Our knowledge of physics and chemistry is relatively well defined. Results from that knowledge are predictable as, largely, are those of their technical offspring such as electrical, chemical, mechanical and civil engineering. By contrast, biology is relatively unconstrained and unpredictable. A factor common to all areas is the trade-off, which provides a means of defining and quantifying a problem and, ideally, its solution. In order to understand the anatomy of the trade-off and how to handle it, its development (as the dialectic) is tracked from Hegel and Marx to its implementation as dialectical materialism in Russian philosophy and TRIZ, the Theory of Invention. With the ready availability of mathematical techniques, such as multi-objective analysis and the Pareto set, the trade-off is well-adapted to bridging the gaps between the quantified and the unquantifiable, allowing modelling and the transfer of concepts by analogy. It is thus an ideal tool for biomimetics. An intracranial endoscope can be derived with little change from the egg-laying tube of a wood wasp. More complex transfers become available as the technique is developed. Most important, as more trade-offs are analyzed, their results are stored to be used again in the solution of problems. There is no other system in biomimetics which can do this.