Believe it or not, I've still been receiving the odd comment on the gun control posts I wrote before Christmas. This rather extraordinary one was left by Epsilon Given a day or two ago, although to begin with you might be hard-pressed to spot any connection with the subject in hand...
"Just for the record, I'd like to clarify just what "counter-intuitive" means to a mathematician.
Intuition is a funny thing. It generally leads us to truth, and a good intuition helps us to discover new theorems, even entirely new lines of thought.
When something we expect to be false, or nonsensical even, turns out to be true, we call such things "counter-intuitive". As we encounter these things, we sometimes adopt them into our intuition--but there is no shortage of things to surprise us!
Historically, we have encountered many counter-intuitive ideas--ideas that often met fierce resistance every step of the way to acceptance. The square root of -1, for example. Or a number for "nothing". Or the irrationality of the square root of 2.
And sometimes, proving something counter-intuitive can lead to your death. The person who first proved that the square root of 2 was irrational, for example, was drowned at sea by his fellow Pythagorians.
I'll give several more counter-intuitive examples that I'd expect to go over your head without deep explanation, unless you are already acquainted with them. You can cut up a unit sphere into nine pieces, and re-assemble them to make two unit spheres (Banach-Tarski Paradox). You can have two intersecting lines both parallel to a third line (hyperbolic geometry). There are more irrational numbers in the interval between zero and one, than there are integers (Georg Cantor's diagonal argument). When we "generalize" the factorial function, the factorial of 1/2 is 1/pi (Gamma function). e^(i*pi)+1=0 (Euler's Formula).
Heck, I spent many hours trying to trisect an angle using a compass and straightedge, and I spent hours trying to integrate e^(-x^2) in terms of "elementary functions", because I was told that these were impossible--and this conflicted with what I was taught in our culture, that "nothing is impossible". Later, I actually read the proof that demonstrated, once and for all, that the former is impossible, and more recently I learned that the latter proof is done along the same lines, so to me, these are no longer counter-intuitive.
The idea "More guns, less crime" is, like all these other things, counter-intuitive. Our intuition tells us that getting rid of guns will decrease violence. But we can find statistics that show when we ban guns, violence increases. And we can find statistically that, internationally, there is no correlation between gun laws, gun ownership, the murder rate, and the suicide rate, from country to country. As I have examined these things closely, I've come to the conclusion that honest people with guns is a good thing, because they can defend their lives against dishonest people determined to do harm.
I have seen the statistics and the studies. I have thought about the philosophies behind the two positions. In all this, I have come to the conclusion that more guns really do mean less crime! And that, more importantly, if you value liberty and security, then you shouldn't depend on the State for protection--it is your duty to protect yourself and those you love--and nothing can change that. Indeed, the State, more often than not, cannot protect you--and occasionally, the State is even your enemy.
And that those who believe otherwise, might as well believe that the moon is made of cheese, or that imaginary numbers really are imaginary, for all the truth that their position holds."
Words fail me. Epsilon, this is not the first time that I've had to make the elementary point to you that I do - honestly, truly - know what "counter-intuitive" means, and have done all along. Your apparent belief that if I take issue with anything you say it must mean that I've simply misunderstood the terminology you use (and require a detailed explanation to bring me up to speed) is...well, a touch bemusing, to say the least. I'll simply reiterate what I said to you before - some things that are counter-intuitive turn out to be true. Many don't. I note that you confirm that at the outset yourself, so your point is...?
The latter part of your comment essentially boils down to this - you've generously had a little think about the statistical evidence on our behalf, you've selectively culled the bits that suit you, you've declared your side of the argument the winner on that basis, and thus regard yourself entitled to feel morally superior to those of us who don't "do our duty" by "protecting" ourselves with a gun.
Well, let me put this to you. Here is the compelling evidence (as opposed to intuition) that those of us on the other side of the argument in Scotland look towards. It suggests overwhelmingly that our approach has succeeded in protecting the public. Might I suggest therefore that we are equally entitled to think - valuing security and liberty as we do - that it would be a disgraceful dereliction of our collective "duty" if we were to suddenly decide to indulge the wishes of a minority to own handguns, and thus compromise the safety and liberty of everyone?