Why we need to be Pi-Shaped
Pi Day has come and gone. Or has it? On Pi Day, we celebrate that famous relationship between the circumference of a circle and its diameter. That relationship in the form of a ratio is known as Pi, an irrational number. It is approximately 3.14159, but actually goes on forever. So even though we can define Pi as a ratio of circular attributes, we cannot define Pi as a rational number — a ratio of integers.
Pi Day results in all kinds of creative energy and output. But, there is a side conversation on Pi. We start with a non-numeric thing: a person. People are said to be I-shaped if they are primarily oriented in a vertical direction. I-shaped people are really good at one thing but they may not be good at anything else. The shape of the letter “I” is meant to describe this. Think of the horizontal as being breadth across several areas, and vertical as being depth in one area or skill. An “I” is deep but other letters connote a combination of breadth and depth.
We might let the letter “T” be a combination of vertical depth and horizontal breadth. This discussion is highlighted in the corporate world. What kind of person are you? If we think of it, like other generalizations, real people are complicated and it is unlikely that there is such a thing as an “I” person or a “T person”. Still, these categories serve as a springboard for discussion. Who should employers hire and how many of each type? Is there an ideal person?
I’d like to strengthen the argument for hybrid depth/breadth, however, by appealing to something more fundamental: abstraction. Supposing your goal is to understand what “horse” means. In a really deep way. A horse is an animal with four legs and a tail. When you read the word “horse”, your mind likely drifted a bit but then settled on some type of mental model of a horse. But the concept “horse” doesn’t exist in real life. It is an abstract category, like “circle” in mathematics. Every circle you might draw or point to is a representation of a circle, not the abstract concept. The concept of circle, like all mathematical concepts, is a mental model.
This situation leads to a conundrum. Let’s hypothesize two things:
- To understand concept X, we need multiple representations of X.
- To understand multiple representations, we form concept X.
For example, to deeply know “horse” one must have seen many horses. So, the concept “horse” cannot live without the representations of different horses. Likewise, individual horse representations by themselves do not permit abstract thought. Concepts and representations are joined at the hip.
Being Pi-shaped is knowing two things in depth — the two vertical parts of the Greek letter:
Knowing multiple things in depth, as well as having breadth, is more complicated so we must resort to physical analogies such as a comb. So, if someone is comb-shaped, they may be a polymath: someone who has serious, but not necessarily expert, knowledge of many things.
In my bridging of art and science, particularly computer science, this idea of mixing the horizontal with the vertical has become a vital consideration. Generally speaking, many computer science representations tend toward the common written language of modern mathematics. But just as we have seen that the concept of circle and its representations complement each other, written mathematics isnot conceptual — the writing captures a conventional representation. The arts tend to be just the opposite: there are different academic departments at a university, where a department matches one way of representing a concept. For example, music, photography, and video.
So, to be T or Pi-shaped means that to understand any concept, such as the concept of iteration or branching (in code), we must become Pi-shaped. We need multiple representations of branching — how else can we deeply come to know this concept? One cannot truly get branching only by writing computer programs. Similarly, it is not enough for someone to know only one sort of representation of a concept any more than knowing one type of drawing of a horse to understand the horse concept. One needs to link the multiple representations together using formalism to yield abstract concepts.
If nothing else, this discussion suggests why the arts and sciences need each other. Celebrating concepts with multiple representations is fundamental to understanding them in a deep sense. At the same time, we cannot dwell in singular representations without losing sight of the abstraction.
We need to see the forest and the trees.
