Differences in Celsius & Fahrenheit

Here’s an unexpected bit of innumeracy.

I’m about to finish up a book by Colin Tudge called The Time Before History : A Million Years of Human Impact (New York : Scribner, 1996; 366 pages). I expect there will be a book note soonish.

Anyway, here are two quotations from two nearby pages. See if you spot the problem.

We know, too, as related in chapter 2, that when the ice ages ended, they could, in any one place, end fast. Twenty years could see a 7°C (44°F) rise in temperature; the difference between a frozen landscape and a temperate one. [p. 301]

Besides, at the trough of the last ice age, 18,000 years ago, the surface of the sea in the eastern Mediterranean is known to have cooled by more than 6°C (43°F), which in ecological terms is huge, and yet the elephants and their miniaturized neighbors came through those harsh times. [p. 302]

Your reaction may be different, but the author’s–or editor’s!–error in converting the temperature differences from Celsius to Fahrenheit stands out to me as though written in flashing neon. Could they really believe that the temperature of the Mediterranean had changed by an amazing 43°F? “Huge” is one thing, but that’s huge!

Not so long ago I wrote at excessive length about how to convert values on one temperature scale to values on the other. What I didn’t talk about was how to compare temperature differences.

Look again at the formula for converting Celsius temperatures to Fahrenheit temperatures:

If we talk a bit about this equation, there are two things that it is telling us:

1. That Celsius degrees are bigger, nine-fifths bigger, than Fahrenheit degrees, which means that it takes fewer Celsius degrees to express a temperature change than Fahrenheit degrees; and
2. That the zero points on the two scales are offset by 32°F.

But this equation and this explanation refer to converting temperature values on one scale to the other. If we want to talk about temperature differences, that’s another matter, and that’s why it’s good to talk/think about what the equation above is saying.

Suppose we have two temperature values specified on the Celsius scale; call them and . Then, to find the corresponding temperature difference expressed in terms of Fahrenheit degrees, we need to write down these two equations:

and then subtract one from the other. Do the algebra and you find

You’ll notice that the offset value of 32 disappears when you do the subtraction. This is as we expected because we had just talked about how Celsius degrees are nine-fifths bigger than Fahrenheit degrees.

But now you can see the error made by the author or his editor: they erroneously used the equation to convert temperatures on the Celsius scale to temperatures on the Fahrenheit scale, rather than merely change a temperature difference from degrees of one size to degrees of another size.

The innumeracy aspect is that, before using the conversion equation, one should know what it is saying. This simple step would alert anyone that 6°C could never be 43°F. Knowing that Celsius degrees are nine-fifths bigger than Fahrenheit degrees let’s us write the correct values for these temperature differences immediately:

Bjørn Jørgensen: Arctic Photo

A recent story from Science@NASA (“Spring is Aurora Season“, 20 March 2008) told an interesting story about how the aurora borealis seems to be more active near the equinoxes. The apparent reason has to do with “magnetic tubes” whose creation is favored when the Earth’s magnetic poles have the alignment relative to the Sun that they exhibit around the equinoxes.

Fine. Very interesting. But who could possibly pay attention to that when this was the image illustrating the article?

This stunning photograph (reduced to fit in this column better) was taken on 1 March 2008 in Tomso, Norway by photographer Bjørn Jørgensen.

His website is called “Arctic Photo” (direct to the English version).

Now, go ahead and give me one good reason why you would not want to click over to his site and see the beautiful photographs of the aurora borealis, not to mention sections like “The Sun at Night”, “Traditional Boatbuilding”, and “North Norway Winter” in his portfolio?

Huler’s Defining the Wind

Back in the days when we roamed at video stores looking for something that might pique my interest, my attention would invariably be drawn to any movie that reviewers blurbed as–and publicists dared print on the package–”quirky”. So, when my eyes landed on Scott Huler’s Defining the Wind : The Beaufort Scale, and How a Nineteenth-Century Admiral Turned Science into Poetry (New York : Crown Publishers, 2004, 290 pages), it looked guaranteed to be quirky. I grabbed it.

As I expected I enjoyed it. What I hadn’t expected was to enjoy it quite so much as I did. The subject is indeed odd, the style idiosyncratic, the topics covered diverse and wide-ranging, but in Huler’s hands it all adds up to a delightful and informative adventure of research and discovery that the author shares vividly with the reader in an unexpectedly intimate way.

Huler is not a scientist but his approach to discovering and understanding the times and circumstances surrounding the creation of Beaufort’s Scale is remarkably scientific; he is aware of this and seems to ascribe it to an awakening of a high-definition awareness of the natural world that resulted from spending so much time contemplating the Beaufort Scale. All this makes the book itself a thing of high scienticity; reading it is to hone one’s intuition about how science actually works.

In fact, the book is akin to what the author came to call a Beaufort Moment: “A Beaufort moment is any moment where instead of merely passing through my surroundings I notice them, notice them in a way that engenders understanding. [p. 242]” I loved this realization that he described late in the book, the summation of his experience as it transcended a mere research project:

And that is what I finally figured out the Beaufort Scale was trying to tell me. The Beaufort Scale is about paying attention. It’s about noticing whether smoke rises vertically or drifts, whether it’s the leaves shaking or the whole branches, whether your umbrella turns inside out or just rattles around some. More, it’s about taking note of those details, filing them away, in memory or, as the Manual of Scientific Enquiry would have it, in the notebook you’d never leave the house without (along, of course, with your pencil and your map and compass). It’s about being able to express what you’ve seen simply and clearly, in as few words as possible, so that others can share it. It’s about the good of sharing that knowledge, of everyone paying attention so that, together, we can all learn as much as possible.

The Beaufort Scale is a manual, a guide for living. It’s like a cross between the Boy Scout Handbook and the Old Farmer’s Almanac: a bunch of cool information that you’ll never be sorry you have, and a general policy of being prepared to deal with it: to notice that information and share it for the good of everybody involved. It’s a philosophy of attentiveness, a religion based on observation: an entire ethos in 110 words. One hundred ten words, that is, and four centuries of backstory. [pp. 237—238]

If, by the way, you need to see a version of the Scale to see what he refers to by the “110 words”, this version from the [UK] Meteorological Office comes the closest to Huler’s original inspiration. (After you’ve read the book you’ll appreciate the futility of trying to define the Beaufort Scale.) Personally, I think my favorite phrase is “umbrellas used with difficulty” (which is, therefore, how I know that the stormy afternoon when I arrived in New York City a few weeks ago was accompanied by Beaufort Scale 6 winds of roughly 25-30 mph).

It’s a book I can recommend most heartily to non-scientists and scientists alike; everyone is certain to find plenty to stimulate their thoughts and refine their perceptions of the natural world.

Lienhard’s Inventing Modern

When I went recently on my cultural trip to New York with Bill, I traveled with a couple of books: reading for the train trip and for those quiet moments at the hotel. One of the books I took was John H. Lienhard’s Inventing Modern : Growing up with X-Rays, Skyscrapers, and Tailfins (Oxford : Oxford University Press, 2003. 292+ix pages). Fortunately I started reading first thing on the train, and I made sure there were enough quiet moments at the hotel for me to finish the book in a couple of days. What a page turner! My book note is here.

Lienhard observes that in the early part of the 20th Century there was a feeling of Modern. It was something more than just modern, more than just new technology or new science–there was some indefinable spirit of adventure, feeling of invention, and optimistic attitude that seemed to dominate American culture. Naturally, given something indefinable like Modern, Lienhard set out to define it.

Lienhard, Anderson Professor of Technology and Culture, Emeritus, at the University of Houston was there for much of the Modern adventure, and his first-hand experiences adds heft to his discussion of the ideas, technology, and cultural currents of the time that met up in Modern.

I had previously read his book How Invention Begins, which impressed me very much, so I was excited to start on this one and I wasn’t disappointed. I did think that Invention had more profound insights on offer, but that doesn’t mean that Inventing Modern was an intellectual lightweight, although its tone was much more personal and somewhat more casual. They are both eminently readable and thoughtful and stimulating, but likely to stimulate different trains of thought.

I admit that there was an extra little frisson from reading about the nearby Empire State Building, which we could see from the street in front of our hotel, and the Chrysler Building, which we could see from the Brooklyn Bridge and which we visited one day. I’m certain however, that readers can enjoy the book without being in Manhattan to read it.