I've always gotten a kick out of deriving formulas from mathematical principles. Waaay back in 9th grade, I remember taking a science test where there was an extra-credit question that went something like: "Water boils at 420 degrees on the linear Kolian scale and freezes at -12 degrees Kolian. What is 52 degrees Fahrenheit on the Kolian scale."
There's no such thing as a Kolian scale and we'd never been taught the way to solve something like that. The idea was to see if you could reason your way through it. Although most of the students did fine in converting Fahrenheit to Celsius or Kelvin, or vice versa, because they'd memorized formulas for doing so, they had never thought about why those conversion formulas were what they were. If you understood the principle, though, it was easy to convert to any scale where you knew two fixed points (assuming it was a linear scale, rather than logarithmic or something). In the entire grade, there were only two of us who got it right.
I wish they'd do more to teach that kind of reasoning, rather than encouraging the memorization of formulas by rote. You're going to forget the vast majority of formulas you memorize, but if you understand the concept behind them, it doesn't matter. I don't know, by rote, the formula for converting Celsius to Fahrenheit, for example, but I remember what boiling and freezing are for each, so I can convert easily between the two by mentally deriving the formula.
There's no such thing as a Kolian scale and we'd never been taught the way to solve something like that. The idea was to see if you could reason your way through it. Although most of the students did fine in converting Fahrenheit to Celsius or Kelvin, or vice versa, because they'd memorized formulas for doing so, they had never thought about why those conversion formulas were what they were. If you understood the principle, though, it was easy to convert to any scale where you knew two fixed points (assuming it was a linear scale, rather than logarithmic or something). In the entire grade, there were only two of us who got it right.
I wish they'd do more to teach that kind of reasoning, rather than encouraging the memorization of formulas by rote. You're going to forget the vast majority of formulas you memorize, but if you understand the concept behind them, it doesn't matter. I don't know, by rote, the formula for converting Celsius to Fahrenheit, for example, but I remember what boiling and freezing are for each, so I can convert easily between the two by mentally deriving the formula.
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Ian Jeffrey
