I would like to fully appreciate the concepts behind, and the motives for, the idea of “off-diagonal long range order”. I want to found this on the basic idea of the matrix, and why it is a useful way of looking at things. (Please represent mathematical expressions in text mode.)

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I have a line of thought that finds the mathematics of quantum physics to be interesting because it deals with the unknown structure statistically. I am seeing these concepts as being a result of the statistical nature of the entity definitions. Now, to me this is interesting because psychology, sociology, political science, and economics all also deal with statistical entities. My interest is to promote distributed intelligence within the global community, and it seems likely that understanding the modes of expression of quantum physics will allow for the community to find metaphors which bridge the distance between the realms of these sciences, and are likely to be especially useful as a means to understand our larger social condition and situation. (Please represent mathematical expressions in text mode.)