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There was nothing strange about zero for our distant ancestors. There are only two things that have been understood much later about zero, that it is a quantit

There was nothing strange about zero for our distant ancestors. There are only two things that have been understood much later about zero, that it is a quantity that in many circumstances should be treated in the same way as any other numbers and that it requires a special symbol in order to implement a positional system for writing numbers. The concept of zero itself had already been known many thousands of years before the invention of the positional system for writing numbers. All the recorded ancient languages were able to answer to the question "How many sheep do you see there?" not only with words meaning "one", "two", "three", "four", "few", "many" and so on, but also with a word meaning "none". Similarly for the answers to a question like "How much barley do you have?". Nevertheless, the concept of the quantity "zero" must have been understood later than the concepts of "one", "two", "many" and of negation, because in most languages the words similar in meaning to "none", "nobody", "nothing", "null" are derived from negation words together with words meaning "one" or denoting small or indefinite quantities. Because the first few numbers, especially 0, 1 and 2 have many distinctive properties in comparison with bigger numbers, not only 0 was initially perceived as being in a class somewhat separate from other numbers, but usually also 1 and 2 and sometimes also 3 or even 4. In many old languages the grammatical behavior of the first few numbers can be different between themselves and also quite different from that of the bigger numbers, which behave more or less in the same way, consistent with the expectation that the big numbers have been added later to the language and at a time when they were perceived as a uniform category.

bugbuddy 2y ago
There are other factual problems with this article. Most jarring is that it repeats this old incorrect information: > Inside the Chaturbhuj Temple in India (left), a wall inscription features the oldest known instance of the digit zero, dated to 876 CE (right). It is part of the number 270. This is the real oldest known zero: > Because we know that the Çaka dynasty began in AD 78, we can date the artifact exactly: to the year AD 683. This makes the “0” in “605” the oldest zero ever found of our base-10, “Hindu-Arabic” number system. > But the Cambodian stone inscription bears the first known zero within the system that evolved into the numbers we use today. Maybe the Khmers came up with it or maybe they got the idea from India. Either way, we should set the facts straight. https://time.com/3845786/my-quest-to-find-the-first-zero/ https://time.com/3845786/my-quest-to-find-the-first-zero/
- westurner 2y ago
  0 (number) > Classical antiquity; https://en.wikipedia.org/wiki/0#Classical_antiquity https://en.wikipedia.org/wiki/0#Classical_antiquity : > By AD 150, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero ( — ° ) [25][26] in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest. [27] This Hellenistic zero was perhaps the earliest documented use of a numeral representing zero in the Old World. [28]
poincaredisk 2y ago
>In many old languages the grammatical behavior of the first few numbers can be different between themselves Not even old languages, in many languages today (notably slavic) nouns decline differently with "1", "2", "3", "4" and say "5". In many languages, including existing ones (Lithuanian, Irish and Slovenian come to mind) there exists a concept of a grammatical number "dual", in addition to singular and plural.
- david_allison 2y ago
  For anyone looking for more information: https://www.unicode.org/cldr/charts/46/supplemental/language_plural_rules.html https://www.unicode.org/cldr/charts/46/supplemental/language... grep for "two" (note: "two" means 'dual', not literally '2') Spec: https://cldr.unicode.org/index/cldr-spec/plural-rules https://cldr.unicode.org/index/cldr-spec/plural-rules
- cperciva 2y ago
  Not even old languages, in many languages today (notably slavic) nouns decline differently with "1", "2", "3", "4" and say "5". Hence a wonderful piece of Soviet humour: A factory needs 5 fireplace pokers, but none of the workers knows the correct plural form for 5 fireplace pokers; not wanting to appear ignorant when they send their request to management, they request "3 fireplace pokers and 2 more". Some months later they receive the fireplace pokers with a note saying "here are 4 fireplace pokers and 1 more" -- because management didn't know the word either!
  - 5- 2y ago
    that's a tough one! i'm a native russian speaker (though i have been living in an english-speaking country for a while), yet it took me a few moments, and i compulsively consulted wiktionary to check myself: "five fireplace-pokers" would be "пять кочерёг", marked as 'irregular' in the table. https://en.wiktionary.org/wiki/кочерга#Declension https://en.wiktionary.org/wiki/кочерга#Declension
TheRealPomax 2y ago
Except there is, because the zero the article is talking about is the mathematical zero, not the natural language one. In your experience of natural language, zero is a quantity. In math, it's very much not: it's a singularity. Sure, as "that number between -1 and 1 on the number line", zero is mostly unremarkable, but math doesn't really care about number lines that much: as a singularity that arises from mathematical operations, its behaviour, and its "so what is it, really?" is a proper brain twister.
drewcoo 2y ago
Zero was not a "counting number." It wasn't used in early calculations. To an ancient Roman, tomorrow is 2 (ok, II) days from now. Today . . . one . . . tomorrow . . . two . . . two days! > Because the first few numbers, especially 0, 1 and 2 Considering zero one of "the first few numbers," or even considering zero being a number, or for that matter considering zero at all are very recent concepts for humans. A millennium ago, asking someone to count all the sheep in a field that had no sheep would be like today asking the sound of one hand clapping.
- johnisgood 2y ago
  I have a hard time believing this though. If there are no sheep, then would it really not be "obvious" to them that there are no sheep, i.e. zero sheep, or none to be found? What would have been their answer if not something akin to this?
  - thfuran 2y ago
    It's not that there's no concept of the absence of sheep, it's that there's no concept that that can be represented as some number of sheep.
    - adrian_b 2y ago
      This may sound clever, but it fails the experimental tests. In most modern grammar theories and already in some of the works of the Ancient Greeks and Romans, a group of words is recognized as having the same nature if any of those words can be substituted for another of them in a given sentence. Given the sentences (which have one-to-one correspondences in the ancient languages): I see zero sheep. (In Latin, "null-" is the word stem for zero.) I see one sheep. I see two sheep. I see three sheep. ... both a modern grammarian and also some of the ancient ones will conclude that zero, one, two, three ... have the same nature. So zero was a concept that represented a certain quantity of sheep. The Romans might have not used the word "number" in reference to zero, but there is no doubt that they understood the concept of a set whose members are 0, 1, 2, 3 and so on. The proof is that the normal way of saying "some" in Latin, i.e. an unknown number that is at least 1, was to say "not zero", i.e. by identifying the subset 1, 2, 3, ... with the complement of the subset that contains 0 in the set of what now are called natural numbers. While they did not have standardized words for concepts like set, subset, complement, membership or quantifiers, these concepts of the modern set theory were nevertheless well understood by the educated people in the Ancient World as they were studied within Logic a.k.a. Dialectic.

bugbuddy 2y ago

There are other factual problems with this article. Most jarring is that it repeats this old incorrect information: > Inside the Chaturbhuj Temple in India (left), a wall inscription features the oldest known instance of the digit zero, dated to 876 CE (right). It is part of the number 270. This is the real oldest known zero: > Because we know that the Çaka dynasty began in AD 78, we can date the artifact exactly: to the year AD 683. This makes the “0” in “605” the oldest zero ever found of our base-10, “Hindu-Arabic” number system. > But the Cambodian stone inscription bears the first known zero within the system that evolved into the numbers we use today. Maybe the Khmers came up with it or maybe they got the idea from India. Either way, we should set the facts straight. https://time.com/3845786/my-quest-to-find-the-first-zero/ https://time.com/3845786/my-quest-to-find-the-first-zero/

westurner 2y ago
0 (number) > Classical antiquity; https://en.wikipedia.org/wiki/0#Classical_antiquity https://en.wikipedia.org/wiki/0#Classical_antiquity : > By AD 150, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero ( — ° ) [25][26] in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest. [27] This Hellenistic zero was perhaps the earliest documented use of a numeral representing zero in the Old World. [28]

poincaredisk 2y ago

>In many old languages the grammatical behavior of the first few numbers can be different between themselves Not even old languages, in many languages today (notably slavic) nouns decline differently with "1", "2", "3", "4" and say "5". In many languages, including existing ones (Lithuanian, Irish and Slovenian come to mind) there exists a concept of a grammatical number "dual", in addition to singular and plural.

david_allison 2y ago
For anyone looking for more information: https://www.unicode.org/cldr/charts/46/supplemental/language_plural_rules.html https://www.unicode.org/cldr/charts/46/supplemental/language... grep for "two" (note: "two" means 'dual', not literally '2') Spec: https://cldr.unicode.org/index/cldr-spec/plural-rules https://cldr.unicode.org/index/cldr-spec/plural-rules
cperciva 2y ago
Not even old languages, in many languages today (notably slavic) nouns decline differently with "1", "2", "3", "4" and say "5". Hence a wonderful piece of Soviet humour: A factory needs 5 fireplace pokers, but none of the workers knows the correct plural form for 5 fireplace pokers; not wanting to appear ignorant when they send their request to management, they request "3 fireplace pokers and 2 more". Some months later they receive the fireplace pokers with a note saying "here are 4 fireplace pokers and 1 more" -- because management didn't know the word either!
- 5- 2y ago
  that's a tough one! i'm a native russian speaker (though i have been living in an english-speaking country for a while), yet it took me a few moments, and i compulsively consulted wiktionary to check myself: "five fireplace-pokers" would be "пять кочерёг", marked as 'irregular' in the table. https://en.wiktionary.org/wiki/кочерга#Declension https://en.wiktionary.org/wiki/кочерга#Declension

TheRealPomax 2y ago

Except there is, because the zero the article is talking about is the mathematical zero, not the natural language one. In your experience of natural language, zero is a quantity. In math, it's very much not: it's a singularity. Sure, as "that number between -1 and 1 on the number line", zero is mostly unremarkable, but math doesn't really care about number lines that much: as a singularity that arises from mathematical operations, its behaviour, and its "so what is it, really?" is a proper brain twister.

drewcoo 2y ago

Zero was not a "counting number." It wasn't used in early calculations. To an ancient Roman, tomorrow is 2 (ok, II) days from now. Today . . . one . . . tomorrow . . . two . . . two days! > Because the first few numbers, especially 0, 1 and 2 Considering zero one of "the first few numbers," or even considering zero being a number, or for that matter considering zero at all are very recent concepts for humans. A millennium ago, asking someone to count all the sheep in a field that had no sheep would be like today asking the sound of one hand clapping.

johnisgood 2y ago
I have a hard time believing this though. If there are no sheep, then would it really not be "obvious" to them that there are no sheep, i.e. zero sheep, or none to be found? What would have been their answer if not something akin to this?
- thfuran 2y ago
  It's not that there's no concept of the absence of sheep, it's that there's no concept that that can be represented as some number of sheep.
  - adrian_b 2y ago
    This may sound clever, but it fails the experimental tests. In most modern grammar theories and already in some of the works of the Ancient Greeks and Romans, a group of words is recognized as having the same nature if any of those words can be substituted for another of them in a given sentence. Given the sentences (which have one-to-one correspondences in the ancient languages): I see zero sheep. (In Latin, "null-" is the word stem for zero.) I see one sheep. I see two sheep. I see three sheep. ... both a modern grammarian and also some of the ancient ones will conclude that zero, one, two, three ... have the same nature. So zero was a concept that represented a certain quantity of sheep. The Romans might have not used the word "number" in reference to zero, but there is no doubt that they understood the concept of a set whose members are 0, 1, 2, 3 and so on. The proof is that the normal way of saying "some" in Latin, i.e. an unknown number that is at least 1, was to say "not zero", i.e. by identifying the subset 1, 2, 3, ... with the complement of the subset that contains 0 in the set of what now are called natural numbers. While they did not have standardized words for concepts like set, subset, complement, membership or quantifiers, these concepts of the modern set theory were nevertheless well understood by the educated people in the Ancient World as they were studied within Logic a.k.a. Dialectic.