You would think that everyone would know this by now.
You are wrong.
Frequently, policy makers, universities and technological supporting institutions erroneously describe innovation according to a linear model that assumes that innovation is applied science. It is assumed to be ‘linear‘ because it is believed that there are a series of well-defined stages that innovations go through, starting with research (science), followed by development and then finally production and marketing. In this linear model scientific research is deemed to be the most important step as it is the first step in the process. Although there are some cases that have followed this route, they are in the minority.
A softer version of the linear process of innovation is where it is assumed that the knowledgeable people are in the academia or business support structures, and that the task of policy makers is to devise ways to transfer the knowledge flows from universities and supporting structures to businesses. The main perceived limitation is the inability of business people to learn by themselves or to absorb knowledge from the system around them.
In the real world, innovation is dynamic and it is complex. It sometimes starts with a clever idea by an entrepreneur about an unmet need in the market. At other times it starts with a customer complaining to a service technician. Often it starts with a problem or obstacles, and in a few cases it is the result of brainstorming. Wherever it starts, innovation is definitely not neat and tidy. In fact, it is quite chaotic.
But there are elements of the innovation process that may appear linear, like a product development process (product innovation). But this scarce and mainly happens in professionally run firms. For most of us, innovation is not a structured process.
Again, it is important to understand that innovation in a systemic context often arise due to the interaction between different social actors like enterprises, technical specialists, suppliers, customers and maybe the odd academic.
 The ‘linear’ innovation process was first criticised by KLINE, S. & ROSENBURG, N. 1986. An overview of innovation. In The positive sum strategy: harnessing technology for economic growth. Landau, R. & Rosenburg, N. (Eds.), Washington, DC: National Academies Press, pp. 275-305.