# Circle E (2)

Circle E is a meditation on the relationship between order, exactness and certainty on the one hand and irrationality, chance and unpredictability on the other. Its name comes from the foundation of the piece, which is the numerical constant “e” and the round sticky labels I have used to represent it, and it is of course a playful reference to the convenience store, Circle K (which, for me, is most closely associated with the movie Bill and Ted’s Excellent Adventure!).

e is an irrational number, like pi, and its first few digits are 2.71828. It is derived from the sum of the reciprocals of the factorials, or 1 + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! + 1/7! and so on, which is more easily understood as 1 + 1/1 + 1/2 + 1/6 + 1/24 + 1/120 + 1/720 + 1/5040 etc. e is the base of the natural logarithm and is thus very important in the world of number theory and it turns out to be very important also in the world of finance where it is used in calculations of continuous compound interest and in the Black Scholes formula for estimating the price of options. I am interested both in the way that e is derived and in the way that a constant is used for something not at all constant, namely the price of a financial instrument like an option, and in the way something as rigorous and as timeless as mathematics can be used in something as volatile as financial forecasting. So in the piece I try to combine the ideas of something that is rigorous and structured with something that has elements of chance or randomness.

The piece is made up of 3620 sticky round labels occupying a grid of 5040 potential spaces which reflects the fact that if you add up 1/2 + 1/6 + 1/24 + 1/120 + 1/720 + 1/5040 you get 3620/5040 or 0.7182, namely the early part of the decimal expansion of e.

To get to the 3620 part I use 7 colors (to reflect 1/7!) and 517 sticky labels of each color. That adds up to 3619. The final 1 is represented by a single black dot at the bottom right hand corner cell in the grid as a kind of period, or “full stop”.

To get to 5040, I’ve created a grid of 71X71 cells, which really appeals to my love of prime numbers and square numbers all at once. 71X71=5041 so I have left the very middle cell empty by design. There's something about including the idea of nothing, or zero, in the middle of the piece that seems very satisfactory to me.

All of that generates the rigor and the structure. The chance is in the fact that I allow my aesthetic judgment rather than logic or formula to dictate where each individual sticky label ends up within the grid, so if I were to make another version of the piece it would be completely different. Part of this judgment is in wanting not to make the piece look entirely random and diffuse so I purposefully create clusters where sticky labels of the same color are situated closer to each other than a uniform distribution would allow. What’s interesting to me is that placing the first dot is an act of almost complete freedom and that each subsequent placement reduces my freedom by degree. I slowly become more and more constrained by my previous choices. And yet, somehow, the last few dots take far longer for me to place than the first. The greater my constraints, the greater the consequences appear of both my previous and my subsequent decisions, or at least that’s how it seemed to me as I was creating the piece.