## Ratcheted up a logarithm?

I really like the Atlantic magazine. Its articles are well-researched, in-depth, interesting, topical, far-ranging and generally a pleasure to read. It is a sign of my enthusiasm for the magazine that I pay the equivalent of US\$15 to buy it here in New Zealand, and I take it to a local cafe/pub overlooking Waiheke (see my New Zealand blog for a couple hundred photos) to savor during one of the few periods I spend away from either work or the ever-fascinating and ever-challenging Alexander. I was reading a typically well-written and persuasive article by Andrew Sullivan on why Barack Obama is the candidate to transcend our political divides (see also his blog entry), when I came across the following:

The war on Islamist terror, after all, is two-pronged: a function of both hard power and soft power.

Consider this hypothetical. It’s November 2008. A young Pakistani Muslim is watching television and sees that this man – Barack Hussein Obama is the new face of America. In one simple image, America’s soft power has been ratcheted up not a notch, but a logarithm.

Ratcheted up a logarithm? What could that possibly mean? I have grown used to the phrasing “increased exponentially” even when the increase is quadratic (as a referee, I see this at least twice a year in professional papers; the popular press is hopeless on this). But can there be a less appropriate term than “ratcheted up logarithmically”? Here are some choices:

• Instead of going up by one (“a notch”) it has gone up by the logarithm of one. Um, no… that would be going up by 0, no matter what base you go with.
• Instead of increasing by one, you take the logarithm of the level. So if you start at 100, instead of going to 101, you go to the logarithm of 100. We’ll go with base 10, so that would take you to 2. Wrong way (and will be for any reasonable base)… no.
• Instead of increasing by 1, you increase by the logarithm of the level. So if you start at 100, you go to 102, instead of 101 (base 10). Well, at least it has the right direction, but I can’t believe this is what Sullivan had in mind.

I do not believe I am overly picky here. If Sullivan had referred to “Congresswoman Clinton”, clearly any fact-checker, editor, or casual reader would correct/castigate as appropriate. Or an illiteracy, “Obama is the bestest choice”, would not possibly make it through the system. But the mathematical illiteracy of the population is sufficient that this can go through in what has to be one of the most closely edited magazines in existence.

This reminds me of the old question. Why is it when I say “I am in Operations Research: the science of using mathematics to make better decisions” (or whatever phrase I am going with at the moment), it is quite common for people to say “Oh, I never understood any mathematics”, expecting me to understand and applaud them for recognizing their limits. But when they refer to a book, if I were to say “Oh, I never understood that reading thing”, I would look like an idiot and they would move on to someone else to talk to. Why is there this difference?

If I am blogging 50 years from now, I am sure I will be complaining “Nice article, too bad it doesn’t mention operations research by name”. But, I would hope that I am not seeing lots of “ratcheted up by a logarithm”!

1. Dan | November 24, 2007 at 1:57 am | Permalink

I agree, it’s a sad thing. I wonder if the writer was envisioning logarithmic scale? Wait, in order to do that he would have to know the inverse relationship between exponential and logarithmic growth… doh!

2. Anonymous | November 28, 2007 at 7:52 pm | Permalink

> Why is there this difference?

Probably because basic knowledge of mathematics is not strictly required in every day life or in most jobs (of course it can be very useful sometimes), but basic knowledge of English/language is required.

3. Kirk | November 29, 2007 at 2:45 pm | Permalink

On the subject of innumeracy, I liked this story from the news of the weird:

In November, Britain’s new weather-themed Cool Cash lottery game was canceled after one day because too many players failed to understand the rules. Each card had a visible temperature and a temperature to be scratched off, and the purchaser would win if the scratched-off temperature was “lower” than the visible one. Officials said they had received “dozens” of complaints from players who could not understand why, for example, minus-5 is not a lower temperature than minus-6. [Manchester Evening News, 11-3-07]

http://www.newsoftheweird.com/archive/index.html