Language of mathematics

WEATHER Eye today might be compared to Galileo's concept of the universe

WEATHER Eye today might be compared to Galileo's concept of the universe. "It cannot be understood," he wrote, "unless one first learns to comprehend the characters in which it is written: it is written in the language of mathematics."

The need for mathematics arises from a letter I received recently that describes how ants can be used to tell the temperature. A scientist of old, apparently, discovered in an idle moment that the speed at which these insects scurry along the footpath is proportional to the square root of the absolute temperature.

But in fact a long list exists of animals from whose behaviour the temperature allegedly can be deduced. Those familiar with rattlesnakes, for example, maintain that at 37 C, they rattle at 100 rattles a second, decreasing to zero just above the freezing point.

The frequency, they say, increases by 2.7 rattles a second for each degree Celsius, so if you are threatened at 60 rattles a second, you know that the air temperature is 22 C, or to put it in mathematical language, T = R/2.7, where R is the rate of the rattle.

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Then there is the cricket rule. Below 13 C, apparently, a cricket or grasshopper does not chirp at all, but at 13, it chirps at around 60 chirps a minute and above 13 the rate of chirping increases steadily with the temperature. The rule here is T = 10 + (N - 40)/8," where T is the temperature in degrees Celsius and N the chirping rate a minute.

Clever readers will be able to work out quickly that if the cricket chirps at 140 chirps a minute, the air temperature is a balmy 22.5.

Now in the case of ants, we are told that their speed is proportional to the "absolute temperature" a concept introduced by scientists who found it difficult to deal with minus, signs. Having discovered that the lowest possible temperature attainable was 273 C or thereabouts, they took this point as zero, so that 15 C, say, becomes 288 K, these being degrees "Kelvin" or "absolute".

The ant rule, therefore, may be written V = c/K which, with a little mathematical manipulation becomes T = AV2 - 273, with T as the air temperature in Celsius, V the speed of the ant and A being what might be called the ant constant, a number with you must discover by observing the behaviour of your local ants at various known temperatures.

"Thus," as Galileo went on to say about the use of mathematics, "do facts which at first seem improbable drop the cloak which has hidden them and stand forth in their naked and simple beauty."