Practically perfect in every wayClifford E. Swartz Citation: Phys. Teach. 36, 134 (1998); doi: 10.1119/1.879983 View online: http://dx.doi.org/10.1119/1.879983 View Table of Contents: http://tpt.aapt.org/resource/1/PHTEAH/v36/i3 Published by the American Association of Physics Teachers Related ArticlesPressure Beneath the Surface of a Fluid: Measuring the Correct Depth Phys. Teach. 51, 288 (2013) Accurate Determination of the Volume of an Irregular Helium Balloon Phys. Teach. 51, 93 (2013) About the International System of Units (SI) Part VII. Numerical issues, unit conversions, and basic handling ofdata Phys. Teach. 50, 280 (2012) Measuring Systematic Error with Curve Fits Phys. Teach. 49, 54 (2011) Linear least squares, the spreadsheet, and Filip Am. J. Phys. 75, 619 (2007) Additional information on Phys. Teach.Journal Homepage: http://tpt.aapt.org/ Journal Information: http://tpt.aapt.org/about/about_the_journal Top downloads: http://tpt.aapt.org/most_downloaded Information for Authors: http://www.aapt.org/publications/tptauthors.cfm

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e d i t o r i a l

134 THE PHYSICS TEACHER Vol. 36, March 1998 Editorial

There’s a lot that I admire aboutthe new computer-based instru-ments. They can measure force at apoint without having to stretchsprings beyond that point. They canmeasure temperature with little tinyprobes that don’t appreciably inter-fere with the temperature of thematerial. They can measure the posi-tion of an object to within the widthof a laser beam. They can stretchtime or compress it, doing away withthe uncertainties of triggering stopwatches with laggard fingers. Bestof all, they present the results not aspositions on some analog scale butwith digits. Lots of digits.

But that’s just the recording func-tion. Computers can analyze data too.They can add and multiply in sepa-rate columns, and then gather theresults all together on a graph, plot-ting the line of least mean squares

to provide great accuracy. There issome point in learning how to dealwith errors big enough to drown in.Let students see how 2% uncertaintyin �x and 3% in �t creates 5% uncer-tainty in v. Error analysis at the intro-ductory level is very simple and neednot involve standard deviations andall the associated arithmetic.

I used to require error bars on allgraphs submitted to The PhysicsTeacher. In recent years I’ve beenworn down a bit, but I think that wasa mistake. A measurement withouterror is like a painting without aframe. It might be a great picture, butyou wouldn’t hang it in your livingroom. From now on, we want mea-surements with error analysis andgraphs with error bars. Either that orwell-phrased explanations. After all,even Mary Poppins wasn’t complete-ly perfect.

and yielding the formula of the line.All that’s left for you to do is to pho-tocopy it, staple it to the report, andsend it in to The Physics Teacher.Thanks to the computer, our experi-mental work is now free of errors.Free at last.

Can it really be so? Do three signif-icant figures no longer representuncertainty to somewhere betweenone part in a hundred and one part in athousand? Doesn’t the math programfor least mean squares assume thateach data point is a Gaussian collec-tion? Isn’t it still very difficult to do0.1% experiments — even 1% experi-ments? Most of the research papers Isee in technical journals still showerror bars on their graphs and if theydon’t, the researcher has to explain.

Maybe it’s a mistake to let begin-ning students use instruments thatyield fine precision and are calibrated

Practically Perfect in Every Way

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