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Thursday, 5 November 2020

Exponents of the exponential: a rant.

An exponent of something is someone who recommends it, or explains it (or sometimes someone who performs it: a musician might be an exponent of the violin, for instance. Or the triangle, for that matter.).

If you're doing maths, however, an exponent is something quite different. In fact it's something so different that I wish that the mathematicians used a different word for it.

To a mathematician, an exponent is the small-font number that sits up in the air to the right of a larger-font number. It's an instruction to multiply the big-font number by itself that many times.

For instance

means forty-three multiplied by itself three times: 43 x 43 x 43. (It equals 79,507. Which is a lot, if it's badgers.)  

On the same principle, this means that


will just mean forty three. Because it's forty three just once, and not multiplied at all.


means one. (Sorry, I do not really understand this, but it is.)


however, means a bit over six and a half. Yes, that is smaller than forty-three: it's because a-bit-over-six-and-a-half multiplied by itself two times gives you forty three. 

(Yes, sometimes this idea is called a square root.)

As this is the case, I do wish that scientists would stop using the word exponential to mean getting bigger quickly.

I mean, that's not ordinary speech, and nor is it science. Use it carefully!

Word To Use Carefully Today: exponential. The Latin word expōnere means to set out or expound.

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