Supporters of 350ppm target for atm. C02 <source>
On October 24, 2009, environmental activists around the world gathered in support of a geophysical data point. With their bodies, banners, and balloons, they formed the numeral 350, advocating that governments should adopt 350 ppm as a target for atmospheric carbon dioxide concentration. How remarkable that a number should have such rallying power. How remarkable that humans are able to conceptualize the invisible stuff we live within and breathe into our bodies as a substance made of numbers. Our ability to do so is an end product of a long series of insights and inventions by our scientific predecessors.
For hundreds of year, a major activity and accomplishment of Earth Scientists and our predecessor natural historians, has been to turn experienced reality into numbers. Earth Science is sometimes dismissed as merely a "descriptive" or "observational" science, but such an attitude understates both the vastness and the power (and the pitfalls) of the enterprise of mathematicizing that which had previously only been known through non-quantitative human senses.
I can jump into a pond or the ocean and sense its temperature with sensors in my skin and describe my sensation in words: "Warm," "Not so cold, come on in," "Cold," "Icey." With the invention of the thermometer, approximately 400 years ago, it became possible to turn these feelings into numbers. Over the same 400 year stretch of time, many attributes and processes of the Earth were turned into numbers: the power of an earthquake, the height of a mountain, the swiftness of the wind, the saltiness of the ocean, the density of minerals, etc., etc.
Why was this considered a good thing to do? Why did so many people devote so much effort to inventing ingenious ways to quantify things, especially things that humans could sense with our own senses without instrumentation? And then, why did so many other people devote so much time, effort, and money to going out into nature and measuring everything? Several reasons:
- Numbers are the same across observers. A child from Florida and a child from Maine quite likely would not use the same words to describe the temperature of a swimming hole they visited together. But given thermometers, they would come up with the same number of degrees.
- Numbers stay put over time, whereas sensations do not. If I revisit the same pond in a week or a month or a year, I can't reliably remember how cold it was last year, and can't reliably tell whether it is warmer this year or not. Numbers allow the study of natural changes over time.
- Related to the above, numbers allow before and after comparisons across interventions or events.
- Numbers allow comparison across space. Sensors in different places allow the same parameter to be measured in different places at the same time, which enables spatial reasoning about causes and consequences.
- Numbers enable conceptual models to be turned into computational models, with predictive power.
On the other hand, something important can be lost when complex reality is reduced to a number. Consider three instances:
To continue with the theme of temperature, the average temperature of the atmosphere can be reduced to a single number: 15°C. This is a very powerful number: it allows us to compare and contrast Earth's atmosphere with that of Venus or Mars, to graph how atmospheric temperature has changed across geologic time, and to consider the radiation balance of the planet as a whole. But reducing the Earth to that single number obscures both temporal and spatial variations: the seasonality that makes New Yorkers shiver in winter and swelter in summer, and the spatial variation that lead to igloos in the Arctic and lanais in Hawaii.
Take a second instance: Earth's complexity reduced to "4.5," where 4.5 is the age of the earth in billions of years. Once again, this is a very powerful number: a number whose immenseness enables the theory of evolution and humbles the span of human history. Yet again, reducing the Earth to this single number leaves behind some important information: uncertainty about the possibility that the true number might be somewhat larger or smaller, and duration, the fact that the process of earth formation took a while.
And a final example: Earth reduced to "3," where "3" is the number of the planet counting outward from the sun. In contrast to the first two examples, this mathematicization requires no loss of information. Does this make this "3" a better number than "4.5" or "15"? No, not better, just different.
In all three cases, the output of mathematicizing the Earth looks the same: a number. But the nature of the number, the affordances and the deficiencies of the number, varies depending on the nature of the Earth process or phenomenon being represented. That word "representation" is key: numbers are a representation of the Earth.
How can we help students to appreciate the vastness of humanity's accomplishment of turning Nature into numbers, along with the pitfalls of so doing? I know of many activities in which students collect and interpret numerical measurements of some aspect of the Earth. But I don't know of many curriculum materials which require or encourage students to reflect metacognitively about the process of turning Nature into numbers, why we do it, what we know afterwards that we didn't know before, and how the meaning of numbers depends on their context.
I've made two stabs at this:
- Sensors, Senses: an activity in which students compare weather observations made with their own human senses with numerical data collected at a weather station
- What does an Earthquake Feel Like?: a Data Puzzle, in which students turn eyewitness newspaper accounts of human's felt experiences of a pre-instrument era earthquake into Modified Mercalli scale numbers, and reflect on what can be done with the numbers that could not be done with the prose descriptions alone.
If you know of other examples, please share them with us in the comments.
Sources:
