## Whitney Biennial

George W. Hart

I was invited to present a workshop at the Whitney Museum, as part of the 2010 Whitney Biennial.  I decided to do a performance art piece about slicing bagels into linked halves.

In the spirit of performance art, I decided to try something experimental, which would challenge me in a new direction.  In the past, I've taught many people how to slice a bagel into two linked halves, and written a web page with detailed instructions.  For this workshop, I decided to try to teach the idea to random members of the public without using any words and without the participants knowing what the final result would be.

I used non-verbal sounds and whole-body movements to convey the geometric ideas of cutting a two-twist mobius strip from a torus. As a professor accustomed to lecturing with words, this was a fun challenge for me. Fortunately, everyone was willing to sing and dance along with me as if I knew what I was doing.

After much thought in the previous weeks, I had worked out a way to use sounds ("eeeh", "aaah", and "oooh") to represent high, middle, and low locations, and rising or falling intonations to indicate directions.  Getting everyone to associate those sounds with the positions as they moved their arms up, out, and down was Part I of the activity.

For Part II, everyone was given a pencil and paper.  I drew on a large easel and the participants copied me.  Again, there were "eeeh", "aaah", and "oooh" sounds, but now associated with the top, middle, and bottom of the drawing. Glissandos indicated curved lines connecting different positions.

For Part III, I mapped the sounds to positions on a large styrofoam torus, and inserted knives to indicate the positions.  Incidentally, this was still executed without words.  I punctuated the four parts of the activity with the sounds "bing", "bing-bing", "bing-bing-bing" and "bing-bing-bing-bing".

In Part IV, the participants were given bagels and toothpicks to mark the key positions and directions.

Here, you can see the high, low, and middle positions, which are key landmarks for the necessary cut.

If these positions are understood, the cut is fairly straightforward and the result is automatic.

Finally, when everyone gets a knife and starts making the cuts, it is the moment of truth.

I was standing up in front to demonstrate, so I made the cuts in the air. But I had expected the participants to use the plates. I never figured out how to indicate to everyone (without words) that even though I was demonstrating in the air, they should do it on the plate on the table. I need to work on that for next time...

At the end, when people got it, it was very cool! There was lots of shouting.

The result was quite a surprise for the participants since I hadn't told them what were were working towards.

So I was very happy that most people did succeed. (It makes me feel like a good teacher.)

We celebrated then with some cream cheese and ate our work.

I'd like to thank my assistant Vi Hart for volunteering and helping with everything.

And I'd like to thank the performance artist Aki Sasomoto of Culture Push for inviting me to participate in the Biennial. Her work inspired me to try this. Here, after the workshop, I'm offering her (and everyone) extra bagels to take home.

And finally, I'd like to thank all the participants who bravely worked along with me. This was really fun!

Oh, and it's not quite true that I didn't speak.  I began and ended by saying this poetic preamble/postscript:

Mathematics is full of wondrous ideas, beautiful beyond words, creating surprising links.