ZERO | Nothingness | Origin | Infinity | The Etymology, Cosmogony, Pantheism, and Ontology of “Zero”
Nothingness | Origin | Infinity
The Etymology, Cosmogony, Pantheism, and Ontology of “Zero”
Chapter 1
The idea of the number zero may be the most persistent of enigmas. Zero divided by a number cannot be defined. There is no dividing zero or multiplying it. It is the absolute. Negative numbers take something bigger out of zero and still work. But what is the truth of zero? What was it, to begin with?
The ancient world that we think struggled to eke out a day-to-day existence, was forsooth meditating the very nature of existence through something as simple as zero. They were representing and using their findings on the secrets of the universe in more tangible planes.
We venture into the wonders and stories of zero, while noting that wondrous stories are nothing short of epic sagas. Into why Zero is one…
Early Number Systems: Zero, Bases, Place-Value, and Calculations
The more archaic cultures around the world did not have a zero or at least did not use it for simplifying, advancing, or effectuating the number system.
Egyptian hieroglyphs used from the 3rd millennium BCE to the 1st millennium CE had a base-10 system. [1] The calculations though, were rendered unreliable as they were not positional and because they rounded off numbers to any random and convenient higher powers. [2]
Mathematicians of the 2nd millennium BCE Babylonia had a base-60 number system. It also accounted for the concepts of 60 seconds and 360 degrees. [3] They were close to developing a true and elaborate place-value system. [4] American science historian Carl Benjamin Boyer observes that they even used a symbolic zero. He concludes though, that Babylonians failed at the elaboration simply because the zero was not used right. [5] The number system also involved the rote memorization of at least 60 number symbols.
Until Empress Wǔ introduced the Zetian characters in 690 BCE, ancient Chinese numerals consisted of rod numbers. Each important number had to be memorized in ‘parrot-fashion’ since there was no fixed base. [6] The symbol "〇" was first used by the Chinese as a word in the 8th century. Later, it became a word for the number zero. [7] The numbers still did not have a base 10 or positional calculations.
The Maya numeral system involved a dot-and-rod base-20 (arguably base-5) number system which used a shell-like symbol for zero and twenty. The calculations were positional, but not in the convenient rows and columns we use today. [8] The culture was mostly destroyed by the advent of the Common Era.
The Aztec pictorial systems (and fate) were similar to the Mayan symbolatry. It was a vigesimal (base-20) system with dots and glyphs. [9]
In the 3rd or 2nd century BCE, Acharya Pingala of India used binary systems similar to modern-day Morse codes. He uses the number zero, the word śūnya, and a place-value system. [10] [11]
The American philologist Walter Eugene Clark translated the major works of Indian thinker Aryabhata in 1930. The 5th-century book titled Aryabhatiya used the positional form of the base-10 system explicitly. [12]
Boyer divulges that by the 7th century, Indian mathematicians used zero and the positional base-10 system to develop the decimal digit. The symbols are the same as the modern Hindu–Arabic numeral system. Brahmagupta contributed several concepts of geometry, Euclidean geometry, and Algebra (the Brahmagupta theorem, Brahmagupta's identity, and Brahmagupta's formula). [13] [14]
Indian temples founded before the 9th century have the circular zero inscribed as glyphs. [15]
Story: Representation of Zero, First Use, Spread, and its Modern Etymology
The place value notation was spread into common use in India in the first century of the Common Era (CE). The Bakhshali manuscript is the earliest available evidence for using the hollow elliptical symbol for zero as per Oxford professor Marcus du Sautoy. Its age is carbon-dated to the 3rd century CE. [16] [17] The manuscripts were found in the Mardan region of Pakistan. The region was under the rules of the Maurya and Gupta empires in those centuries. [18] Taxila or Takshashila, an ancient center of learning was active and not far away either. [19]
Numbers were denoted using symbols in the numeral system. Zero was represented by the very symbol we use today. [20] The ancestor of this system was the Brahmi system that used a high dot instead of the blank oval we know (and owe to and are in awe of) today. [21] [22]
Mathematician Dr. Russ Rowlett and the University of North Carolina assert that Persian and Arabic mathematicians adopted what they called the "Hindu numerals" in the 9th century. Arab merchants who traded with the West are said to have passed on important knowledge. Arabs introduced to the West the most convenient way of using numbers they had come across. [23]
But the converse is suggested by a few others. To start with, Dutch astronomer, socialist revolutionary, and Marxist theorist Antonie Pannekoek identifies that the Arab world obtained knowledge of science and mathematics from the Greeks. In his Pulitzer Prize-winning series of books, Dr. Will Durant identifies Hindu influences on Greek science. Durant pins down that Indian knowledge came to the Arabs through the Greeks. [24]
Either way - Europe to Arab or vice versa - the origins are asserted as Indian.
Durant goes on to observe that Muḥammad ibn Mūsā al-Khwārizmī used Hindu numerals in AD 813. (Kindly pardon the long name, as the parts ‘Musā’ and ‘al-Khwarizmi’ will soon come in handy.) Tony Abboud identifies that the same Persian mathematician used both Greek and Hindu knowledge bases to spread the use of zero to the Arab world. [25]
A century and a half later, Muhammad ibn Ahmad al-Khwarizmi (and not ‘Musa’ al-Khwarizmi) suggests that “a little circle” can be used "to keep the rows" in calculations when no number appears “ in the place of tens”. He called the handy little circle “ṣifr.”
Likely by the works of Pope Sylvester II (or Gerbert of Aurillac), Spanish Muslims, and the Moors, the Hindu–Arabic numeral system that involved a base 10 and the oval zero spread among the thinkers of the 11th century. [26] Modern math experts like Sigler and Grimm maintain that Fibonacci explicitly propounded the Indian numeral concept. [27] [28]
In the 12th century, the works of Al-Khwarizmi (unsure if Musa or Ahmad) were translated into Latin as Algoritmi de numero Indorum or "Al-Khwarizmi on the Numerals of the Indians". The word “Hind” (likely used by foreigners for the Himalayan Sindh valley-land) was Latinized as “Indo”, paving the way for the land of Bharat to be later dubbed India. The name Al-Khwarizmi was turned into "Algoritmi" setting the stone for "Algorithm". [29]
The Bhūtasaṃkhyā System of Numbers Amazes!
The Bhūtasaṃkhyā (or Bhūtasaṅkhyā) system of representing numbers used the digits from 0 to 9. The words eyes and hands would represent the number two since they usually come in pairs. "Veda” gives the value four, as there are four of them. “Bhūt” is five, because there are five elements, and so on. It was developed by astronomers and mathematicians who expressed their findings in poems as was standard at the time.
Some of the words used in the curious stead of zero would amaze the modern cosmologist. [30] [31] Interestingly, the Bhūtasaṃkhyā notation system used the word “sky”, “ether”, or the “vast emptiness” (vāna, vyoma, ambar, ākāśa, and nabhas) to denote the number zero! [32]
“Bindu (बिन्दु)” means a point or dot, referring to the universe beginning from nothing but a point. “Randhra (रन्ध्र) means “entry point” either connoting that the universe is just a passageway or referring to the universe coming into existence through nothing but a point. “Śūnya (शून्य)” or emptiness was used in the Bhūtasaṃkhyā system for zero.
Around the World with Nothing(ness): The Etymology of “Zero”
Various sources trace the origins of zero back to the Sanskrit word śūnya. [33] [34] [35] The idea is that pre-Islamic Arabs and Persians may have translated the word to ṣifr. That sound became ṣafira. In turn, the word became zefiro in Italian and zevero in the Venetian tongues. The French adapted it to zéro. English finally got “zero” by the end of the 16th century CE. [36] [37] [38] [39] 20th-century linguist John Baker Opdycke opines that the Portuguese, Catalan, and Romanian languages may have obtained zero around the time too. [40]
Owing to their Spanish roots, "zero" and "cipher" are considered doublets - words that took different routes into English but have the same roots. The Romanians took in cifră from the Spanish cifra and cifre in Old French. Opdycke wrote in 1949 that modern French and English may have picked up "chiffre" and "cipher" respectively from there. Modern Spanish uses cero. [41]
The tendencies of the words used for zero in various languages are stark and striking. A list of the different words used all over the world shows four main kinds of words betoken zero, based on their utterance: [42]
1. The Origin is “Śūnya”
Sanskrit, Hindi, Punjabi, Gujarati, Telugu, and Tamil (the language credited as the oldest one) are examples.
2. The Origin is “Sifr” as a Translation of “Śūnya”
The Arabic and Urdu languages use the original sifr to this day. Under the influence of the two, Hindi still has the word sirf meaning ‘just a little’. The Turkish language modifies the root as sifir.
Notably, the “Semitic cousin” of Arabic, Hebrew uses “אֶפֶס (efes)”. The language though is written from right to left. Reading it from left to right feels like “esef”.
Zero is used today in English, Spanish, Polish, Portuguese, Romanian, and French. Haitian Creole uses zewo. ‘Cipher’ is also in use in English. ‘Decipher’ something, and you get “everything” from a code, whether it is Morse (yes-and-no) or Binary (0 and 1)!
3. The Origin or “Śūnya” is revered or worshipped by the language
The word “pūja” refers to worship in many Indian languages. Telugu, Kannada, Odia, Sinhala, and Marathi agree to this.
Zero is pūjyam in Tamil and Malayalam - the two languages infamous for adding the “m” sound at the end of words, like some words in Sanskrit. In Telugu, pūjya means both nothingness and revered.
4. The Origin is “N” with or without “L”
The sound “na” represents nothingness in Sanskrit. Depending on the context, the sound takes the forms “ne”, “nahi”, “neti”, “no”, “nau̇”, “nato”, “nōyam”, “navā”, et cetera, if we go through ancient Sanskrit literature. The root sound, while passing through the ports of Tamil Nadu (Tamil) and Kerala (Malayalam) may have taken on the “il” sound the people used for “no”.
English (nil and naught), Chinese, Czech, Dutch, German, Indonesian, Lojban, Korean, and Russian languages exemplify the use of the “N” sound for zero.
Side notes:
Egyptians used the character nfr (𓄤) (or nefer) (i) to symbolize zero, (ii) for the words beautiful, perfect and complete, and (iii) as a baseline for glyphs. [43] [44] [45]
“Love” is the term used for zero in Tennis. It comes from the French term l'œuf meaning "the egg". “Duck” is zero in Cricket. It is short for “duck’s egg”. [46] But more on zero, egg, and the oval shape later.
[...to be continued in Chapter 2...]
References and Citations:
[1] "Egyptian numerals". MacTutor - School of Mathematics and Statistics. University of St. Andrews.
[2] "The Story of Numbers" by John McLeish
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