18 ms·

The Elusive Origin of Zero

71 points by Hooke 4y ago

deleted 4y ago
[deleted]
RcouF1uZ4gsC 4y ago
> The stone bore a Khmer epigraphic inscription that included the date for the Khmer year 605, reckoned within the Hindu Saka system, a historical calendar based on the rule of the Indian emperor Shalivahana. Seems there is a pretty good chance that the origin of zero is still Indian and was adopted by the Khmer just as they adopted the Indian calendar.
- drieddust 4y ago
  Isha Upnishad[0] was written in 1st half of 1st millennium BCE as per the conservative estimates. Its Shanti Mantra(wishing peace to all living beings) of says: ॐ पूर्णमदः पूर्णमिदं पूर्णात्पूर्णमुदच्यते । पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥ ॐ शान्तिः शान्तिः शान्तिः ॥ Om Puurnnam-Adah Puurnnam-Idam Puurnnaat-Puurnnam-Udacyate | Puurnnasya Puurnnam-Aadaaya Puurnnam-Eva-Avashissyate || Om Shaantih Shaantih Shaantih || Rough Translation: That (god) is complete(puurnnam), this living being is complete. From completeness emerges completeness. When this completeness (living beings) emerges from that completeness (god), only completeness remains. This verse describes God. But it can also be describing concept of zero and infinity. Buddhist philosophy emerging in 500 BCE is based in shoonyata[1] (nothingness) so concept of zero was definitely known for a long time. As far as mathematical applications are concerned, we can't say for sure as a lot of knowledge was lost to invasions which specifically targeted universities like Nalanda[2]. Hindus imagined time scales of microseconds to trillions of years which in IMHO difficult to imagine without zero based mathematics[3]. Having said that there are a large number of manuscripts in the hands of small groups and families are yet to be discovered so these dates. [0] https://en.wikipedia.org/wiki/Isha_Upanishad https://en.wikipedia.org/wiki/Isha_Upanishad [1] https://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81 https://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81 [2] https://www.myindiamyglory.com/2017/09/11/nalanda-9-million-books-burnt/ https://www.myindiamyglory.com/2017/09/11/nalanda-9-million-... [3] https://en.wikipedia.org/wiki/Hindu_units_of_time https://en.wikipedia.org/wiki/Hindu_units_of_time
  - KingOfCoders 4y ago
    The idea of zero is that it's used in a positional numeric system, not just as a symbol for nothingness, like in 1305 + 0935 ---- 2240 or in calculations ((5-5)+2)*0 = (0+2)*0 = 2*0 = 0
    - drieddust 4y ago
      Thanks, but that's such a narrow definition of the concept. Shukla Yajurveda[0] conservatively estimated to be written in 1200- 800 BCE period in 17.2.20 constructs powers of 10 upto a billion by names by adding shunya successively to 10. [0] https://en.m.wikipedia.org/wiki/Yajurveda https://en.m.wikipedia.org/wiki/Yajurveda
      - KingOfCoders 4y ago
        This is the concept of zero. The title said "The Elusive Origin of Zero". Widening the definition to something else doesn't expand understanding but creates confusion.
  - braindead_in 4y ago
    As Swami Sarvapriyananda is fond of saying, this verse encapsulates the essence of Advaita Vedanta. This verse is in fact his favourite. He has given hours and hours of talks on it. There is a lot packed into it.
- xhevahir 4y ago
  Maybe. It would be odd, though, not to find any Indian examples of zero from earlier than ~200 years after the oldest Khmer one if the invention came from India. That area first came under Indian influence centuries before these dates. Some parts of the country, Chenla, were dependent on states in Java and Srivijaya (the one mentioned in the article) later on. The Indian cultural sphere as a whole covered a huge area and the Subcontinent itself certainly did not have a monopoly on culture there.
moralestapia 4y ago
LOL, how could two "emeritus professors" write an article like this without a single mention of the Mayan civilization, which is regarded by many as the earliest use of an explicit zero in a numerical system. Are they not aware of this?
- melissalobos 4y ago
  Not sure, but maybe because it isn't a positional zero.
- xhevahir 4y ago
  The Mayans may or may not have been first, but due to their isolation their use of zero was unknown to the rest of the world. By the time Europeans and Mayans met, the Hindu-Arabic numeral system was well established and that was the system that became the world's.
WhitneyLand 4y ago
Looking far enough back in time it becomes difficult to imagine the context in which the “concept of nothing” was a novel idea. How intuitive is counting starting from no foundational knowledge? I mean, every day you knew if you had 1 or 2 pieces of food to eat right? It seems realizing when you had zero pieces of food would be top of mind.
- jcranmer 4y ago
  The difficulty, I think, is in establishing that "nothing" is a tangible object that can be manipulated as if it were a "regular" number. This may be a little easier to grasp if you look at language. In many languages (most? nearly all?), you generally don't express lacking food as saying "I have 0 food" but as saying "I do not have food"--the concept of nothing is essentially reflected as turning the verb (or clause/sentence as a whole) into a negative mood, rather than indicating that the count of an object is 0.
  - madmoose 4y ago
    I like to imagine the situation of a tax collector in ancient Mesopotamia, going around and asking the farmers how many animals they have. If the farmer has 5 cows, they have a number of cows that you can put in a form on a clay tablet. If the farmer has no goats, they don't have "a number of goats", they have no goats to count. Writing a number on the tax form doesn't make sense. If numbers are only used to count actual things in the real world, zero is a very odd concept. We realized later that having "a number" to represent "none" simplifies many things and rids us having to deal with special cases. And if we teach it to children early enough it isn't too confusing.
    - dr_dshiv 4y ago
      Yes, but when you have a set of goods to proportion out and you are complete, then there is a zero. So it may be quite common. The Egyptians indicated a concept like zero with the NFR sign, for perfect. That’s the one with a circle and a cross on top. But, no decimal placeholder system, like described in the article. http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egypt_zero.html http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_e...
wintorez 4y ago
For me the importance of zero is not about assigning a symbol to nothing. It’s about to come up with the idea that the symbol for the number of things one more than 9 should be 10 instead of another arbitrary symbol. This concept seems intuitive at first, but when you think about it, it’s such an genius idea.
- dataflow 4y ago
  > For me the importance of zero is not about assigning a symbol to nothing. It’s about to come up with the idea that the symbol for the number of things one more than 9 should be 10 instead of another arbitrary symbol. By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. [...] The Babylonian placeholder was not a true zero because it was not used alone, nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60) looked the same, because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them. From https://en.wikipedia.org/wiki/0 https://en.wikipedia.org/wiki/0
cat_plus_plus 4y ago
"We are out of stuff" is not a concept that can be traced to recorded history, because it much predates humans. Literal single cell life forms behave differently under conditions of scarcity vs abundance.
makach 4y ago
My hero Zero, by the Lemonheads. Yeah, Zero is a wonderful thing In fact, Zero is my hero! How can Zero be a hero? Well, there are all kinds of heroes, you know A man can get to be a hero For a famous battle he fought Or by studying very hard And becoming a weightless astronaut And then there are heroes of other sorts Like the heroes, you know, from watching sports But a hero doesn't have to be a grown up person, you know A hero can be a very big dog Who comes to your rescue Or a very little boy who's smart enough to know what to do But let me tell you about my favorite hero My hero, Zero, such a funny little hero But 'til you came along We counted on our fingers and toes Now you're here to stay And nobody really knows How wonderful you are Why we could never reach a star Without you, Zero, my hero How wonderful you are What's so wonderful about a zero? It's nothing, isn't it? Sure, it represents nothing alone But place a zero after 1 And you've got yourself a 10 See how important that is? When you run out of digits You can start all over again See how convenient that is? That's why with only ten digits including zero You can count as high as you could ever go Forever, towards infinity No one ever gets there, but you could try 10 billion zeros From the cavemen to the weirdos Who invented you They counted on their fingers and toes Or maybe some sticks and stones, rocks and bones Their neighbors' toes Yeah yeah And nobody really knows How wonderful you are Why you could never reach a star Without you, Zero, my hero Zero, how wonderful you are Place one zero after any number And you've multiplied that number by 10 See how easy that is Place two zeros after any number And you've multiplied that number by 100 See how simple that is Place three zeros after any number And you've multiplied that number by 1, 000 Et cetera, et cetera, ad infinitum, ad astra, forever and ever With zero, my hero, how wonderful you are
chunkyguy 4y ago
India as a whole didn't even exist back then. Why don't historians describe only in terms of ancient kingdoms or whatever geographical entities existed back then and then describe what current political boundaries contains that area today?
- reil_convnet 4y ago
  > India as a whole didn't even exist back then. Given the only entity you think of India to be is a Nation State, it didn't. Which for most "west" educated people is the only type of state that can exist. But entities can exist beyond concept of a Nation State. Unfortunately, its not very easy to unlearn years of "one good way" to think. Did Germany exist during Roman Empire or during Holy Roman Empire ? It did not as a nation state, but the people almost always felt connected. India had much stronger bonds among people than say typical Germany, the religion/culture had elements from the entire nation, created by leaders from different parts of continent. Hinduism has verses conveying rivers and Gods from around the subcontinent as important aspects of life. Adi Shakaracharya, the religious teacher who is considered the person who made Hinduism the dominant form from among other existing interpretations of "Dharma" belongs to the southernmost tip of the region and created hindu institutions in all corners of subcontinent. Bhakshali Manuscript is one of the oldest Indian documents with use of Zero in Maths written by Buddhist scholars in Sanskrit. https://en.wikipedia.org/wiki/Bakhshali_manuscript https://en.wikipedia.org/wiki/Bakhshali_manuscript . This was discovered in modern day Pakistan [then British India]. You could argue that this is a part of Pakistan's history, but what is Pakistan's History then ? You can somewhat imagine if a Mesopotamian state survived till today, parts of it unconverted to Islam in a sub area of fertile crescent. Would you call it the successor state to entire Mesopotamia or you would say Uruk history is not their history because the region is now part of nation state of Iraq. That is the case with India as well ! There is a reason we read Mesopotamian history as a composite and as a different topic than say Egyptian History, because Mesopotamia was a different and connected civilization. Institutions like that don't survive now and hence a modern western scholar has no ontology to relate it to, but India exists as an outlier. That is the reason what most orientalists write and what we observe on ground about India are super disconnected.
- thowieuro2343 4y ago
msaharia 4y ago
I think this article is confusing the discovery of an inscription of zero to the concept of zero. The latter would predate the former.
- reil_convnet 4y ago
  > The latter would predate the former. Agree, I think it would have existed from the day a cat ate all chickens and one had to tell their neighbor they have no more chicken in house. Just that the neanderthal or Cro-Magnon did not need to write it down for the modern paleontologist to discover.
Ekaros 4y ago
Just use of Abacus would make one think that there must have been some thinking about concept of zero. Just using ten system and having 123 and removing 3 from that would mean that you have 0 left for 1s. What is this zero, clearly it is not none as there is 1 100 and 2 10s... Now how to notate this is different question.
dschuetz 4y ago
'Zero' was most likely invented for the same reason Complex Numbers were invented: to make some rare cases of contradictory mathematical formulas work. Zero is more a mathematical device than a number.
- Sharlin 4y ago
  On the contrary, complex numbers are one of the most "number" things that exist. It could be convincingly argued that either ℕ or ℂ are the most "real" of all sets of numbers; ℝ is a rather artificial restriction of the true richness of structure of its less popular superset.
  - sumitviii 4y ago
    >It could be convincingly argued Go on. Argue that please.
    - Sharlin 4y ago
      Your comment has a needlessly confrontational tone. Anyway, the field of complex numbers is algebraically closed. Reals are not.
  - dahart 4y ago
    FWIW I don’t think this is contrary to the comment you replied to, but I started reading your comment hoping you’d have the convincing argument. Are there some examples you’re thinking of? There’s no denying the mathematical utility of complex numbers, they are a great mathematical device. There’s also no question that natural and real numbers existed in math and language for thousands of years before complex numbers were invented. But why would complex be more “number” or more “real” than scalars, what does that mean? How are reals an artificial restriction of complex numbers? (Does it make real number sense to have 2+3i dollars or apples?) Surely the choice to include the real number line in the complex plane isn’t the only reason? Otherwise, I’d argue that vectors are the more natural choice for what you’re trying to say.
    - 4y ago
fleddr 4y ago
"The tracing of zero’s heritage has been elusive. For a country to be able to claim the number’s origin would provide a sense of ownership and determine a source of great nationalistic pride." As seen in some of the comments below. As if they personally made it possible. It's like your country winning a sports tournament and claiming that "WE" won. No, you didn't. You just watched it.
- Bost 4y ago
  Almost. Behind "WE/US" is the society which builds and runs sports facilities (operating quite often at loss) implements sport education programmes for children and youth etc. So, no it is us being represented by the few talented ones.
- Abishek_Muthian 4y ago
  Yeah, Because Nationalism across the world is all time low! Besides, The two main contenders for the title from Cambodia and Indonesia have stone inscriptions with 'Zero' for the 'Saka' calendar year; So even if the inscriptions are older, The origin of zero likely points to somewhere in Indian subcontinent of Saka Era. The author seems to conflate between 'Origin of zero' and 'Latest evidence for oldest occurrence of zero'. I don't think professors dealing with Epigraphy, Philology (or) Archeology can make such a mistake unless writing a click-bait article with misleading content was the goal.
dr_dshiv 4y ago
* * * * * * * * * * This is a Pythagorean Tetractys. It is a mystical symbol that shows how 1+2+3+4=10, which supposedly shows the presence of harmony in pure numbers. Harmony in numbers was believed to manifest in the physical cosmos (eg, Harmony of the Spheres). This Tetractys relates also to musical harmony (which was famously formalized by the Pythagoreans). The top dot shows that, when you press a lyre string in the middle, you produce an octave. The two dots show where you can press a string to produce a musical fifth (3:2), and so on. The presence of zero is represented esoterically in the open string, which has no dot. Whether or not this was actually discussed by the Pythagoreans cannot be known—and clearly the concept of zero was otherwise unknown to the Greeks. But, who knows what might have been: the Pythagoreans were nearly all massacred by their enemies in the 5th century BC.
Bubble_Pop_22 4y ago
I think most likely it was a representation of an empty circular enclosure for animals. Enclosure empty = O
contingencies 4y ago
IMHO the big picture is missing. Examples of Indic scripts are found inside of China, as far northeast as central Vietnam, at some (later) sites in Japan and Korea, and all over Southeast Asia. Most of the use of these scripts is related to religion and to a lesser extent record-keeping. Unfortunately, the majority of these scripts were written on palm leaves which do not keep very well, so we are only left with the relatively rare inscriptions on stone and inscriptions on metal. The Indian seafaring polities which are associated with Southeast Asia (ie. Srivijaya et al) are from India's south and eastern coasts. The south of India is also the traditional home of the Tamil, a Dravidian (non-Aryan) people whose language and script predate and differ from the prakrit languages which dominate Aryan-influenced northern and western India. What is interesting about the Tamil is that they had a record keeping culture in which inscriptions were made in to metal plates which were then bound on giant keyrings like a giant keychain. There are a great deal of these preserved. One wonders if zero exists in this corpus, whether or not it goes back to a directly contemporary period. If not, then the origin would appear to be clearly non-Tamil and could be ascribed to the subset of enthusiastically seafaring empires of the southern and eastern Indian coasts. The apparent main Tamil/Dravidian seafaring polity was called the Chola. https://en.wikipedia.org/wiki/Chola_dynasty https://en.wikipedia.org/wiki/Chola_dynasty but there was also the Pandyas https://en.wikipedia.org/wiki/Pandya_dynasty https://en.wikipedia.org/wiki/Pandya_dynasty and Cheras (west coast, modern Kerala) https://en.wikipedia.org/wiki/Chera_dynasty https://en.wikipedia.org/wiki/Chera_dynasty Some of the non-Tamil seafaring polities: the Pallava, the Gupta (central-northern India), the Pala (Bengal coast and northward). https://en.wikipedia.org/wiki/Pallava_dynasty https://en.wikipedia.org/wiki/Pallava_dynasty https://en.wikipedia.org/wiki/Gupta_Empire https://en.wikipedia.org/wiki/Gupta_Empire https://en.wikipedia.org/wiki/Pala_Empire https://en.wikipedia.org/wiki/Pala_Empire Any of these could have been the Indic culture at which "zero" moved eastward with merchants or religious record keeping.
mihaic 4y ago
I get a bit annoyed on these claims of "the first zero", since it never bothers to be very explicit about defining what first "zero" they're talking about. Is it the first symbol for no quantity? If you're only working with positive numbers you're not missing much by just saying "nothing". Having a zero matters a lot in positional number systems, since it means something else there. The Babylonians still got by with just putting a space instead of a symbol. Lastly, when using negative numbers on top of this, being able to work with the number between -1 and 1 just as any other becomes more necessary. All these examples of "first zero" originate from the need to simplify and strengthen an already innovative system, and each individual first zero needs to be tied to that concept of number.

71 points by Hooke 4y ago

deleted 4y ago

[deleted]

> The stone bore a Khmer epigraphic inscription that included the date for the Khmer year 605, reckoned within the Hindu Saka system, a historical calendar based on the rule of the Indian emperor Shalivahana. Seems there is a pretty good chance that the origin of zero is still Indian and was adopted by the Khmer just as they adopted the Indian calendar.

drieddust 4y ago
Isha Upnishad[0] was written in 1st half of 1st millennium BCE as per the conservative estimates. Its Shanti Mantra(wishing peace to all living beings) of says: ॐ पूर्णमदः पूर्णमिदं पूर्णात्पूर्णमुदच्यते । पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥ ॐ शान्तिः शान्तिः शान्तिः ॥ Om Puurnnam-Adah Puurnnam-Idam Puurnnaat-Puurnnam-Udacyate | Puurnnasya Puurnnam-Aadaaya Puurnnam-Eva-Avashissyate || Om Shaantih Shaantih Shaantih || Rough Translation: That (god) is complete(puurnnam), this living being is complete. From completeness emerges completeness. When this completeness (living beings) emerges from that completeness (god), only completeness remains. This verse describes God. But it can also be describing concept of zero and infinity. Buddhist philosophy emerging in 500 BCE is based in shoonyata[1] (nothingness) so concept of zero was definitely known for a long time. As far as mathematical applications are concerned, we can't say for sure as a lot of knowledge was lost to invasions which specifically targeted universities like Nalanda[2]. Hindus imagined time scales of microseconds to trillions of years which in IMHO difficult to imagine without zero based mathematics[3]. Having said that there are a large number of manuscripts in the hands of small groups and families are yet to be discovered so these dates. [0] https://en.wikipedia.org/wiki/Isha_Upanishad https://en.wikipedia.org/wiki/Isha_Upanishad [1] https://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81 https://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81 [2] https://www.myindiamyglory.com/2017/09/11/nalanda-9-million-books-burnt/ https://www.myindiamyglory.com/2017/09/11/nalanda-9-million-... [3] https://en.wikipedia.org/wiki/Hindu_units_of_time https://en.wikipedia.org/wiki/Hindu_units_of_time
- KingOfCoders 4y ago
  The idea of zero is that it's used in a positional numeric system, not just as a symbol for nothingness, like in 1305 + 0935 ---- 2240 or in calculations ((5-5)+2)*0 = (0+2)*0 = 2*0 = 0
  - drieddust 4y ago
    Thanks, but that's such a narrow definition of the concept. Shukla Yajurveda[0] conservatively estimated to be written in 1200- 800 BCE period in 17.2.20 constructs powers of 10 upto a billion by names by adding shunya successively to 10. [0] https://en.m.wikipedia.org/wiki/Yajurveda https://en.m.wikipedia.org/wiki/Yajurveda
    - KingOfCoders 4y ago
      This is the concept of zero. The title said "The Elusive Origin of Zero". Widening the definition to something else doesn't expand understanding but creates confusion.
- braindead_in 4y ago
  As Swami Sarvapriyananda is fond of saying, this verse encapsulates the essence of Advaita Vedanta. This verse is in fact his favourite. He has given hours and hours of talks on it. There is a lot packed into it.
xhevahir 4y ago
Maybe. It would be odd, though, not to find any Indian examples of zero from earlier than ~200 years after the oldest Khmer one if the invention came from India. That area first came under Indian influence centuries before these dates. Some parts of the country, Chenla, were dependent on states in Java and Srivijaya (the one mentioned in the article) later on. The Indian cultural sphere as a whole covered a huge area and the Subcontinent itself certainly did not have a monopoly on culture there.

moralestapia 4y ago

LOL, how could two "emeritus professors" write an article like this without a single mention of the Mayan civilization, which is regarded by many as the earliest use of an explicit zero in a numerical system. Are they not aware of this?

melissalobos 4y ago
Not sure, but maybe because it isn't a positional zero.
xhevahir 4y ago
The Mayans may or may not have been first, but due to their isolation their use of zero was unknown to the rest of the world. By the time Europeans and Mayans met, the Hindu-Arabic numeral system was well established and that was the system that became the world's.

WhitneyLand 4y ago

Looking far enough back in time it becomes difficult to imagine the context in which the “concept of nothing” was a novel idea. How intuitive is counting starting from no foundational knowledge? I mean, every day you knew if you had 1 or 2 pieces of food to eat right? It seems realizing when you had zero pieces of food would be top of mind.

jcranmer 4y ago
The difficulty, I think, is in establishing that "nothing" is a tangible object that can be manipulated as if it were a "regular" number. This may be a little easier to grasp if you look at language. In many languages (most? nearly all?), you generally don't express lacking food as saying "I have 0 food" but as saying "I do not have food"--the concept of nothing is essentially reflected as turning the verb (or clause/sentence as a whole) into a negative mood, rather than indicating that the count of an object is 0.
- madmoose 4y ago
  I like to imagine the situation of a tax collector in ancient Mesopotamia, going around and asking the farmers how many animals they have. If the farmer has 5 cows, they have a number of cows that you can put in a form on a clay tablet. If the farmer has no goats, they don't have "a number of goats", they have no goats to count. Writing a number on the tax form doesn't make sense. If numbers are only used to count actual things in the real world, zero is a very odd concept. We realized later that having "a number" to represent "none" simplifies many things and rids us having to deal with special cases. And if we teach it to children early enough it isn't too confusing.
  - dr_dshiv 4y ago
    Yes, but when you have a set of goods to proportion out and you are complete, then there is a zero. So it may be quite common. The Egyptians indicated a concept like zero with the NFR sign, for perfect. That’s the one with a circle and a cross on top. But, no decimal placeholder system, like described in the article. http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egypt_zero.html http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_e...

wintorez 4y ago

For me the importance of zero is not about assigning a symbol to nothing. It’s about to come up with the idea that the symbol for the number of things one more than 9 should be 10 instead of another arbitrary symbol. This concept seems intuitive at first, but when you think about it, it’s such an genius idea.

dataflow 4y ago
> For me the importance of zero is not about assigning a symbol to nothing. It’s about to come up with the idea that the symbol for the number of things one more than 9 should be 10 instead of another arbitrary symbol. By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. [...] The Babylonian placeholder was not a true zero because it was not used alone, nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60) looked the same, because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them. From https://en.wikipedia.org/wiki/0 https://en.wikipedia.org/wiki/0

cat_plus_plus 4y ago

"We are out of stuff" is not a concept that can be traced to recorded history, because it much predates humans. Literal single cell life forms behave differently under conditions of scarcity vs abundance.

makach 4y ago

My hero Zero, by the Lemonheads. Yeah, Zero is a wonderful thing In fact, Zero is my hero! How can Zero be a hero? Well, there are all kinds of heroes, you know A man can get to be a hero For a famous battle he fought Or by studying very hard And becoming a weightless astronaut And then there are heroes of other sorts Like the heroes, you know, from watching sports But a hero doesn't have to be a grown up person, you know A hero can be a very big dog Who comes to your rescue Or a very little boy who's smart enough to know what to do But let me tell you about my favorite hero My hero, Zero, such a funny little hero But 'til you came along We counted on our fingers and toes Now you're here to stay And nobody really knows How wonderful you are Why we could never reach a star Without you, Zero, my hero How wonderful you are What's so wonderful about a zero? It's nothing, isn't it? Sure, it represents nothing alone But place a zero after 1 And you've got yourself a 10 See how important that is? When you run out of digits You can start all over again See how convenient that is? That's why with only ten digits including zero You can count as high as you could ever go Forever, towards infinity No one ever gets there, but you could try 10 billion zeros From the cavemen to the weirdos Who invented you They counted on their fingers and toes Or maybe some sticks and stones, rocks and bones Their neighbors' toes Yeah yeah And nobody really knows How wonderful you are Why you could never reach a star Without you, Zero, my hero Zero, how wonderful you are Place one zero after any number And you've multiplied that number by 10 See how easy that is Place two zeros after any number And you've multiplied that number by 100 See how simple that is Place three zeros after any number And you've multiplied that number by 1, 000 Et cetera, et cetera, ad infinitum, ad astra, forever and ever With zero, my hero, how wonderful you are

chunkyguy 4y ago

India as a whole didn't even exist back then. Why don't historians describe only in terms of ancient kingdoms or whatever geographical entities existed back then and then describe what current political boundaries contains that area today?

reil_convnet 4y ago
> India as a whole didn't even exist back then. Given the only entity you think of India to be is a Nation State, it didn't. Which for most "west" educated people is the only type of state that can exist. But entities can exist beyond concept of a Nation State. Unfortunately, its not very easy to unlearn years of "one good way" to think. Did Germany exist during Roman Empire or during Holy Roman Empire ? It did not as a nation state, but the people almost always felt connected. India had much stronger bonds among people than say typical Germany, the religion/culture had elements from the entire nation, created by leaders from different parts of continent. Hinduism has verses conveying rivers and Gods from around the subcontinent as important aspects of life. Adi Shakaracharya, the religious teacher who is considered the person who made Hinduism the dominant form from among other existing interpretations of "Dharma" belongs to the southernmost tip of the region and created hindu institutions in all corners of subcontinent. Bhakshali Manuscript is one of the oldest Indian documents with use of Zero in Maths written by Buddhist scholars in Sanskrit. https://en.wikipedia.org/wiki/Bakhshali_manuscript https://en.wikipedia.org/wiki/Bakhshali_manuscript . This was discovered in modern day Pakistan [then British India]. You could argue that this is a part of Pakistan's history, but what is Pakistan's History then ? You can somewhat imagine if a Mesopotamian state survived till today, parts of it unconverted to Islam in a sub area of fertile crescent. Would you call it the successor state to entire Mesopotamia or you would say Uruk history is not their history because the region is now part of nation state of Iraq. That is the case with India as well ! There is a reason we read Mesopotamian history as a composite and as a different topic than say Egyptian History, because Mesopotamia was a different and connected civilization. Institutions like that don't survive now and hence a modern western scholar has no ontology to relate it to, but India exists as an outlier. That is the reason what most orientalists write and what we observe on ground about India are super disconnected.
thowieuro2343 4y ago

msaharia 4y ago

I think this article is confusing the discovery of an inscription of zero to the concept of zero. The latter would predate the former.

reil_convnet 4y ago
> The latter would predate the former. Agree, I think it would have existed from the day a cat ate all chickens and one had to tell their neighbor they have no more chicken in house. Just that the neanderthal or Cro-Magnon did not need to write it down for the modern paleontologist to discover.

Ekaros 4y ago

Just use of Abacus would make one think that there must have been some thinking about concept of zero. Just using ten system and having 123 and removing 3 from that would mean that you have 0 left for 1s. What is this zero, clearly it is not none as there is 1 100 and 2 10s... Now how to notate this is different question.

dschuetz 4y ago

'Zero' was most likely invented for the same reason Complex Numbers were invented: to make some rare cases of contradictory mathematical formulas work. Zero is more a mathematical device than a number.

Sharlin 4y ago
On the contrary, complex numbers are one of the most "number" things that exist. It could be convincingly argued that either ℕ or ℂ are the most "real" of all sets of numbers; ℝ is a rather artificial restriction of the true richness of structure of its less popular superset.
- sumitviii 4y ago
  >It could be convincingly argued Go on. Argue that please.
  - Sharlin 4y ago
    Your comment has a needlessly confrontational tone. Anyway, the field of complex numbers is algebraically closed. Reals are not.
- dahart 4y ago
  FWIW I don’t think this is contrary to the comment you replied to, but I started reading your comment hoping you’d have the convincing argument. Are there some examples you’re thinking of? There’s no denying the mathematical utility of complex numbers, they are a great mathematical device. There’s also no question that natural and real numbers existed in math and language for thousands of years before complex numbers were invented. But why would complex be more “number” or more “real” than scalars, what does that mean? How are reals an artificial restriction of complex numbers? (Does it make real number sense to have 2+3i dollars or apples?) Surely the choice to include the real number line in the complex plane isn’t the only reason? Otherwise, I’d argue that vectors are the more natural choice for what you’re trying to say.
  - 4y ago

fleddr 4y ago

"The tracing of zero’s heritage has been elusive. For a country to be able to claim the number’s origin would provide a sense of ownership and determine a source of great nationalistic pride." As seen in some of the comments below. As if they personally made it possible. It's like your country winning a sports tournament and claiming that "WE" won. No, you didn't. You just watched it.

Bost 4y ago
Almost. Behind "WE/US" is the society which builds and runs sports facilities (operating quite often at loss) implements sport education programmes for children and youth etc. So, no it is us being represented by the few talented ones.
Abishek_Muthian 4y ago
Yeah, Because Nationalism across the world is all time low! Besides, The two main contenders for the title from Cambodia and Indonesia have stone inscriptions with 'Zero' for the 'Saka' calendar year; So even if the inscriptions are older, The origin of zero likely points to somewhere in Indian subcontinent of Saka Era. The author seems to conflate between 'Origin of zero' and 'Latest evidence for oldest occurrence of zero'. I don't think professors dealing with Epigraphy, Philology (or) Archeology can make such a mistake unless writing a click-bait article with misleading content was the goal.

dr_dshiv 4y ago

* * * * * * * * * * This is a Pythagorean Tetractys. It is a mystical symbol that shows how 1+2+3+4=10, which supposedly shows the presence of harmony in pure numbers. Harmony in numbers was believed to manifest in the physical cosmos (eg, Harmony of the Spheres). This Tetractys relates also to musical harmony (which was famously formalized by the Pythagoreans). The top dot shows that, when you press a lyre string in the middle, you produce an octave. The two dots show where you can press a string to produce a musical fifth (3:2), and so on. The presence of zero is represented esoterically in the open string, which has no dot. Whether or not this was actually discussed by the Pythagoreans cannot be known—and clearly the concept of zero was otherwise unknown to the Greeks. But, who knows what might have been: the Pythagoreans were nearly all massacred by their enemies in the 5th century BC.

Bubble_Pop_22 4y ago

I think most likely it was a representation of an empty circular enclosure for animals. Enclosure empty = O

contingencies 4y ago

IMHO the big picture is missing. Examples of Indic scripts are found inside of China, as far northeast as central Vietnam, at some (later) sites in Japan and Korea, and all over Southeast Asia. Most of the use of these scripts is related to religion and to a lesser extent record-keeping. Unfortunately, the majority of these scripts were written on palm leaves which do not keep very well, so we are only left with the relatively rare inscriptions on stone and inscriptions on metal. The Indian seafaring polities which are associated with Southeast Asia (ie. Srivijaya et al) are from India's south and eastern coasts. The south of India is also the traditional home of the Tamil, a Dravidian (non-Aryan) people whose language and script predate and differ from the prakrit languages which dominate Aryan-influenced northern and western India. What is interesting about the Tamil is that they had a record keeping culture in which inscriptions were made in to metal plates which were then bound on giant keyrings like a giant keychain. There are a great deal of these preserved. One wonders if zero exists in this corpus, whether or not it goes back to a directly contemporary period. If not, then the origin would appear to be clearly non-Tamil and could be ascribed to the subset of enthusiastically seafaring empires of the southern and eastern Indian coasts. The apparent main Tamil/Dravidian seafaring polity was called the Chola. https://en.wikipedia.org/wiki/Chola_dynasty https://en.wikipedia.org/wiki/Chola_dynasty but there was also the Pandyas https://en.wikipedia.org/wiki/Pandya_dynasty https://en.wikipedia.org/wiki/Pandya_dynasty and Cheras (west coast, modern Kerala) https://en.wikipedia.org/wiki/Chera_dynasty https://en.wikipedia.org/wiki/Chera_dynasty Some of the non-Tamil seafaring polities: the Pallava, the Gupta (central-northern India), the Pala (Bengal coast and northward). https://en.wikipedia.org/wiki/Pallava_dynasty https://en.wikipedia.org/wiki/Pallava_dynasty https://en.wikipedia.org/wiki/Gupta_Empire https://en.wikipedia.org/wiki/Gupta_Empire https://en.wikipedia.org/wiki/Pala_Empire https://en.wikipedia.org/wiki/Pala_Empire Any of these could have been the Indic culture at which "zero" moved eastward with merchants or religious record keeping.

mihaic 4y ago

I get a bit annoyed on these claims of "the first zero", since it never bothers to be very explicit about defining what first "zero" they're talking about. Is it the first symbol for no quantity? If you're only working with positive numbers you're not missing much by just saying "nothing". Having a zero matters a lot in positional number systems, since it means something else there. The Babylonians still got by with just putting a space instead of a symbol. Lastly, when using negative numbers on top of this, being able to work with the number between -1 and 1 just as any other becomes more necessary. All these examples of "first zero" originate from the need to simplify and strengthen an already innovative system, and each individual first zero needs to be tied to that concept of number.