Mathematics: An Unseen Force

We recently recommended The Joy of X: A Guided Tour of Math, from One to Infinity by Steven Strogatz.  One of the more interesting essays explains some of the mathematics behind interesting phenomena.  He offers the architecture of New York’s Grand Central Station whispering galleries as one such example. In the whispering galleries two people can stand at two points 40 feet across the hallway from each other. If one person whispers “sweet nothings” the second person can clearly hear each word, but passersby cannot hear a word.

While this phenomenon seems like magic, it’s actually based on mathematics. The gallery is elliptically shaped (or oval shaped) which means there are two focus points on the floor where all sound waves will bounce from the walls.

One of my favorite examples of elliptical shaped architecture is the National Hall of Statues in Washington, DC. This is where the U. S. House of Representatives held their sessions from 1807-1857. There are two bronze plaques on the floor. If two people stand on those plaques across the hall from each other, they can talk to one another in a normal conversational tone and not miss hearing a word.

The first time a tour guide told me about these two points, I knew immediately that the two points were focal points of the elliptically-shaped hall. But the tour guide also shared that John Adams had his desk sitting at one of those bronze plaques on the floor and pretend he was sleeping. Actually, he could hear every word that was said among the other representatives. This is because his desk was at the point where all sound waves would bounce off the walls and over to the focal points. One of those points was where John Adams was sitting.

So what is wrong with this story?  John Adams served as our second president from 1797 to 1801. At the end of his one and only term, he retired and moved back to his home in Massachusetts.  While I love the math that is demonstrated in a beautiful and historic buildings, I also appreciate and know enough about  U.S. history to realize that John Adams did not serve as a representative in the original US capital in Washington, DC.  But I still can’t help but smile when I hear the story, as it so beautifully illustrates how much mathematics influences our world in unseen ways.

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