At the heart of civilisation, or at least civilisation as defined by Western European culture, lies mathematics. And at the heart of mathematics lies the concept of infinity, denoted by the lemniscate.
This study takes as its departure point information available on the Internet, most notably information on the worldwide web and Usenet. How is the infinity symbol viewed and put to use on the Internet? Is it a taboo in this giant conversation spanning all languages, nations and cultures? Merriam-Webster define “taboo” as “forbidden to profane use or contact because of what are held to be dangerous supernatural powers”, or “banned on grounds of morality or taste”. Is the use of the infinity symbol prohibited in some or all cultures? What are its emotive associations?
…a figure-eight shaped curve; New Latin lemniscata, from feminine of Latin lemniscatus with hanging ribbons, from lemniscus
Merriam-Webster Online Dictionary
…the locus of the foot of the perpendicular from the centre of a conic upon a tangent; Latin lemniscatus – ribboned; Greek lemniskos – a ribbon or bandageChambers Twentieth Century Dictionary
Signs and symbols have always been fundamental means of delivering messages. Their meaning and their content of information depend on the cultural contexts, so the same symbols could have distinctive meanings in different cultures.
The Internet symbol library at Symbols.com states that “this sign, or the Western graph for the number 8 positioned horizontally, is a sign to denote the idea of infinitely great or infinity, referring to distances or numbers.
Although both the lemniscate as symbol and as concept of infinity come to us from the start of human civilisation, its introduction into modern scientific usage only dates back to medieval times. The term lemniscate refers to the shape itself, and the Swiss mathematician Jacob Bernoulli (1654-1705) first called the shape a lemniscus (Latin for ribbon) in an article in Acta Eruditorum in 1694.
The English mathematician John Wallis (1616-1703) used the infinity symbol to represent mathematical infinity in his book Arithmetica Infinitorum (first published in 1655). He wrote: Cum enim primus terminus in serie primanorum sit 0, primus terminus in serie reciproca erit 8 vel infinitus. (Florian Cajori, “A History of Mathematical Notations”).
Another important name in the history of the lemniscate was that of Giulio Carlo de’ Toschi di Fagnano, a mathematician born at Sinigaglia, Italy, in 1682. He is best known on account of his investigations on the length and division of arcs of certain curves, especially the lemniscate; which in his own estimation seems to have been his most important work, since he had the figure of the lemniscate with the inscription: Multifariam divisa atque dimensa Deo veritatis gloria, engraved on the title-page of his Produzioni Matematiche, published in 1750, which he dedicated to Benedict XIV. The same figure and the words Deo veritatis gloria also appear on his tomb.
The origins of the lemniscate can be traced to various sources:
- The numeral 8 lying on its side, closed in on itself and physically representing infinity;
- The Etruscan sign CD, signifying 1000, which evolved into the Roman letter M;
- A lowercase omega, the last letter of the Greek alphabet; or
- A representation of the Möbius strip, a flat surface forever folding in on itself.
The modern depiction of the infinity symbol may also have been influenced by early typesetters simply using a horizontal character 8, which saved them having to create new characters.
The role of the symbol 8 used in Western numerical systems (also sometimes known as “Arabian numerals”) does not appear to have played a significant part in the development of the infinity symbol. The Arabic numerals (in fact of Indian origin) first appeared in European manuscripts in the 12th century, and date back to 8th century India. Europeans started to use them widely after 1202, when Leonardo of Pisa explained and detailed their use in his Liber Abaci (sometimes mistranslated as “Book of the Abacus).
Use of the lemniscate and its family of related symbols can be traced back to ancient esotericism. The symbol was described by Plato in The Timaeus, with later commentaries by Latin writer and philosopher Macrobius and the Stoics, and eventually this symbol becomes the gyres (a circular or spiral motion or form) of St. Thomas Aquinas (describing the circular movement of angels) and the divination tables of English mathematician and magus John Dee.
On the origins of the lemniscate, Symbols.com state that “the most common similar medieval symbol is the snake biting its own tail, or the empty circle […]. It is as if [the symbol] represents a double endlessness or eternity.”
The snake devouring itself, the ouborous or ouroboros, also takes the form of a lizard or a dragon. The symbol is emblematic of ancient Egypt and Greece, represented with its tail in its mouth, continually devouring and being reborn from itself. A Gnostic and alchemical symbol, ouroboros expresses the unity of all things, material and spiritual, which never disappear but perpetually change form in an eternal cycle of destruction and re-creation. In the 19th century, a vision of ouroboros gave the German chemist Friedrich August Kekule von Stradonitz the idea of linked carbon atoms forming the benzene ring.
Mathematically, the symbol of infinity can be interpreted as a graph of the following equations:
(x^2 + y^2) = a^2 (x^2 – y^2) and r^2 = a^2 cos (2 Theta)
The lemniscate is a special case of a Cassinian Oval, described in 1680 by Gian Domenico Cassini, the Italian-born French astronomer. However, the general properties of the lemniscate were first discovered by Giovanni Fagnano in 1750.
An example of a Cassinian Oval
The infinity symbol can be found in several branches of science. In botany, the lemniscate has been used to denote a great number of stamens (more than 20), while in meteorology the sign has sometimes been used to represent heat haze or sun haze. In photography the lemniscate refers to infinity focus. The infinity symbol is structurally similar to the symbol, which is used to indicate marriage in genealogy.
The lemniscate is also structurally similar to the symbol for the astrological sign Taurus (), which carries the meaning of variation in both astronomy and mathematics. The sign of Taurus is sometimes used in mathematics as a synonym for the infinity symbol.
The infinity symbol can be clearly seen in the astronomical occurrence called an analemma, defined by Merriam-Webster as “a plot or graph of the position of the sun in the sky at a certain time of day (as noon) at one locale measured at regular intervals throughout the year that has the shape of a figure 8; also a scale (as on a globe or sundial) based on such a plot that shows the sun’s position for each day of the year or that allows local mean time to be determined”. This association with the sun accounts for the lemniscate or analemma’s common use on sundials.
The mathematical equations represented by the lemniscate have applications in quantum theory, and the graph is used in marginal science to prove the theoretical possibility of time travel. This serves to strengthen the infinity symbol’s associations with science and the future.
Non-Western and non-European Culture
The relatively infrequent use of the lemniscate in non-Westernised culture might be attributable to the complex mathematical process involved in calculating and understanding the lemniscate. A greater emphasis on “holy geometry” in European and Arabic culture could have led to greater esoteric meaning being read into geometric patterns, while non-European cultures often tend to associated their holy symbols with patterns found in nature.
The Metis people (a Canadian community of mixed native Indian and European ancestry) incorporated the lemniscate into their traditional flag. In Calvin Racette, Flags of the
Métis, (Regina: Gabriel Dumont Institute of Applied Native Studies, 1987) the Metis flag is interpreted as follows: “the infinity symbol has two meanings, the joining of two cultures and the existence of a people forever. The infinity symbol has also emerged in the traditional dances of the Metis; the quadrille, in which the dancers move in a figure eight pattern, is a perfect example. Historically, the red of the first Metis flag was associated with the main colour of the Hudson’s Bay Company. However, later conflicts with this company led the Metis to favour trades with the North West Company who rather used blue as a main colour.”
In Ghana, the biribi wo soro closely resembles the lemniscate, and is seen as a symbol of hope. The similarities can also be seen in the hye wo nyhe (or symbol of forgiveness) and the nkonsonkonso (the symbol of human relations).
The hye wo nyhe
In Chinese symbolism, the figure 8 expresses the totality of the universe, and can be seen mirrored in the yin-yang design. The concept of infinity is symbolised by the Chinese swastika, called Lei-Wen, meaning roll of thunder. In earlier references, Lei-Wen was also used to designate the number 10,000. The swastika represents “the heart of the Buddha Shakyamuni, resignation of spirit, all happiness that humanity desires, mind, infinity, all and many.” In Buddhist culture the Endless Knot (Chang or P’an-Chang) receives and forwards abundance, and is a symbol of longevity, infinity and eternity.
Art, Popular Culture & Underground Culture
Some traditional weddings in Britain used to incorporate the lemniscate as part of the ceremony. The couple would “join hands, his right to her right, his left to her left, so from above they looked like an infinity symbol. […] This was called ‘handfasting’ and was used extensively in the rural areas where priests and ministers didn’t go all that often.”
The lemniscate appears in the official emblem of the 2002 FIFA World Cup Korea/Japan. The designers of the emblem note that the “two zeros in the year 2002 in the text […] are intertwined, representing the symbol for infinity.”
The Ultima series of fantasy computer games, a Dungeons & Dragons-style environment into which players totally immerse themselves, uses the lemniscate as symbolic of a fictitious religious system. Richard Garriott, the creator of the Ultima series, states: “I thought it would be fun to put my personal philosophy of life into my future games, which I call Ethical Hedonism. Ethical Hedonism has the following basic premises: Hedonism, in the sense of one should at least be trying to enjoy one’s life, or one wasting the short time they have; and Ethics as the limiting factor one should put on one’s hedonism so that others will treat you ethically as well. The symbol for this philosophy that a few friends and I now espouse looks like a one, for the hedonistic self, and an infinity symbol, for the balance against the fact that we live in a limitless society.”
In computer and console gaming, the lemniscate is also often used to indicate an infinite number of games (in other words eternal life), usually activated using a “cheat code” or secret key sequence. Programmers and developers usually build these back doors into their games for testing purposes.
An Internet community based around the Usenet newsgroup alt.lifestyle.furry uses the infinity symbol inside a paw print as its unofficial logo. The ALF FAQ (or list of Frequently Asked Questions) states that “alt.lifestyle.furry (or ALF) is a newsgroup for and about people who relate strongly to animals […] in a way that impacts their personalities and/or way of life.”
In a glossary developed for the television series Poltergeist: The Legacy (Metro-Goldwyn-Mayer 1996-1999), the lemniscate is said to signify “eternity, infinity, regeneration, the Holy Spirit, infinite wisdom, and higher consciousness. Its serpentine shape has no beginning and no end, and represents the endless spiralling and balancing of opposing forces in the universe.”
The infinity symbol appears as an image on the barrels of a brand of paintball sporting gun named the Dark Angel.
In Pixar’s animated film Toy Story, the character Buzz Lightyear uses the catchphrase: “To Infinity, and Beyond!”
In fan fiction based on the Japanese anime series Sailor Moon, the character Sailor Hades’s uniform includes boot tops bearing an infinity symbol. Symbolism in anime is often based on an amalgam of Eastern and Western culture, and seldom depicts purely Japanese icons.
The self-declared “micronation” Kingdom of TorHavn uses the infinity symbol on its coat of arms and official seal. “The coat of arms and seal of the Kingdom of TorHavn is a round shield of space black; resting within this circle is a classical scales, a twin-edged daggar (sic) as the fulcrum, point down, surmounted by a simple crown, all over an infinity symbol below the scales.”
In the Body Modification subculture, the lemniscate is often used in designs for tattoos, brandings and ritual scarring. Used in conjunction with a name, the infinity sign denotes eternal love. In a ritual scarring ceremony performed in Britain, the design was described as consisting of “2 major parts, the infinity symbol in the middle and 10 ‘rays’ coming out around it. […] The infinity symbol is there for the everlasting love we will share with each other, as we grow old together.”
Tattoos involving lemniscates
Religion, Esoteric Culture and the Occult
It is in the esoteric world that the infinity symbol is most often found (outside of mathematics), where the lemniscate has become symbolic of the future and futurist thought, depicting eternal life, harmonious interaction between conscious and subconscious, serenity, harmony and dominion over the physical plane. Simply because of the lemniscate’s symbolically laden but (at the same time) symbolically neutral nature, newly founded modern religious and philosophical groups often tend to associate with it and appropriate it as their own. In turn, even newer communities form and draw upon the symbols of the slightly older groups, lending historical rights and perpetuation to an otherwise neutral symbol.
In mainstream Western religion, the infinity symbol can be found on the cross of St. Boniface, a Latin cross entwined with a lemniscate. However, the lemniscate more often appears in New Age writings and philosophies, where the usage appears to have very little historical basis. References to the lemniscate can be found in (relatively recent) marginal esoteric works such as the Rosicrucian manuscript Gleanings of a Mystic by Max Heindel (1865-1919).
The cross of St. Boniface
In spiritual terms, the lemniscate represents eternity, the numinous and the higher spiritual powers. The Magus, the first card in the Major Arcana of the tarot, is often depicted with the lemniscate above his head or incorporated into a wide-brimmed hat, signifying the divine forces he is attempting to control. The lemniscate often appears in Russian tarot designs dating from the early twentieth century, also in association with the Magician or Strength cards. Cynthia Giles writes: “The Magician was based on the Tinker, or flimflam man as he’s been known in today’s culture. The lemniscate over his head, mathematical symbol of infinity is winged, an unusual choice probably signifying the great Hermes, messenger to the Greek gods.”
In the Heptameron of Petrus de Abano, a magician and medical doctor in Italy in the late 13th century, features a seal reportedly used in Cabalist thought and ritual magic. “The seal itself is that of the Sun. It forms the basic type for all the planetary seals of this work by d’Abano. In the center circle and ring, the one with the cross, are the words: Agla, Eloy, Adonay and Tetragrammaton. Inside these [appear] Alpha, the name of the first letter of the Greek Alphabet, and the infinity symbol.”
The use of a figure eight to represent infinity is an interesting choice, as eight is linked to the pre-creational infinity through the Ogdoad, the primeval forces of chaos in Egyptian mythology, represented as eight deities which existed before the creation of the sun god (the gods and their corresponding goddesses being Heh and Hauket, Amun and Amaunet, Nun and Naunet, Kek and Kauket).
The use of the figure eight can also be linked to a cyclical sense of infinity through the eight pagan festivals of the year and the octagram (an eight-pointed star symbolic of fullness and regeneration).
The symbol of a snake eating itself, the ouroboros or ouborous already mentioned, is often found in ancient religious and esoteric groups as a portrayal of infinity. The symbol appears principally among the Gnostics and is depicted as a dragon, snake or serpent biting its own tail. In the broadest sense, it is symbolic of time and the continuity of life. It sometimes bears the caption Hen to pan – ‘The One, the All’, as in the Codex Marcianus, for instance, of the 2nd century A.D. It has also been explained as the union between the chthonian (Greek for “of the earth”) principle as represented by the serpent and the celestial principal as signified by the bird (a synthesis which can also be applied to the dragon). “The Ouroboros biting its own tail is symbolic of self-fecundation, or the primitive idea of a self-sufficient Nature – a Nature which, à la Nietzsche, continually returns, within a cyclic pattern, to its own beginning.”
The lemniscate is often used to illustrate abstract concepts, such as the concept of reincarnation n Buddhism. However, the symbol does not seem to appear in traditional Buddhist writings. In Zen Buddhism, a single circle represents infinity.
Some 18th century manuscripts on alchemy and mysticism, believed to have been produced by the Comte de St Germain, depict “a dragon of magical influences with a tail in lemniscate formation with a small head on its end. The main head and the headed tail are pointing in opposing directions, and the figure is winged with an arrow-shaped tongue protruding from the main head.”
References can be found in Usenet conversations to a mythological interpretation of the lemniscate as “love lace”, most likely derived from Celtic infinity designs.
The Church of Civilization, described as “a religion for skeptics, agnostics [and] atheists” uses the lemniscate as an alternative to the Christian cross. “Hand actions activate parts of the brain not used by the voice. […] Moving your hands when doing something gives it greater psychological impact. It is possible that the action of making the sign of the Cross or other similar actions in religious ceremonies increases their placebo effect by engaging more of the brain in the actions. In imitation of this the Church of Civilization should have a hand gesture to make like the Cross. Looking at the two C’s and tracing them in the air produces a horizontal figure 8. A horizontal figure 8 is the mathematical symbol for infinity. So, this makes a nice piece of serendipity. The infinity symbol becomes the cross of the Church of Civilization. ”
In her book Interstellar Flight Portals (quoted at length on the Internet) Claire Watson writes: “The Great Pyramid was known to the Isis-Osiris sect as Secret House, where they practiced their journeys in the afterlife by traveling [sic] in light-body to the 8th dimension, called the Ogdoad. This Heaven-Sphere, symbolized by the sphere atop the cross of the Egyptian Ankh, was called Thoth’s celestial City of 8 and is symbolized by the infinity sign, or the figure 8. This appears on the Rod of Hermes as the intertwined serpents, Ida and Pingala, the subtle nervous system of the chakra system that is part of the mechanism for astral travel and mental projection. Thoth’s City of 8 was believed to be the destination of souls after death when the material body is abandoned and the soul re-ascends the planetary spheres to merge with the dead god-man Osiris and with God. By building Merkabas, the members of the sect could preclude death by passing through the portal, thus negating the wheel of time and fatality.”
A purifying ritual of supposedly (but doubtful) Asian origin, used in Feng Shui, describes the use of the lemniscate: “The following is a marvellous, energizing, healing ceremony that really does make a radical and lasting, difference in your life. You are about to clear negative energy from your home or apartment and create a sacred space around you. […] On a saucer sized piece of paper draw a clockwise spiral (like a nautilus shell). Or you can draw the powerful figure of infinity (a figure eight lying on its side). Draw one for each corner of your room. If you have two rooms in your apartment draw eight, etc., and put one spiral or infinity symbol on a round plate or basket in each corner of the room. Starting in the corner closest to the north and walking around the room clockwise, sprinkle two teaspoons of salt on each spiral.”
Other reports of meta-physical rituals also contain references to the lemniscate: “The ritual preparation started for me at the Winter Solstice when I volunteered during a semi-public ritual in London to be one of those calling down the sun-child so the Sun could be reborn. […] I became aware that there was within me a room filled with white light. Then, into this room came a spiralling light formed in the shape of a figure of eight. […] Then I recognised the light form. It was in the ancient shape of an infinity symbol, it was God himself. ”
In the practice of alternative medicine, the lemniscate is often used in reiki and seichem, alternative healing methods incorporating the infinity symbol into rituals as a powerful “secret” symbol. Reiki practicioner Lee Carroll writes: “Ahnya began to reveal to me the figure-eight fibers that radiate from the chakras and connect us to Core energy. These are the self-balancing loops of the UCL. They form the infinity symbol, representing the infinite connection between you and Creator. I observed these light fibers feeding information back into the human biology from the universe. When I saw the biology sending information back out through the figure-eight loops, I realized we had taken a sizable evolutionary leap with the activation of this part of the energy anatomy.”
Associations between the infinity symbol and meta-physical healing abound. The following is a personal account by Bob Manrodt, suffering from throat cancer: “While in the midst of very powerful experiences, in a sort of ‘break’ from strong and heady waves of experience, I look up at the sky and see an infinity symbol. One half is red and the other is blue. I am aware that I have experienced one half of the infinity symbol in my visions, now I am to work through the other half.”
In another article, Manrodt states: “This infinity symbol has shown up for me repeatedly on other significant occasions, a powerful symbol that seems to transcend time/space.”
British mystic and occult writer Alistair Crowley describes the infinity symbol as representing “heaven on earth or lower sephiroth plus Daath (or 7 planets plus Sothis); Mercury; Hod, Ogoad, the Buddhist & other 8 path. Perfection. Strength, fortitude, everlastingness. It is the first cubic number, hence it stands for the cube itself, or earth. Splendour of endurance.”
The infinity symbol plays a central role in Scientology founder L. Ron Hubbard’s book Scientology 8.8008. Hubbard turned lemniscate upright, and explained that the book’s title meant “the attainment of infinity (the first 8) by the reduction of the physical universe’s command value to zero (the 80), and the increase of the individual’s personal universe to an infinity (the last 08).” Through the application of the techniques given in the lectures, the “individual would become a god”.
It is often alleged that Hubbard freely borrowed symbolism and philosophy from the writings of Alistair Crowley. Both Crowley and Hubbard use an equilateral triangle pointing up in a circle as one of their group’s symbols.
An anonymous author interprets the lemniscate as “sexual union and sense of perfection – two becoming one (two uniting circles, one representing man and the other woman). It also shows male, I believe the right, connected with female the left, this demonstrates equality because one is not above the other.”
In a text entitled Building the Sky Ladder: The 13th Tribe of Levi-Levitron (associated with the Bartonian Metaphysical Society), reference is made to the lemniscate as the “universal constant”: “FORCE (like countless billions of goldfish tails) has propelled the planetary mind over evolutionary DISTANCE at a growing VELOCITY carrying the MASS by means of WORK and hi-tec ACCELERATION into conjunction with the UNIVERSAL CONSTANT (-1) (infinity symbol 8) = Home again in INFINITY.”
Various sects with an emphasis on outer space tend to use the infinity symbol in their religious texts, the most famous of which is the Heaven’s Gate cult, whose members committed mass suicide in the late 1990s. The cult used the symbol to illustrate infinity, and the concept of infinity and eternal life features prominently in their scientific belief system. Science played an integral part in their core philosophy, and most of their members were scientific members of the digital community. It was clearly thought that the lemniscate conveyed a sense of seriousness and scientific empiricism.
The International Raelian Movement states that “life on Earth is not the result of random evolution, nor the work of a supernatural ‘God’. It is a deliberate creation, using DNA, by a scientifically advanced people who made human beings literally in their image.” The movement claims that these scientists used the lemniscate as their symbol, and that references to this symbol can be found in the ancient texts of many cultures.
Economic, Commercial and Political Context
In a political context, the lemniscate is most often used to symbolise the eternal and stable nature of a group. In the South African coat of arms adopted in 1999, the structure of the infinity symbol can be seen to give birth to a secretary bird (sagittarius serpentarius). The secretary bird symbolises growth and speed, and combined with the infinity symbol represents the rebirth of the spirit of the nation.
The Humanist Party (Partido Humanista) of Argentina uses the lemniscate as a symbol in their official flag. The Humanist Party in other countries (notably Portugal) also sporadically make use of the symbol at official meetings.
Flag designs used by the Humanist Party of Argentina
The upright infinity symbol (8) often appears in late twentieth century neo-nazi symbolism, usually as 88, representing double the eighth letter of the alphabet, HH, an abbreviation in turn for Heil Hitler.
A standard set by the U.S. National Information Standards Organization (NISO) for archival quality permanent (or non-degradable) paper uses the “mathematical symbol for infinity set inside a circle”. The symbol was introduced in ANSI Z39.48-1984, and is also part of ANSI/NISO Z39.48-1992. The symbol is also used in ISO 9706 with the permission of NISO.
The Australian National Archives incorporate a lemniscate into their logo.
The infinity symbol and its associated designs are featured extensively in a particular school of jewellery design, often in conjunction with the heart icon, symbolising eternal love. In modern interpretations of ethnic and ancient designs, the Celtic infinity symbol and the ouroboros can also often be found.
The Fujitsu electronics groups uses an “Environmental Emblem”, consisting of “a miniature of the earth, a pair of eyes, and an infinity symbol, which is used as part of the Fujitsu Logo. The meaning is that the Fujitsu Group will always conduct its business caring for the Earth.”
Fujitsu environmental logo
The lemniscate is sporadically used as logo by small businesses. A company called Lemniscate Inc produces educational toys, and uses the infinity symbol. A group in Raleigh, N.C. in the USA called The Cosmic Lemniscate describes itself as “an eclectic community center” and offers crafts based on “alternative religions”.
A web design company named Web Essentials use a lemniscate as their logo, and interprets the symbolism as follows: “Our infinity symbol with our company logo shows just how the odds have been evened out and what small business can now offer people that was never before theirs to take.”
Another Internet-based company named WebGate explains their use of the infinity symbol as logo and slogan: “A lot of ideas had been suggested but one of those that really made an impact is the slogan ‘explore the infinite web’. This slogan was preferred, since WebGate want Internet browsers to discover the web’s limitlessness. To match with the Company’s slogan, a logo was created with a globe in the center of an infinity sign. The globe represents the abundance of information that one can get from the Internet, bridging the gap of distance in between continents throughout the world. The infinity symbol represents the web’s boundlessness or continuum. The company’s logo and slogan is a manifestation of the Company’s determination to provide quality Internet service to its customers.”
Although the origins of the lemniscate or infinity symbol lie shrouded in the mists of time, it still conveys symbolic meaning and evokes an emotional response. In mainstream Western culture the symbol appears to carry a mainly scientific and mathematical association, with no explicit taboo, although non-specific enough to allow marginal esoteric applications.
Man is a pattern-matching animal, and receives positive feedback in a feeling of well-being when patterns can be matched in nature. This recognition stirs a primal instinct of comfort and safety. Perhaps in the infinity symbol we recognise something basic, the eyes of a predator, or human eyes staring back at us. In esoteric culture the symbol has come to denote eternal life, harmonious interaction between conscious and subconscious, infinite reality, the removal of borders, infinite possibility and the eternal nature of God.
However, the repeated occurrence of the lemniscate pattern in various ethnic cultures could mean more ambiguous tribal and religious interpretations of its symbolism. Infinity as birth and rebirth can also be made to include death, and as such may carry secondary associations in addition to traditional Western notions of infinity.