Thursday, September 10, 2015

On algebra

In my post yesterday, at the linked article there was a link to Paul Krugman's TWO CHEERS FOR FORMALISM. In it there is this paragraph:
In 1997 the editor of Governing magazine published an op-ed attacking the economics profession for denying the obvious fact that globalization was having devastating effects on the economy (Ehrenhalt 1997). As an example of just how bad economists are, he quoted an unnamed "prominent economist" (the reference was actually to Krugman 1996), who had written that "there are ... important ideas in economics that are crystal clear if you can stand algebra, and very difficult to grasp if you can't". This, according to the op-ed writer, was an "insult", a "charge of illiteracy"; he went on to assert that algebra could not be essential to economic understanding, because if it were this would delegitimize the opinions of people who had not studied algebra when young and were now too old to retool.
The editor is not just ignorant in complaining about the algebra, but also ignorant of the history of mathematics. There is nothing quite so ironic as saying algebra could not be essential to economic understanding.

Mathematics had two major purposes in its development; broadly, "counting/accounting" and "measuring". The latter culminates in calculus, and the former -- and older -- purpose culminates in algebra.

Algebra was developed to figure out how to allocate abstract quantities among heirs, calculate interest and in general conduct business. It arrives in Europe primarily through Fibonacci along with 'Arabic' (i.e. Indian) numerals and is used for that purpose.

How does one even begin to understand the concept of an interest rate without algebra?

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