field of information

systems and systems theory. A high-level

framework will be proposed, based on known

elements with the potential to serve as the

blueprint for a futuristic lifestyle system. Finally,

this paper identifies future research goals

necessary to make such a system a reality.

4. FINDINGS

The understanding of the flow of universal

energies in nature within time and space as an

information system represents the foundation of

feng shui, the ancient Chinese art of geomancy. It

is helpful to refer to Webster’s Revised Unabridged

Dictionary (Porter, 1913), for definitions

regarding such terms:

Geomancy \Ge"o*man`cy\, n. [OE. geomance,

geomancie, F. g['e]omance, g['e]omancie, LL.

geomantia, fr. Gr. ge`a, gh^, the earth + mantei`a

divination.] A kind of divination by means of figures

or lines, formed by little dots or points, originally on

the earth, and latterly on paper.

Feng-shui \F[^e]ng"-shu`i\, n. [Chin. feng wind +

shui water.] A system of spirit influences for good

and evil believed by the Chinese to attend the natural

features of landscape; also, a kind of geomancy

dealing with these influences, used in determining

sites for graves, houses, etc.

The idea that feng shui translates directly as “wind

and water” makes it rather evident that the

system originated in a flood culture of antiquity

when the study of nature and attempting to

predict its iterations was essential to survival; it

is speculated that slightly different flood stories

associated with the legends of the Xia and Shang

dynasties are explicable as originating

respectively in both the south and north regions

of the Yellow River delta in areas traditionally

associated with the beginnings of these two

lineages (Watson, 1966). The earlies recorded

flood disaster in China occurred around 2000

BC, causing immense damage and accounting

for many deaths across the country (Luo et al.,

2015). The Great Yu, a hero of the Chinese

people, was assigned to flood control by King

Shun and was successful by dredging channels

instead of building levees, as had been done by

his father, which allowed the water to flow in a

controlled manner to the seas (Gu, 2006). The

Han Daoists believed he used the information

system underlying feng shui to accomplish his

feats:

According to legend, the Great Flood endured

for many decades throughout the reign of Yao

and Shun, causing heavy damage to all

inhabitants of the earth. It was the Great Yu who

dug thousands of canals, rivers, and streams from

the Yellow River to help strengthen the

movement of water towards the sea. Yu labored

for almost thirteen years, often using just a

bucket and shovel; legend states that because his

legs were always in the water, there was no hair

left on them. Dressed in skins and cloths made

from the hides of animals and the barks of trees,

5

Yu worked through fierce winds and strong

rainstorms to bring about a change to the world;

finally, he was able to contain the flood, using

geomancy (e.g., feng shui) to make marks in the

ground that helped direct the flow of water to

where he had built tributaries and reservoirs.

Because of his popularity amongst the people,

Shun had no choice but to name him as successor

to the throne in 2200 BC, which began the start

of the Xia dynasty, the first of the three ancient

dynasties of China whose founders were of

model virtue. It was said that on this day, 10,000

tribes came to pay homage to what then became

their unified leader. (“Gourd Meditation,” C. Y.

Hsiang, personal communication, July 27, 2003)

Through anthropology, the history of Chinese

civilization, dating back to prehistoric times,

provides a rich cultural landscape examining the

development and evolution of human behaviors

and ideas. While there are serious questions

about the content and sequence of civilizations

that existed as early as the Xia dynasty due, in

part, to a lack of written record combined with

both the influence of Western ideology in the

1920s and an absence of scientific evidence, even

if one takes a horizontal view, we know such

people existed along the Yellow River at such

time and created ancient texts that contained the

details of these early systems and the

information behind them (Chang, 1999). In fact,

a golden saying handed down from generation to

generation in the Chinese nation states “a man

who wishes to run the country well should give

priority to flood control” (Cheng, 2005). As to

policy, there was a preponderance for

conformity to nature, on the back of Daoist

concepts; hence a lack of support for dykes,

which were time-consuming to dig and

expensive to maintain, especially when

compared to drawing water off canals, which

boasts the advantages of reclamation, increased

fertility, and transportation (Bates, 1935). It is no

wonder that during these ancient times, Daoist

and Confucian ideals ultimately combined

together and became the framework for the Six

Arts (Table 1, below) which were the subjects

taught in the first Chinese schools introduced

during the Western Zhou (1046-256 BCE)

dynasty (Street & Matelski, 2009).

Table 1. The Six Arts of the Zhou Dynasty

rt Description

禮 lǐ Ritual This art, which also correlates with meditation and Qi Gong, represents the

reverent observation of the laws and forces of nature.

樂 yuè Music

This art relates to how one can become in tune with the divine harmony of the

universe. It also relates to the power of regulating the frequency, timing, and

rhythm of energy.

射 shè Archery

This art refers to the martial idea of ‘yielding to achieve a return.’ It also pertains

to the focus and concentration of power when storing and releasing energy.

御 yù Charioteering

This art symbolizes the discipline and cultivation of the mind, body, and spirit.

It also relates to the ability to harness, control, and direct energy to where it needs

to go.

書 shū Calligraphy

This art represents refinement in calligraphy, charms, and the Daoist and

Confucian classical studies. It can also pertain to one's clarity of expression.

數 shù Mathematics

This art refers to mystical calculations and divination used to influence and

interpret patterns of nature, which often delineate one’s fate or destiny.

By the third century BC, the formation of the six

arts brought together an amalgamation of

philosophical schools that, upon reaching the

Song Dynasty (960–1279), had integrated

yin/yang, five phases, the Confucian classics, and, at

the center of it all, the art of mathematics in the

Yi Jing 易經, known in the West as the Book of

Changes; it is the oldest of all Chinese classical

manuscripts, written in a primal language during

times when ancient clan-commune beings would

record events by tying knots in cords of rope

strung around the village during ceremonies

(Feuchtwang, 1974). A solid line, or a rope

segment without a knot in it, represented yang 陽

or 1 in binary code; when the solid line is broken

into two by a knot, yin 陰 or 0 in binary code is

formed; this represents the basis of yin/yang

theory that remains extant to this very day in

Chinese culture.

The Yi Jing thus establishes a mathematical

system of organized chaos in nature. Since

research has illustrated that the universe is

fundamentally composed of data, understood as

dedomena, patterns or fields of differences, instead

of matter or energy (Floridi, 2010), one could

surmise that the Yi Jing taps into this dedomena to

arrive at quantitative variables of the state of the

natural environment at any given time. One yin

and one yang (21) is thus often called dao in that

it represents the polar quality of all effects in our

natural environment; the system is enhanced

complexity-wise by the introduction of infinitely

endless qualitative gradations and combinations

(see Figure 1, below) which has practical limits

only as to the relative significance of the object

being measured (Porkert, 1974).

This underlying system of yin and yang forms one

of the earliest known examples of a mathematical

theory of communication (Shannon, 1948), best

described today as quantum entropic logic,

representing a non-linear source of reality

existing simultaneously, at both the macro and

micro levels, embracing a multitude of local

forms and elements of reality, thus creating a

gigantic, monstrous density of a primary matter

negentropy (complexity of a structure). It

postulates that natural information is actually

described by means of quantum equations and

that particles exist in nature which can transfer

such data in various forms (Nesterov, 2011);

information, in this light, functions as a material

category reflecting the levels of structural

organization in objects and interrelating with

such basic characteristics as energy and mass.

Sharing commonality with yin/yang theory, both

the classical and quantum versions of logical

entropy have simple interpretations as two-draw

probabilities (Ellerman, 2017). As two-draw

probabilities, like tossing a coin or arranging

yarrow stalks, are performed three times (23),

eight possible combinations result, forming, in

antiquity, the Ba Gua 八卦 or Eight Trigrams;

after six times (26), sixty-four combinations

result, forming the Hexagrams of the Yi Jing that,

when moving, can result in up to 4,096

combinations (212)). The basis of the

mathematics of this system is equivalent to the

binary system of numbers and its use of

probabilities (Yan, 1991); this ancient system also

closely identifies with the concepts of bits and

bytes that form the working principle found in

our current computing environment and in the

structure of deoxyribonucleic acid (DNA).

Figure 1. Gradations and Combinations of Yin and Yang, 21 – 26

7

Yin and yang are

traditionally illustrated

by way of the tai ji 太極

symbol (Figure 2, right),

which translates as the

Absolute or Supreme

Ultimate, and the

relationship between

these two forces follows

four distinct aspects:

opposition, interdependence, mutual

consumption, and inter-transformation

(Maciocia, 1989). Opposition is illustrated with

yang represented as white on the left, and yin

represented as black on the right.

Interdependence is illustrated as the two forces

making up one complete circle, often referred to

as dao 道, which loosely translates as the way or

the path. Part religion and part philosophy, the

Chinese understood the dao, or nature, from

which all beings are conceived; they believed all

life was embodied with an unseen life force, a

force that can be cultivated and developed to

enable one to live life more fully (Siou, 1975).

Mutual consumption is illustrated by the tapering

of one aspect while the other grows; inter-

transformation is represented by the opposite

color dot within each main aspect. As such, the

tai ji symbol, while simplistic in appearance,

actual portrays the fundamental four laws of yin

and yang, which, according to the ancient

Chinese, governs the entirety of life in the

universe (Jing-Nuan, 1993).

When yin and yang expand into 22, a more

thorough evolution occurs, as illustrated in

Figure 3 (below). Old or utmost yin, represented

by two broken lines, takes the darkest period,

midnight; old or utmost yang, represented by two

solid lines, takes the lightest period, noon. Yang

within yin, or a solid line below a broken line,

shows how yang grows out of yin and represents

the time period of dawn; yin within yang, or a

broken line below a solid line, shows how yin

grows out of yang and represents the time period

of dusk. These assignments (Mann, 1973) can

also represent the four seasons and the four

directions: Winter/North (Old Yin),

Spring/East (Yang within Yin), Summer/South

(Old Yang), and Autumn/West (Yin within

Yang).

As discussed in the Yi Jing (Wilhelm & Baynes,

1950) yin and yang as 23 represents what is known

as the Eight Trigrams or ba gua; three lines each,

solid or broken, continuing to denote evolutions

of yin and yang, the bottom line symbolizes the

form (earth), the top line symbolizes the content

(heaven), and the middle line symbolizes the

subject (humankind). Table 2 on the following

page illustrates the Eight Trigrams, their

meanings, relationships, times, and associations;

over time, they have been arranged in two

separate ways, influenced by two ancient

mathematical maps called the He Tu 河圖

(Figure 4a, below) or Yellow River map and the

Luo Shu 洛書 (Figure 4b, below) or Luo River

map (Cammann, 1990). Myths associated with

these maps (images courtesy Wikipedia) go back

to the earliest days depicted earlier in this paper,

when floods ravaged ancient China.

Figure 3. Yin and Yang Expressed as a daily cycle

(Aarons, 2004).



Figure 2. Yin and

Yang Expressed as the

Tai Chi symbol.



8

Table 2. The Eight Trigrams (Wilhelm & Baynes, 1950).

Chinese Pin Yin Name

rigram English

ttribute Family/Area Direction/Fx

乾 qián Heaven

☰

Creative Rulership;

strength Father; head

Northwest; light

and dark mingle

together

兌 duì Lake

☱

Joyous Pleasure

Youngest

Daughter;

mouth

West; time of

rejoice

離 lì Fire

☲

Clinging Warmth;

dependence

Middle

Daughter; eye

South; brightness

under which we

perceive one

another

震 zhèn Thunder

☳

Arousing Movement Oldest Son;

foot

East; brings forth

all living things

巽 xùn Wind

☴

Gentle Dispersion;

penetrating

Oldest

Daughter; thigh

Southeast; brings

to completion

坎 kǎn Water

☵

Abysmal Moisture;

danger Middle Son; ear North; time of toil

艮 gèn Mountain

☶

Keeping

Still

Standing

still

Youngest Son;

hand

Northwest;

beginning and end

is completed

坤 kūn Earth

☷

Receptive Shelter;

yielding Mother; belly

Southwest and

center; cares by

nourishing



Figure 4a. The He River Map.



Figure 4b. The Luo River Map.



9

The He River

map alignment

of the Eight

Trigrams is

called the Fu

Hsi, Earlier

Heaven, or

Primal

arrangement;

it represents

the dynamic

actions of

opposites, or

the law of polar reversal, in that opposite pairs

have opposite symbology and mathematics, in

the sense that where on one side is a solid line,

on the other is a broken line (Wing, 1982). The

Luo River map alignment of the Eight Trigrams

is called the King Wen, Later Heaven, or Inner-

World arrangement; as compared to the prior

illustration, this scheme represents the law of

periodicity, depicting cycles and rhythms of

nature, such as the changing seasons, and

suggests the constant transformation of all

things, considered by some to be the external

manifestation of cosmic order (Wing, 1982).

Thus, within one

binary system,

, we have one

polar

arrangement,

indicating the

stability of

nature and of all

things, and one

period

arrangement,

indicating the

cycles of nature

and of all things.

The King Wen arrangement and the Luo River

map are also patterned in the same manner as the

3x3 magic square, an arrangement of the

numbers one through nine where, in every

direction, the three sets of numbers add up to 15

(Figure 7, below). Odd and even numbers also

alternate in the periphery; the 4 even numbers are

at the four corners, and the 5 odd numbers form

a cross through the center of the square. It has

been said that number is the origin of all things,

and the law of number is a potential key to

unlock the secrets of the universe; example of the

magic square can be found in Chinese literature

around 1125AD but were evidently copied from

still older documents (Andrews, 2004). These

numbers also occur in a possibly earlier

mathematical text called Shushu jiyi (Memoir on

Some Traditions of Mathematical Art), said to be

written in 190BC; this is believed to be the

earliest appearance of a magic square on record

and references its use for feng shui and astrology

(Yoke, 2008). But, up to now, no one has truly

attempted to analyze its inherent mathematical

properties, or the numerical significance of its

numbers – singly or in combination – and then

tried to consider these in light of Chinese

cosmological concepts and practices (Cammann,

1961).

While yin/yang theory is fundamentally expressed

qualitatively in binary code, representing the

polar Fu Hsi arrangement of the Eight Trigrams,

the King Wen version represents the

mathematical base of the five phases, whom

constitute qualitative stretches of time, temporal

segments of exactly defined measurements that

follow each other in cyclical order at reference

positions defined in space; there are several

Figure 7. 3x3 Magic Square

4 9 2

3 5 7

8 1 6

Figure 5. Fu Hsi arrangement of

the Eight Trigrams (Wing, 1982).

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Figure 6. King Wen

arrangement of the Eight

Trigrams (Wing, 1982).

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10

geometrical arrangements that illustrate these

changing energetic qualities, one of which being

the 3x3 magic square (Porkert, 1974). The three

key aspects are depicted in Figure 8 (below). The

sheng or Creation Cycle of nourishment and

generation is a circle that connects the elements,

represented by the wide arrows. The ke or

Control Cycle allows for the Five Phases to hold

each other in check, symbolized by the solid

arrows; earth, for example, earth contains water,

while water rules out fire, etc. The wei or

Protective Cycle operates superficially to audit

the Creation and Control Cycles to ensure they

remain in balance and in harmony with nature.

These three systems closely mirror the first three

systems in Beer’s (1985) Viable Systems Model,

whereby the ongoing nature of life represents the

system-in-focus, the Creation Cycle; the Control

Cycle acts in an anti-oscillatory manner, not in

command, but both flexible and rigid depending

on what is happening to the system-in-focus –

real life. The Protective Cycle (identified by

dotted arrows in Figure 8) acts like an external

audit function to see what is being done well and

what is being done not-so-well so that

adjustments can be to the Control Cycle. It

ensures self-organization and autonomic

regulation. To complete the operation, yin and

yangrepresent the monitoring of the external

environment, acting like Systems Four and Five

according to Beer (1985), rooting the system-in-

focus to reality and what is happening at any

point in time with larger and smaller systems.

The five phases thus possess the ability to

function as a system of checks and balances

created by the background forces of yin and yang,

representing a system for how all organic and

inorganic things were formed; this fundamental

theory generated the later development of

theories relating to medicine, chemistry, physics,

biology, mathematics, business, music, and

political strategy, to name a few (Lu, 2013).

Worsley (1998) states that the five phases of

Wood, Fire, Earth, Metal, and Water are not just

foundations of feng shui but of many of the

systems used throughout Chinese history,

representing the spirit of nature in and all around

us. Veith (1949) reminds us that classical texts

note that the diseases of the four seasons react to

the five flavors, which corresponds, via yin/yang

and five phases theory, to a calendar of time and

space, connecting our bodies and environment

through diet, based on cosmological principles.

Therefore, one can surmise that the entire system

of Chinese culture, their way of natural living, is

based on a system that is intellectually coherent

and embedded in cultural premises and symbols;

it cannot be fully understood outside of the

context of history, and unfortunately, to this day,

does not reconcile with the scientific concept of

causality (Leslie, 1976). Yet the randomness that

has come to be called chaos generated by

complex systems is, according to some, shaking

science to its very foundation; for the first time,

an alternative to linear, reductionist thinking that

has dominated science since Newton appears

possible (Larsen-Freeman, 1997).

There now however exists a structure, a system-

in-focus that is life, based on yin/yang and five

phases theories, that functions like entropic

geometry, consisting of logic, flow, initiation, and

termination, as a way to mathematically explain

probabilities in life (Coecke, 2003). In addition,

using at least two different strategies, when

applied to the processes of the brain, for

instance, to reach any result is oftentimes

Figure 8. Relationship systems among the

Five Phases (Lu, 2013).

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considered quantic in nature; the natural world

teaches us about inherent flexibilities inside

atoms, molecules, organelles, cells, tissues,

organisms, ecosystems, and planets (Castro-

Chavez, 2011), just like the underlying system of

feng shui attempts to manage. When the trigrams

are combined together, as noted before as 2

sixty-four variations occur (Table 3, below),

which, according to the Ta Chuan or Great

Treatise, “contains the measure of heaven and

earth; therefore (they) enable us to comprehend

the dao of heaven and earth and its order”

(Wilhelm & Baynes, 1950). Interestingly, Secter

(1998) illustrated the idea of reframing problems

and making use of different, possibly surprising

new perspectives, also belongs to an old

‘culturally inherited method of mental mapping,

relating, and strategic planning’ rooted in the

Book of Changes, and it is ‘coincidentally

compatible with digital information and

communication technology.”

Table 3. The sixty-four hexagrams of the Yi Jing (Xun arrangement).

qiàn

乾

Vital Spirit

jué

夬

Breakthrough

dàyǒu

大有

Great Harvest

dàzhuàng

大壯

Great Power

xiǎo chù

小畜

Small Taming

xū

需

Waiting

dàchù

大畜

Great Taming

tài

泰

Peace

lǚ

履

Treading

duì

兌

Joyousness

kuí

睽

Opposition

guīmèi

歸妹

Marrying Girl

zhōngfú

中孚

Insight

jiē

節

Limitations

sǔn

損

Decrease

lín

臨

Approach

tóngrén

同人

Gathering

gé

革

Revolution

lì

離

Radiance

fēng

豐

Abundance

jiārén

家人

Family

jìjì

旣濟

After End

bēn

賁

Decoration

míngyí

明夷

Light Darkens

wǔwàng

五妄

Innocence

suí

隨

Following

shìkē

噬嗑

Bite Through

zhèn

震

Shock

yì

益

Increase

tún

屯

Difficulty

yí

頥

The Cheeks

fù

復

Return

gòu

姤

Rendezvous

dàguò

大過

Great Excess

dǐng

鼎

Cauldron

héng

恒

Duration

xùn

巽

Gentle Mvmt

jǐng

井

The Well

gǔ

蠱

Work

shēng

升

Ascending

sòng

訟

Conflict

kùn

困

Oppression

wèijì

未濟

Before End

jiě

解

Deliverance

huàn

渙

Dispersion

kǎn

坎

Danger

měng

蒙

Youthful Folly

shī

師

Army

dùn

遯

Retreat

xián

咸

Influence

lǔ

挔

Wanderer

xiǎoguò

小過

Small Excess

jiàn

漸

Development

jiǎn

蹇

Obstruction

gèn

艮

Keeping Still

qiān

謙

Modesty

否

Stagnation

cuì

萃

Massing

jìn

晉

Progress

yù

豫

Enthusiasm

guān

觀

View

bǐ

比

Union

bāo

剝

Split Apart

kūn

坤

Receptivity

One way to understand the information system

of the Yi Jing is that it was shaped by and reflects

correlative thinking, in contrast to causal

ideology; in effect, it employs analogical

associations in a non-logical process, in that it is

not based on the kind of causal implications

utilized in Western logic (Hall & Ames, 1995). In

fact, according to Fung (1983), the Yi Jing is one

of the few texts of Asian descent that has no

counterpart in the West; written as early as 820

BC, it is predicated in part by representing

qualitative concepts with binary symbols, with

yin/yang theory representing one of the oldest, if

not the earliest, works on the subject of change

and transformation. Each of the sixty-four

hexagram symbols are assigned a distinct set of

attributes and characteristics, thus establishing a

correspondence between binary or quantitative

values on the one hand (the measurement of the

six lines as yin or yang), and descriptive or

qualitative values on the other (the description of

what the six lines represent, both separate as

individual lines and together as the hexagram);

the qualitative characteristics take on three key

measures, namely qualitative-quantitative,

cooperative-competitive, and risk easy-risk

adverse (Secter, 1993). The results form a model

of probability and change which, while most

people view or interpret as divination, could, in

an era of big data analytics, be remodeled as a

system of relative predictability with a

framework, constraints, rules, and a process for

implementation; the system compels decision

makers to examine issues from an unexpected

perspective, representing a fundamental

reframing of the issue, generating and

encouraging a fresh line of thought, creating

alternatives or solutions, reducing one’s chances

of getting stuck procedurally, discourages agents

from imposing their own intentions, and lays

responsibility at the hands of the parties

concerned (Secter, 1998).

Moving on from the decision-making guidance

of the Yi Jing, which in fact attempts to pattern

an organized type of chaos that exists in life on

earth, the rotation of planetary bodies in the solar

system lends to a more prescribed, systematic

observation of the universe. It was common

knowledge in antiquity that the Chinese state

regarded the maintenance of a sharply accurate

luni-solar calendar as a basic function, one that

led to annual predictions that were well-guarded

secrets of the emperor’s inner chamber

(Needham, 1959). While many believe such

intricate calendric systems were adopted to

improve agricultural processes (Changhao,

1981), the truth of the matter was the emperor

had desires to act as mediator between the

human and celestial orders of existence, linking

political ideology with astronomical truths as

early as 221BC (Sivin, 1969). New emperors

would oftentimes take the advice of scholars who

interpreted the successes and failures of past

dynasties in terms of a complex arrangement of

celestial stems and terrestrial branches which, at

its root, are derived from yin/yang and five phases

theories (Graham, 1989).

As noted above, the five phases, which rest in the

North (Water), East (Wood), South (Fire), West

(Metal), and Center (Earth), follow one another

in order, similar to nature, a smooth process with

overlapping patterns; when divided up into yin

and yang components, the five phases manifest

naturally into the ten Celestial Stems (Table 4,

above), following the composition of the Yellow

River map in counting numbers from one to ten.

Because of these correspondences, the Celestial

Stems are principally Yang in nature, symbolizing

Heaven, and denote the place in the cycle of time

and space, with odd numbers corresponding to

Table 4. The ten celestial stems (Wei-Pang, 1946).

# Name Symbo

Nature Element

1 Jiǎ 甲 Yang Wood

2 Yǐ 乙 Yin Wood

3 Bǐng 丙 Yang Fire

4 Dīng 丁 Yin Fire

5 Wù 戊 Yang Earth

6 Jǐ 己 Yin Earth

7 Gēng 庚 Yang Metal

8 Xīn 辛 Yin Metal

9 Rén 壬 Yang Water

10 Guǐ 癸 Yin Water

13

Yang and even numbers corresponding to Yin.

Thus, stems 1, 3, 5, 7, and 9 represent the five

pure yang stages, whereas stems 2, 4, 6, 8, and 10

represent the five yin stages of yang.

The five phases are also reflected in the King Wen

arrangement of the Eight Trigrams and evolve

into the Twelve Terrestrial Branches (Table 5,

below); it is interesting to note that four trigrams

maintain the cardinal directions, each

corresponding to one branch, while the trigrams

in the corner directions divide apart into two

branches each, one relating to earth, being

terrestrial, and the other relating to a cardinal

direction element. Thus, eight (8) plus four (4)

equals twelve, providing insight into how the

eight basic patterns of the universe are embedded

into the effects of the cycles of nature,

corresponding to a wealth of things including,

but not limited to, the qi meridians of the body,

the organs of the body, times of day in two hour

intervals, months, zodiac signs, compass

directions, etc. (Wei-pang, 1946). The Twelve

Terrestrial Branches denote the effect in the cycle in

relation to time and space and are listed in

numerical order from one to twelve, with even

numbers representing yin and odd numbers

representing yang. Branches 1, 3, 5, 7, 9, and 11

represent the six yang phases of yin, whereas

branches 2, 4, 6, 8, 10, and 12 represent the six

pure yin phases.

Table 5. The twelve terrestrial branches (Wei-Pang, 1946).

Trigram Name Branch Name # Element Time Zodiac Month Direction

☵ Water 子 Jiǎ 1 Water 11-1AM Mouse December North

☶ Mountain

丑 Chǒu 2 Earth 1-3AM Ox January North

Northeast

寅 Yín 3 Wood 3-5AM Tiger February Northeast

☳ Thunder 夘 Wān 4 Wood 5-7AM Rabbit March East

☴ Wind

辰 Chén 5 Earth 7-9AM Dragon April Southeast

巳 Sì 6 Fire 9-11AM Snake May South

Southeast

☲ Fire 午 Wǔ 7 Fire 11-1PM Horse June South

☷ Earth

未 Wèi 8 Earth 1-3PM Ram July South

Southwest

申 Shēn 9 Metal 3-5PM Monkey August Southwest

☱ Lake 酉 Yǒu 10 Metal 5-7PM Rooster September West

☰ Heaven

戌 Xū 11 Earth 7-9PM Dog October Northwest

亥 Hài 12 Water 9-11PM Boar November North

Northwest

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Diagram 1. The sixty cycles of nature (Wei-Pang, 1946).

Stem 1 2 3 4 5 6 7 8 9 10 1 2