4 ms·

How would you know whether an ancient culture had zero?

69 points by ibobev 2mo ago

gmuslera 1mo ago
Looks like translating a positional numbering system from ancient cultures than ruling out or not if they had the concept of zero. It may be a single use symbol, here is nothing, instead of being part of bigger amounts. Numbering systems doesn't have to be positional (nor go too far).
- whatsThisBtn4 1mo ago
  Gosh I love Wittgenstein for this. I highly recommend suffering through both early and late Wittgenstein (only wrote 2 books and essentially invented one of the 3 branches of philosophy). Expect to only understand 10% of what he says, but that is normal. Separately, pragmatism by William James is an easy 4 hour read and you can have 2/3 of the branches of meta philosophy.
  - verisimi 1mo ago
    What do you think Wittgenstein would say?
    - heresie-dabord 1mo ago
      Alas, Wittgenstein can only explain it like you are 0.5.
lisp2240 1mo ago
Zero has two roles: as a positional placeholder and as a cardinal value (nothingness or net-zero). This only addresses the former.
- j16sdiz 1mo ago
  Afaict, most ancient civization have conception of "nothingness" or "emptiness". The dispute is often whether they consider it as a number or not
  - philipov 1mo ago
    We have both. Zero and Null are different data types.
    - wahern 1mo ago
      I once had a statistics professor (teaching a programming class using, IIRC, SAS) in college who worked as a data analyst in the federal government, possibly the Labor Department. Part of his job was working with polling and form data. After class he once tried to explain a paper he wrote arguing for an additional null-like type in the formal analytics system in his domain. I was young and stupid (took it as an easy programming course; was not skilled at abstract math) and impatient (wanted to meet up with friends at a pub) so didn't follow along well enough to even properly remember his argument, let alone understand it. But I've always distinctly recalled that he was arguing for a 4th, or possibly 5th type, yet whenever I survey the literature I've only found at most such 2 types. But I've probably been looking in the wrong places. For context, NULL/missing was a type. N/A was a type (i.e. a question irrelevant to someone). I can't remember the 3rd, and of course not the additional (4th or 5th) type he was proposing. If anyone knows a good resource that describes this problem domain, that would be much appreciated. I've been haunted for over 20 years by the regret of not fully appreciating what he was trying to explain to me, both because I could've learned something that day, but also because I almost immediately felt like an a*hole for not showing enough interest in and respect for a piece of scholarly work he was clearly proud of and wanted to share with me. EDIT: I think the third pre-existing type was for a situation where someone abstains from answering a question like, "Sex: male/female", because they consider themselves neither. So something like an Other type. In retrospect this was presumably related to set theory, and he felt there was a gap in the pre-existing formal models.
      - Someone 1mo ago
- Beijinger 1mo ago
  [dead]
- rendaw 1mo ago
  Doesn't the placeholder imply nothingness? E.g. 10 means 1 ten and 0 ones.
  - idoubtit 1mo ago
    No, that implication is not automatic. The Babylonian numeral system evolved over milenaries, and the simple space noting the absence of a digit between two digits was later noted by a "0" digit. But this symbol was never used by itself, so it did not mean "nothingness". In the same way, a civilization having the concepts of addition and subtraction does not automatically induce the concept of negative numbers. On the other side, ancient Egyptian numerals did have a zero, but it was only for nothingness. But they did not have a placeholder zero, because their systems was similar to Greek and Roman numerals.
- amelius 1mo ago
  The article has quite some assumptions. They also assume a base-N system with big-endian lexicographic ordering from left to right. Has the author not heard of Roman numerals?
  - Ekaros 1mo ago
    It is very big assumption to me. It is now used very widely. But I am not sure if it was at all common back in the history. Most systems were kinda different from it.
NotBenny 1mo ago
[dead]
conartist6 1mo ago
What I wonder is: why has nobody noticed that code editors lack a concept of 0? When you're writing code, you can express any concept except that of an unfilled hole. We've rearranged every part of the coding process in a twisted-up way, all for the lack of a way to express lack. If you want to be more clear about what I mean, look to tools which can express holes like https://scratch.mit.edu https://scratch.mit.edu and https://hazel.org https://hazel.org. They give the feeling of letting things snap together like lego bricks. Indeed, lego bricks themselves function because of the negative space (the holes) in them!
- onestay42 1mo ago
  How about an `extern` variable in C?
  - conartist6 1mo ago
    A million variations exist. I'm looking for a programming-language-agnostic concept. The closest you'll find are templating languages like Handlebars
    - skew-aberration 1mo ago
      Delimited continuations? Though I'm not totally clear what you're asking for. Semantics or syntax?
      - deleted 1mo ago
        [deleted]
      - conartist6isme 1mo ago
        Syntax. Delimited continuations would be a similar concept but for semantics
    - Someone 1mo ago
      Function arguments are unfilled holes. So are interface declarations. Both are (fairly) programming language agnostic, but in the context of an editor, would become specific. The editor would have to know _how_ to represent them in the code’s language.
thaumasiotes 1mo ago
> If you knew somehow that some symbol corresponds to 20, then you’d know they didn’t use base 20 because base b doesn’t have a single symbol for b. Well, this is plainly false.
- CamperBob2 1mo ago
  I suppose Roman numerals would be one counterexample, but are there any number systems based on place/position value that qualify as counterexamples?
  - thaumasiotes 1mo ago
    Of course. The Chinese number system is base 10 (or, if you scale way up, base 10,000) with a positional writing system. The symbol for ten is 十. Heck, there's also a symbol for twenty, 廿, and it exists despite the number system being base 10. Anything that has to be written a lot is likely to have a convenient written form. If you're curious, zero is 零. Successive zeroes are combined, so 一千零一 is 1001. 5147 would be 五千一百四十七. 10, as previously mentioned, is 十.
    - card_zero 1mo ago
      > 5147 would be 五千一百四十七 "Five thousand one hundred four tens seven". So each order of magnitude is explicitly labeled. Where's the positional part?
      - thaumasiotes 1mo ago
        That is the positional part. If you were to rearrange it, you'd get something invalid. 二十三百 isn't a number at all. Recall that the use of zero is necessitated by using positional notation, and that is what we see here: you must explicitly zero any magnitudes you're not using. (At least, any that are below one you are using.) I should also note that while there is no symbol for the number 10,000 - there is a place value, but the number is 一万, not 万 - the number 10 is still written 十.
    - 1mo ago
idoubtit 1mo ago
The question is the title is left unanswered by this shallow article. At least it's not AI slop since there are spelling mistakes ("You’re best hope"). > Say you’ve found 17 numeric symbols. You might infer that the writing used a base 20 system Reals numerical systems are much more diverse than that. For instance, Babylon used a base 60 (hence our minutes and hours). But there were much less than 60 numeric symbols, since they had a symbol for 1 and 10. So 2 symbols for a base 60! > never appears at the beginning of a number, you might infer that is a zero In the later times Babylonians had a kind of zero, but it was very limited, only used to point the lack of a number between two, i.e. "2∅1" but never "21∅∅" which was written "21" (so numbers were ambiguous if the context didn't give the magnitude). And Babylonians had floating numbers. So "4" could also mean 4/60. What I mean is that Babylon had a zero, but it only covered a part of the positional modern zero. They could not write 0 - 3. And if their zero had been fully positional, there would have been numbers beginning with it, i.e. sexagecimals floats.
- leoc 1mo ago
  > Reals numerical systems are much more diverse than that. For instance, Babylon used a base 60 (hence our minutes and hours). But there were much less than 60 numeric symbols, since they had a symbol for 1 and 10. So 2 symbols for a base 60! It's oddly similar (obviously not identical) to bi-quinary: https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal .
- Aerroon 1mo ago
  >In the later times Babylonians had a kind of zero, but it was very limited, only used to point the lack of a number between two, i.e. "2∅1" but never "21∅∅" which was written "21" (so numbers were ambiguous if the context didn't give the magnitude). Was it really like this or could it have been like "21 h" meaning "2100"? Did they write things like "5 talents of grain"?
ZeroDayDreamer 1mo ago
The Chinese counterexample is important. The author says "base b doesn't have a single symbol for b" - but Chinese has a symbol for 10 (十) and even 20 (廿). Having a symbol for the base doesn't mean the system isn't positional. It just means you have shortcuts for common numbers. So the article's main diagnostic is flawed
jamesjolliffe 1mo ago
Is this the perfect clickbait title for nerd sniping? One of the best I can recall.
vintermann 1mo ago
It has been pointed out before that although we know of no cultures which used a bijective base number system (well, besides base 1!) it might not be immediately obvious if they did. I think it was in a paper which was about how many times the bijective base system had been independently reinvented by mathematicians.

69 points by ibobev 2mo ago

Looks like translating a positional numbering system from ancient cultures than ruling out or not if they had the concept of zero. It may be a single use symbol, here is nothing, instead of being part of bigger amounts. Numbering systems doesn't have to be positional (nor go too far).

whatsThisBtn4 1mo ago
Gosh I love Wittgenstein for this. I highly recommend suffering through both early and late Wittgenstein (only wrote 2 books and essentially invented one of the 3 branches of philosophy). Expect to only understand 10% of what he says, but that is normal. Separately, pragmatism by William James is an easy 4 hour read and you can have 2/3 of the branches of meta philosophy.
- verisimi 1mo ago
  What do you think Wittgenstein would say?
  - heresie-dabord 1mo ago
    Alas, Wittgenstein can only explain it like you are 0.5.

lisp2240 1mo ago

Zero has two roles: as a positional placeholder and as a cardinal value (nothingness or net-zero). This only addresses the former.

j16sdiz 1mo ago
Afaict, most ancient civization have conception of "nothingness" or "emptiness". The dispute is often whether they consider it as a number or not
- philipov 1mo ago
  We have both. Zero and Null are different data types.
  - wahern 1mo ago
    I once had a statistics professor (teaching a programming class using, IIRC, SAS) in college who worked as a data analyst in the federal government, possibly the Labor Department. Part of his job was working with polling and form data. After class he once tried to explain a paper he wrote arguing for an additional null-like type in the formal analytics system in his domain. I was young and stupid (took it as an easy programming course; was not skilled at abstract math) and impatient (wanted to meet up with friends at a pub) so didn't follow along well enough to even properly remember his argument, let alone understand it. But I've always distinctly recalled that he was arguing for a 4th, or possibly 5th type, yet whenever I survey the literature I've only found at most such 2 types. But I've probably been looking in the wrong places. For context, NULL/missing was a type. N/A was a type (i.e. a question irrelevant to someone). I can't remember the 3rd, and of course not the additional (4th or 5th) type he was proposing. If anyone knows a good resource that describes this problem domain, that would be much appreciated. I've been haunted for over 20 years by the regret of not fully appreciating what he was trying to explain to me, both because I could've learned something that day, but also because I almost immediately felt like an a*hole for not showing enough interest in and respect for a piece of scholarly work he was clearly proud of and wanted to share with me. EDIT: I think the third pre-existing type was for a situation where someone abstains from answering a question like, "Sex: male/female", because they consider themselves neither. So something like an Other type. In retrospect this was presumably related to set theory, and he felt there was a gap in the pre-existing formal models.
    - Someone 1mo ago
Beijinger 1mo ago
[dead]
rendaw 1mo ago
Doesn't the placeholder imply nothingness? E.g. 10 means 1 ten and 0 ones.
- idoubtit 1mo ago
  No, that implication is not automatic. The Babylonian numeral system evolved over milenaries, and the simple space noting the absence of a digit between two digits was later noted by a "0" digit. But this symbol was never used by itself, so it did not mean "nothingness". In the same way, a civilization having the concepts of addition and subtraction does not automatically induce the concept of negative numbers. On the other side, ancient Egyptian numerals did have a zero, but it was only for nothingness. But they did not have a placeholder zero, because their systems was similar to Greek and Roman numerals.
amelius 1mo ago
The article has quite some assumptions. They also assume a base-N system with big-endian lexicographic ordering from left to right. Has the author not heard of Roman numerals?
- Ekaros 1mo ago
  It is very big assumption to me. It is now used very widely. But I am not sure if it was at all common back in the history. Most systems were kinda different from it.

NotBenny 1mo ago

[dead]

conartist6 1mo ago

What I wonder is: why has nobody noticed that code editors lack a concept of 0? When you're writing code, you can express any concept except that of an unfilled hole. We've rearranged every part of the coding process in a twisted-up way, all for the lack of a way to express lack. If you want to be more clear about what I mean, look to tools which can express holes like https://scratch.mit.edu https://scratch.mit.edu and https://hazel.org https://hazel.org. They give the feeling of letting things snap together like lego bricks. Indeed, lego bricks themselves function because of the negative space (the holes) in them!

onestay42 1mo ago
How about an `extern` variable in C?
- conartist6 1mo ago
  A million variations exist. I'm looking for a programming-language-agnostic concept. The closest you'll find are templating languages like Handlebars
  - skew-aberration 1mo ago
    Delimited continuations? Though I'm not totally clear what you're asking for. Semantics or syntax?
    - deleted 1mo ago
      [deleted]
    - conartist6isme 1mo ago
      Syntax. Delimited continuations would be a similar concept but for semantics
  - Someone 1mo ago
    Function arguments are unfilled holes. So are interface declarations. Both are (fairly) programming language agnostic, but in the context of an editor, would become specific. The editor would have to know _how_ to represent them in the code’s language.

thaumasiotes 1mo ago

> If you knew somehow that some symbol corresponds to 20, then you’d know they didn’t use base 20 because base b doesn’t have a single symbol for b. Well, this is plainly false.

CamperBob2 1mo ago
I suppose Roman numerals would be one counterexample, but are there any number systems based on place/position value that qualify as counterexamples?
- thaumasiotes 1mo ago
  Of course. The Chinese number system is base 10 (or, if you scale way up, base 10,000) with a positional writing system. The symbol for ten is 十. Heck, there's also a symbol for twenty, 廿, and it exists despite the number system being base 10. Anything that has to be written a lot is likely to have a convenient written form. If you're curious, zero is 零. Successive zeroes are combined, so 一千零一 is 1001. 5147 would be 五千一百四十七. 10, as previously mentioned, is 十.
  - card_zero 1mo ago
    > 5147 would be 五千一百四十七 "Five thousand one hundred four tens seven". So each order of magnitude is explicitly labeled. Where's the positional part?
    - thaumasiotes 1mo ago
      That is the positional part. If you were to rearrange it, you'd get something invalid. 二十三百 isn't a number at all. Recall that the use of zero is necessitated by using positional notation, and that is what we see here: you must explicitly zero any magnitudes you're not using. (At least, any that are below one you are using.) I should also note that while there is no symbol for the number 10,000 - there is a place value, but the number is 一万, not 万 - the number 10 is still written 十.
  - 1mo ago

idoubtit 1mo ago

The question is the title is left unanswered by this shallow article. At least it's not AI slop since there are spelling mistakes ("You’re best hope"). > Say you’ve found 17 numeric symbols. You might infer that the writing used a base 20 system Reals numerical systems are much more diverse than that. For instance, Babylon used a base 60 (hence our minutes and hours). But there were much less than 60 numeric symbols, since they had a symbol for 1 and 10. So 2 symbols for a base 60! > never appears at the beginning of a number, you might infer that is a zero In the later times Babylonians had a kind of zero, but it was very limited, only used to point the lack of a number between two, i.e. "2∅1" but never "21∅∅" which was written "21" (so numbers were ambiguous if the context didn't give the magnitude). And Babylonians had floating numbers. So "4" could also mean 4/60. What I mean is that Babylon had a zero, but it only covered a part of the positional modern zero. They could not write 0 - 3. And if their zero had been fully positional, there would have been numbers beginning with it, i.e. sexagecimals floats.

leoc 1mo ago
> Reals numerical systems are much more diverse than that. For instance, Babylon used a base 60 (hence our minutes and hours). But there were much less than 60 numeric symbols, since they had a symbol for 1 and 10. So 2 symbols for a base 60! It's oddly similar (obviously not identical) to bi-quinary: https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal .
Aerroon 1mo ago
>In the later times Babylonians had a kind of zero, but it was very limited, only used to point the lack of a number between two, i.e. "2∅1" but never "21∅∅" which was written "21" (so numbers were ambiguous if the context didn't give the magnitude). Was it really like this or could it have been like "21 h" meaning "2100"? Did they write things like "5 talents of grain"?

ZeroDayDreamer 1mo ago

The Chinese counterexample is important. The author says "base b doesn't have a single symbol for b" - but Chinese has a symbol for 10 (十) and even 20 (廿). Having a symbol for the base doesn't mean the system isn't positional. It just means you have shortcuts for common numbers. So the article's main diagnostic is flawed

jamesjolliffe 1mo ago

Is this the perfect clickbait title for nerd sniping? One of the best I can recall.

vintermann 1mo ago

It has been pointed out before that although we know of no cultures which used a bijective base number system (well, besides base 1!) it might not be immediately obvious if they did. I think it was in a paper which was about how many times the bijective base system had been independently reinvented by mathematicians.