Part Three: Modeling Innovation as a Complex System



For many reasons, innovation strategy is poorly understood and even more poorly executed.


This series of posts will discuss some of my thinking on innovation and creativity, and as such outlines a concept I have developed: the Combinatorial Theory of Innovation from first principles. Others may have written something like this in the past, and if so, super. My concepts draw on methodologies and frameworks in high-dimensional combinatorial spaces that I both created and used at places like NASA and for the DoD for complex systems. For me, these could (and should) be applied everywhere, but especially to how we think about innovation.


I would also like to acknowledge that there are a handful of superb scholars in the field of innovation theory, and I hope there is some overlap in our thinking. There are unfortunately also some less superb innovation scholars roaming the halls of academia and policy and I hope that by outlining my theory of combinatorial innovation, I can more adequately explain why some of their policies are bad, and maybe even at times immoral.

[NB: This set of posts in particular comes from a series of ongoing discussions between myself and Turlough Downes as we create an innovation policy working paper using combinatorial and chaos theory, focusing on Ireland's innovation ecosystem. Thanks Turlough!]



Art by Amina McConvell: "A Combinatorial Explosion"


As mentioned in Part One and Part Two, the goal is to create an understanding of innovation strategy such that sound economic and social policy can be created, which is often hampered due to (1) complexity and (2) a lack of visible policy feedback. By way of deriving the first principles of the innovation ecosystem’s behavior, this theory will then enable:


1. A transparent understanding of innovation strategy (reduce complexity)

2. A generalizable input-output response model for implemented policy (create feedback loop)


This will be achievable by modeling the innovation ecosystem as a complex system, and moving from a mathematics-based economics solution based on system equilibrium (bad!), to a complex system solution based on dynamic and adaptive behavior (good!). The process being pursued is as follows:


1. Map ecosystem constituents*

2. Map ecosystem drivers*

3. Derive system first principles


[Only * will be included in this post.]




1. Mapping Ecosystem Constituents


The innovation ecosystem lacks a formal and widely accepted definition for terminology and mapping around the nature of innovation, stakeholder involvement and measured outcomes. This clearly adds to the complexity of the nature of industrial strategy and measuring policy feedback: without a defined map of the innovation ecosystem, it is not possible to do activities such as compare two policies or even comprehend policy outcomes qualitatively or quantitatively. This leads to increased reliance on narrative and as such further creates discordant economics.


Table 1 below demonstrates some of the terminology involved when comparing several economic policies on innovation strategy, thus adding to complexity:


It is a necessary first step to map the constituents of the innovation process such that a strategy can be created and

(1) actors in the ecosystem are defined,

(2) roles are assigned to those actors and

(3) expected input-output mapping can be created.


Firstly, I will break down the constituents within the table by activity, and the constituent outputs described in terms of complexity theory, which will allow activities to be modeled not as a linear set of processes, but instead as a ‘space (mapping) of behaviors and likely outcomes.


The innovation ecosystem is broken down into three distinct set of processes, as follows:


Discovery: is the activity of discovering the basic science of the universe. Actors in this space only discover existing relationships between a fixed number of variables that allow us to better understand phenomena about the world in which we live, such as quantum mechanics, fluid mechanics, electricity or mathematical relationships. The discovery space is finite: actors in this space only find what already exists, they do not create anything new. This is a critical aspect of discovery. There are a finite number of discoveries that can be made about our universe; the universe itself does not change, only our understanding of it as we discover it.


People in the discovery space produce building blocks of basic science. Once they have produced a building block, they produce another, and then another. Actors in this space seek only to produce basic building blocks, nothing more and nothing less, of which there is a finite amount. The space is so large that it may seem that, when compared to achievable accomplishments within our lifetime, there are infinite building blocks that can be created, but it is important that we realize and model it as a finite space. Big but finite.


Application: activity in the application space takes as an input the output of the discovery space seeks (building blocks). The output of the application process is the creation of variations of the discovery space. For example, if the discovery space produces building blocks A, B, C and D, the application space will create combinations of these blocks (such as AA, AC, AD, BAC, DDAC). Agents in this space will play with the building blocks and build variation after variation of building blocks, each variation known as an application block. An application block is a combination of building blocks. Whereas the discovery space is finite, the size of the application space is a combinatorial explosion (has an exponential growth rate of application space outputs to application space inputs).


Commercialization: activity within this space takes application blocks (from the application space) and combines them with the real-world of markets, people, businesses, society, etc. to create outputs with inherent value (societal or financial value for example). These are known as commercial blocks. The size of the commercialization space is infinitely large: it takes inputs from a combinatorial explosion (the application space), and combines it with the chaos-driven space of markets, businesses, humans and policy. It is like multiplying one space of extraordinarily high dimensions with another space of even higher orders of dimensions, and the result is an infinite dimensionality space. Unlike discovery and application spaces (which are both large but not infinite), the commercialization space is infinite. For example, an application block “DDAC” may not be commercializable with the first ten billion interactions with the ‘real-world’, but it may be commercializable with the ten-billionth-and-one interaction.



Thus, this report defines innovation as the entire process of three sub-processes:


Taking this new innovation process definition, and reconsidering Table 1, we can create more clarity and reduce complexity around definitions. Each of the “Innovation Activities” can be defined in terms of what they produce: basic building blocks, application blocks (combinations of basic building blocks), or commercial blocks (interaction of application blocks with the real world).


For example, basic science research is a discovery activity, research and design (R&D) is an application activity and transformations usually take place in the commercialization space.


We can now start to better understand what the inputs and outputs should be at each stage of the innovation process. Why do we care about inputs and outputs per stage? Because we want to better understand how different policy decisions impact the entire innovation ecosystem, and this is a good place to start.


A visual representation of a combinatorial explosion space: high dimensionality. Each point on this graph is represented as a value along x dimensions.










2. Mapping the Ecosystem Drivers


Before we discuss the relationship between system inputs and outputs, we first need to understand the natural behavior of the innovation process as a system, without external inputs.


If system was modeled using an economics approach by assuming system equilibrium, looking at the resting behavior of the system wouldn’t be necessary. This is, and this needs to be explicitly stated, reinforced and highlighted, because a classical economics approach to innovation theory would assume that the system without input is in equilibrium. We know, however, that the innovation ecosystem is not an equilibrium-driven system and that it is a complex adaptive system that is always moving: never still, never constant.


So before we can understand input-to-output mapping, we must consider the system without public or private sector inputs and, if left untouched, how it behaves. This will enable policy-makers to reduce the conflation of output as a response to policy input and the natural system behavior. This is difficult to do in today’s economy, which is highly interconnected and therefore nearly impossible to isolate the innovation process. However, we can look historically and think philosophically about the system at each stage of the innovation process.


Discovery: Looking historically at innovation processes, we can see that discoveries happen with and without external intervention. The easiest way to see this is to read historical accounts of the process for notable discoveries. Take for example the theory of evolution by natural selection, the creation of the internet mathematics (networkability), or even mathematics behind chaos theory- universality. All of these discovery processes outlined historically show paths that are highly non-linear and, when you look at the series of events that led to the discovery, appear extraordinarily random. In a description of Feigenbaum’s discovery of universality, the author writes:


“It was Hohenberg, in the end, who brought the theorist and the experimenter together [several years later]. On his way home, Hohenberg happened to stop and see Feigenbaum in New Mexico. Not long after, Feigenbaum paid a call on Libchaber in Paris. They stood amid the scattered parts and instruments of Libchaber’s laboratory… and let Feigenbaum explain his latest theory.”


Most descriptions of discovery are like this- random, spontaneous and non-linear with chance meetings and the lucky discovery of new, adjacent information.


However, as much as these discoveries may appear as miraculous (the chance of these random events happening at all seems against the odds), the outcome of the discovery is nearly guaranteed. For at any given moment when Feigenbaum was working towards his theory of universality, so were others. In fact, when the mathematician Benoit Mendelbrot gave his Nobel Symposium address in Sweden, he referred to the Feigbenbaum sequence as “Myrberg sequences”, having found a similar twenty-year-old paper by a Finnish mathematician Myrberg. Similarly, the theory of natural selection was independently discovered by both Charles Darwin and Alfred Wallace, and many aspects of the internet (networkability) were discovered by scientists within the UK, France and the US simultaneously.


From this, we can learn that there are two key properties of the behavior of discovery:

(i) Non-linearity

(ii) Certainty in outcome


Discovery is a non-linear process that is certain to happen within a finite time frame. Digging a little deeper, discoveries are driven by an often unaccounted for phenomena in economic models: human desire. There is evidence as far back as records go that some humans have always been driven to the process of discovery, with or without external motivation (financing, investment, targets); their motivation is both intrinsic and deep.


This leads to the most important characteristic of the process of discovery: given that the space is finite (although very large), and that with and without external motivation discovery will happen, the undisturbed behavior of the discovery process is not zero equilibrium but instead is moving at a positive speed. That is: without any external perturbations, all discoveries in the finite discovery space will be produced by itself in a finite amount of time.


Thus, the only influence that any policy can have in the innovation space is to speed up or slow down the rate of discovery. It cannot create or delete it.


Applications: The role of the application space is to take discovery building blocks and to create alternative combinations of discoveries to be applied. Being adjacent to both discovery and commercialization processes, the space is much better defined by specific inputs from the discovery process.


Like the discovery space, the application space exhibits two properties of

(i) Non-linearity

(ii) Uncertainty in outcome


You'll notice now that the application space moves from certainty to uncertainty in outcome. Whereas multiple scientists may make the same discovery in the discovery space, the applications space is magnitudes bigger given it is a combinatorial explosion of alternative application blocks that could be created to produce successful ‘innovation’ outcomes. Thus, it is not certain that successful outcomes will be produced without intervention as the number of possible combinations of applications is so high, in any time period.


There are additional similarities between the discovery and application space: that in both spaces, humans are intrinsically motivated and driven to produce outcomes in this space. Thus, without external influence, the application blocks would be created. However, speed of creating these building blocks is much more important to innovation process outcomes: this is a combinatorial explosion space and if all application blocks are to be explored, moving through the alternatives must be done very quickly. Again- given the size of this space, the speed of creating alternatives becomes incredibly important to create successful outcomes.


Similarly, to the discovery process, the only influence that policy can have in this space is to speed up or slow down the rate of applications created. That is to say again- speed of creating application blocks in this space is crucial to creating increased innovation ecosystem outcomes.


Commercialization: This space is unbound and infinite. Taking as an input a combinatorial explosion of application blocks, there are infinite ways these blocks can be combined with the alternatives provided by markets, society, human behavior and policy. The commercialization process is defined by being

(i) Non-linear

(ii) Uncertain


Following the progress of successful and failed startups in the commercialization space shows how highly non-linear the process is. How so? Similar to the discovery process, the commercialization process is one filled with chance encounters, ‘lucky’ timing and an against-all-odds chance of success. However, unlike the discovery process, certainty is not guaranteed. The infinite number of ways to take an application block and apply it to the ‘real-world’ means that only an infinitely small number of combinations and alternatives are ever tested for success, and a tiny number of these alternatives achieve success.


Again, similarly to discovery and application processes, people who operate in this space are intrinsically motivated to do so, and this intrinsic motivation creates a powerful positive speed and momentum to commercialization dynamics. This space, even more so than the application space, needs speed. With an infinite number of possible combinations of applications to the real world, successful commercial outcomes require a really rapid movement through those possible alternatives.


The only impact that can be created here is speeding up or slowing down combinations creation. If it takes one billion combinations to create one successful commercial outcome, clearly the best way to create this successful outcome is to iterate and fail nearly one billion times, cumulatively, as fast as possible. Successful outcomes in this space are driven by fast iterations of successive failures (non-successful alternatives).


In summary


The innovation process (Discovery – Application – Commercialization) is comprised of processes that, if left unperturbed, will continue to evolve and create ‘innovation’ output by itself. Therefore, as the system (viewed through the lens of complexity theory) shows, innovation outcomes are directly linked to the combinatorial problem of needing to create, combine and iterate through ‘innovation blocks’. The faster these iterations can be done, the higher the successful outcome. Thus, the external influence that will have outsize impact in creating successful innovation outcomes will be that of inducing speed.