Measurement and Scale

Fukushima Prefecture (photo by Lincun)

On March 11, 2011, just off the east coast of Japan, a 9.0 magnitude earthquake occurred. When we talk about an earthquake having magnitude, we attempt to understand its seismic energy. That number is a notch on the Moment Magnitude Scale (MMS), which, in the 1970s, replaced the colloquial Richter scale that had held sway since the 1930s. Since 1990, just one other quake of greater size than last week’s Japan quake has been recorded. (For more info on earthquakes, see the U.S. Geological Survey.)

Because of the subsequent events unfolding at the Fukushima Daiichi nuclear power plant, we made an unexpected connection between the Richter scale and the nuclear age. The Wikipedia entry table for Richter Magnitude examples includes a few atomic and thermonuclear weapons tests, most uncomfortably assigning the fifty-megaton Tsar Bomba—or Big Ivan—with a magnitude of 8.35 on the Richter scale. In our post entitled “Measuring the Unthinkable” (December 8, 2010), we claimed that the measurement of fifty megatons was relatively meaningless, that we couldn’t really comprehend the explosion that was Tsar Bomba. But now, in the wake of Japan’s seismic event, we are trying to do just that. We want to understand what 9.0 means.

Fukushima Daiichi 2002 (photo by Theanphibian)

Last week, before the earthquake hit Japan, we were already thinking about scale because we watched the documentary film Powers of Ten (see video below and more here). The opening scene is of a man and a woman indulging in a leisurely, early fall picnic close to the shore of Lake Michigan. The film is narrated by MIT physicist and Manhattan Project veteran Phillip Morrison. (As an aside, Morrison was also the dissertation director for Chapman University’s Dean of Schmid College, Menas Kafatos.) Morrison tells us what is important in this scene: we are viewing a one-meter square image from a distance of one meter. His next statement provides the plotline for the entire documentary: “Now, every ten seconds, we will look from ten times farther away and our field of view will be ten times wider.”

With every new vantage in Powers of Ten, Morrison offers a physically meaningful context. When the field of view is a hundred meters, he tells us that this is the distance a man can run in ten seconds. Ten thousand meters become the distance that a supersonic aircraft can travel in ten seconds, and so on. Every ten seconds, we are ten times further away. After reaching 1024, the journey stops and returns to where it began. Then, the camera travels inward. As we pan back to the starting point, every ten seconds, the perspective travels ninety percent of the remaining distance. The perspective continues moving beyond the starting point, ultimately reaching what Morrison terms the “limit of our understanding” at 10-16 meters, deep in the subatomic structure of matter.

What Powers of Ten so effectively communicates are the concepts of logarithms (in this case, logarithms of base 10) and orders of magnitude (each power of ten is equivalent to an order of magnitude). By providing rough visual cues tied to our understanding of our bodies (at one meter, about half of the man is in the frame), things that our bodies can do (a man running a hundred meters), and things our bodies can see happening (an airplane flying overhead), Powers of Ten makes an intuitive appeal to take us into realms not ordinarily comprehensible, like the distance between stars.

Decibel Scale

Noise, like a seismic event, is measured by a logarithmic scale, using the unit of the decibel. Your refrigerator hums at about 45 decibels, and heavy traffic can reach 85 decibels, a level at which lengthy or repeated exposure can cause hearing loss. The danger is one of scale: for every ten-decibel increase—from the highest volume on an mp3 player (100 dB) to a rock concert (110 dB)—the sound is actually ten times as powerful. Energy, intensity—these are not the areas in which ordinary addition will do.

(If you eat a cookie, let’s say that’s 200 calories. If you eat a second, 200 + 200 = 400 calories. Imagine if the caloric intake of cookies worked on a logarithmic scale instead. That second cookie would be 2000 calories, and a third would be another 20,000 calories. That third cookie would be the equivalent of more than five pounds of body fat.)

Tomorrow, we’ll attend a reception for the closing of Measure for Measure, an art exhibit built, according to the accompanying booklet, on the “idea that we can organize and understand objects by incorporating a sense of their size—both in relation to ourselves and in relation to other physical quantities.” The curators—artist Lia Halloran and physicist Lisa Randall—chose the exhibit’s name to echo both William Shakespeare’s play and Tom Levenson’s book (the subtitle of which is A Musical History of Science). Lia Halloran was the person who reminded us, last week before the earthquake, of the film Powers of Ten.

One installation, by artist Meeson Pae Yang, of mirrored sculptures suspended from the ceiling tells us that the ocean isn’t what it appears to be, that 90% of its creatures are microscopic algae. Susan Sironi’s self-portraits use the size of her body parts to carve out layered illustrations in the books Gulliver’s Travels and Alice in Wonderland, two classics that toy with our sense of scale. The artwork by the seven artists in this exhibit reveals how our interpretation of scale “makes us question and perceive the world in new and various ways.”

Fukushima 1 NPP, Reactors 1-5 (National Land Image Information, Color Aerial Photograph)

As we write this, Japan’s death toll is currently relatively low, though there are more than 10,000 estimated dead in the province of Miyagi alone. The bodies—not yet those missing—are being counted. As the weeks go by, the bodies will accumulate, the missing will be tallied, and our way of measuring death will shift. Several of the largest earthquakes since 1990 caused no deaths, in large part because the epicenters were far from populated areas. Last year’s earthquake in Haiti, though, was just a 7.0—100 times less powerful than 9.0—but it caused 222,570 fatalities, in part because Haiti is, according to Newsweek, the poorest country in the Western hemisphere. Magnitude is one way to measure, fatalities another. Each way of measuring reveals different relationships to ourselves and the world around us.

As we finish this post, France’s nuclear safety authority says that the Fukuskima Daiichi catastrophe can now be categorized as a 6. The International Nuclear and Radioactive Event Scale (INES) is 1 through 7 and is another attempt at understanding the world around us. Three-mile island was a 5 (an accident with wider consequences), and Chernobyl was a 7 (a major accident). Tokyo, the metropolitan area where 13 million people reside, is less than 150 miles from the nuclear power plant in the town of Okuma, population of more than 10,000, presumably almost all of them evacuated. Clearly, we’ll be thinking about these ways of measuring for a very long time.

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