Every day, we toss around ‘official numbers’ we only dimly, at best, understand. But now the next time you apply sunscreen, take shelter during an earthquake, check the weather, or turn up the volume of your music, you might just have a better idea of what’s really going on.
If there’s an SPF 60 sunscreen, surely SPF 30 sunscreen is only half as effective, right? And as for SPF 15, well, you may as well just spread milk on your arms, right? Actually, no. An SPF 30 sunscreen blocks nearly 97 percent of ultraviolet B radiation (the wavelength that causes sunburn and plays a key role in skin cancers). But an SPF 15 sunscreen blocks 93 percent of UVB. So what does the number mean?
A sunscreen’s SPF number is determined, horribly, through tests on human subjects. Essentially, you round up a group of people and see how long it takes for them to burn without sunscreen, then repeat the test with sunscreen. Divide the number of minutes to burn with sunscreen by the minutes to burn without, round down to the nearest five, and that’s your extremely precise and scientific SPF number.
If you’re willing to experiment on yourself, which we don’t recommend, you could theoretically reverse the formula to determine how often to reapply sunscreen, by multiplying your minutes-to-burn without sunscreen by the SPF number. So, if you normally burn after five minutes outside, and apply 30 SPF sunscreen, you could expect to last outside for 5 x 30 = 150 minutes without burning.
Increased SPF numbers offer sharply diminishing returns: An SPF 50 sunscreen blocks 98 percent of UVB, just over 1 percent more than SPF 30. A sunscreen’s effectiveness also drops thanks to water or sweat, and people tend to not apply as much sunscreen as they need.
The familiar Richter scale rating earthquake magnitudes employs a base-10 logarithmic scale. That means each whole-number “step” (say, going from a 4.0 to a 5.0) on the scale corresponds to a tenfold increase in the shaking amplitude of the quake recorded by a seismograph. Even more dramatically, each whole-number step corresponds to around a 32-fold increase in the amount of energy released by the quake. So while a 5.0 earthquake releases the equivalent of 200 tons of exploding TNT, a magnitude 6.0 quake releases the equivalent of 6,270 tons. In the 70s, the Richter scale was professionally replaced by the moment magnitude scale, a product of the distance a fault moves and the force required to move the fault. For smaller quakes the Richter scale and the moment magnitude scale are roughly equal; it’s only when you start getting to the really big quakes, like magnitude 8.0 and above, that the moment magnitude scale starts to diverge, and gives a more useful reading.
When the weatherman says there’s a 30 percent chance of rain tonight, it doesn’t exactly mean you’re 3/10 likely to get wet. The way that meteorologists calculate the probability of precipitation depends on two factors: the portion of the area that should experience rain (coverage), and the confidence that rain will occur. Multiplied together, those two percentages give you your prediction—technically called the probability of precipitation (or POPS for short).
So, after looking at a number of factors— including satellite and radar imagery, computer models, and data from local weather observation stations—a weatherman in Atlanta might offer a 30% prediction. This might mean he feels 75 percent certain that around 40 percent of the metro area will experience some rain, which would yield a POPS of (.75 x .40 =) 30 percent. Or he might have been 50 percent confident that 60 percent of the area would get rained on—also yielding a POPS of 30 percent.
Alcohol proof is simply twice the percentage of alcohol by volume (ABV) in a drink (or 7/4 times the ABV, if you’re in the U.K., historically, although they seem to be begrudgingly adopting the ABV standard now).
Why bother with a simple doubling formula? Stories of the origin of alcohol proof differ: We have to thank either the scrupulous 17th-century British sailors who would not accept watered-down rations of rum, or the scrupulous British tax collectors trying to impose a higher tax rate on stronger stuff. Allegedly, both sailors and tax collectors employed the “gunpowder test,” wherein a bit of spirit is poured on gunpowder and lit. If the flame burned steadily, this was deemed “proof” of high alcohol content, as any spirit less than around 57 percent alcohol would not burn. Eventually, the British settled on a more precise test: 100 proof spirits were those where the weight of the spirit was 12/13 the weight of an equal volume of distilled water at 51 degrees Fahrenheit.
In 1824, French chemist Joseph-Louis Gay-Lussac came up with probably the most reasonable standard of proof: 100 percent alcohol is 100 proof, while 100 percent water is 0 proof. “Thus 100 proof on the American scale is 50 proof on the French scale and about 87.6 proof on the British scale,” University of Cincinnati chemist William Jensen wrote in the Journal of Chemical Education. “All in all it is a good example of what happens when standards are set by politicians instead of scientists.”
It’s enough to drive one to drink.
Like earthquake magnitude, comparing the intensity of sounds relies on a logarithmic scale. Decibel units measure the sound energy flowing through a particular area, rating each sound according to the exponent of its intensity, relative to the threshold of human hearing, multiplied by ten (hence the ‘deci’ part of decibels). Huh? Take a bird call that’s 10,000 times more intense than the threshold of human hearing. 10,000 is equal to 104; we take the exponent, 4, and multiply it by 10, giving us 40 decibels.
Why multiply by ten…why do we measure things in decibels, but not bels? A single decibel’s difference, it turns out, is just at the limit of what humans can normally detect. We wouldn’t notice an increase from 40.0 to 40.1 decibels, but we can just pick up the difference between 40 and 41 decibels.
Purdue University offers a chart comparing decibel sounds. 20 decibels is about the sound of whispering. 60 DB is the ambient noise level in a typical office; 80 DB a garbage disposal, 90 DB a motorcycle. 110 DB is the threshold of human pain endurance and—coincidentally?—the sound level rock concerts usually deliver. At 150 decibels (the sound of a jet engine), eardrums can rupture.