Friday, February 20, 2015

Answer: A couple of odd questions...

One week, two curious questions.   Two interesting answers... 

1.  Those equations are really interesting, but WHAT do they mean?  And why would Woody Paul put them on his concert performance gear?  (For extra points: Where did Woody go to college?)  

Woody Paul's awesome shirt with mysterious equations.

It's not hard to figure out from a quick query who Woody Paul really is: 

     [ Woody Paul "Riders in the Sky" ] 

Here I quoted the name of the band just to make sure I didn't get anything spurious.  (It turns out not to matter too much.)  

Woody Paul is his stage name.  Real name:  Paul Chrisman. My favorite article was from MIT's Technology Review magazine which points out that he got his PhD in nuclear engineering from MIT in 1976.  When he graduated there were two job offers waiting--an assistant professorship at Columbia University or a recording gig in California.  (Other versions of this story have him heading to Nashville.) It's clear he chose music in either case. 

A little more poking around finds that his thesis was "Inertial, Viscous, and Finite-Beta Effects in a Resistive, Time Dependent Tokamak Discharge", Thesis Nuc. Eng. 1976, PhD, supervised by James E. McCune. 

This is all relevant because it gives us a clue about what these symbols on his shirt might be. 

If you already recognize the symbols involved, you've got a headstart.  But suppose you DON'T recognize any of these symbols, how do you start?  

You might remember that earlier I've written about "Symbol Search" using either the Shape Catcher web app, or the Google Docs symbol search tool.  

In both cases, you draw the character and look through the list of recognized symbols.  Here's my screenimage from using  (it works with Google Docs symbol reco as well)... 

 The trick here is to notice (look carefully!) that the symbol on Woody's shirt has a special, thickened left side on the downward pointing triangle.  That's what makes it a "nabla" symbol.  (Note:  It's not a delta--that's a triangle that points up, not down!) 

Once you know that, you can do a query for: 

     [ nabla ] 

and learn that it is the name of the symbol in mathematics that (quoting Wikipedia) "... is used in mathematics to denote the del operator, a differential operator that indicates taking gradient, divergence, or curl..."  

That might look scary, but hold on a second--stay with me here.  The key idea here is that nabla isn't the big thing, that's just the character's name (it's a bit like saying "virgule" for the slash, or divide, character).  The important term to notice here is that it's the del operator.  

Okay, so what's del?  

If you [ define del ] you'll find it's an operator used in vector mathematics.  

So now I just searched for the most obvious natural language translation of this, which I put down as: 

     [ del dot b equals 0  ]

Sure enough, once you do that, you land in the land of physics discussions.  

It only takes a minute or so of looking around there (in to find out that his "del dot E" is one of Maxwell's equations.  A quick search for that takes us to the Wikipedia entry (or any of a thousand textbooks, all with exactly the same information): 

Adapted from Wikipedia entry on Maxwell's Equations

As you can see, Woody has Gauss's law in his collar, Gauss's law of magentism and  Faraday's law of induction embroidered into his western-style, fringed shirt.  And as Luis cleverly spotted in an image I hadn't seen before, assume Ampère's circuital law is on the back of the yoke.  (You can just see it riding up over his right shoulder here.)  

Except of image from

Maxwell's equations are four equations that form the foundation of electrodynamics, classical optics, and electric circuits. They describe how electric and magnetic fields are generated and altered by each other and by charges and currents. These equations are named after the Scottish physicist and mathematician James Clerk Maxwell, who published an early form of those equations between 1861 and 1862.

They are, of course, equations that Woody would have used extensively in his thesis writings.  A Tokamak reactor is one that uses a strong torus-shaped magnetic field to contain a plasma.  It was (and still is, in some circles) the best approach for possibly generating a viable fusion reactor. 

2.  Have crows become suddenly much more common in the Bay Area?  Is it just crows, or have ravens also turned into frequent guests?  

You know, sometimes things don't work out the way you'd expect.  I'd fully expected that the only good way to answer this would have been to look at data pulled from the annual Audubon bird counts.  (Such as this entry for the 2014 counts of crows.) 

But people other than me have noticed this crow / raven trend.  Consequently, the first searches you might do:  

     [ crow population statistics san francisco bay area ] 

end up pretty much answering the question.  The lesson for me is obvious--pre-test the questions!  

Several people pointed to one of the three articles about crow population expansion.  

SFGate (a local media service) wrote an article in 2012 about "Why ravens, crows are more common now in the Bay Area" quoting an ornithologist from Cornell, and giving crow counts from the Audubon census of 1991 (17 crows and 54 ravens in San Francisco; 60 crows and 23 ravens in Oakland), and 2011 (SF tallied 566 crows and 599 ravens;  while Oakland had 1,152 crows and 193 ravens).  

They also pointed out that crows were "relatively rare" back in 1927, so this really is a recent phenomenon.  

The San Jose Mercury News also had an article that same year, except giving similar numbers for crows growth in the penninsula (where I live) and the South Bay (where San José is).  Their article, "Counting crows: Number of black birds on the rise in Bay Area" also has a lovely chart showing the growth rate over time.  

Chart from SJ Mercury story on crows, 2012, by Aaron Kinney.  

As you can see, the growth rate the South Bay (San Jose) has been nothing short of spectacular.  

But just this past month, the Mercury wrote another article about crows.  "They're everywhere! Crows, ravens overrun Bay Area" (Nicholas Wieler, Santa Cruz Sentinel, 2/14/15)  which repeats the same basic data, but adds a new graph showing crows v. ravens.  

Graph from SJ Merc article.  

The findings here are clear enough:  Yes, both crows and ravens have been skyrocketing in populations--with crows more common in the South Bay, and ravens more common in San Francisco.  

Search Lessons: 

1.  Remember the search tools you know about!  Finding the nabla is easy, IF you know about the symbol finding tool.  (And if you don't, try describing it in the simplest way possible-- something like:  [ downward pointing triangle symbol ]  )  
2.  Once you've found the symbol name, trying searching for the way it's commonly used.  In this case, it was to discover that the symbol was also called "del" and under that name, it's easy to find in the physics literature. (Which is why it was helpful to know about Wood Paul's previous writings...)  
3.  When searching for analyses (e.g., crows population over time), always search for a completed report.  You never know (I certainly didn't!) when someone will have already done the analysis for you.  Double check the data and the sources, but all of these articles refer to data from Audubon Society and/or the Cornell Lab of Ornithology--both extremely respected resources in the birding world.  

Search on! 


  1. …had forgotten about the "Symbol Search" lesson — good reminders and examples, danke Dan.
    sorry, I was having a 90's moment del/∇

  2. Maxwell's equations make an appearance — still searching for a complete report.
    Hover cursor on comic… it will appear like gravity.
    Fundamental Forces

  3. SearchReduxSearch… …had forgotten about the "Symbol Search" lesson — good reminders and examples, danke Dan.
    sorry, I was having a 90's moment del/∇…again

    1. Hi Remmij, [maxwell equation comics] [maxwell equation t-shirts] shows fun stuff

      "Symbol Search" lesson, I did remember. However searched [Character] and only saw the Google Translate. My mistake.

      On other topic, maybe some of you like this Lost Sherlock Holmes story discovered. BBC

      Dr. Russell, why searching crop part of equation does not give good results?

      Nice week!

  4. …don't ask…but Crow related — kinda cool — there is a kindness/randomness appeal. that may be my 3 watt - .25 amp - 13.5 volt - T3.25 - Miniature Wedge bulb… wondered where it got to.
    …worth the time/listen… if you are corvid inclined.
    Episode 51: CROWS [Rome]
    MISSING: Bob the Bulb
    John Marzluff at TEDxRainier
    Seattle Crows
    fb/JohnMarzluff, (corvid expert)
    Avian Conservation Laboratory, UoWA
    check the Raven @ Levi's Stadium in San Fran
    and from the BitterSweet Life episode Michelangelo Merisi (or Amerighi) fragment… —
    Amor Vincit Omnia, Caravaggio, c. 1602
    BSP twitter
    Tony Angell
    wiki - Angell
    Angell interview