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.
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.
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.
> 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.
It is equally common to say: "I have no food" or "I have nothing".
I can go on: "I have no money". "I have no cattle".
So I don't know that your argument is a compelling one.
No is a boolean operator, not a number. "Do you have any bread?" ... "No. I have no bread." It's the opposite of yes, or some. No or none isn't countable, it's the opposite of any positive quantity, that's why the concept of zero was so counter-intuitive.
It's far more common to say "I haven't got any bread". There's no word or phase in there that's proxying for a number.
Your example ("No. I have no bread"), however, uses "no" in two different ways.
The first is negation and the second represent the null/empty set ("no bread"). And the empty set is not the same as zero.
You don't have to go back to the Middle Ages to find people having difficulty with the concept of zero. A couple of more recent examples from a paper by Eric Hehner (http://www.cs.toronto.edu/%7Ehehner/RPUTP.pdf):
"In the 1991 Toronto phone book, there is a page that helpfully gives the time difference to various places in the world; to the U.K. it says "+5", and to Costa Rica it says "-1". But to Cuba it says "NA", and the legenda explains "time difference not applicable". By 1996 they tried to correct it; for Cuba it says "=", with the same explanation. In 1997 they discovered the number 0 , but they felt the need then, and still do today, to explain that 0 means "no time difference"
"The Fortran language of 1955 had a loop construct, but its body had to be executed at least once; I suppose it seemed senseless to have a loop whose body might be executed 0 times. The error was corrected in Algol in 1958, and in PL/I, and in Pascal, in part: iteration might be 0 times, but the data structure over which one is iterating, the array, had to have at least one element. In Pascal that meant there was no null string. And that put the algebra of data structures back where the algebra of natural numbers was prior to 1930."
The article, and the overall discussion is really about having a symbol in your numeric alphabet for "none," not about having a conception of nothing. Even more particularly, it's about the use of that symbol in a positional symbolic system for representing natural numbers. That is the breakthrough generally accredited to India, not the idea that before you have 1 thing, you have no (zero) things.
I'd say it is about answering the question "How many?".
It becomes natural to give a distinct symbol for each answer smaller than a given limit say 10. If you have symbols 1, 2, 3, .... 9 then it would be pretty obvious you would also want a symbol for zero.
The positional way of expressing numbers is a separate more evolved development of course.
In Roman numbers you had I, II, and III, ... So why didn't they have say '-' to symbolize less than "I"? Maybe they just expressed it with the word "none".
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.