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THOUGHTS:  Thinking by Orders of Magnitude

9/23/2013

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Early in my last year of university, my most energetic geology professor asked his class to give the rate of drift for Earth’s tectonic plates. The other students and I – exercising the habits of memorization that come from three years of education in the natural sciences – looked to the ceiling or floor and began to recall previous classes. Did he want the faster drift rates of the Pacific plate (7-12 cm/year) or the slower rates of the North American plate (2-4 cm/year)? The Antarctic plate hardly moves at all. . .

The professor waved his arms enthusiastically and told us to stop thinking. “Orders of magnitude only!” he explained. “Let’s call it 1 cm/year. What about rates of mountain uplift in active regions, like the Himalayas and New Zealand?” The answer, to an order of magnitude, was 0.1 cm/year.

Now his point was obvious: plates drift faster than mountains rise, but both move at similar speeds.  This relationship – normally hidden behind numbers like 7.3 and 0.4 – was suddenly clear in the comparison of 1 and 0.1.  We had lost some precision, but had gained clarity, which we would easily remember.

An order of magnitude is a group of measurements (all of the same type) that fall within one power of ten. So 2 and 7 are the same order of magnitude, but 12 is one order of magnitude greater and 70,000 is four greater. Each could be approximated as 100, 100, 101, and 104, respectively. This simplicity makes orders of magnitude excellent for quickly comparing very large (and very small) numbers.

Picture
Comic by Randall Munroe, creator of xkcd.com.

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REPORT: On the Increasing Complexity of Scientific Research

9/10/2013

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The James Webb Space Telescope
Credit: NASA
The James Webb Space Telescope (JWST) is a wonder of human engineering.  Its primary mirror – a collection of smaller mirrors – is 6.5 meters wide.  To operate, JWST’s mirror and sensors must be chilled to within 50 degrees Kelvin of absolute zero (-370ºF), with one instrument operating at only 7 Kelvin.  To help achieve these temperatures, it will be shielded by a sunshade the size of a tennis court.  To fit JWST into the top of an Ariane rocket for launch, the whole spacecraft (tennis court included) will be folded into a space only 4.5 meters in diameter.  Once the telescope leaves Earth orbit for its final destination, orbiting the Sun 1.5 million miles outside of Earth’s orbit, it will unfold and begin observing.

JWST will be capable of imaging an incredible array of targets. Peering across the Universe – and thus back in time – it will observe the formation of the first galaxies, only 250 million years after the Big Bang. It will be able to detect the presence of planets around other stars and search for water in their atmosphere (a step toward finding potential homes for life). It will even give us more detailed views of the outer planets in our own solar system.  But there is another side to JWST. . .

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Contact: HarrisonDreves@gmail.com | (615)-349-7300