This is not a difficult question. Growing complexity can stop everything when it peaks, then, it can stop innovation. However, my discussion is not related to the effects of complexity on a certain area of the society, but how complexity at the technological process destroys the capability of a society or company to get successful results of technology.
Complexity in any process drives to ineffectiveness and inefficiency. In management terms, inefficiency is related to non optimal expenses. A complex organization must cope with a lot of internal uncertainty, and the planned actions with a certain budged are not resolved with precision enough. This fact produces that the final costs of the projects go farther the expected costs. If we spend more money to get a result, we will have less money to get the rest. In a small organization, this effect is trivial, but in a large one, we cannot see so easily how the organization is wasting money.
In every organization there are areas with larger priority than others. Short term activities are usually considered before long term ones, when the complexity of the organization grows, if short-term tasks must be executed under a lot of uncertainty that makes them inefficient, it is very common that long term tasks do not receive funds enough to be effective.
Looking only at the innovation process, as technology makes itself more complicated, it requires the integration of several issues from different knowledge areas to provide new products. As technology developers are experts only in a certain area, the integration of knowledge is making more difficult every time.
Specialization introduces structure in the way as innovation is managed, making the process itself more complex. In this structured process, the information about new knowledge is structured too, flowing through certain channels instead of being spread all over the scientific community.
In my country as in other European countries, superior engineering was a six years degree that covered many knowledge areas providing professionals with a lot of capability to integrate knowledge from different areas to make new products, however, in order to fit some European directives this time has been reduced eliminating general scientific education in order to provide the most practical knowledge on a certain area. Politicians justify this fact saying that the new educative model will fit better the needs of the labor market. I do not think that this can be correct because more knowledge does not produce a worker that cannot occupy a certain job; it produces a worker that can fit a larger number of jobs. The reason is more related to the use of public education resources to reduce the time required in order that a young worker can be productive. They are searching for a more structured market labor substituting the training required to fit job by the education period, but the greater the structure, the higher the complexity.
A society based on knowledge needs captains accustomed to sail a sea of uncertainties trying to determine the position of the ship and the proper direction looking at the sun with a sextant by day and looking at the position of stars by night, or with a compass, not only with a GPS, because if the GPS device is broken, the ship will not remain stopped.
There are many things that can be used to critique these new educative trends from the complexity viewpoint. Under unexpected events the new model can be more fragile, producing a longer period of unemployment, because it cannot fit so well randomness, but now I am only interested in its effects on innovation.
Although science has taken advantage of specialization many years ago, innovation, linked to the practical use of the acquired knowledge requires in order to provide economic value the integration of different areas. For instance, in order to fly, it was necessary, not only the development of fluid dynamics but the development of gasoline engines too.
The specialization of scientists lets to develop technologies in deeper, but puts limits to the diffusion of knowledge among areas. As technology development is doing more structured, it is necessary to establish mechanisms to move knowledge from a field to other ones. In previous times, scientific work was published and it was accessible at libraries, today we have technological tools through internet to make the acquired scientific knowledge more accessible, however, there are new limits imposed to the diffusion of knowledge among fields due to the degree of specialization of the scientists that need to access that knowledge, and the reduction of fundamental knowledge in the education of technicians required to understand the scientific works.
Probably in the future, the complexity of the technological development process can become itself a barrier to sharp innovation where this complexity source is not being considered at political and strategic levels.