The Amazing Trisociation Cube: A Visual Model of Creation

Product managers don’t create things the way people often think of creating. We usually aren’t writing the code or crafting pixel-perfect designs. Instead, our role is to synthesize diverse inputs from customers and contributors into a singular direction; a narrative that guides the team who hands-on builds the product.

On the surface, synthesis feels different from creation. Creation suggests introducing something new into the world while synthesis implies blending existing elements. However, Arthur Koestler explains in The Art of Creation that synthesis is not only a key part of the creative process but near to its essence. He uses the term “bisociation” to describe the fusion of two otherwise disparate matrices of thought. Koestler demonstrates that the greatest creative breakthroughs spanning science, art, and humor can be understood in terms of bisociation. Gutenberg’s invention of the printing press bisociated the techniques of the wine-press and the seal. Kepler’s laws of planetary motion bisociated the previously unconnected fields of astronomy and physics. In my post, When the Tension Snaps in Silicon Valley, I used Koestler’s concept of bisociation to explain the hilarity of HBO’s Silicon Valley show.

In reading The Art of Creation, I’ve been struck by Koestler’s illustrations of the creative process, such as his representation of humor.Screen Shot 2016-08-27 at 4.52.31 PM

The underlying pattern, Koestler writes, “… is the perceiving of a situation or idea, L, in two self-consistent but habitually incompatible frames of reference, M1 and M2. The event L, in which the two intersect, is made to vibrate simultaneously on two different wavelengths, as it were. While this unusual situation lasts, L is not merely linked to one associative context, but bisociated with two.”

A simple example is a pun, where a single word takes on simultaneous meaning in two associative contexts. One can imagine similar diagrams representing other forms of discovery. In the above illustration, M1 could be physics, M2 could be astronomy, and L could be Kepler’s law of planetary motion.

Within each discourse, technique, or scientific paradigm, some patterns of behavior are intelligible while others are not. One can’t readily apply principles of military strategy when decorating a house for a party. Koestler uses chess as a metaphor to explain the dynamics of a thought matrix. Each matrix comes with a set of permissible moves, like the moves a rook or bishop can make on a chess board.


Another way of representing the permissible moves in a domain could be a maze, like the one I’ve drawn below. The walls of the maze dictate where you can wander and where you can’t. The red path illustrates one possible train of thought through the matrix.


Koestler’s visualizations of the creative process illustrate the fusing of two matrices of thought. Product managers, as I’ve explored starting with The Product Management Triangle, must synthesize input from three domains: business, users, and technology. Thus, I was inspired to visualize a model of trisociation, using mazes as metaphors for the constructs of each domain.

I created three maze forms; one for business, one for users, and one for technology. Each form represents a distinct way of thinking. The business dimension of product development requires an understanding of economics and the motivations of investors. Building a product that users love requires a mastery of behavioral psychology and design.  Engineering the product requires a grasp of physical possibility and deep knowledge of the chosen technology. Each one of these areas is independently deep, worthy of graduate-level study. Each one has its own language, history, and perceived dead-ends.


Building a product requires trisociating a business model, market (user group), and technology. Unfortunately, it’s impossible to be certain that a certain blend will work together. The options are endless. It requires an abductive leap to choose the elements from each matrix for an attempted synthesis. The below illustration represents a possible area of focus within each domain; a business model, target market, and a technology.


In this visual model, the trisociation stage is set by placing the chosen matrix regions in the shape of a three-dimensional cube, like this:



Let the attempted synthesis begin! As Marty Cagan says, the goal of product is to create something that’s “valuable, usable and feasible.” As entrepreneurs know, achieving just two of these conditions is hard. Attaining all three at once is magical.

The below maze cube represents the success state — a connected loop touching all three matrices; tech, users, and business.



Reaching the success state requires many things to go right.

For one, you need to choose matrix regions that can be trisociated. Some attempted syntheses fail to generate durable progress, like the fusion of astronomy and religion.

Let’s say we picked a different region from the users matrix. Maybe instead of focusing our app on the pet owners market, we focus on clowns.


We could end up in a formation where it’s impossible to create a connected loop touching all facades of the trisociation cube. We’re blocked.


You can think of a pivot as swapping in one matrix region for another. Flickr swapped in photo sharing in place of gaming. Groupon swapped in shopping for political movements. With many of the same pieces, they moved from blocked to trisociated.

But even when you have compatible matrices fused together in your discovery process, it’s not guaranteed that you’ll find the path to synthesizing them. Freud took the right abductive leap to connect cocaine with medicine, but he missed the use case as a topical anesthetic.

As Koestler conveys in The Art of Creation, the person who originally juxtaposes two matrices is not always the one who makes the breakthrough connection. Just as Karl Koller, not Freud, is credited with the discovery of cocaine as a local anesthetic, Darwin wasn’t first to bisociate biology and the struggle for existence. But Darwin was the one who most rigorously established the connection and demonstrated its validity.

This last diagram shows a combination of matrices that can be connected with a loop, but the traveler is yet to discover the path. The explorer, with their own biases and tunnel vision, can’t know for sure that there is a solution. Tragically, they may give up, or pivot, before finding it.



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