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Comment by jcranmer | Hacker News Reader

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.

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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.

http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_e...

> 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.

I agree that "no" is not equivalent to "zero".

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.

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