The Mathematics of Innovation
Posted by Plish on December 18, 2008
I’ve been reading and re-reading The Innovation Equation . It is an excellent book and I highly recommend it.
One of the things I love about this book is that they define Innovation with an equation: Innovation= Creativity x Risk Taking.
I think there is merit to this formula as I also believe, with the authors, that true innovation is possible for anyone.
Being the person I am, I decided to dig deeper into this formula and try stretching the mathematics to see what can be learned from its manipulation. (If you’re math averse, please skip to the bottom for the DISCUSSION)
Innovation doesn’t occur out of the context of time, so I figured, why not differentiate the formula with respect to time and see what impact that has and what it can perhaps teach us about innovation. The formulas are below:
By differentiating we can determine how Innovation changes with respect to time as Creativity and Risk Taking change with respect to time. I summarized the results using various functions in the table below. The lines represent the rough shapes of the curves of what the variable is doing over time. So a straight line means the variable is constant over time. A slant means a linear increase. A curve means the form of y= ax^2 + bx +c (but it could be a higher order as well but thiswould impact the results)
So what does this all mean?
A- When Creativity and Risk Taking are constant in a company, Innovation is constant. This means there is no Innovation Velocity and no Innovation Acceleration
B- When Creativity is constant and Risk Taking increases over time, Innovation increases because of Risk Taking. This means Innovation over time changes at a constant rate – the Innovation Velocity changes. There is still no Acceleration.
C- When Risk Taking is constant and Creativity increases over time, Innovation increases because of increases in Creativity. This means Innovation over time changes at a constant rate – the Innovation Velocity increases. There is still no Acceleration.
D- When Creativity over time is increasing in a non-linear second order fashion, and Risk Taking is constant over time, Innovation increases, Innovation Velocity increase linearly and Innovation Acceleration stays constant. But there is Acceleration!
E-When Risk Taking over time is increasing in a non-linear second order fashion, and Creativity is constant over time, Innovation increases, Innovation Velocity increase linearly and Innovation Acceleration stays constant. But there is Acceleration!
F-When Risk Taking and Creativity both are increasing linearly, Innovation increases, Innovation Velocity increases and Innovation Acceleration stays constant. But there is Acceleration!
DISCUSSION: In those cases where there is constant Creative output and constant Risk governing strategies, Innovation occurs but isn’t accelerated. In fact, it’s not moving, dynamic Innovation. It’s Innovation by definition-that’s all.
Dynamic Innovation (Innovation Velocity) is constant or increases only when Risk Taking gets riskier and/or Creativity increases. There needs to be a constant effort to either get riskier or be more creative to get Innovation moving. The problem is that according to the research of Dr. Byrd, as people get more encultured by the corporation, there is a tendency for creativity to decline (p.127) – they become prisoners of their culture. Innovation will suffer as a result.
Is it possible to Accelerate Innovation? Yes, but it’s not easy. You either need Hyper-Creativity, (second-order or higher Creativity), Super High Risk Tolerance (also of the second-order or higher), or everyone firing on all cylinders (which is probably the likelier path). Even when this occurs, though, Innovation Acceleration is constant.
So what’s the take away?
Remember, Risk Taking in most corporations rarely gets more aggressive with time and success. If anything, it grows more cautious. There may be times when this or that project may be more risky, but somewhere there are usually safety nets. If a project is too risky it gets killed.
The implications of killing projects and the signals sent by mitigating risk can directly impact creativity in a negative way and based upon the results above, we don’t want that! After all, if Risk Taking is constant or declining, Creativity is all that’s left to keep Innovation moving!
There are two solutions.
1. Individuals start exercising more risk and go out on limbs to keep projects going. If they succeed, great. If they fail, unless the company knows what it means to be innovative (and too many companies aren’t sure), the person pays the consequences and again, Creativity could take a hit on the Corporate level. Death Spiral…
2. Start treating each individual as a unique source of brilliance, training and enabling people to be more fully alive, fully authentic humans who utilize their creativity freely. (The culture that does this is itself being creative–a two-fer!)
When confronted with the choices, can we afford not to start investing in the creativity of people?