What are mental concepts? Why do they work the way they do? How can they be captured in language? How can they be captured in a computer? The authors describe the development of, and clearly explain, the underlying linguistic theory and the working software they have developed over 40 years to store declarative knowledge in a computer fully to the same level as language, knowledge accessible via ordinary conversation. During this 40 year project there was no epiphany, no "Eureka moment," except perhaps for the day that their parser program successfully parsed a long sentence for the first time, taking into account the contribution of every word and punctuation mark. Their parser software can now parse a whole paragraph of long sentences each comprising multiple subordinate clauses with punctuation, to determine the paragraph's global meaning. Among many practical applications for their technology is precision communication with the Internet. The authors show that knowledge stored in language is not unstructured as is generally assumed. Rather they show that language expressions are highly structured once the rules of syntax are understood. Lexical words, grammaticals, punctuation marks, paragraphs and poetry, single elimination tournaments, "grandmother cells," calculator algorithms are just a few of the topics explored in this smart, witty, and eclectic tour through natural language understanding by a computer. Illustrated with flow-of-meaning-trees and easily followed Mensa tables this essay outlines a wide-ranging theory of language and thought and its transition to computers. John W. Gorman, a Masters in Engineering from the University of Auckland, joined his father, John G. Gorman, Lasker Award winning medical researcher, in their enterprise twenty years ago to solve the until now intractable problem of computer understanding of thought and language. An Essay Concerning Computer Understanding will provoke linguists, neuroscientists, software designers, advertisers, poets, and the just plain curious. The book suggests many opportunities for future research in linguistic theory and cognitive science employing hands on experiments with computer models of knowledge and the brain. Discover the theory and practice of computer understanding that has computational linguists everywhere taking notice.