08.15.07

Reductio Ad Retardum

Posted in Math, Politics, Wingnuts at 10:38 pm by Cangrejero

A common practice in mathematics is the proof by contradiction, or reductio ad absurdum (literally Latin for ‘reduction to the absurd’). when faced with a complicated theorem, mathematicians will sometimes assume that the opposite is true, and show how that assumption leads to a contradiction. An example is a proof for the fact that there are infinite prime numbers.

Suppose that the primes are finite. Call the list of primes p₁, p₂, p₃, …, p_n. Now construct a new number P such that P = (p₁ * p₂ * p₃ * … * p_n) + 1. This new number P cannot be composite, as it is not divisible by any of the primes p₁ through p_n. Therefore it is a prime, which contradicts our original assumption. Hence the primes are infinite.

Another technique for lazy mathematicians is the beloved counter-example. When faced with a complicated positive statement, one need only to find a single counter-example to disprove it. If I said all primes are odd, a simple proof would be to point out that 2 is prime and even, and you’re an idiot Cangrejero for saying otherwise.

Sadly, the concept of counter-example is used (and misused) in desperation way way way too often in our national political discourse. Two cases come to mind. The first is the (now really old, but bear with me) Dan Rather business. Mr. Rather and CBS news fucked up immensely with that memo. They should have done their homework blah blah blah etc… Yeah we know. The problem is, that issue prematurely ended any discussion of the President’s service records. It was a classic misapplied proof by contradiction, which will hereafter be known at The Midpoint as Reductio Ad Retardum.

I bring this up because of the ongoing Scott Beauchamp saga. (If you don’t know what I’m talking about, I envy you) I’ll spare you the details, but this guy fucked up too and the noise from the ongoing right-wing circle jerk is deafening. In short, this is being used as a Reductio Ad Retardum for the idea that the liberal emm ess emm has ever gotten anything right when they’re not busy troop-hating.

Another example of Reductio Ad Retardum is ‘Clinton Did It!!!1!!’ This is probably the most commonly seen form. Never mind that the claims are often dubious; this is too often seen as an argument destroyer by people who don’t understand how to argue.

Finally, I’ll leave you with one of my favorite RAR’s in humorous form.

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