Hidden figures: 2.303, slide rules and classrooms mired in the last century

A five -place table of logarithms from my dad's CRC Handbook of 

Mathematics (why is that set of values circled?) and a circa 

1958 Hemmi 257 slide rule designed for chemical calculations.  

 Wonder why random values of 2.303 are "hidden" in formulae? To make them easier to use with a slide rule.¹ 

A slide rule?  The last slide rule slid out the door of Keuffel & Esser in 1975 (they sent their engraving equipment to the Smithsonian).  You can still find them, used and even new - still packaged up to sell to engineers and scientists.  The Oughtred Society has a online museum, as well.

We still have my mother-in-law's K&E, in it's leather case with her name impressed into it.  Family history says she bought it with the money she earned tutoring Jackie Robinson in chemistry at UCLA.

I have an essay out in this month's Nature Chemistry, "It figures", about how the computational tools we use shapes what we teach and not necessarily in good ways. Given that slide rules were obsolete by the time many of my student's parents were born, why does their use still linger in general chemistry book?  (The 2.303's in texts are lowly going away. I checked texts running back about a decade.)

More critically to my mind why, several decades after  digital computing tools became ubiquitous on college campuses do many physical chemistry texts eschew any discussion of numerical techniques for solving the rate equations for a chemical reaction?  I suspect the chasm between the computational tools used in the field and those used in the classroom is a result of apathy. We teach what we learned as we learned it.  As I note in the article, I don't think it is defensible on intellectual grounds.

Don't know how to use a slide rule?  It's fun, it's geeky. No need to buy one to play, check out this simulator and the instructions at Nature Chemistry!

You can read the article here:  http://rdcu.be/sY5Q

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1.  2.303 is the natural log of 10. To change the base of logs recognize that
x = b^log_bx
so
ln(x) = ln(10^log₁₀x)
ln(x) = log₁₀x ln(10)
ln(x) =(log₁₀x)(2.303)
ln(x) = 2.303(log₁₀x)

Changing exams

I just handed out a math assessment in my physical chemistry class, the same one I’ve used for the last several years. I generally don’t re-use exams (though I know colleagues who do), though I do re-use questions. By now I’ve been creating exams for more than a quarter of a century, and I wonder what the drift has been like over that time. How are the questions I ask now different (or not!) from what I asked 25 years ago? Or have the questions remained the same, and just the answers changed?

Fueling my introspection are the selections from the University of London’s 19th century bachelor’s degree exams. (H/T to a tweet from Nature Chemistry and the RSC). The chemistry question is one I could envision asking my students on an exam: “Explain the nature, from a chemical point of view, of the chief operations involved in the production of a photograph.”

The only catch, of course, is that the answer I’m expecting could be quite different than what the examiners in 1892 expected. In 1892, production of a photographic print necessarily involved silver, developers and fixing agents — and a darkroom. In 2011, production of a print could involve silicon and germanium, and a clean room. The theoretical underpinnings are less about pH and solution chemistry and more about semi-conductors and quantum mechanics.

What other reasonable exam questions might I ask, where the answers have changed so dramatically?

(And you have to love the example English question - just how important were werewolves in the 19th century?)

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Photo of 39/365 Kodak Vigilant Six-20 Antique Camera, by M.Christian on Flickr.

Two thousand mockingbirds

I'm writing final exams for two intro chem courses. I try for a light touch brush of humor on at least a couple of the questions, it's stressful enough without every question probing deeply important things.

Some useful (in this context) unit conversions:

2000 mockingbirds = 2 kilomockingbirds
10^-6 fish = 1 microfiche
454 graham crackers = 1 pound cake
10 millipedes = 1 centipede
10 monologs = 5 dialogues
2 monograms = 1 diagram
8 nickels = 2 paradigms
10^-2 mental = 1 centimental

Have more to suggest?

Lab Notes: Walking the walk

Some days you have to be willing to walk the walk as well as talk the talk. My primary care physician keeps copious, real time notes on her encounters with her patients. She starts every visit with her pad in her lap - writing notes to herself (and best, yet, notes to me on what I need to follow-up on, complete with phone numbers and details) as the visit proceeds. So when she inquired about my immunization status during my physical yesterday, and she asked about tetanus, I thought I recalled getting a booster in 2008. Nothing in her notes on that.

Do we trust my memory or her notes? We'd chatted about my science writing, and given my expressed thoughts about (good) field notes - it was no contest. I have a sore arm, but no regrets.

The book I really want to read about field notes is not yet out (but I've ordered a copy) - Field Notes on Science and Nature edited by Michael Canfield of Notes from the field. The cover is beautiful and the contents look intriguing.

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Image is from Wikimedia commons. A 1964 poster boosting boosters.

Weird Words of Science: Hypsometer

Every time I write an exam, I think about this story, where a physics professor asks on an exam how to measure the height of a building using a barometer. A student answered that he would tie a string to the barometer, lower it down, then measure the length of the string. Given no credit, he protests, and the professor offers him a second chance to provide an answer that is both correct and demonstrates some knowledge of physics taught in the course. The student goes on to give several answers (in some versions the student is averred to be Niels Bohr - though the origin of the story is apparently in a textbook on the teaching of math and science by Alexander Calandra, and unrelated to Bohr) all demonstrating a knowledge of physics, and none the one he seems to know the professor is fishing for (which has to do with the - probably unmeasurably small - pressure differential between the ground and the top of the building).

Here is a chemistry exam question I sometimes ask - how would you measure the height of a mountain with a thermometer? This is a well-known technique,not a trick question, the apparatus is called a hypsometer, from the Greek for "height-measure". The underlying science is that the boiling point of a liquid changes in a known way with altitude. Hypsometers were used before portable aneroid barometers became widely available, and were used in high altitude balloon measurements of pressure as late as the 1960s.

Bonus question: Is it easier to drink a liquid using a straw at the top of Mt. Everest or on the beach in Florida? (Disregard temperature differences and explain your answer for full credit!)