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Comment by osigurdson | Hacker News Reader

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.

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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.

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

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.

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.

There are cultures where the basic directions are north, east, south, west, which they use pervasively in preference to forward/back/left/right. People from such a culture are very good at keeping track of their absolute orientation and are uncomfortable with body-relative directions.

"Hey I ran out of arrows" is a different construct than "there is such a thing as a number that is independent of particulars like arrows and zero is one of those numbers"

The perspective of modern computer science (with its zero-based indexing etc) or modern algebra (with its need for neutral element for addition) certainly makes it clear that zero is just another integer. However, without those perspectives I doubt it is so obvious.

For example, people normally count things by starting from one, so, at least following this usual procedure, counting to zero is technically speaking impossible. Also, we can't distinguish between zero apples and zero oranges, but we can tell two apples and two oranges apart.

In fact, even with the perspective of modern algebra zero remains special. For example, it is the only element of a field without a multiplicative inverse.

I'd be surprised if zero didn't take any extra effort to discover. It's clearly different than other integers.

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.

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