|Tahrir Square, 24th Nov. An injured protester wakes up.|
Photograph: Tara Todras-Whitehill/AP
Any decent revolution comes in two stages roughly eight months apart, and now that Egypt is in the throes of stage 2, I'm looking at what was written earlier in the year. And I find this in The Guardian of 12th August, under the heading "The Arab Spring's Bottom Line", by Khaled Diab.
He asks why the Arab spring concentrated on political reforms, without addressing economic injustice. The strapline to his article is “You can have all the democracy in the world, but without addressing economic injustice, reforms will be hollow”.
In Egypt and Tunisia trade unions and workers were a vital driving force behind the protests, holding regular strikes and sit-ins, Diab writes. Even the 6 April youth movement, which called for the first protest of the Egyptian revolution on 25 January, was originally set up to express solidarity with textile workers. So why have demands for social justice been sidelined?
One reason, he suggests, is that in order to topple the old order, the Tunisian and Egyptian popular uprisings needed to appeal to all strata of society – young and old, rich and poor, socialist and conservative. To do this they focused on the lowest common denominator: regime change, the creation of a level political playing field and the protection of human rights.
But incompatible class interests meant that on economic issues such as pay and workers rights, there could be no consensus about how to proceed; so the once-united opposition splintered into political factions.
You can read the article here.
At this juncture I must come clean and confess I've been toying with you. This post isn’t actually about politics, it’s a rant in defence of mathematics, and against the persistent abuse of a particular mathematical term, the "lowest common denominator".
But first, another example. It’s a reader's letter in the London Independent on 6th September, about the glut of media commemoration of the tenth anniversary of the 9/11 attacks.
The letter is from one Paul Harper who notes with considerable disappointment that The Independent has joined the rest of the media in commemorating the anniversary by what he calls “mindless wallowing”. A time for dignified reflection on the causes and effects of 9/11 has been squandered in favour of “sensationalist ratings-grabbing specials. It is lowest common denominator bottom-feeding journalism feeding off crocodile tears of fake emotion. … The media should be ashamed of itself.”
Now I ask: what do Khaled Diab and Paul Harper mean with this expression "lowest common denominator"?
In the piece about the Arab Spring, it appears to mean something like “the only issue shared by the disparate opposition groups and classes”. (I'll return to this example at the end).
In the letter about the 9/11 commemorations, it appears to mean something like “the lowest of the low”; little more than a piece of vulgar abuse, in fact.
An elegant mathematical procedure
4/15 + 5/9
Outside of a classroom it’s actually quite unlikely that you would want to do this, you would express the amounts as decimals instead. But just as a mental exercise, say we do wish to add 4/15 and 5/9, how do we do it? We express both fractions with a common denominator; preferably the lowest common denominator.
This will neatly lead you to the answer, which is 37/45.
In this answer, 45 is the lowest common denominator. It’s an elegant procedure, and it's all in this pdf file in case you want to see how it works.
My point at the moment is this.
How, exactly, is this piece of maths connected to the phrase "lowest common denominator" as used by journalists, politicians, business pundits and letters to the editor? Do these people understand the above procedure?
I suspect they do not.
Moreover, suppose we skip the maths, and just for the time being take my word for it that 45 actually is the lowest common denominator of 4/15 and 5/9. What do we notice about this number 45?
That it's larger than any number we started with. So the lowest common denominator isn't even a low number. It’s a high number. Hah!
Moreover the lowest common denominator is also the best common denominator. Other common denominators can be used, but none is as neat as the lowest common denominator.
Yet those who employ the phrase lazily convey the impression that the lowest common denominator is a riffraff number, a base, degraded species of entity.
Consequently I declare "lowest common denominator" the third most annoying expression in the English language, I anathematise it and ban it altogether.
For an epilogue, let me just return to my first example, from The Guardian. Whilst in most instances I've come across, "lowest common denominator" is used lazily, often (as in the readers letter about 9/11) as a stand-in for vulgar abuse, such may not be the case here.
In the piece about the Arab Spring, we've noted that "lowest common denominator" appears to mean something like “the only issue shared by the disparate opposition groups and classes”. I thinks it’s fair to deduce therefore that the writer, Khaled Diab, does perhaps have in mind the phrase's actual mathematical meaning. If he's genuinely keen on a mathematical metaphor, then I would suggest the apt one to use is highest common factor. (As in 15 is the highest common factor of 30 and 45).
Thus he could have written “To do this they focused on their highest common factor: regime change, the creation of a level political playing field and the protection of human rights.” I don’t necessarily recommend this. But it works a whole lot better than lowest common denominator.
I could multiply examples but it would become tedious. Woody Allen is fond of using “lowest common denominator” about Hollywood, and I've found an example in the writing of Tony Cliff, late guru of the SWP. See this pdf file if interested.