One Matrix, Inverted

Another gem from The Lady Tasting Tea.

The mathematical theory of input-output analysis requires that the matrix that describes the economy have a unique inverse … Leontief’s initial set of sectors led to a 12 x 12 matrix, and Jerry Cornfield proceeded to invert that … It took him about a week, and the end result was the conclusion that the number of sectors had to be expanded. So, with trepidation, Cornfield and Leontief began subdividing the sectors until they ended with the simplest matrix they thought would be feasible, a 24 x 24 matrix … During World War II, Harvard University had developed one of the first, very primitive computers … Cornfield and Leontief decided to send their 24 x 24 matrix to Harvard … When they sought to pay for this project, the process was stopped by the accounting officer of the Bureau of Labor Statistics. The government had a policy at that time; it would pay for goods but not for services. The theory was that the government had all kinds of experts working for it. If something had to be done, there should be someone in government who could do it. They explained to the government accountant that, while this was theoretically something that a person could do, no would be able to live long enough to do it. The accountant was sympathetic, but he could not see a way around the regulation. Cornfield then made a suggestion. As a result, the bureau issued a purchase order for capital goods. What capital goods? The invoice called for the bureau to purchase from Harvard “one matrix, inverted.”

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One Response to One Matrix, Inverted

  1. Alex Gittens says:

    Nice story :) . I wonder if it’s really that hard to invert a 24×24 matrix.

    BTW, I really like the new design.

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