# The parity of zero

| Comments (3) | Misc
Over at the Volokh Conspiracy, Eugene Volokh asks people to weigh in on whether 0 is even or odd. This is, as they say, a simple question with a simple answer: 0 is even. Despite this, nearly half the people in Volokh's poll (around 1500) get the answer wrong. (Most of those people say it's neither odd nor even). Moreover, this question spawned two threads of over 100 comments each, with people seriously arguing—despite extremely clear arguments to the contrary from people with real mathematical expertise—that zero was not even.

Part of the problem is educational: apparently some schools, textbooks, etc. teach that zero is neither odd nor even. Volokh cites McGraw Hill's Catholic High School Entrance Exams:

An integer is even if it is a member of the following set: [...,-6,-4,-2,2,4,6,...]. An integer is odd if it is a member [of] the following set: [...,-5,-3,-1,1,3,5,...]. The number zero (0) is neither even nor odd.

Reading the comments, though, there seems to be something else going on: many of the commenters seem to assume that they can just reason out the answer from (incorrect) first principles, and that expert opinion doesn't matter. For no doubt bad reasons (primarily boredom), I have read through a number of Volokh Conspiracy threads on other scientific topics and this seems to be a fairly common pattern. Usually, though it's usually confined to discussions where the scientific questions have some political implications (global warming, evolution, etc.), but in this case it just seems to be that people have the wrong intuitions and don't want to listen to anything that contradicts them—and at some level are actively hostile to being told that actual expertise might count for something... I'd be interested to see whether there's any correlation between commenter's positions on the zero parity issue and issues with more political weight behind them.

My 1st grader has already been taught that 0 is even.

Suppose Monty Hall offered you the choice of three different answers to the question, "what is the parity of zero?"...

To be more explicit, I think the problem is the same in both cases--if you answer incorrectly the first time, based on faulty intuition or reasoning, you then have the option of admitting error and looking at least a little bit foolish, or brazening it out by arguing that your answer is actually correct, no matter what the experts say. At least some people appear to find the second option less painful.

This is somewhat different from the phenomenon of politicized judgment about scientific matters. In the latter case, the issue is whether "the experts" are themselves trusted or biased, as much as it is about the technical details of the disputant's view vs. the consensus view. One rarely hears, for example, that "evenist" or "switchist" experts have ulterior motives for claiming that zero is even, or that the contestant should switch his or her choice of doors in the Monty Hall game. Rather, it's likely purely personal pride and sense of expertise that's at stake in the mind of someone arguing that zero isn't even or that contestants should stick with their choice of doors.

I read those threads, and took part a bit.

I think there may be a domain specific issue with the commenters there - a large fraction of them are lawyers. Most lawyers have comparatively little schooling in hard sciences, leaving a lot of ignorance there. But I think worse for threads like this is that they tend to internalize the notion that persuasive argumentation will *actually change the outcome* of what they're arguing about, because, in a professional context, it does. This leads them down a bad road when they find themselves on the wrong side of actual facts that cannot be argued with.

### October 2012

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