To me, the circle is a symbol of negative entropy. Simply, it confines space, imposing boundries and structure upon chaos. It is a frame where that which is captured inside is seen in a new light, a different focus from that which is outside its walls. There is now a beginning, and an end (which is amusing, considering the fact that the circle is, by definition, a line that does not have a beginning or an end), a starting and stopping point for anything inside.
Paradoxially, I feel that negative entropy is in itself entropic. When you pull back far enough to look at all the chaotic information available, an ordered pattern placed in the midst of it seems out of place. For example, look at a mandelbrot set, or any fractal pattern. Pretty, isn't it? That picture is created using a mathamatical formula that creates waves of randomness. Now take any section of that pattern, and draw a smiley face, or any other ordered, structured design. Look at the picture again. The design seems out of place, doesn't it? It seems almost... random, hmmm?
Negative entropy is self-referential. It only applies to the things it contains. You cannot apply negative entropy upon the universe, just as you cannot draw a circle around the universe. Negative entropy is only possible if you have a boundry beyond which randomness occurs again. Also, negative entropy is only possible if you don't look beyond the boundries. In a sense, creating order actually increases entropy, when the entire universe is taken into consideration.
Circles (negative entropy) are useful in that it implies structure and order, which brings to light the absolute chaos around us (if you're looking for it). Just as in Taoist thought (hey, their symbol uses a circle too, right?), you cannot see the chaos without order, and you cannot think of order without chaos.
In other news, one of the definitions of entropy is a measure of information in a system. Simply put, a mathematical definition of entropy is the amount of unpredictability withing a given message. It therefore stands that the phrase "Colorless dreams battle furiously with Starsky and Hutch" is chock full of information, while a presidential speech has almost none, because we cannot predict the following words in the former, but we know what a politician will say almost all the time. This implies that a circle has an infinitesimal amount of information (because of it's instant predictability and pattern recognition), while a shape decided by the role of a die has an almost infinite amount of information (because of its shape is formed by chance, therefore unpredictable).
On a contradictory note, let's say you roll a die 360 times, each determining a direction for your shape to go. In some amazing coincidence, you randomly make a shape that turns one degree to the left 360 times. you've made a circle, right? Initially, you might think that this circle is the same as all the others, that is, devoid of information. But this circle is unique in that the very creation of the circle involved a random process, and that the absolute unpredictability (and improbibility) of coming up with the same roll 360 times is so surprising, this circle is almost 100% information.
So now we have a circle that is both entropic and non-entropic. Go figure.
-Lex Marburger