Gödel's proposition can be applied to human creativity; people can come up with solutions that could not be derived within the formal system

Design is a creative process; we all know that. But how does the process really work? Which mechanism enables the brain to come up with solutions to a design problem? What is the source of the "creative spark"?

In information theory terms, knowledge and experience allow a designer to come up with a solution. If we were to measure the output information of a deterministic system conditional on the input information, this measure would be zero. In the case of a creative act like design, the output is correlated to the input problem the designer wants to solve but is not deterministically derived from it (unless we are dealing with an EDA tool, which cannot create information; an EDA tool cannot get to a solution unless we have added the derivation rules it needs to apply).

I proposed this problem in 1978 at a conference on Systems, Man and Cybernetics in Tokyo. To help solve it, I invoked one of my icons: mathematician Kurt Gödel, hailed for having laid the basis of formal reasoning about formal systems.

The proposition that made Gödel famous states that within each self-consistent recursive axiomatic system, which is powerful enough to describe the calculus of the natural numbers, there exists a true proposition about the natural numbers that cannot be proved on the basis of the axioms of the system. In everyday language, the proposition states that within a formal system (math, an electronic circuit, a logic circuit) it is possible to come up with a solution that cannot be proved from the axioms and rules of that system.

Gödel's creative mind crafted the proposition that led me to understand the basis of human creativity: People can come up with solutions that could not be derived within the formal system.

Einstein's theory of relativity predicted that light that passes close to the sun is bent, but the postulate could not be scientifically confirmed until 1922. During a solar eclipse that year, light from a star near the sun was indeed bent, leading to a noticeable change in the star's observed location.

In physics, the creative mind discovers a law of nature that explains previously unknown or poorly understood phenomena. In technology, we come up with an electronic component or function with which novel solutions can be designed. One might say the design process is one in which solutions are created.

You can you measure the information created during design by examining a design process in which two quantities are modified: the selection (or creation) of the right components for obtaining a solution to an electronic design problem, and the creation of the interconnection pattern between these components.¹ The information that figures into a connection pattern between components is much larger than the information for the choice of components: The first is a quadratic function of the number of termination points, the second a proportion between numbers.

Let's follow the reasoning of a designer thinking at the level of the end components. Suppose we start with a design consisting of 49 components, each with three connectors, for a total of 147 connectors. That gives C = 147 * (147 – 1) / 2, or 10,731, possible connections between the 49 components.

Each connection can be present or not; that gives 2^C interconnection patterns between all components. The amount of information the designer has to come up with in order to select one particular interconnection pattern is the 2 logarithm of C.

Now consider a designer who thinks in levels of abstraction according to a structured design methodology. Suppose he selects the top-level design to have one component with three connection points. At the next design level, he decomposes this top-level component into seven more-detailed components (each with three connections) and subsequently implements each of those components at level 3, selecting from seven basic level components at the same final level as in the earlier example. In that case, 21* (21 – 1) / 2, or 210 bits, are created in each of the detailing steps or 420 bits for the two steps--smaller than the unstructured example by a factor of 25!

I am indebted to Gödel for leading me to the link between creativity and logic.

References

¹Koomen, C.J. 1991. The Design of Communicating Systems: A System Engineering Approach. Boston: Kluwer.

—Cees Jan Koomen is founding partner of Point-One Innovation Fund and previously was an executive at Philips.