The real world isn't that way. Real things differ from each other quantitatively and qualitatively along spectra, and sometimes multi-dimensional spectra, rather than in discrete boxes. The variations may be time-varying, and the things' boundaries may not even be definable. The ultimate time-varying, multiple-spectrum, indefinable-boundary thing is human behavior.
Related to this categorizing is the compulsion to define. An inventor whose mind is constrained to think in sharply defined categories with sharply defined elements won't make it. Even the mathematicians are now talking about "fuzzy sets."
This is not an argument to discard our mathematical and engineering education. It is a warning not to distort your understanding of reality by dividing it into hard boxes, and it is a statement that the process of invention is not an exercise in Aristotelian logic.
Tradeoffs and Two-Way Winners
It is routine engineering practice to trade off the magnitude of one virtue or parameter of a design against that of another to get the best combination. In airplanes one trades off range against payload. In automobiles one trades off power against fuel consumption. There are probably many such duels in your own field, and in many cases there are clusters of parameters to be proportioned. The process of optimizing the parameters has been the subject of mathematic analysis, and there are textbooks on the subject. Often there is no choice, and such optimizing studies must be performed with no alternative in sight.
Many suggest that with sufficient effort and ingenuity you may be able to find two-way winners. A two-way winner is a modified or different design which has the advantages of the best in both parameters that must otherwise be traded off. You may be able to devise a change which is both better and cheaper. Proper selection of proportions and materials may result in a structure which is both stronger and lighter.
Sometimes with a little bit of luck and a great deal of effort a multiple-way winner can be devised. A superb example of this is the container system for ocean shipping. For thousands of years ships were loaded with loose parts, jars, boxes, crates, and barrels. Loading and unloading were laborious, pilferage was common, and damage was frequent. Then a system was devised in which cargo was loaded at the factory or warehouses into large steel containers the size of a trailer truck body. Large cranes were built to handle these containers and to transfer them between ship and shore. Ships were designed to accommodate these containers in neat stacks. The containers themselves were sized to fit onto flatbed truck trailers and onto rail container cars for land transportation. The result is the now almost universal system which has reduced handling costs, pilferage, loading and unloading time, packaging and crating cost, and damage. All of this has been done with a highly cost-efficient technology. The classical approach of optimizing parameters would trade off the comparative cost of security systems versus pilferage loss and the like. The ship container system is a triumph as a multiple-way winner.
In fields other than engineering the search for multiple-way winners is incessant. Such fields include business deals, political policies, and many others where the consequence of a decision is human behavior. All the non-engineering inventors described above are in constant search for two-way and multiple-way winners.
In many large companies senior managers have a relatively short tenure in each of their assignments. Therefore they have little motivation to start spending money and effort on long-term programs whose benefits will be credited to their successors and not to them-selves.
Most companies have suggestion boxes for employee proposals. The proposals which are accepted are those which yield immediate profits and not those requiring investment in what might be very much greater long-term profits.
The resistance to innovation of company managers pales before that of venture capital managers and investment bankers. These people boast that their profession is the seeking out of innovation. In fact they seek small increments of innovation in a few fashionable fields. If your innovation is not based on semiconductors, DNA, or coherent light, you will have a tough time promoting investment.
Be of good cheer, all is not dark. There are companies and managers who not only talk about loving innovation but behave and invest as if they mean it. They treat innovators with friendliness, encouragement, praise, tolerance of error, and rewards for success. They read books on how to manage creative people.
How do you find jobs working for such people and avoid jobs working for their opposites? Many have only a few suggestions.
Certain industries are more progressive than others. The electronics, pharmaceutical, and chemical industries tend to promote innovations. Certain groups in the aerospace industry (but by no means all) are encouraging. The aerospace industry receives large amounts of government money to encourage and pay for innovation, and it is hard not to seek and accept money. Many government agencies give grants for innovative work to universities and companies. Some R&D groups in universities encourage engineering innovation.