Similarity, Self-Similarity, and Intermediate Asymptotics

Professor Grigorii Isaakovich Barenblatt has written an outstanding book that contains an attempt to answer the very important questions of how to under­ stand complex physical processes and how to interpret results obtained by numerical computations. Progress in numerical calculation brings not only great good but also notori­ ously awkward questions about the role of the human mind. The human partner in the interaction of a man and a computer often turns out to be the weak spot in the relationship. The problem of formulating rules and extracting ideas from vast masses of computational or experimental results remains a matter for our brains, our minds. This problem is closely connected with the recognition of patterns. It is not just a coincidence that in both the Russian and English languages the word "obvious" has two meanings-not only something easily and clearly understood, but also something immediately evident to our eyes. The identification of forms and the search for invariant relations constitute the foundation of pattern recognition; thus, we identify the similarity oflarge and small triangles, etc.