[popctrl]

The idea that zero was "invented" at a certain time by recent humans and not in use until then has always seemed absolutely absurd to me. I will admit I haven't read deeply into it, but there's just no way people didn't have a concept for "none of a thing" until a couple millennia ago.

One of the justifications used for this reasoning is "You don't go to the market and buy 0 fish". But all that tells us is: There's no reason to record buying 0 fish or owning 0 acres of land. Another justification given is the difficulty children experience with 0 - but we don't teach children to start counting with 0, so it makes sense that they would get tripped up there.

I guess the argument sometimes seems to be that we didn't have a symbol for 0, and that this was somehow more confusing to adopt than other symbols? But if that's the case, then isn't claiming any culture "invented" zero the same as claiming a culture "invented" any concept they came up with a word for?

I'd love to hear all the reasons I am wrong and stupid.

[OscarCunningham]

I think the thing which came surprisingly late in history wasn't having a concept of 'none' but rather of allowing it to be considered a number with the same status as 1, 2, 3 and the rest.

Indeed some of the ancient Greeks were of the opinion that 1 was not a number (since numbers were for counting a plurality of things).

It's quite the realisation that you can use the usual rules of arithmetic for 1 and 0, and not have anything go wrong. (Except of course division does go wrong!)

[martincmartin]

You see this in programming languages too. Many languages distinguish between one of something and a collection of them, e.g. int x vs vector<int> x. In other languages, like Matlab, everything's a vector, and a scalar is just a vector of length one.

[burnished]

Well, its not that they distinguish between one of something and a collection, its that one of something is different from a collection of things. So, int x is a handle to an integer value, whereas an array handle (your collection) is a handle to a pointer, which points to the start of your data structure and you can get the other elements by using an offset etc. etc. My point being that they are differentiated because they are different things.

[martincmartin]

Having a concept of "none of a thing" is one thing. Abstracting that to a number is a different thing.

Even today, when you ask someone "how many kids to you have," and they don't have any, they say "I don't have any," not "zero." In other words, they respond with a phrase, often one with a negation (not), instead of a number.

[DiggyJohnson]

What if they're thinking "zero" but just don't have the word for it. I.e. what if this is just a linguistic deficit?

Please err on the side of me understanding your question well.

[srean]

Even the question whether one can 'think' of something without having a linguistic representation is a topic of active debate. My personal take is that its possible, predators plan ambush, but do they have a linguistic representation ? Its not clear that they do.

[sellyme]

> Even the question whether one can 'think' of something without having a linguistic representation is a topic of active debate.

This seems fairly trivially true just based on how common it is for someone to have 100% full understanding of a concept and then be completely incapable of remembering the word describing it, or even a phrase that conveys a decent approximation.

[srean]

Linguistic representation can deal with what's-the-word-again place holders though. So, not being able to recall the name of an object or concept does not prevent linguistic thinking.

[DiggyJohnson]

I agree with the context that you described. In fact, I'm delighted that we agree on that context.

I agree its not clear, though I might lean the other way. Who knows.

[srean]

Hellen Keller's writings may interest you. Her recollections from a time when she did not have an internal language is very interesting.

Many believe that animals do not have an "I" the self reflective "I", that they are not aware of themselves etc etc. This runs contrary to my beliefs, I have had several conversations/arguments on HN along those lines, but lets not dwell on mere beliefs.

What I find interesting is what test/experiment can one perform that can demonstrate that a human, who is not allowed to communicate linguistically, has the attributes mentioned above. If we cannot design such a compelling experiment that shows are inability to detect those attributes in animal even if those attributes maybe present.

We need the restriction of no-linguistic-communication so that animals and humans are on the same playing field. Hellen Keller, when she did not have language she would have been on the same playing field.

My position is that if I cant even prove/demonstrate to others that you are sentient in the senses described above, how can we even claim that animals aren't sentient. We have no way of demonstrating it even if they were.

[anigbrowl]

Seems contrived. 'None' is an equally valid answer, and easy to conceptualize as a number, eg 'start with three, take away two, take away one, now you have none.'

[throwaway192874]

There's a book called "Zero: The Biography of a Dangerous Idea" that goes into the history of zero in detail, admittedly I haven't finished reading the book myself but got at least partway through and it was fascinating to read about it and I'll one day finish it :)

What you said about it not being in the numeric system is definitely part of it (ex: roman numerals not having it) but also all the problems that come up with zero have to be dealt with (e.g allowing dividing by it allows you to prove anything, and there's a great proof that winston churchill is a carrot in the book showing as such), and there's some overlap with religions in fearing "nothing" and what that might mean

[gugagore]

I more or less had understood that what was meant by "zero was invented" is zero as used in a positional number system. In other words, the digit zero, not the quantity zero.

[nwallin]

Zero is an overloaded concept. There are at least like 5 or so different things that we use the word "zero" for, some of which are very sophisticated.

On the one hand, it means there's none of a thing in there. Most animals understand this. There is zero food here. There are zero predators on that island. Pretty sure crows have this one down pat.

Taking it one step further, you have zero as a number. Zero which is on equal footing as numbers like one or seven-- it is a number that you can perform arithmetic on or with. You can multiple by zero, you can add by zero, you can divide by -- wait, you can't divide by zero! The Greeks understood this. But lots of people say the Greek's "didn't have/didn't invent zero" because they used the word "nothing" instead of its own word. But Aristotle did say "nothing and nothing, added together, make nothing" and "there is no ratio of nothing to a number".

Crows probably don't understand that you cannot divide by zero. Maybe you could teach a crow that if two crows got ten total nuts, each crow would get five nuts, and so on. If you told that crow to split ten nuts between no crows, and ask the crow how many nuts each crow would get, the crow might tell you ten nuts, but it's not going to tell you that that operation is undefined.

Then there's the use of zero as a digit in a place-value system, like the one we use, as opposed to Roman numerals or Chinese numerals or so forth. Before there was a symbol for zero, you couldn't write one hundred and four as 104, it would just be 14 which was ambiguous. So when the Indians "invented zero" in the 7th century or whatever, it wasn't zero that they were inventing, it was the place-value system we use today to conduct our daily lives with, which is a shitload better than Roman numerals or trying to do arithmetic with a straightedge and compass or whatever.

There are a lot of people who claim that, for instance, the Maya were more mathematically advanced than the ancient Greeks, because the Maya had a symbol for zero (which looks sorta like a French baguette and an American football had a baby) and the Greeks didn't. While the Mayan way of writing down a number was much better than the Greek method, we don't have any evidence that the Mayans had much in the way of math beyond counting and extrapolating. The Mayans primary method of calculating is by drawing out tables: they knew the cycle of Venus is (roughly) 585 days, they knew the cycle of Mercury was 117 days, so you'd get a table with thousands of entries counting up the cycles. The Dresden codex has a table with 2340 entries, with 585 entries for Venus repeated 4 times and 117 entries for Mercury repeated 20 times. With a place-value system that used zeroes for zero digits. Which... ok, the place-value system was more advanced than the Greeks, but the Greeks would have done that same 'calculation' with a lot less tedium.

Then you have zero as in the additive identity, which opens whole new worlds of mathematics to you. Now you can start talking about things like rings, fields, and groups, and can have all sorts of fun. Pretty sure crows haven't sat down and discusses abelian vs non-abelian groups, but I wouldn't put it past them.

So anyway, any time someone starts talking about inventing or understanding the concept of zero but do not, themselves, display an understanding the concept of zero, (by explaining what it means in that context) it's generally a good time to stop listening.