7 ms·

The Invention of Zero

150 points by Anon84 2y ago

lamp_book 2y ago
Interesting enough, the oldest recorded use of the symbol zero in mesoamerica is older. From https://baas.aas.org/pub/2021n1i336p03/release/2 https://baas.aas.org/pub/2021n1i336p03/release/2 - “The oldest representation of the Mesoamerican zero, dating from the year 31 BCE, is found in Stela C in the ancestral Olmec site of Tres Zapotes in Veracruz, Mexico.”
- adrian_b 2y ago
  Older than the use of zero in India, but hundreds of years later than the use of zero in Mesopotamia. In any case, this must have been an independent invention of zero.
  - deleted 2y ago
    [deleted]
  - kragen 2y ago
    unless it was brought over by the flying saucers (now where did i put my aluminum foil)
adrian_b 2y ago
Speaking about the "invention of zero" is not a good choice of words. All languages have had words for "zero", for at least a few thousand years. For instance English has inherited "null" from Latin, whose literal meaning was initially "not even a small one", but whose meaning has become "zero". Latin also used very frequently the word "non-null", with the meaning "one or more". Latin had a few more other words that could be used to express the quantity "zero". The same was true for Ancient Greek and for the languages for which even older records exist. What the parent article intends to discuss is the invention of a purely positional system for writing numbers. Before the invention of such a system for writing numbers, the words meaning "zero" were used in all languages only for the unique quantity "zero". They were not used as components of the numerals used to name bigger numbers. The necessity to write very big numbers for accounting or computational purposes has made desirable the invention of a system that would be less cumbersome for such big numbers than the system used for the spoken numerals. That was the positional number system, where a small set of symbols is sufficient to write even very big numbers. Any purely positional number system needs some kind of symbol for zero, which must be usable in any position. When the sexagesimal Mesopotamian number system began to be used positionally, a symbol for "zero" had to be added. So nobody thought directly about a "zero" symbol. They just wanted to reuse the same symbols in all positions, and sooner or later someone understood that adding a symbol for "zero" is the solution to this problem.
- mensetmanusman 2y ago
  Null is closer to ‘empty set’ than to zero, and the two concepts are similar but different enough to be distinct.
  - dayjaby 2y ago
    In German, it's the same. I hope you are not talking about null in coding? Because I'm pretty sure human 2000 years ago did not know any programming code or even empty sets.
    - deleted 2y ago
      [deleted]
    - rdtsc 2y ago
      Empty set idea doesn’t seem so abstract. A bag of stuff can have nothing in it, so it’s empty. Combining and splitting up containers of items would have been an everyday occurrence.
  - kreetx 2y ago
    I'm just nitpicking, but it's unlikely that the inventors of both had empty set and zero formalized to a degree to make them distinct.
    - adrian_b 2y ago
      While the empty set and the number "zero" are distinct concepts, the relationship between them is much closer than between any other sets and numbers. The cardinal numbers are equivalence classes of the sets. For any other cardinal number except "zero", the equivalence class of that number contains a huge number of sets, potentially infinite. For "zero", the equivalence class contains only a unique set, the empty set. Because of this one-to-one correspondence between the empty set and "zero", they may be interchanged in many contexts without causing any ambiguities.
      - 2y ago
constantcrying 2y ago
I am very unconvinced by this "history of zero". Definitely the Greek geometers were aware of that concept, they just expressed it geometrically not numerically. Putting the concept at some specific geographic location seems very strange to me. To me there is no doubt that in each mathematical culture there was some notion of it, just weaved into that conceptions of that particular culture. Of course then there is zero as a symbol and positional number systems. The first one seems very uninteresting, the later one definitely more so, but the question of how to express numbers is definitely more interesting and broad than the history of just one component of it.
- rusticpenn 2y ago
  Mesopotamians were at least a millennium ahead of Greeks though..
  - constantcrying 2y ago
    No. They weren't even in the same category, even the comparison doesn't make sense. In Mesopotamia mathematics seems to have been a tool, a method for business and construction planers to drive certain quantities. Mathematics to the Greeks was "mathematics" in the sense we understand it today. From a system of axioms they derived a complex system of theorems, which allowed for an abstract description of reality. It was mathematics as a system of truth, which then could be used for other purposes. E.g. with Archimedes who discovered integration, but also was a prolific engineer. The Greeks were so far ahead of anything the Mesopotamians did, that even the comparison is unfair.
    - derstander 2y ago
      > No. They weren't even in the same category, even the comparison doesn't make sense. The comparison does make sense if you interpret the parent’s post simply to state that Babylonian mathematics (in Mesopotamia) were developed (and seemingly stagnated) before Greek mathematics began in earnest. Which seems to be pretty uncontroversial. There are extant clay tablets from 1800 to 1600 BC that would indeed predate the Greek Geometers by a millennia — and that’s if you’re counting Thales as the beginning. Ie. your parent post is using “ahead of” == “temporally before” not as in “more advanced”.
plasticeagle 2y ago
Zero is important because it is the first abstraction. If your notion of numbers includes the idea of zero as a number, then you have broken through the first intellectual barrier of mathematics. Without this, it remains tempting to still consider numbers as existing for the purpose of counting _things_. But with zero, this idea converges on the same thing. No matter what things you were counting, if you have zero of them, you have the same idea. And so you take a step towards the idea of a number being a concept in its own right, rather than existing purely for the purpose of counting or measurement. It is the same sort of conceptual freedom that allows you to do things like add a number to a square. To deal with an equation like x + x ^ 2 = 0. If you're stuck with numbers "meaning" something beyond themselves, then you'll never add x to x^2. One is a length, the other an area. They are different objects. This intellectual leap is one that must be made by all students of mathematics - and many young people do not.
- traject_ 2y ago
  Yeah, a lot of these articles conflate use of zero as placeholder, numeral and number. But the real critical conceptual step is the last step of using zero like any other number (mostly) in arithmetic.
- roywiggins 2y ago
  I am pretty sure early European mathematicians did treat polynomials as areas or volumes, x can be just a rectangle x units long in one dimension and 1 in the other, x^2 is a square, etc. This meant they had to go through contortions to avoid negative coefficients since they made no geometric sense. If a coefficient would otherwise be negative it would have to move to the other side of the equality, and be solved using a different method. Instead of a single quadratic formula they needed several different cases depending the exact form of the polynomial.
- dahart 2y ago
  > Zero is important because it is the first abstraction I’m not sure what this even means, but Sumerians had abstract mathematics, in addition to art and literature which are abstract by their nature. They were using numbers in the abstract sense before the number zero was named, and so while it seems like a logical and tempting narrative that naming zero is what abstracted numbers, history doesn’t seem to support this particular post-facto rationalization. Naming zero is very important in the history of math, it just isn’t the first abstraction. https://en.wikipedia.org/wiki/Sumer#Mathematics https://en.wikipedia.org/wiki/Sumer#Mathematics
chrisweekly 2y ago
Two things: 1. I'm a huge fan and long-time supporter of Maria Popova; IMHO themarginalian.org is one of the finest websites ever, with a breadth and depth of consistently worthwhile content. Check it out! 2. This post reminds me of a book I really enjoyed maybe 10 years ago -- "Zero: the History of a Dangerous Idea". Recommended.
nyc111 2y ago
"This concept of the infinite in a sense contoured the need for naming its mirror-image counterpart: nothingness." Is infinity the mirror image of nothingness? I cannot conceive infinity let alone its mirror image. Same with nothingness.
ArnoVW 2y ago
If you have young kids that you would like to infect with the virus of mathematics, I highly recommend "the story of 1" by Terry Jones (of Monthy Python fame) They cover how we went from objects to abstract concepts, and how 1 and 0 were "invented". https://www.youtube.com/watch?v=1Tm18iapVlI https://www.youtube.com/watch?v=1Tm18iapVlI
osigurdson 2y ago
I don't understand how the concept of zero could have taken so long for humans to discover: "I had two apples, I ate one and gave one to a friend". They must have had a word for the concept of running out of things as soon as any level of cognitive ability emerged.
- dahart 2y ago
  That’s right; the concept of nothing was already there, both as an idea, as well as in written language. It’s the use of a written numeral zero for arithmetic, and the implications of using zeroes in algebra that this article is discussing.
- xigoi 2y ago
  What took long to find out is that zero is a number like any other. That having no apples is just a special case of having some quantity of apples, not something completely separate.
- mkoubaa 2y ago
  Some living languages in amazonian tribes don't have a word for left or right. Their directions are downriver, upriver, towards river, and away from river. The language we speak and the concepts we are taught literally form into structures in our brain, and we can't understand what it would be like not to have them, because those structures are part of the organ of understanding
  - osigurdson 2y ago
    I don't think the analogy holds. River based directions can be mapped to NESW. It does't hold that the concept of "hey I ran out of stuff" would not exist in their minds. It is impossible that they didn't understand this concept.
    - avz 2y ago
      Well, the may have understood the concept of "running out of stuff" and yet not realize it naturally belongs with numbers (of which they would have known other examples like one and two). I can imagine ancient folks putting the notion of "running out of stuff" with ideas such as "hungry", "empty", "dead" etc. Formation of the more abstract concept of zero-the-number is certainly a few cognitive experiences further down a line.
ks2048 2y ago
Shoutout to the Maya who also had zero (as a placeholder in base 20 number system), it seems by at least 36 BC
kouru225 2y ago
I just finished Zero: A Biography of a Dangerous Idea. One of the best books I’ve read in a while. Really gives a great story about the evolving history of thought.
gumby 2y ago
This article is really just a gloss on Kaplan's book (which I have read so it stands out) with a bit of gratuitous randomness thrown in. Much as I have a rather low-level atavistic desire to credit India with the zero/nil, as there was so much exchange between mesopotamia and the early indus regions (just look at the idea of the alphabet going one way and then digits going the other), the sumerian "origins" are quite likely. More importantly, the vedic tradition didn't give rise to the formalisms developed by the later Greeks and, centuries later, their Islamic students. Thus for a long time, scholarly dissertations from the subcontinent on mathematics, philosophy etc tended to essays and explorations of conjectures, which makes pinning responsibility hard to do, the way you can, say, "Wiles did prove Fermat's Last Theorem". Personally I find invention requires so much history and intertwined communication that the idea of "inventor" is kind of bogus anyway. BTW in case this sounds like I'm dissing ancient indian scholars: you see this in the early days of any scientific field: early neuroscience in the early 20th century, the same with cognitive science in the mid 50s-70s (at least) etc. In fact most of contemporary ML just has a light layer of formalism painted on too. It feels like fields need names, but only really get them when they have attained some early level of abstraction and emerging rigor. Sorry, that moved on beyond zero!
- jacobolus 2y ago
  The real problem is there are too many people who treat mathematical/scientific history as some kind of olympic games, where the goal is to rack up medals for your preferred team (country, region, religious group, ...), with the result that any discussion becomes counterproductively politicized. Trying to argue about whether one tribe's or another tribe's 50-generations-ago ancestor was the first one to do this or that thing seems to me like completely missing the point, when all of these steps were part of a long and gradual historical process, building ideas and tools up over centuries. (Similarly, it's annoying how many debates center on various ancient figures' ethnicity or religious affiliation, usually without much evidence.) To anyone who tries researching ancient (or more recent) mathematics, it's clear that there usually isn't a single aha moment changing everything, but a broader culture that gradually evolves. We can see different flavors/aspects of a concept like "zero" which were developed different times and places (China, Mesopotamia, India, Greece, North America), none of which really draws any obvious line in the sand. With regard to Indian innovations, however, it seems pretty clear that written arithmetic per se (performed on a "sand board") was developed there, as credited by all of the oldest extant texts on the subject from writers in Arabic (which call it something like "Indian arithmetic" or "Indian numbers"). Written arithmetic was then substantially elaborated in the Islamic world with a switch to using pen and paper, before making its way to Europe where it eventually kicked off the development of modern mathematical notation. The earlier Mesopotamian/Egyptian/Greek/European tradition, as well as the Chinese tradition, were generally based on using finger counting or some form of counting board, with written numerals used as a serialization format rather than a calculation tool. Arguably the invention and spread of physical materials like cheap good quality paper, writing implements, ink, and eventually printing presses were as important as the theoretical developments.
m463 2y ago
I think of Dilbert's "Tell me why you need a new server" https://i.pinimg.com/originals/cd/55/b5/cd55b56cd40e1fa16e0b659c96c0c8bb.gif https://i.pinimg.com/originals/cd/55/b5/cd55b56cd40e1fa16e0b...
raleighm 2y ago
Obligatory link to My Hero Zero by Schoolhouse Rock https://www.youtube.com/watch?v=tK9qE81uAGU https://www.youtube.com/watch?v=tK9qE81uAGU
poulpy123 2y ago
I'm a bit baffled by the concept of "pre-Arab Sumer", knowing that Sumer disappeared 2500 years before the arab invasion
tumidpandora 2y ago
The concept of zero wasn't a single invention, but the credit for the initial zero concept goes to India. Around 500 AD, Indian mathematicians, like Aryabhata, figured out a way to use zero as a placeholder in their number system. This was a huge deal because before that, nobody had a good way to show "nothing" in a way that worked with other numbers. Even though others like the Arabs built on this idea later, India got the whole zero ball rolling.
cushpush 2y ago
Don't forget `nil` for when you need something in your collections more naught than "not"

150 points by Anon84 2y ago

Interesting enough, the oldest recorded use of the symbol zero in mesoamerica is older. From https://baas.aas.org/pub/2021n1i336p03/release/2 https://baas.aas.org/pub/2021n1i336p03/release/2 - “The oldest representation of the Mesoamerican zero, dating from the year 31 BCE, is found in Stela C in the ancestral Olmec site of Tres Zapotes in Veracruz, Mexico.”

adrian_b 2y ago
Older than the use of zero in India, but hundreds of years later than the use of zero in Mesopotamia. In any case, this must have been an independent invention of zero.
- deleted 2y ago
  [deleted]
- kragen 2y ago
  unless it was brought over by the flying saucers (now where did i put my aluminum foil)

adrian_b 2y ago

Speaking about the "invention of zero" is not a good choice of words. All languages have had words for "zero", for at least a few thousand years. For instance English has inherited "null" from Latin, whose literal meaning was initially "not even a small one", but whose meaning has become "zero". Latin also used very frequently the word "non-null", with the meaning "one or more". Latin had a few more other words that could be used to express the quantity "zero". The same was true for Ancient Greek and for the languages for which even older records exist. What the parent article intends to discuss is the invention of a purely positional system for writing numbers. Before the invention of such a system for writing numbers, the words meaning "zero" were used in all languages only for the unique quantity "zero". They were not used as components of the numerals used to name bigger numbers. The necessity to write very big numbers for accounting or computational purposes has made desirable the invention of a system that would be less cumbersome for such big numbers than the system used for the spoken numerals. That was the positional number system, where a small set of symbols is sufficient to write even very big numbers. Any purely positional number system needs some kind of symbol for zero, which must be usable in any position. When the sexagesimal Mesopotamian number system began to be used positionally, a symbol for "zero" had to be added. So nobody thought directly about a "zero" symbol. They just wanted to reuse the same symbols in all positions, and sooner or later someone understood that adding a symbol for "zero" is the solution to this problem.

mensetmanusman 2y ago
Null is closer to ‘empty set’ than to zero, and the two concepts are similar but different enough to be distinct.
- dayjaby 2y ago
  In German, it's the same. I hope you are not talking about null in coding? Because I'm pretty sure human 2000 years ago did not know any programming code or even empty sets.
  - deleted 2y ago
    [deleted]
  - rdtsc 2y ago
    Empty set idea doesn’t seem so abstract. A bag of stuff can have nothing in it, so it’s empty. Combining and splitting up containers of items would have been an everyday occurrence.
- kreetx 2y ago
  I'm just nitpicking, but it's unlikely that the inventors of both had empty set and zero formalized to a degree to make them distinct.
  - adrian_b 2y ago
    While the empty set and the number "zero" are distinct concepts, the relationship between them is much closer than between any other sets and numbers. The cardinal numbers are equivalence classes of the sets. For any other cardinal number except "zero", the equivalence class of that number contains a huge number of sets, potentially infinite. For "zero", the equivalence class contains only a unique set, the empty set. Because of this one-to-one correspondence between the empty set and "zero", they may be interchanged in many contexts without causing any ambiguities.
    - 2y ago

constantcrying 2y ago

I am very unconvinced by this "history of zero". Definitely the Greek geometers were aware of that concept, they just expressed it geometrically not numerically. Putting the concept at some specific geographic location seems very strange to me. To me there is no doubt that in each mathematical culture there was some notion of it, just weaved into that conceptions of that particular culture. Of course then there is zero as a symbol and positional number systems. The first one seems very uninteresting, the later one definitely more so, but the question of how to express numbers is definitely more interesting and broad than the history of just one component of it.

rusticpenn 2y ago
Mesopotamians were at least a millennium ahead of Greeks though..
- constantcrying 2y ago
  No. They weren't even in the same category, even the comparison doesn't make sense. In Mesopotamia mathematics seems to have been a tool, a method for business and construction planers to drive certain quantities. Mathematics to the Greeks was "mathematics" in the sense we understand it today. From a system of axioms they derived a complex system of theorems, which allowed for an abstract description of reality. It was mathematics as a system of truth, which then could be used for other purposes. E.g. with Archimedes who discovered integration, but also was a prolific engineer. The Greeks were so far ahead of anything the Mesopotamians did, that even the comparison is unfair.
  - derstander 2y ago
    > No. They weren't even in the same category, even the comparison doesn't make sense. The comparison does make sense if you interpret the parent’s post simply to state that Babylonian mathematics (in Mesopotamia) were developed (and seemingly stagnated) before Greek mathematics began in earnest. Which seems to be pretty uncontroversial. There are extant clay tablets from 1800 to 1600 BC that would indeed predate the Greek Geometers by a millennia — and that’s if you’re counting Thales as the beginning. Ie. your parent post is using “ahead of” == “temporally before” not as in “more advanced”.

plasticeagle 2y ago

Zero is important because it is the first abstraction. If your notion of numbers includes the idea of zero as a number, then you have broken through the first intellectual barrier of mathematics. Without this, it remains tempting to still consider numbers as existing for the purpose of counting _things_. But with zero, this idea converges on the same thing. No matter what things you were counting, if you have zero of them, you have the same idea. And so you take a step towards the idea of a number being a concept in its own right, rather than existing purely for the purpose of counting or measurement. It is the same sort of conceptual freedom that allows you to do things like add a number to a square. To deal with an equation like x + x ^ 2 = 0. If you're stuck with numbers "meaning" something beyond themselves, then you'll never add x to x^2. One is a length, the other an area. They are different objects. This intellectual leap is one that must be made by all students of mathematics - and many young people do not.

traject_ 2y ago
Yeah, a lot of these articles conflate use of zero as placeholder, numeral and number. But the real critical conceptual step is the last step of using zero like any other number (mostly) in arithmetic.
roywiggins 2y ago
I am pretty sure early European mathematicians did treat polynomials as areas or volumes, x can be just a rectangle x units long in one dimension and 1 in the other, x^2 is a square, etc. This meant they had to go through contortions to avoid negative coefficients since they made no geometric sense. If a coefficient would otherwise be negative it would have to move to the other side of the equality, and be solved using a different method. Instead of a single quadratic formula they needed several different cases depending the exact form of the polynomial.
dahart 2y ago
> Zero is important because it is the first abstraction I’m not sure what this even means, but Sumerians had abstract mathematics, in addition to art and literature which are abstract by their nature. They were using numbers in the abstract sense before the number zero was named, and so while it seems like a logical and tempting narrative that naming zero is what abstracted numbers, history doesn’t seem to support this particular post-facto rationalization. Naming zero is very important in the history of math, it just isn’t the first abstraction. https://en.wikipedia.org/wiki/Sumer#Mathematics https://en.wikipedia.org/wiki/Sumer#Mathematics

chrisweekly 2y ago

Two things: 1. I'm a huge fan and long-time supporter of Maria Popova; IMHO themarginalian.org is one of the finest websites ever, with a breadth and depth of consistently worthwhile content. Check it out! 2. This post reminds me of a book I really enjoyed maybe 10 years ago -- "Zero: the History of a Dangerous Idea". Recommended.

nyc111 2y ago

"This concept of the infinite in a sense contoured the need for naming its mirror-image counterpart: nothingness." Is infinity the mirror image of nothingness? I cannot conceive infinity let alone its mirror image. Same with nothingness.

ArnoVW 2y ago

If you have young kids that you would like to infect with the virus of mathematics, I highly recommend "the story of 1" by Terry Jones (of Monthy Python fame) They cover how we went from objects to abstract concepts, and how 1 and 0 were "invented". https://www.youtube.com/watch?v=1Tm18iapVlI https://www.youtube.com/watch?v=1Tm18iapVlI

osigurdson 2y ago

I don't understand how the concept of zero could have taken so long for humans to discover: "I had two apples, I ate one and gave one to a friend". They must have had a word for the concept of running out of things as soon as any level of cognitive ability emerged.

dahart 2y ago
That’s right; the concept of nothing was already there, both as an idea, as well as in written language. It’s the use of a written numeral zero for arithmetic, and the implications of using zeroes in algebra that this article is discussing.
xigoi 2y ago
What took long to find out is that zero is a number like any other. That having no apples is just a special case of having some quantity of apples, not something completely separate.
mkoubaa 2y ago
Some living languages in amazonian tribes don't have a word for left or right. Their directions are downriver, upriver, towards river, and away from river. The language we speak and the concepts we are taught literally form into structures in our brain, and we can't understand what it would be like not to have them, because those structures are part of the organ of understanding
- osigurdson 2y ago
  I don't think the analogy holds. River based directions can be mapped to NESW. It does't hold that the concept of "hey I ran out of stuff" would not exist in their minds. It is impossible that they didn't understand this concept.
  - avz 2y ago
    Well, the may have understood the concept of "running out of stuff" and yet not realize it naturally belongs with numbers (of which they would have known other examples like one and two). I can imagine ancient folks putting the notion of "running out of stuff" with ideas such as "hungry", "empty", "dead" etc. Formation of the more abstract concept of zero-the-number is certainly a few cognitive experiences further down a line.

ks2048 2y ago

Shoutout to the Maya who also had zero (as a placeholder in base 20 number system), it seems by at least 36 BC

kouru225 2y ago

I just finished Zero: A Biography of a Dangerous Idea. One of the best books I’ve read in a while. Really gives a great story about the evolving history of thought.

gumby 2y ago

This article is really just a gloss on Kaplan's book (which I have read so it stands out) with a bit of gratuitous randomness thrown in. Much as I have a rather low-level atavistic desire to credit India with the zero/nil, as there was so much exchange between mesopotamia and the early indus regions (just look at the idea of the alphabet going one way and then digits going the other), the sumerian "origins" are quite likely. More importantly, the vedic tradition didn't give rise to the formalisms developed by the later Greeks and, centuries later, their Islamic students. Thus for a long time, scholarly dissertations from the subcontinent on mathematics, philosophy etc tended to essays and explorations of conjectures, which makes pinning responsibility hard to do, the way you can, say, "Wiles did prove Fermat's Last Theorem". Personally I find invention requires so much history and intertwined communication that the idea of "inventor" is kind of bogus anyway. BTW in case this sounds like I'm dissing ancient indian scholars: you see this in the early days of any scientific field: early neuroscience in the early 20th century, the same with cognitive science in the mid 50s-70s (at least) etc. In fact most of contemporary ML just has a light layer of formalism painted on too. It feels like fields need names, but only really get them when they have attained some early level of abstraction and emerging rigor. Sorry, that moved on beyond zero!

jacobolus 2y ago
The real problem is there are too many people who treat mathematical/scientific history as some kind of olympic games, where the goal is to rack up medals for your preferred team (country, region, religious group, ...), with the result that any discussion becomes counterproductively politicized. Trying to argue about whether one tribe's or another tribe's 50-generations-ago ancestor was the first one to do this or that thing seems to me like completely missing the point, when all of these steps were part of a long and gradual historical process, building ideas and tools up over centuries. (Similarly, it's annoying how many debates center on various ancient figures' ethnicity or religious affiliation, usually without much evidence.) To anyone who tries researching ancient (or more recent) mathematics, it's clear that there usually isn't a single aha moment changing everything, but a broader culture that gradually evolves. We can see different flavors/aspects of a concept like "zero" which were developed different times and places (China, Mesopotamia, India, Greece, North America), none of which really draws any obvious line in the sand. With regard to Indian innovations, however, it seems pretty clear that written arithmetic per se (performed on a "sand board") was developed there, as credited by all of the oldest extant texts on the subject from writers in Arabic (which call it something like "Indian arithmetic" or "Indian numbers"). Written arithmetic was then substantially elaborated in the Islamic world with a switch to using pen and paper, before making its way to Europe where it eventually kicked off the development of modern mathematical notation. The earlier Mesopotamian/Egyptian/Greek/European tradition, as well as the Chinese tradition, were generally based on using finger counting or some form of counting board, with written numerals used as a serialization format rather than a calculation tool. Arguably the invention and spread of physical materials like cheap good quality paper, writing implements, ink, and eventually printing presses were as important as the theoretical developments.

m463 2y ago

I think of Dilbert's "Tell me why you need a new server" https://i.pinimg.com/originals/cd/55/b5/cd55b56cd40e1fa16e0b659c96c0c8bb.gif https://i.pinimg.com/originals/cd/55/b5/cd55b56cd40e1fa16e0b...

raleighm 2y ago

Obligatory link to My Hero Zero by Schoolhouse Rock https://www.youtube.com/watch?v=tK9qE81uAGU https://www.youtube.com/watch?v=tK9qE81uAGU

poulpy123 2y ago

I'm a bit baffled by the concept of "pre-Arab Sumer", knowing that Sumer disappeared 2500 years before the arab invasion

tumidpandora 2y ago

The concept of zero wasn't a single invention, but the credit for the initial zero concept goes to India. Around 500 AD, Indian mathematicians, like Aryabhata, figured out a way to use zero as a placeholder in their number system. This was a huge deal because before that, nobody had a good way to show "nothing" in a way that worked with other numbers. Even though others like the Arabs built on this idea later, India got the whole zero ball rolling.

cushpush 2y ago

Don't forget `nil` for when you need something in your collections more naught than "not"