Up to 11, up to 100

On the weekend my wife and I took the opportunity to rewatch the finest rock/mock-umentary ever made, This is Spinal Tap (sorry, Unicode still hasn’t got around to n-diaeresis). We’re going to see the boys from Spinal Tap / every other Christopher Guest movie ever made, unwigged and unplugged, in concert in Detroit on the 29th, so this was sort of preliminary research.

As you know if you’ve been reading for a while, or at least if you’ve been reading and paying attention, I study cultural aspects of numbers and mathematics, and so today I’d like to talk to you about one of the greatest phrases coined in the past quarter-century, ‘up to eleven’ – check out this strikingly long list of pop-cultural references as evidence of its ubiquity, or just so you know what I’m talking about here if you’re unfamiliar with the movie. The core idea is that a higher number represents more (in this case, more volume –> better!), rather than simply being a more fine-grained division of a continuum (i.e., 1 to 10 –> 1 to 11 –> … 1 to 100, etc.).

Okay, it’s hilarious, and I’m making it sound all technical and such, but I have a point here. It’s an example of what I call conspicuous calculation, the use of (often unnecessarily) large numbers for discursive effect. This is highly prevalent in Western societies, but is by no means limited to them – one of the earliest pieces of Egyptian text, the Narmer mace-head, contains a set of numerals ranging into the millions boasting of a large quantity of livestock and people taken as plunder. Particularly in state societies that have a focus on quantification and enumeration, numbers can become a tool to overawe, manipulate, and obfuscate. The argument is longer (and still in development), but you get the idea.

But in one of those fantastic serendipities, a fascinating article came out in the New York Times a few days ago, ‘Confused by SPF? Take a Number‘ by Catherine Saint Louis. It’s a fascinating look at how an objective measurement (Sun Protection Factor / SPF: the measured ratio of the time it takes to burn with sunscreen on to the time it takes to burn without it) can be used as part of a rhetorical advertising war and can exaggerate the actual protection you are receiving. Although dermatologists are aware that there is little practical difference between SPF 30 and SPF 100 – and that far more significant factors include how much sunscreen you use, and how thoroughly you apply it – the numbers war has significant effects, as discussed in the article:

“It captures the consumers’ attention, the high SPF,” said Dr. Elma D. Baron, an assistant professor of dermatology at Case Western Reserve University who sees patients at hospitals in Cleveland. “Just walking down the drugstore aisle and seeing a SPF 90 or 95, they assume, ‘This is what I need.’ ”


When told of Neutrogena’s 100+ lotion, Ms. Bigio worried that the sunscreen she always wears when rock climbing and bicycling to work isn’t enough. “It makes me feel like SPF 45 is inadequate,” she said.

Now that there is such a thing as SPF 100, there is a real danger that 100 will be interpreted as complete protection. Living in a decimal society permeated by scientific discourses, we tend to associate 100 with 100%. It’s no coincidence that the new Neutrogena product is advertised as SPF 100+, not SPF 104 or SPF 106.4. In contrast no one would advertise SPF 25 as ’20+’. The spurious roundness of the number allows the consumer to associate 100 with completeness and thus to be confident of full protection. But SPF isn’t a measure of the percentage of the sun’s rays blocked, and it doesn’t have an upper limit.

When I was a kid, we had SPF 6 or SPF 8 around the house, and we rarely wore it (even though I’m pretty pale for someone of partially Mediterranean heritage, and one half of my family is particularly burn-prone). Was I well-protected? Probably not. I also should have been wearing a hat (still to this day I am a non-hat person). Today you can’t even find such low SPFs anywhere, and you will find people who think that putting anything less than SPF 30 on your child is tantamount to abuse. But make no mistake: this is a discursive battle as much as it is a scientific one, one ultimately governed not by laboratory practice but by the need of an industry to outmanoeuver competitors, literally, by outnumbering them.


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