Math is really a beautiful framework with which we can analyze several ideas. For instance, beauty can be seen through the lenses of math using symmetry and geometry, and the study of complex systems can be cast through calculus and probability theory.

Given this premise, can we use math to understand what creativity is. Here is my attempt:

How can creativity be defined?

Let us run the following thought experiment. Imagine you’re an enthusiastic pursuer of truth. The whole universe is simply an empty space. In this void, in front of you are a some numbers and two operators: + (ordinary addition) and * (ordinary multiplication)1.

Science, or the discovery of knowledge, is analogous to discovering new numbers. You randomly add two numbers, 1 and -1 and discover 0. Then you add 1 to 1 and obtain 2. Repeating this process, you end up discovering all the integers. Furthermore, you can find patterns that lead to theorems among the integers, such as properties of commutativity, transitivity and distributivity.

However, from a metaphysical point of view, addition and multiplication over integers is closed in this set, therefore you can’t discover anything beyond the horizon of integers.

Can you discover anything else?

Creativity, in this scenario, would be proposing another operator such as division. Having this new operator in your mind’s eye to perceive reality, you can now compute a new class of numbers, the rationals and thus discover the set of all real numbers.

In either case, prior and after the discovery of the division operator, the infiniteness of numbers is analogous to the infinity of knowledge.

Creativity can also materialize by introducing the square root, and this new operator extends our perceptual horizon to encompass the realm of complex/imaginary numbers.

More analogies

A different civilization from another point in space, using a different set of symbols to encode numbers, may make similar discoveries, i.e., numbers obtained following the same principles of computation using + and *. Moreover, they may also discover commutativity, transitivity and distributivity. This analogy represents the universality of knowledge.

In the above thought experiment, I’ve ignored letters, phonemes, and words to simplify this overly-idealized world to get my ideas on what is creativity across.

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The thumbnail is generate by Dall-E powered MS Bing Image Generator given the prompt "your interpretation of what creativity is".

PS: Demis Hassabis, Deepmind CEO, also comments on another definition of creativity, or AGI. This is going beyond statistical interpolation and extrapolation of training data. An AGI model that is creative should be able to give an output to an instruction such as “design a game that has simple rules, but is extremely hard to master, and can be played for hours”.

  1. Perhaps these numbers and operators existed there a priori, maybe they emerged from a Creator, or perhaps they emerged from a singularity. ↩