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We explore role of software modeling in semiconductor manufacturing and contrast it with the roles that modeling plays in other fields of human activity. Major trends and challenges in physical and compact process modeling are discussed. We contemplate complexities arising from their multi-dimensional nature. The landscape of Optical Proximity Correction and satellite applications is surveyed. Instructive examples are collected that demonstrate shortcomings of our intuition while dealing with complex systems and parameter interactions. We ponder over the scientific and business opportunities of new promising techniques and prospective applications.