Answer: Why is she wearing that kind of hat?

Sorry about the delay--as I mentioned, I'm traveling, and it's tough being on the road, teaching, moving from point A to point B and finding both a decent internet connection and time to write.  Especially in places where my cell provider doesn't have service.  (Yes, I'm deep in the backwoods of New Hampshire...)  

Back our regularly scheduled program... 

Our challenge was to figure out the hat.  The woman on the right in the above image is wearing a fairly peculiar kind of hat.  I mentioned that I recognized that hat from a totally different context, and was curious why the artist would portray her as wearing this particular kind of hat.

First, quick answers for insatiably curious.  

1.  What's the name of that style of hat?  

     A:  A Phyrgian cap.  

2.  Who is she?  (Or, more precisely, what does she represent?)  

A:  She is Columbia (aka Pallas Columbia), the female personification of the United States.  

3.  Can you find another artistic portrayal of someone else wearing a hat like this?  

     A:  Yes, see below.  

First, kudos to everyone who solved this challenge.  It's a fairly good problem that starts with a vaguely defined information goal, but one that's recognizably correct (when you find it).  I try to set up all of our challenges that way--intrinsically interesting, but clearly correct when you solve it.  (Not always, but mostly.) 

I solved this challenge (as did Fred and many others) by using "Search by Image."  I dragged the image into the Image search bar and found that it appeared on many sites.  I first looked at the Smithsonian site, thinking that they most likely would have a good attribution and some context for the picture.  Sure enough, from the Smithsonian page I found it was called, "The Teddyssey" and it was by "Otto Cushing."  The next query is obvious: 

     [ Teddyssey Otto Cushing ] 

Knowing that it was a book, I went to Google Books and searched for "Teddyssey," which took me to the book. 

If you scroll through the book, you'll find it came from the Harvard library (ah, the Massachusetts connection mentioned earlier), and you'll quickly find that the woman is named "Pallas Athena," and that she's seated next to the male personification of the US, "Uncle Sam."  

Now, how about that hat?  How can we find that?  

A search like: 

     [ Columbia hat ] 

gives a lot of commercial, obviously incorrect results.  (Turns out that Columbia is a sportswear brand name.)  Now what? 

Well, I knew that Columbia was personifying the United States, so I tried that as a query to find out more--who is she?  What's the background story?  (I need to know a bit more to focus my next query.) 

     [ Columbia personification ] 

The first result here was for the Columbia (name) entry on Wikipedia, which not only told me that the name "Columbia" is a recent word coinage (combining a stem Columb- based on the surname of the explorer Christopher Columbus combined with the ending -ia, common in Latin names of countries (e.g. Britannia "Britain", Gallia "Gaul").

BUT on that same page, there's a picture with a caption saying "Personified Columbia in American flag gown and Phrygian cap."  If you do the obvious checks, you'll find that Phrygian caps come from (surprise!) the Phrygian region of Turkey, and have been worn since antiquity.  It's a little unclear HOW they came to signify freedom and liberty, but by the time of the Roman empire, they came to be worn by freed slaves, and the association was made. 

It's then been worn by revolutionaries throughout time and around the world.  Popular in the French Revolution, it was adopted by the US as a symbol of freedom and liberty.  

Finding other artistic representations of the Phrygian cap is easy.  Just search for it in Images: 

     [ Phrygian cap artwork ] 

Here're a few images I grabbed (from Wikipedia's commons area).  

Phrygian Caps: US, Attic Greece, French Revolution, US Department of the Army

And the Seal of the US Senate, the herald of Haiti, etc etc.  

Now you know. 

Search on!