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Chapter 8:
Templates for Invention in the Mathematical and Physical Sciences with Applications to Optics
Over many years of friendship, Adolf Lohmann and I have never written a paper together. Surely one of the reasons is that every time we have private time together, we do not talk about optics. Instead, we talk about invention. Not only is that the only thing either of us can do at a professional level (Adolf never tried professional tennis), but also it is what we both enjoy doing. Yet we find our minds are not always our willing servants, allowing us to invent on demand (although with experience, it gets easier). We have abundant theories and superstitions about our invention capabilities, but we have also picked up “tricks” over the years that serve us well. In honor of Adolf, I propose to share some of my favorite tricks here - illustrating them with enough examples to make the patterns clear. This chapter claims no (or at least little) originality in that almost every aspect of optics discussed here has been done before. Rather, it claims to be a synthetic chapter in the sense that it gathers previously disconnected concepts together under several easy-to-understand templates and shows what underlies all of those concepts. My purpose is to stimulate readers to invent, along with those previous scientists and mathematicians, but to do so not accidentally but systematically. If some new area can be made to fit one of these templates, inventions should be both easy and useful. My exposition will be somewhat deductive. I will illustrate multiple examples of each scheme (emphasizing optical applications) before I seek to define the paradigm or pattern or template precisely. My hope is that you will be as surprised as I to realize that these templates have never been described as such, despite their remarkable usefulness.
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