Thursday, December 29, 2011

How can you easily draw dotted chalk lines on a blackboard?

On Monday I discussed the hour-long video celebrating Professor Walter Lewin’s book For the Love of Physics. During the question and answer period (at 52:30), one of his former students comments:

“So, I sat in on your lectures here, I think about twenty years ago, and I’d forgotten one thing that I learned from you was how to draw dotted lines on chalkboards - which I actually used myself when I was a professor (at Northwestern) for some number of years , so very useful skill.”

Then he asks how did your lectures evolve over time? Professor Lewin replies:

“I think I was always eccentric. It’s true, and so from day one my lectures were always different from the mean. But, of course, they evolved in a way that grew substantially, and that is not because of the dotting of the line - because I could already do that in high school.

....But, it is amazing that many physics professors want to know how I make those dotted lines. There is a two-minute videotape which someone made. Someone looked at all the dotted lines I ever drew in 8.01, and put that in one videotape. It’s a riot!”

Here is that video:

Can you see how he makes those dotted lines? I had to look carefully before I saw what he does differently. When you pull the chalk along behind your hand. you get a normal solid line. Look carefully at 0:50 on that video, as shown in the following still photo:

When you instead push the chalk ahead of your hand you can get a dotted line. In a comment on another video by Walter Lewin someone said:

“I know chalk boards are hard to find nowadays. but it's easy to do: hold the chalk loosely in your hand and hold it at an angle so that it's ahead of your hand. Push it in the direction of your line and it skips making a dotted line. Too easy.”

Is it easy to explain in detail though? No! Look at this University of Bristol web page. (Benjamin Hall did both a web site and report about it). There also is a 28-page paper (Hall's Ref. [10]) on Periodic Motion and Bifurcations Induced by the Painlevé Paradox about all the math involved in this and similar situations.

Added January 4, 2012

Another place this trick would be useful is in laying out chalk art.


Donn King said...

Very cool! Indeed, chalkboards are rare these days, and I miss them. Too bad it won't work on these new-fangled whiteboards. :)

Richard I. Garber said...


I suspect that wet markers on either whiteboards or flip charts have too little friction to permit making dotted lines.

The slip-stick friction transition (like in chalk) also is important in bowing of musical instruments.


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V Line said...

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Chalk Line

Anonymous said...

These are so much fun to draw. I found an unused classroom at my school today and spent 15 minutes covering the blackboard with Lewin lines :)