The Fractal Geometry of Invention

INTRODUCTIONA fundamental question in patent-related disputes is, "What did the patentee (or patent applicant) invent?"1 The claims of the patent define the invention, in so far as "the invention" means the sphere of activity reserved exclusively to the patentee.2 The disclosures of the pa- tent specification describe and enable the invention, in so far as "the invention" means the patentee's substantive contribution to the art.* * 3 Before it can be claimed or described, "the invention" begins as an idea formed in the mind of the inventor.4 In a perfect world, a world in which the patent system operated as a smooth-running and wellregulated machine, "the invention" would be a single thing-one thing conceived, reduced to practice, disclosed, and claimed. The reality is more complicated, and the multi-faceted nature of "the invention" in our world is the source of much tension, friction, and potential mishaps. Partly this is a problem of communication. As the U.S. Supreme Court has observed, the shortcomings of vocabulary produce "idea gaps" when one translates a conception into the language of a claim.5 Similar problems may impair the completeness of the patent disclosure. This Article suggests, however, that the source of the difficulty in pinning down "the invention" is even more fundamental, and begins in the nature of invention itself.Few inventions are singular entities, unconnected to broader networks of technological advancement.6 Most inventions are variations on what has come before and have the potential to generate further variations or refinements.7 Whether it is the work of an individual researcher or the community of all researchers, invention is a complex web of questions and answers. Each insight may suggest a host of new paths to follow in the search for technological solutions to the needs of mankind. One might visualize invention as an ever-expanding island, each advancement pushing out a new headland, itself the root of newer promontories, each generation mirroring the last, ad infinitum.A mathematician would recognize that island as a Koch island-a species of fractal.8 A fractal is a geometric figure of inexhaustible detail.9 The closer one examines a fractal, the more detail one finds.10 Structures with fractal properties can be found in nature-in the contours of an actual island, for example.* 11 A map might approximate the shape of the island, but would inevitably miss twists and turns too small to be depicted.12 A larger scale map could correct those deficiencies, but only up to a point.13 Closer examination of a coastline always reveals more detail-twists upon twists, turns upon turns.14Certain properties are typical of fractals, and the real-world objects that mimic them. One of these properties I call "multiplicity," in reference to that inexhaustible supply of detail. A second property I call "latency," in reference to the fact that the fractal details reveal themselves only on examination-an examination that can never be completed. A third property, well-known in the field of fractals, is "self-similarity."15 A fractal is self-similar when its structure appears the same at any scale.16 These properties are all characteristics of invention. Invention leads to a seemingly inexhaustible supply of technological solutions, even to comparatively simple problems.17 The potential of an inventive insight to produce such solutions does not reveal itself immediately; further investigation typically reveals more paths to explore. To some degree, inventive contributions are also self-similar. A refinement many steps removed from one path-breaking advancement may seem, in its own context, just as fundamental.These properties underlie the difficulty of defining the invention to which a patentee is legally entitled. If inventions are, as a rule, only promontories on a larger continent, and themselves the source of elab- orations to come, to what territory is an inventor entitled to stake a claim? …