When 2 plus 2 Equals 5, plus Another Unsettling Equation


I just wanted to note for folks who don’t read The Straight Dope — the first two books of which were unimaginably important to the teenage me, hundreds of pages of neat stuff to know delivered in a powerful style, that overwhelmed even The People’s Almanac 2 if you can imagine — that the Straight Dope Science Advisory board tried to take on the question of Does 2 + 2 equal 5 for very large values of 2?

Straight Dope Staffer Dex takes the question a bit more literally than I have ever interpreted the joke to be. I’ve basically read it as just justifying a nonsense result with a nonsense explanation, fitting in the spectrum of comic answers somewhere between King Lear’s understanding of why there are seven stars in the Pleiades and classic 1940s style double-talk. But Dex uses the equation to point out how rounding and estimation, essential steps in translating between the real world and the mathematical representation of the world, can produce results which are correct at every step but wrong in the whole, which is worth considering.


Also, in a bit of reading I’m doing and which I might rip off^W^W use as inspiration for some posts around here the (British) author dropped in an equation meant to be unsettling and, yeah, this unsettles me. Let me know what you think:

3 \mbox{ feet } + 2 \mbox{ tons } = 36 \mbox{ inches } + 2440 \mbox{ pounds }

I should say it’s not like I’m going to have nightmares about that, but it feels off anyway.

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

13 thoughts on “When 2 plus 2 Equals 5, plus Another Unsettling Equation”

  1. To me British Imperial measures like the long ton (which is only half a smoot longer than a short ton) pretty much sum up the problem the British also have making reliable cars. And landing things on Mars, when one half of the team is using Imperial and the other half metric.

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    1. As best I can tell the short ton is an invention of the Americans, so the British aren’t directly at fault for the long ton/short ton divide. Granted that 2240 pounds is a superficially weird number of pounds to put into any unit, but that is at least a nice convenient twenty hundredweights, which admittedly moves the problem back to why a hundredweight is a hundred pounds. In that case it’s because a hundredweight was a nice convenient eight stone, which had been twelve and a half pounds avoirdupois, until King Edward III yielded to the convenience of the wool trade and increase the stone to fourteen pounds (making a sack of cloth, 28 stone, more conveniently measured without cheating on available scales and also a nice (nearly) round 500 Florentian libbrae, and the rest followed from there.) Which is to admit that it’s daft, but every step made sense at the time, which is the best we can ever hope for.

      Now, the Imperial/Metric problem with the space probe is interesting because while the difference in units is the proximate cause of the vehicle’s loss, it’s not the real cause. There were hints, from earlier maneuvers, that something was wrong in the way thrusts were being calculated or executed, but those weren’t followed up on. Had they been, a correction would’ve been straightforward. It’s a lesson in the importance of having good project management, and that project management has to include people signaling clearly when they suspect there’s problems and exploring adequately whether these suspicions are well-founded.

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  2. It was not until recently that I learned how ‘ton’ is used in engineering (related to air conditioning). I learned a lot of – maybe a ton of – new units when trying to respond to questions in the comments section on my blog :-)

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    1. I did not know there were custom uses of the ‘ton’ for engineering purposes until just now, and I’m fascinated to see how many different “big mass of the thing we’re measuring” get called tons, now. (Panama Canal Net Ton? Who ordered that?)

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