2 x 4s, hamburgers, and driveways [draft]

A friend of mine recently observed that a 2 x 4 isn't actually two inches by four inches (it isn't two feet by four feet, either). The reasons for this, as I understand, is that lumber was originally measured by what came off the saw - in other words, wood was cut to a dimension of two inches by four inches, and that was your two by four - pretty straight forward. Problems arose, however, regarding the surface of the wood, which, having just been sawed, was rough and splintery. Customers started asking for the wood to be smoothed down, and the lumber yard was happy to oblige, but the smoothing process takes off some of the wood, leaving an ostensible 2 x 4 actually 1 & 1/2 inches by 3 & 1/2 inches.

But the point of this is that it got me thinking about language. Even though our wood may be 1 & 1/2 inches by 3 & 1/2 inches, we call it a 2 x 4, and if you ask a carpenter for a 2 x 4, she'll know what it is that you're looking for. As a society, we seem to have agreed that 2 x 4, in the context of lumber, does not refer to the actuality of the thing that it describes. It's kind of like the quarter-pounder hamburger whose weight was a quarter of a pound before cooking, but now weighs something other than a quarter of a pound (something less than a quarter pound, I imagine). And this isn't too far removed from the oft repeated "why do we park in driveways and drive on parkways." Words don't always mean what they mean; sometimes we agree that they mean something else.

If you're not confused yet, don't worry: things get worse.

If we take a step back, we realize that there is nothing inherent in the word two that indicates a whole number between one and three. Nor is there anything inherent in four, or 4, for that matter, that indicates a whole number between three and five. We can see this on one level if we recognize that 2 isn't two to all people. For those speaking Spanish, 2 is dos, while for those speaking German, 2 is (I think) zwei. All of these languages have 2 in common, but if we were to go to ancient Rome, the number between one and three would be II.

So the word or label that we apply to the concept of two is non-intrinsic. If we had all decided that two meant three, for instance, the world wouldn't be functionally different. All that matters is that we agree on a word's meaning, not what we agree that that word means.

Our 2 x 4 becomes increasingly removed from reality.

Because our use of 2 x 4 is an agreement to assign a meaning to the phrase 2 x 4, in the context of lumber, that differs from the generally agreed upon meaning of 2 x 4. We agree to consistently disagree with what we have all previously agreed upon, but only to do so in certain well-defined situations, viz lumber.

We can make this all even more complicated by observing that we make our agreement on the meaning of two by using terms that also lack inherent meaning, but which we have assigned an agreed meaning to. We ultimately have a house of cards built by M. C. Escher, in which each piece looks fine, but the totality is absurd; but I'll spare you that discussion.

[Edit (21 May 2008): yes, the 2nd to last paragraph is deliberately obscure]