Putting two and two together: mathematical expressions
As somebody who loves words and English literature, I have often been assumed to be a natural enemy of the mathematical mind. And, if we’re being honest, my days of calculus and the hypotenuse are behind me, but, with those qualifications under my belt, I did learn that the worlds of words and numbers are not necessarily as separate as they seem. Quite a few expressions use numbers (sixes and sevens, six of one and half a dozen of the other, one of a kind etc.) but a few are more closely related to mathematics than you’d expect…
Put two and two together
Let’s start with an easy one. It doesn’t take a mathematical whizz to know that 2 + 2 = 4, and, indeed, that’s the heart of this expression. To put two and two together is used to mean ‘draw an obvious conclusion from what is known or evident’. Conversely, if you say that somebody might put two and two together and make five, you’re suggesting that they are attempting to draw a plausible conclusion from what is known and evident, but this conclusion is ultimately incorrect. 2 + 2 = 5 was famously used in George Orwell’s Ninteen Eighty-Four as an example of a dogma that seems obviously false, but which the totalitarian Party of the novel may require the population to believe: ‘In the end the Party would announce that two and two made five, and you would have to believe it.’
Fly off at a tangent
I remember a moment of surprise in the middle of one of my mathematics A Level classes. It made a nice change from the almost unbroken moments of bewilderment which characterized the experience. It was when we were looking – as you do – at the equations relevant to what happens when something rotating on an axis suddenly stopped. Well, guess what? It would go off at a tangent.
So, what is a tangent? It’s a straight line that touches a curve at a point, but (when extended) does not cross it at that point. (It’s also apparently ‘the trigonometric function that is equal to the ratio of the sides [other than the hypotenuse] opposite and adjacent to an angle in a right-angled triangle’, but the less said about that the better.)
In common parlance, of course, it simply means ‘a completely different line of thought or action’. While we’re mentioning the hypotenuse, you may well recall that it is ‘the longest side of a right-angled triangle, opposite the right angle’, but may not know the word’s origin: it ultimately comes from the Greek verb hupoteinein, from hupo ‘under’ + teinein ‘stretch’.
The lowest common denominator
In a fit of pique, you might have described a person or a group as the lowest common denominator. It is often said, in a derogatory way, to mean ‘the level of the least discriminating audience’, for example ‘they were accused of pandering to the lowest common denominator of public taste’. But what actually is a denominator?
Cast your mind back (if you will) to the world of fractions – specifically vulgar fractions (those that are expressed by one number over another, rather than decimally). The number above the line is the numerator and the number below the line is the denominator. In ½, for instance, the numerator is 1 and the denominator is 2. In mathematics, the lowest common denominator is ‘the lowest common multiple of the denominators of several vulgar fractions’. For instance, the lowest common denominator of 2/5 and 1/3 is 15, as that is the lowest common multiple of the denominators 5 and 3; the fractions would become 6/15 and 5/15 respectively. It isn’t entirely clear how this sense transferred to the broader, non-mathematical sense.
Can you think of any other expressions that developed from the world of mathematics? Let us know in the comments!