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Comment by jmrodgers | Hacker News Reader

Development of zero https://en.wikipedia.org/wiki/0

Is it though? All languages have the word 'nothing'.

Better candidates: a) place-value numbering aka the positional numeral system, b) the Cartesian coordinate system. Forced to choose, I would pick (b).

"nothing" is not the same the same as "zero". "zero apples" means something different to "nothing", but that difference is subtle and difficult to explain, which is what makes the invention of zero such an achievement.

ok, "no apples."

Also not the same. You can't say "the number of apples is no", but you can with "zero".

And that is an all-time great innovation outpacing the Cartesian coordinate system, you say, being able to word a sentence differently

The wording was just an attempt to illustrate the point. There are cases where you can rephrase a sentence with "zero" to get basically the same meaning, but the important thing is that "zero" falls into the same semantic class as other numerals, which other ways of negatively qualifying existence don't.

Put another way, the invention was not literally the word "zero", or anything to do with language per se. It was the idea that you can think about lack of existence in the same was that you think about counting, i.e. treating the idea of there being two apples and the idea of there being zero apples as two examples of the same thing in your mind, instead of treating one as being in some way fundamentally different.

Being raised with a maths education from a young age now, it's easy to see this as obvious, but there was a time in human history when it wasn't.

Also, I wasn't disagreeing with the Cartesian coordinate system being more significant.

I think ppl really do overrate the "mind shift" needed for zero. That's my honest opinion. I think ppl don't think about it hard enough.

The fact is, zero's usefulness is a bookkeeping device. "There are zero apples" is not better or more useful than "there are no apples." That's not why zero survives. You can wax poetic day and night about what a mind shift "lack of existence is." You're not getting it. You're missing the point. What does that _enable_ that "no apples" does not? That's the measure of its usefulness, right?

It enables positional notation. That's zero's primary gift to the world. It is a necessary bookkeeping device for positional notation. And the measure of positional's usefulness over its predecessor, additive numerals a la the Roman system, is so profoundly great that no argument need be made. No waxing poetic is needed. No "it seems obvious now but back then." It's just indisputable.

> Is it though? All languages have the word 'nothing'.

The interpretation of the concept that been different over time. See perhaps The Nothing That Is: A Natural History of Zero by Kaplan:

* https://www.goodreads.com/book/show/3188988

The difference is that zero is explicitly a number, rather than a concept.

Making it a number allows it interact with the rest of mathematics in a consistent way, which I'd argue you can't do with "nothing".

To use your later example of "no apples":

Is no apples the same thing as no bananas? What about no meters? I honestly don't know, the question is a bad one. My gut says yes, nothing in each case is just nothing.

Is zero apples the same thing as zero bananas or zero meters? No, they're different because the unit "apple" is orthogonal to the unit "meter".

The precision of zero is what's so special about it.

Notably, zero persons have chosen to make the explicit case that zero is more ingenious than the Cartesian coordinate system. :)

Which is a better idea, the brick or the building?

In this case, the building. To give bricks the win over any building ever simply because bricks precede buildings is a little - what’s the word - dumb

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