Zero as a Symbol and Aid in 3 Dimensions
[...Continued from Chapter 1 | Chapter 2 | Chapter 3 ...]
Chapter 4. Zero as a Symbol and Aid in 3 Dimensions
Although history has been transmitted in writing and other two-dimensional representations, both remnants and reminders of their three-dimensional versions are available around the world. Circles, spheres, and their generalizations (i.e., ellipses and ellipsoids) are of utmost significance across domains of knowledge, geographies, and times.
A physicist sees how well nature obeys Kepler’s elliptical paths - comet or planet. [1] To a cosmologist, the universe is an ellipsoid - an elongated sphere.
Geodesy uses reference ellipsoids to define the shapes of different planetary bodies. [2] The rotation of launched spacecrafts in their orbits is studied using Poinsot's ellipsoids. [3] Ellipsoidal representations are also significant in robotics, medicine, and crystallography. [4] [5] [6]
An engineer is more specific about the stability of the Jacobi and Dedekind ellipsoids. [7] They are either (i) unconditionally stable or (ii) unconditionally unstable with the chaotic and aberrant “pear-shaped'' equilibria. [8] [9] [10] Maclaurin spheroid, on the contrary, gives a dynamic, secular instability. [11] [12] They go on to illustrate the range of dynamicities offered by ellipsoids in general.
An architect is keen on incorporating ellipsoidal domes for their simplicity and potential. [13] [14] Dr. Krivoshapko notes that “Knowing the geometry of ellipsoids, one can solve various problems in physics, optics, and so on”. [15]
Several structures of spiritual value utilize the potential of ellipsoids in quite a few instances. [16] [17] We come across signs of ancient knowledge about ellipsoidal architecture around the world.
Iranian masonry domes of Chogha Mish and other Middle Eastern examples [18]
Quite a few temples and Buddhist monasteries of ancient India [19] [20]
The Taj Mahal is a fusion of the Persian dome and the widely observed lotus leaf base hip-knob from Hindu temple architecture. [21]
Mediterranean culture [22]
Roman Pantheon [23] [24]
Mesopotamian Halaf and Ubaid [25]
Sumerian Royal Cemetery of Ur [26]
Chinese corbelled domes [27]
Interestingly enough, there are more “signs” of representing zero in three dimensions while also connecting it to the root word sifr or zevero around the world.
A Shiva Linga (śiva liṅga) are ellipsoids, ellipsoidal cylinders, or cylinders finished with ellipsoidal domes. The more elongated lingas are also considered a manifestation of the beginningless and endless form called the “stambha” pillar, a form of Shiva. [28] [29] [30]
The concepts of Shiva and Lingas were connected for millennia. Archaeological evidence is available at least from the 2300 BCE Mohenjodaro artifacts and Indus Valley curio. [31] [32] Harappan sites have yielded both linga forms and pieces identified as a “meditating ascetic Shiva”. [33] The Harappan Civilisation can be dated back to about 6000 BCE. The cities were established by 2600 BCE. [34]
Most other pieces of evidence are actively under religious worship and may not be dated accurately. They are found all over India and other countries.
Pakistan houses the Shri Katas Raj linga. [35] Lingas are also found in Karachi, Tharparkar, Jacobabad, and other districts. [36] [37]
Shiva linga temples are found all over Vietnam. [38] [39] Different lingas of copper, crystal, and stone were excavated at the Cát Tiên Sanctuary of Vietnam. [40]
Pre-Angkorian, Angkorian, Khmer, and Common Era lingas are found in Cambodia. [41] [42] [43]
Mukhalinga (linga structure that features a face) are found in Nepal. [44] [45]
Buddhist and Jain linga worship is found in India, Nepal, and Sri Lanka. The word linga is used in the literature for "sign, evidence, or subtle body". [46] [47] [48] Stupas are also considered lingas. [49]
The Pakistan Defence website shared that Indian master, philanthropist, and environmentalist Sadhguru Jaggi Vasudev discovered a 5-foot-tall linga in Rumi’s Mausoleum, a Museum of Sufism in Konya, Turkey. [50]
Variations are found all over Thailand, Indonesia, China, Sri Lanka, Bangladesh, and other East and Southeast Asian territories. [51] [52] [53] [54] [55] [56]
Why Did Ancient Cultures Across the Globe Revere the Linga?
Unlike popular speculation, these cultures have not adopted the structure as a phallic representation but in congruence with creation. French historian and translator Alain Daniélou found that “linga” means “a sign”. [57] Austrian Sanskrit scholar at Oxford, Moriz Winternitz asserts that there are no historical reasons to relate lingas to any obscene phallic cult. [58]
At birth, the only sign notable between a male child and a female child is the external genitals. [59] The identifier was named linga too, which may have been an arbitrary choice. The word choice may also have been intentional since the organs held the power to procreate. [60]
Analogously, the female genitalia was termed “yoni”. The word also translates to "womb" and the "source" owing to its procreative powers. [61] [62] [63] In recognition of the potential of the female reproductive system, the ovum is recognized as “aṇṭha”. The word is also synonymous with “egg”. The cosmic egg is dubbed “brahmāṇṭha” or “hiraṇyagarbha”, the latter meaning “golden womb”. [64]
According to the Cultural Encyclopedia of the Penis by Rowman & Littlefield Publishers, both linga and yoni were assigned to sex organs only in the 19th century. [65] The word linga translates to Symptomatology in the Ayurvedic works of Charaka. [66]
The 1899 Sanskrit to English Dictionary by Sir M. Monier Williams gives the meaning of linga mainly as a “mark, sign, token, badge, emblem, guise”, “mark or sign from which the existence of something else can be reliably inferred", and “anything having an origin and therefore liable to be destroyed again”. [67]
Lingas are seldom without the yoni. A linga is rooted within the yoni that acts as a pathway or platform. [68] Beyond the juncture of the two, we do not know if the linga and yoni are two or merged; it is not known what the inside end of the linga is. This may be the ultimate union of the masculine and feminine, the duality of matter and energy, and the merging of microcosmos and macrocosmos. [69] [70]
Shiva is said to be without gender. Śiva and Śakti may be simply the expressions of duality - the masculine and the feminine. [71] Professor John A. Grimes avers that Linga is more of an outward symbol of the “formless Reality” which in turn is the union of “'primordial matter' (Prakṛti) with the 'pure consciousness' (Puruṣa)”. [72]
The combined structure contains a microcosm of the universe (since Shiva or masculine is considered matter) and emanates vibrations that are congruent with creation (since Shakti or feminine is considered energy).
For all we know, zero could have come from Shiva or the source. The zeroes and singularities we know of manage to retain the true nature of “The Origin.” Veneration and dissection are up to us, depending on what we are looking to achieve.
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