The Grandeur of the Lowest Common Denominator

You ever get a metaphor wrong? You know, you hear an expression and then use it without really thinking it through? All these years, I've been thinking the term "lowest common denominator" was a pejorative term often used when critics speak dismissively of low-brow culture. But today I learned that I'm wrong.

I've been reading Andrew Hodges new book One to Nine: The Inner Life of Numbers. [Hodges also wrote Alan Turing: The Enigma.] In his chapter about the number Nine, Hodges discusses the term "lowest common denominator," a term that many associate with something that is "small and cheap." But we've got it all backwards:

"A lowest common denominator is generally a rather grand number! This term arises in the context of fractions p/q, where p is called a numerator and a q a denominator.

"To add 1/1 + 1/2 + 1/3 +1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9, the trick is to find the lowest common denominator from 1, 2, 3, 4, 5, 6, 7, 8, 9. That is the smallest number which can be be divided exactly by all of 1, 2, 3, 4, 5, 6, 7, 8, 9 — which turns out to be 2,520. You are supposed to write 1/2 as 1260/2520, 1/3 as 840/2520 . . . 1/9 as 280/2520 and so add them up. [Amazing stuff: as it turns out the lowest common denominator is a special number.]

"In practice, few people add up fractions much more complicated than 1/2 hour + 1/4 hour, and I am not surprised that this complicated theory has left little trace on the collective mind. Probably the misuse of the metaphor [of 'lowest common denominator'] has arisen by people confusing it with the 'highest common factor' of a set of numbers, and this is typically something modest."

That's my lesson for today: over the years, the term "lowest common denominator" has gotten an undeserved bad reputation because it has been confused with something else.

Question: what other commonly used metaphors actually mean something quite different from the ideas we usually associate with them?

Comments

[Dr. Zoltan!]

Although these are not metaphors, this post reminded me that the terms, "Alternative" and "Progressive" (in reference to music) are Relative terms that have been Absolute-ized. Progressive now means music from the 70's, and Alternative has become mainstream.

[JB]

While it is a grand number, it is still the lowest of the "infinitely grander" numbers available to the solution set. :)

nice post, though -- just poking!

[Roger von Oech]

Dr. Zoltan: When I hear the word "Progressive" in a political sense, it usually makes me think of its use in the 1930s-50s as a less alarming alternative to "Workers" and "Socialist."

JB: Thanks for poking! You must agree, though, that in its mathematical sense, LCD is a long way from "modest" and "cheap."

[Katie Konrath]

Until I studied ancient Greek in college, I thought that giving someone "kudos" meant rewarding them with a Kudos candy bar. (http://www.rockofagescandy.com/HTFCandyBars/Products/Kudos.html)

So I was always disappointed that I never actually saw candy change hands, despite all the promises...

...Until I learned in college that "kudos" is actually the Greek word for "honor" and "fame"! Whoops!

Still, I can't fault my mind for always defaulting to the candy bar option - I was swimming 2 hours a day at that time and always hungry!

[JB]

I agree it doesn't mean simple or cheap -- I always thought it implied "the most basic level" and/or "dumbed down." Depending.

So if 2520 is your number, 5040 works too, and so does 10080. In that case, if we assume that larger is better, our LCD does have negative implications. As in this "Value Score" of our design solution is only 2520 when it could be 5040.

But if we take it as simple is better than complex, then it could be positive.

It's an interesting concept: the context, and the accuracy with which it is used. Again, very nice post.

[JB]

I thought about it some more too. Assume all humans have base instincts (2520 of them, including lust and greed). And some rise above those and have higher pursuits (1000 more, not all the same). Then when "this movie" appeals to our LCD, it could mean lowbrow in a way that implies "base" since all the higher pursuits are not in the common set.

I apologize for being geeked about this post. G'day!

[Andrew]

How about "a dog's life"? Watching my golden retriever, an observer would have to conclude this dog's life was pretty good, perhaps even enviable. Yet that is not the commonly understood meaning of this metaphor.

[Randy Bosch]

"Rocket Scientist" and "Brain Surgeon" come to mind -- originally terms of great respect, now of disrepect.

"Architect" and "Engineer" are two others.
Usually, those who are behind a specious scheme are labeled "architects" and those behind successful ones are labeled "engineers". As an actual architect (and not a "software architect" - a contrivence!!), perhaps I should be offended?

[Randy Bosch]

In re: "lowest common denominator".
In our culture, in group work, does consensus often have that definition?

[Business Loan]

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