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Comment by travisjungroth | Hacker News Reader

Please don’t take this as defending this thinking. I’m just guessing at how someone could get to this confusion.

I can see how you’d get there by thinking of numbers as a thing for counting. Even numbers give you piles of two without one left over. Zero fails the first condition since it gives you no piles at all. But it doesn’t leave a pile of one, so it’s not really odd, either.

If you ever find yourself confused in this way about definitions consider: is this definition serving me? Could I adopt a different definition that’s used by people really good at this sort of thing?

(Zero is even because any integer n that can be formed by 2k for integer k is even, and that can be formed by 2k+1 is odd. 2x0=0)

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I am fairly certain I can split an empty pile into two empty piles, without a remainder.

Hmmm by definition an empty pile is not a pile though, is it? So there's nothing to split?

;-)

And an empty plate is not a plate, also by definition? Okay, sure.

Ah I suppose if you see an "empty pile" as still a vessel with nothing on/in it, your point stands.

But a plate is its own thing, in addition to what goes on it. A "full plate" is full of what? And a full plate is the plate plus whatever is on it, not just the stuff on it.

I think of a "pile" of stuff as being it's own thing, that being the pile itself. An empty pile is the absence of the thing.

That was my interpretation, but I see what you meant. :)

Hmm, I think that's how normal people approach the question (implicitly), and that might be how they think zero is not an even number.

At least this would explain their reasoning in terms I can understand.

well that's odd

Yes, it all boils down to definitions. Definitions that have 0 as an even number work well in math.

For most people's daily life, it doesn't really matter which category zero would fall under (as they never really eg consider dividing zero items evenly between people.) So their (implied) definitions can be all over the place.

>Even numbers give you piles of two without one left over. Zero fails the first condition since it gives you no piles at all. But it doesn’t leave a pile of one, so it’s not really odd, either.

This definition does not naively extend to negative numbers, which are anti-piles of things. You are right, of course, about definitions serving their purpose. In this case maintaining the symmetry of alternation requires 0 to be even, and that argument could even be extended to negative numbers. (Of course other numbers, like the rationals and reals, are pure fiction and can safely be ignored negative or otherwise.)

> (Of course other numbers, like the rationals and reals, are pure fiction and can safely be ignored negative or otherwise.)

I think natural numbers are already pretty fictional.

Btw, you might want to look into p-adic numbers.

Your defense boils down to people having an insufficient understanding of zero as an ordinary number, and still clinging to the concept that zero means "nothing" or is otherwise magic.

This hints at a failure of math education.

As an analogy, many (usually, but not always, weaker) programmers still have magic ideas about booleans and comparison operators, and write nonsensical stuff like if (a == true). When you ask them, it's invariably that in their mind, there's mystic connection between comparison operators and if statements.

> Your defense

I literally… never mind.

Ha ha, I didn't even realize this when I typed the answer. I hope it was clear that I didn't mean to imply this was your personal opinion.

It wasn’t clear then, but I can certainly see how you’d mean it that way. It was “mine” as in “I brought it”.

> When you ask them, it's invariably that in their mind, there's mystic connection between comparison operators and if statements.

It doesn't have to be mystic. It's perfectly fine to design a language that works like this. It wouldn't be a good language, but it would be possible.

Just like PHP didn't use to support constructs like `f(10)[2]`, that used to be a syntax error. So you needed something like `x = f(10);` first, before accessing `x[2]`.

If you saw that kind of construction with the intermediate variable, you might also accuse the programmer of imagining mystic connections.

Matlab still doesn't handle f(10)(2)... (The _(_) syntax is both function calls and indexing there.)

You are giving me flashbacks to memories I thought I had successfully repressed.

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