Mathematical Symbols and Scientific Icons
Emily Guerin (20040618; email)
The Equality Symbol
Who was the first person to use the = (equal) sign?
A very elongated form of the modern equality symbol (=) was first introduced in print
in The Whetstone of Witte (1557) by
Robert
Recorde (15101558) the man who first introduced algebra into England.
He justified the symbol by stating
that no two things can be more equal than a pair of parallel lines...
We've been told that a manuscript from the University of Bologna, dated between 1550 and 1568,
features the same equality symbol,
apparently independently of the work of
Robert Recorde (and possibly slightly earlier).
William
Oughtred (15741660) was instrumental in the subsequent popularization
of the symbol,
which appears next in 1618, in the appendix [attributed to him]
of the English translation by Edward Wright of John Napier's
Descriptio
(where early logarithms were first described in 1614).
The mathematical symbol is then seen again, and perhaps more importantly,
in Oughtred's masterpiece Clavis Mathematicae (1631) in which other mathematical
symbols are experimented with, which are still with us today
(including ´ for multiplication).
Instead of the now familiar equality symbol,
many mathematicians of that era used words or abbreviations (including "ae" for the
Latin aequalis) well into the 18th century.
Thomas
Harriot (15601621) was using a slightly different symbol
(),
while some others used a pair of vertical lines (  ) instead.
Earliest Uses of Symbols of Relation
(Jeff Miller)
(Monica of Glassboro, NJ.
20010208)
What's the correct terminology for the line
between the numerator and denominator of a fraction?
When the numerator is written directly above the denominator,
the horizontal line
between them is called [either a bar or] a vinculum.
The overbar part of a squareroot sign or a guzinta
is also called a vinculum, so is the full weight
superbar or overscore used to tie several symbols together
(in particular, groups of letters with a numerical meaning in Greek or
Latin, where such explicit groupings may
also imply multiplication by 1000).
The thinner diacritical mark placed over a single symbol
(e.g., over long vowels in some modern Latin transcriptions) is called
a macron.
When the numerator and denominator appear at the same level,
separated by a slanted line (e.g., "1/2") such a line is called a solidus
(also virgule or slash).
The noun solidus originates from the Roman gold coin of the same name
(the ancestor of the shilling, of the French sol or sou, etc.).
The symbol was originally a monetary symbol, which was still being used for the British
shilling in 1971 (when British money was decimalized).
The related symbol "¸" is called an obelus.
Today, this symbol is virtually unused to separate both parts of a ratio,
but it remains very familiar as the icon which identifies the
division key on electronic calculators...
(20030808)
¥
The infinity symbol introduced by John Wallis in 1655.
This symbol was first given its current mathematical meaning in
"Arithmetica Infinitorum" (1655)
by the British mathematician John Wallis (16161703).
+¥
(resp. ¥)
is simply the mathematical symbol used to denote the "limit" of a real quantity which
eventually remains above (resp. below) any preset bound.
Incidentally,
he above illustrates the proper mathematical usage of "resp." (which is best construed
as a mathematical symbol, as discussed elsewhere on this
site). This remark was prompted by an entry
(20061118) in
the blog of a professional translator (Margaret Marks)
who used this very prose as an example of a usage she was discovering
with the help
of her readers...
In canonical maps
between the complex plane
and a sphere minus a point, the
unsigned symbol (¥) corresponds to
the "missing point" of the sphere,
but ¥ is not a
proper complex number... It's just a convenient symbol for the fictitious
"circle at infinity" beyond the horizon of the complex plane, so to speak.
The symbol itself is properly called a lemniscus,
a latin noun which means "pendant ribbon"
and was first used in 1694 by Jacob Bernoulli (16541705)
to describe a planar curve now called the
Lemniscate of Bernoulli.
The design was a part of Western iconography well before modern times.
In particular, it's found on the cross of
Saint Boniface
(bishop and martyr, English apostle of Germany, né Winfrid c.675755).
The infinity snake, the
ouroboros symbol
(also, uroboros or uroborus)
is a serpent or a dragon biting its own tail
(ourobóroV
means "tail swallower").
The symbol appeared in Egypt as early as 1600 BC, and independently
in Mesoamerica (see a Mayan version at left).
It has been associated with the entire Zodiac and the eternity of time.
It's the symbol of the perpetual cyclic renewal of life.
It has been found in Tibetan rock carvings and elsewhere
depicted in the shape of a lemniscate, although a plain circle is more common
(the circle symbolizes infinity in Zen Buddhism).

The Lemniscate or Infinity Symbol
(20031110)
Symbols of Infinite Numbers
w and
Ào, the other
infinity symbols.
As discussed above, the infinity symbol of Wallis
(¥) is not a number...
However, there are two different approaches that make sense of actual
infinite numbers. Both of them were first investigated by
Georg
Cantor (18451918).
Two sets are said to have the same cardinal number of elements
if they can be put in onetoone correspondence with each other.
For finite sets, the natural integers (0,1,2,3,4 ...) are
adequate cardinal numbers, but transfinite cardinals
are needed for infinite sets.
The symbol Ào (pronounced
"aleph zero", "aleph null", or "aleph nought") was introduced by Cantor to
denote the smallest of these (the cardinal of the set of the integers themselves).
He knew that more than one transfinite cardinal was needed because his famous
diagonal argument
proves that reals and integers have different cardinality.
The second kind of infinite numbers introduced by Cantor
are called transfinite ordinals.
Observe that a natural integer may be represented by
the set of all nonnegative integers before it,
starting with the empty set ( Æ )
for 0 (zero) because there are no nonnegative integers before it.
So, 1 corresponds to the set {0}, 2 is {0,1}, 3 is {0,1,2}, etc.
For the ordinal corresponding to the set of all the nonnegative integers {0,1,2,3...}
the w infinity symbol was introduced.
Cantor did not stop there, since {0,1,2,3...w}
corresponds to another transfinite ordinal, which is best "called"
w+1.
{0,1,2,3...w,w+1} is w+2, etc.
Thus, w is much more like an ordinary number than
Ào.
In fact, within the context of surreal numbers
described by John H. Conway around 1972, most of the usual rules of arithmetic apply to
expressions involving w (whereas Cantor's scheme for
adding transfinite ordinals is not even commutative).
Note that 1/w is another nonzero
surreal number, an infinitesimal one.
By contrast, adding one element to an infinity of
Ào elements
still yields just Ào
elements, and 1/Ào
is meaningless.
Infinite Ordinals and Transfinite Cardinals

The Surreal Numbers of John H. Conway
(20050410)
Cap: Ç
Cup: È
Wedge: Ù
Vee: Ú
Intersection (greatest below) & Union (lowest above).
The chevron (wedge) and inverted chevron (vee) are the generic symbols used
to denote the basic binary operators induced by a partial ordering on a
lattice.

The chevron symbol (wedge) denotes the highest element "less" than (or equal to)
both operands.
aÙb = inf(a,b)
is called the greatest lower bound,
the infimum or meet of a and b.
The operation is welldefined only in what's called a
meet semilattice, a partially ordered set where two elements always
have at least one lower bound
(i.e., an element which is less than or equal to both)._{ }

The inverted chevron symbol (vee) denotes the lowest element "greater" than
(or equal to) both operands.
aÚb = sup(a,b)
is called the least upper bound,
the supremum or join of a and b.
The operation is welldefined only in what's called a
join semilattice, a partially ordered set where two elements always
have at least one upper bound (i.e., an element which is greater than or equal to both).
A set endowed with a partial ordering relation which makes it both
a meetsemilattice and a joinsemilattice is called a lattice
(French: treillis).
In the special case of a total ordering
(like the ordering of real numbers) two elements can always be compared
(if they're not equal, one is larger and one is smaller)
so either operation will always yield one of the two operands:
pÙq = min(p,q) 
Î {p,q} 
pÚq = max(p,q) 
Î {p,q} 
On the other hand, consider the relation mong positive integers
(usually denoted by a vertical bar)
which we may call "divides" or "is a divisor of". It's indeed
an ordering relation (because it's reflexive, antisymmetric
and transitive)
but it's only a partial ordering relation
(for example, 2 and 3 can't be "compared" to each other,
as neither divides the other). In that context,
pÙq is the greatest common divisor
(GCD) of p and q, more rarely called their highest common factor
(HCF). Conversely, pÚq is their
lowest common multiple (LCM).
pÙq = gcd(p,q)
[ = (p,q) ] (*) 
pÚq = lcm(p,q) 
(*) We do not recommend the widespread but dubious notation (p,q)
for the GCD of p and q. It's unfortunately dominant in English texts.
In the context of
Number Theory, the above use of the "wedge" and "vee" mathematical
symbols needs little or no introduction, except to avoid confusion with the meaning
they have in predicate calculus (the chevron symbol stands for "logical and", whereas
the inverted chevron is "logical or", also called "and/or").
In Set Theory, the fundamental ordering relation among sets may be
called "is included in" (Ì or, more precisely,
Í).
In this case, and in this case only,
the corresponding symbols for the related binary operators assume
rounded shapes and cute names:
cap (Ç) and
cup (È).
AÇB and AÈB
are respectively called the intersection and the union of the sets A and B.
The intersection AÇB is the set of all elements that
belong to both A and B.
The union AÈB is the set of all elements that
belong to A and/or B ("and/or" means "either or both";
it is the explicitly inclusive
version of the more ambiguous "or" conjunction, which normally does mean "and/or"
in any mathematical context).
The chevron symbol is also used for the exterior product
(the wedge product).
In an international context, the same mathematical symbol may be found to denote
the vectorial cross product
as well...
(20071112)
Disjoint Union = Discriminated Union Union
of distinct copies of sets in an indexed family.
Formally, the disjoint union of an indexed family of
sets
A_{i} is:

A_{i} = 
È 
{ (x,i) 
x Î
A_{i} } 
iÎI 
iÎI 
However, such an indexed family is often treated as a mere collection of sets.
The existence of an indexation is essential in the above formulation, but the
usual abuse of notation is to omit the index itself, which is considered
mute. This makes it possible to use simple notations like
A+B or
AB
for the disjoint union of two sets A and B.
The squared "U" symbol
() is the preferred symbol
(because the plus symbol is so overloaded).
In handwriting and in print, that "squared U" symbol is best drawn
as an "inverted pi", to avoid any possible confusion with
the "rounded U" symbol (cup symbol) denoting an
ordinary union of sets.
A symbol is said to be overloaded if its meaning
depends on the context. Mathematical symbols are very often overloaded.
The overloading of a symbol usually implies the overloading of related symbols.
For example, the overloading of the addition symbol (+)
implies an overloading of the summation symbol
(S) and viceversa.
What makes additive symbols [somewhat] popular to denote
discriminated unions is the fact that the
cardinal of a discriminated union is
always the sum of the cardinals of its components.
Denoting E the cardinal of the set E,
we have:
 å A 
=
å  A 
(20050926)
"Blackboard Bold" or Doublestruck Symbols
Letters enhanced with double lines are symbols for sets
of numbers.
Such symbols are attributed to Nicolas Bourbaki,
although they don't appear in the printed work of Bourbaki... Some
Bourbakists like JeanPierre Serre advise against
them, except in handwriting (including traditional blackboard use).
One advantage of using those doublestruck letters even in print
(against the advice of JeanPierre Serre) is that they do not suffer
from any overloading, which makes it unnecessary to
build up a context when using them.
ln(x) = 
ó õ 
^{ x} _{1} 
dt 

t 
(20030803)
ò
The integration symbol introduced by Leibniz.
Gottfried Wilhelm Leibniz
thought of integration as a generalized summation,
and he was partial to the name "calculus summatorius"
for what we now call [integral] calculus.
He eventually settled on the familiar elongated "s" for the sign of integration,
after discussing the matter with Johann Bernoulli,
who favored the name "calculus integralis"
and the symbol I for integrals...
Eventually, what prevailed was the symbol of Leibniz, with the name advocated by Bernoulli...
(20020705)
Q.E.D.
[ QED =
Quod Erat Demonstrandum ]
What's the name of the endofproof box, in a mathematical context?
Mathematicians call it a halmos symbol, after
Paul
R. Halmos (19162006)
who is also credited with the "iff" abbreviation for "if and only if".
Typographers call it a tombstone, which is the name of the symbol in any
nonscientific context.
Before Halmos had the idea to use the symbol in a mathematical context,
it was widely used to mark
the end of an article in popular magazines (it still is).
Such a tombstone is especially useful for an article which
spans a number of columns on several pages,
because the end of the article may not otherwise be so obvious...
Some publications use a small stylized logo in lieu of a plain tombstone symbol.
See Math Words...
Here's a halmos symbol, at the end of this last line!
Jacob Krauze
(20030420; email)
As a math major, I had been taught that the symbol ¶
(used for partial derivatives) was pronounced "dee",
but a chemistry professor told me it was actually pronounced "del".
Which is it?
I thought "del" was reserved for [Hamilton's nabla operator]
Ñ = < ¶/¶x,
¶/¶y,
¶/¶z > ...
"Del" is indeed a correct name for both
¶ and Ñ.
Some authors present these two as the lowercase and uppercase versions of the same
mathematical symbol, although the terms
"small del" and "big del" [sic!] are rarely used, if ever...
Physicists and others often pronounce
¶y/¶x
"del y by del x".
In an international scientific context, the possible confusion between
¶ and Ñ
is probably best avoided by calling the
Ñ mathematical symbol "nabla del",
or simply nabla.
William Robertson Smith (18461894) coined the name "nabla"
for the Ñ
mathematical symbol, whose shape is reminiscent
of a Hebrew harp by the same name (also spelled "nebel").
The term was first adopted by Peter Guthrie Tait (18311901)
by Hamilton and also by Heaviside.
Maxwell
apparently never used the name in a scientific context.
The question is moot for many mathematicians, who routinely read
a ¶ symbol
like a "d" (mentally or aloud).
I'm guilty of this myself, but don't tell anybody!
When it's necessary to lift all ambiguities without sounding overly pedantic,
"¶" is also routinely called
"curly d", "rounded d" or "curved d".
It corresponds to the cursive "dey" of the Cyrillic alphabet and is sometimes
also known as Jacobi's delta, because
Carl Gustav Jacobi
(18041851)
is credited with the popularization of the symbol's modern mathematical meaning
(starting in 1841,
with the introduction of Jacobians in the
epochmaking paper entitled
"De determinantibus functionalibus").
Historically, this mathematical symbol was first used by Condorcet in 1770,
and by Legendre around 1786.
Geetar (20070718) The Staff of Aesculapius
What's the symbol for the 13th zodiacal constellation, Ophiuchus?
Ophiuchus is the name (abbreviated Oph)
of a constellation also known as Serpentarius
(French: Serpentaire). The serpent bearer.
 
This "snake handler" is actually the demigod Asclepios/Aesculapius,
the Greek/Roman god of medicine, a son of Apollo who was taught the healing arts
by the centaur Chiron.
Asclepius served aboard Argo as ship's doctor
of Jason (in the quest for the Golden Fleece)
and became so good at healing that
he could bring people back from the dead. This made
the underworld ruler (Hades) complain to Zeus, who
struck Asclepius with a bolt of lightning but decided to honor him with a place
in the sky, as Ophiuchus.
The Greeks identified Asclepius with the deified Egyptian doctor
Imhotep
(27th century BC).

The Rod of Asclepius, symbol of medicine,
is a single snake entwined around a stick.
Originally, the symbol may have depicted the treatment of
dracunculiasis
(very common in the Ancient World) in which the long parasitic worm was
traditionally extracted through the patient's skin
by wrapping it around a stick over a period of days or weeks
(because a faster procedure might break the worm).
Any symbol involving a snake would seem natural for medicine:
The snake is a symbol of renewed life out of old shedded skin,
not to mention the perpetual renewal of life evoked by the
ouroboros
symbol (a snake feeding on its own tail).
A snake around a walking stick is also an ancient symbol of supernatural powers
which can triumph over death, like medicine can
(biblically, the symbol of Moses' divine mission was his ability to change his
walking stick into a snake).
The large Ophiuchus constellation
is one of the 88 modern constellations. It was also one
of the 48 traditional constellations listed by Ptolemy.
In both systems, it's one of only 13 zodiacal constellations.
By definition, a zodiacal constellation is a constellation which
is crossed by the ecliptic
(the path traced by the Sun on the celestial sphere, which is so named because that's
where solar eclipses occur).
As a path charted against the background of fixed stars,
the ecliptic is a remarkably stable line (since it's tied to the orbital motion
of the Earth, not its wobbling spin). It does not vary with
the relatively rapid precession of equinoxes
(whose period is roughly 25772 years). What does vary is the location on
the ecliptic of the socalled "gamma point"
(the position of the Sun at the vernal equinox).
Ophiuchus is the only zodiacal constellation which has not given
its name to one of the 12 signs of the zodiac associated with
the 12 traditional equal subdivisions of the solar year, which form the
calendar used by astrologers.
However, some
modern
astrologers are advocating a reformed system
with uneven zodiacal signs, where Ophiuchus has found its place...
Astrological belief systems are not proper subjects
for scientific investigation.
Nevertheless, we must point out that it's a plain error to associate Ophiuchus
with the caduceus symbol
(two snakes around a winged staff)
since that symbol of Hermes
(messenger of the gods) is associated with
commerce, not medicine.
Ophiuchus is indeed properly associated with the
Staff of Asclepius symbol
(one snake around a plain stick) the correct symbol of the
medical profession,
which is mythologically tied to the Ophiuchus constellation.
In 1910, the House of Delegates of the American Medical Association
issued a resolution stating that
"the true ancestral symbol of healing art is
the knotty pine and the [single] serpent of Aesculapius".
Rod_of_Asclepius

Modernized
Zodiac 
Astrological Attributes of
Ophiuchus by Betty Rhodes
(20071125)
The Caduceus (Scepter of Hermes)
Image of dynamic equilibrium. Symbol of commerce.
Several explanations exist for this ancient
overloaded symbol.
In Greek mythology, the Caduceus
symbol inherited by Hermes (called
Mercury by the Romans) is often said to have originated
with the blind seer
Tiresias,
the prophet who experienced both sexes.
Tiresias was a son of Zeus and the nymph Calypso
(daughter of the titan Atlas).
After he had separated two copulating serpents with a stick,
Tiresias was changed into a woman for 7 years by Hera, experiencing
marriage and childbirth before returning to his original male form.
This experience of both sexes uniquely qualified him to settle
a dispute between Zeus (Jupiter) and his wife Hera (Juno).
He sided with Zeus by stating that women experience ten times
more sexual pleasure than men.
This displeased Hera who made him blind
(in another version, it's Athena who blinded him, because he had
surprised her bathing in the nude).
Zeus tried to make up for this by giving him foresight and
allowing Tiresias to live 7 lives.
The caduceus symbol evokes a dynamic equilibrium
emerging from a confrontation of opposing principles
(male and female).
As an alleged symbol of peace, it represents a balance of powers
rather than a lack of tensions.
The oldest depiction of two snakes entwined around an axial
rod is in the Louvre museum.
It appears on a steatite vase carved for
Gudea of Lagash
(who ruled from around 2144 to 2124 BC)
and dedicated to the Mesopotamian underworld deity
Ningizzida
who is so represented.
The name means "Lord of the Good Tree" in Sumerian, which is reminiscent of
Zoroastrian righteousness
(Good and Evil) and of the biblical
Tree of Knowledge of Good and Evil,
also featuring a serpent...
Curiously, the gender of Ningizzida seems
as ambiguous as the sexual identity
of Tiresias.
Coincidentally or not, Ningizzida is associated
with the large vonstellation Hydra whose name
happens to evoke Hydrargyrum, the latin name of the metal
mercury (symbol
Hg).
The Hydra constellation is either associated to the Hydra of Lerna
(the multiheaded reptilian monster defeated by Heracles)
or, interestingly, to the serpent cast into the
heavens by Apollo (who ended up giving the caduceus emblem to
his brother Hermes/Mercury).
The two facing serpents have also been said to be symbols for water and fire,
two opposing elements entwined around the axis of the Earth.
The wings evoke the spiritual or spatial dimension linked to the
fourth element : sky, wind or air.
Also, the copulating serpents have been construed as a fertility symbol
involving two complementary forces revolving around a common center.
This makes the caduceus a western counterpart of the
oriental YinYang symbol.
Hermes was the god of alchemists,
for which this unification of opposites was a fundamental credo
(in which the element mercury held center stage).
By extension, the caduceus has been associated with
chemistry and pharmacy.
It's a common mistake, dating back to the 16th century, to associate
the Caduceus with medicine.
The misguided heraldic use of the
symbol by military medicine started in the 19th century
and culminated with the unfortunate adoption
of the symbol by the Medical Department of the US Army, in 1902.
It's still the official emblem of the
US Navy Hospital Corps.
Yet, the correct symbol for medicine is definitely the
Staff of Asclepius (no wings and a
single serpent) so recognized
as a "true ancestral symbol" by the American Medical Association (AMA)
in 1910.
The caduceus is also associated with communication, eloquence,
trade and commerce,
the traditional attributions of Hermes, messenger for the gods and protector of
all merchants, thieves, journalists, tricksters and... inventors.
(20030610)
Borromean Symbol. Borromean Links.
What are Borromean rings?
These are 3 interwoven rings which are pairwise separated (see picture).
Interestingly,
it can be shown that such rings cannot all be perfect circles
(you'd have to bend or stretch at least one of them)
and the converse seems to be true:
three simple unknotted closed curves may always be placed
in a Borromean configuration unless they are all circles
[no other counterexamples are known].
The design was once the symbol of the alliance between
the Visconti, Sforza and Borromeo families.
It's been named after the Borromeo family who has perused the threering symbol,
with several
other interlacing patterns!
The three rings are found among the many symbols featured on the
Borromeo
coat of arms (they are not nearly as prominent as one would expect,
you may need a closer look).
The Borromean interlacing is also featured in other symbols which do not involve rings.
One example, pictured at left, is [one of the two versions of] the socalled
Odin's triangle.
In a recent issue of the journal Science
(May 28, 2004)
a group of chemists at UCLA reported
the synthesis of a molecule with the Borromean topology.
At a more fundamental level, the logic of the Borromean symbol
applies to a type of quantum entanglement first conjectured by
Vitaly Efimov in 1970, where ternary stability may exist in spite of pairwise repulsion.
Such an Efimov state
was first observed (for three cesium atoms confined below 0.000000001 K)
by the group of Rudolf Grimm
at the University of Innsbruck (Austria)
in collaboration with Cheng Chin of Chicago (Nature,
March 16, 2006).
(20030623)
The taichi mandala: Taiji or YinYang symbol.
Niels Bohr's coatofarms (Argent, a taiji Gules and Sable) illustrates
his motto: Contraria sunt complementa.
The Chinese Taiji symbol (TaiChi, or taijitu)
predates the Song dynasty (9601279). Known in the West as the
YinYang symbol,
it appears in the ancient I Ching (or YiJing,
the "Book of Changes").
It is meant to depict the two traditional types of complementary principles
from which all things are supposed to come from, Yin and Yang,
whirling within an eternally turning circle representing the primordial void
(the Tao).
The Confucian TaiChi symbol represents actual plenitude,
whereas the Taoist WuChi symbol (an empty circle) symbolizes undifferentiated emptiness,
but also the infinite potential of the primordial Tao...
Yin and Yang are each divided into greater and lesser "phases"
(or "elements"). A fifth central phase (earth)
represents a perfect transformation equilibrium.
To a Western scientific mind, this traditional Chinese classification may seem entirely
arbitrary, especially the more recent "scientific" extensions to physics and chemistry,
which are highlighted in
the following table:
 Yin  Yang 

Etymology  Dark Side (French: ubac)  Bright
Side (French: adret) 
Gender  Female, Feminine  Male, Masculine 
Celestial  Moon, Planet, Night  Sun, Star, Day 
Ancient Symbol  White Tiger  Green Dragon 
Colors  Violet, Indigo, Blue  Red, Orange, Yellow 
Greater Phase Equinox Transition, Young  West, Metal
and Autumn Potential Structure  East, Wood
and Spring Potential Action 
Weak Nuclear Force  Gravity 
Lesser Phase Solstice Stability, Old  North, Water
and Winter Actual Structure  South, Fire
and Summer Actual Action 
Strong Nuclear Force  Electromagnetism 
General Features 
Dark, Cold, Wet Solid, Heavy, Slow Curling, Deep Soft voice,
Sad Yielding, Soft,
Relaxed Stillness, Passivity Coming, Inward, Pull Receive,
Grasp, Listen Descending,
Low, Bottom Contracting, Preserving Small, Interior, Bone Mental, Subtle Buy 
Bright, Hot, Dry Gas, Light, Fast Stretching, Shallow Loud voice,
Happy Resistant, Hard,
Tense Motion, Activity Going, Outward, Push Transmit,
Release, Talk Ascending,
High, Top Expanding, Consuming Large, Exterior, Skin Physical, Obvious Sell 
Food  Sweet, Bitter, Mild Vegetable, Root Red meat 
Salty, Sour, Hot Fruit, Leaf Seafood 
Geometry Topology  Space, Open angle Finite, Discontinuous 
Time, Closed circle Infinite, Continuous 
Logic  Cause  Effect 
Orientation  Dexter, Negative, Loss Front, Counterclockwise  Sinister,
Positive, Gain Back, Clockwise 
Binary
Arithmetic  0, Zero, Even, No
 1, One, Odd, Yes

Chemistry  Acidic, Cation, Oxidant  Alkaline,
Anion, Reductant 
Genetic
Code  Pyrimidines: Cytosine, Thymine  Purines:
Guanine, Adenine 
Particle Physics 
Matter, Particle, Fermion 
Energy, Force, Boson 
 Yin  Yang 
The traditional Chinese taiji symbol became a scientific icon
when Niels Bohr made it his coatofarms in 1947
(with the motto: contraria sunt complementa)
but the symbol was never meant to convey any precise scientific meaning...
The oldest known TaiChi symbol
was carved in the stone of a Korean Buddhist temple in AD 682.
A stylized version of the YingYang symbol
(EumYang to Koreans) appears on the modern [South] Korean Flag
(T'aeGukKi)
which was first used in 1882, by the diplomat YoungHyo Park on a mission to Japan.
The flag was banned during the Japanese occupation of Korea, from 1910 to 1945.
