More Thoughts on Ames, and the Value of Nothing

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If all the other front-runners decide to skip Ames and leave the dog-and-pony show to Romney, it’ll be interesting to see how the campaign spins whatever results come of it. They’ll likely win, but it could be close to meaningless for them — and could give those who do even marginally well despite not participating (i.e., not shipping in voters but still putting their names on the ballot) a huge boost.

Speaking of Mitt and meaninglessness, his answer last night about invading Iraq has been bothering me. Not because he, you know, apparently is reading some alternative science fiction history of the war, but because he kept referring to the question Wolf asked being a “null set”:

Knowing everything you know right now, was it a mistake for us to invade Iraq?

MR. ROMNEY: Well, the question is kind of a non sequitur, if you will, and what I mean by that — or a null set.


MR. ROMNEY: Well, I answered the question by saying it’s a — it’s a non sequitur, it’s a null set kind of question, because you can go back and say, if we knew then what we know now, by virtue of inspectors having been let in and giving us that information, by virtue of if Saddam Hussein had followed the U.N. resolutions, we wouldn’t be having this — this discussion. So it’s a hypothetical that I think is an unreasonable hypothetical.

“Null set” answer means no answer, not a hypothetical answer or even an unknown set of answers. But I wasn’t sure. For clarification, I turned to SwampDad, who has a PhD in this kind of thing; he writes:

You are correct. What Romney said does not make sense. By the way there is only one null set. It would be better to say “the null set” rather than “a null set.” The set that contains no elements is unique. There is only one set that contains nothing.

Maybe Romney meant that the set of correct answers to the question is null.

This is interesting. I can remember in the late 1960s a few older professors did not accept some ideas of set theory, which was well established by then, or category theory which was relatively new. One professor would not let us use the term “null set”‘ in our proofs or presentations. Category theory admits objects that are not sets. In this theory the category of sets, for example, contains all sets. As B. Russell pointed earlier, the category of sets itself is not a set. This is Russell’s paradox.

There were several professors who would not accept the ideas of category theory, but it has become part of modern mathematics. Another version of Russell’s paradox involves the town in which the barber shaves (the face) every one who does not shave their own face. Who shaves the barber?


I know, I know! John Edwards, right?