11 April 2010

"Three times smaller" makes no sense to me

I was reading an article this week about an early hominid, and the description of the skull indicated that the creature's brain would have been "three times smaller" than that of a modern human.

It's a commonly used phrase (800K Google hits), and I know what the author meant.  He/she was saying that the brain was "one-third the size of a modern human brain."  But to me "three times smaller" is a dreadful construction because it could just as well mean "one-fourth the size" ("two times smaller" would be one-third the size, and "one times smaller" would be half-size).


  1. I think the bigger problem is that 'smallness' isn't a terribly meaningful concept. It's easy to see why "the human brain is three times bigger than..." is wrong because we understand 'bigness' (size) but 'smallness' is alien.

    Some reciprocal pairs, like resistance and conductance, are both meaningful. Even distance and proximity are both fairly useful. We have an intuitive understanding of proximity. We don't explicitly use it much, but one could formulate Newton's law of gravity, for example, in terms of proximity: F=Gm₁m₂p²

    But 'smallness' doesn't work that way. It doesn't make sense to us to say the human brain is 885m⁻³ small, so saying something's three times smaller than that, whatever is meant by that, is unhelpful.

    But at least it's better than 'hotness' and 'coldness'. People casually say it's 'three times hotter' when the temperature increases from 10°C to 40°C, but it should be measured from -273°C, absolute zero. Otherwise -20°C is "three times hotter" than -5°C. Instead people call that "three times colder". But it's totally meaningless, because what's "three times colder" than -5°C changes when you use Fahrenheit. It's 23°F, so "three times colder" is nearer 5°F, which is -15°C (the same figure you'd get by misinterpreting the phrase 'three times').

    Basically people need to start using intuitive language to describe quantities. I don't see why that's hard. Just tap the figure into Wolfram Alpha, and it'll tell you that the brain you've found is about the size of a can of soda. Surely that's more useful than a comparison of smallness?

  2. I think three times smaller means two below none. If you think how small is one time smaller...


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