A historical Pachinko machine, a relative of Francis Galton's
Quincunx and the AAKKOZZLL, and the predecessor of the widely popular amusement
in today's Japan. Click here for more info – photo
by Gnsin.
Knowledge of the nature of mathematical method pays dividends
to the average man who seeks to understand and cope with political,
religious, and economic problems. When carefully
analyzed, different political doctrines, as well as religious and
economic doctrines, differ essentially in the postulates on which
they are based. Statements acceptable to some people as fundamental
truths are regarded by others as unacceptable and sometimes unreasonable
assumptions. It follows, therefore, that the conclusions correctly
deduced from such postulates will not be equally acceptable to all
people.
A glance at current economic theories illustrates the remarks of the proceeding
paragraph. The differences between social and economic systems, such as
socialism and capitalism, might well be reduced to differences in fundamental
assumptions concerning the acquisition and ownership of wealth. Shall natural
resources such as coal and waterpower be the property of a few people or
of the whole population? Shall profits be unlimited or should the tax rate
be larger for corporations with higher profits. Is the contribution of
men’s labor to a business an investment as is money, or is labor
to be paid for as a commodity, on the basis of the supply and demand? Does
the government have obligations to employ people who are not employed by
industry and, if so, can it tax to secure money to pay those people? Such
fundamental issues are at the heart of economic systems. Once a person
commits himself to one or another side of the issues like these, the whole
body of his economic beliefs follows as a consequence. Much
dispute would be avoided if people would recognize the importance of unearthing
the fundamental assumptions on which differing economic beliefs are based
and concentrate their discussions on these assumptions.
A person’s decision to adopt one or another
set of basic economic assumptions is entirely analogous to the scientist’s
decision to one or another system of geometry. This analogy goes further.
When scientists found that non-Euclidean geometry fitted observations and
experience better than Euclidean geometry, the latter was rejected and
the former installed in its place. A revolution took place
in scientific thought.
The same happens in economic thought. Individuals and sometimes nations
find that an economic system does not meet the needs of the people. Individuals
react by changing their economic beliefs. Nations sometimes
react by revolution, for often the economic system is tied to the political
system.
In a political system, too, basic assumptions determine
entire theories.
...
The influence of mathematics on our civilization through the medium of the sciences, and the direct influence of mathematics on all fields of thought as a major method of attacking problems, are the larger values of the subject. These values together with the uncountable applications and relationships of mathematics to engineering, art, philosophy, music, logic, religion, and social sciences, establish mathematics as having unchallengeable importance for our civilization. It will be noted that the importance of mathematics extends beyond the ways in which man earns his daily bread. It includes those higher forms of human activity such as art, philosophy, and music, which are commonly referred to as the cultural fields.
Cooley, Hollis R., David Gans, Morris Kline, and Howard Wahlert, Houghton Mifflin Company 1937. Reprinted in Mathematics, edited by Rapport, Samuel and Helen Wright, New York University Press, 1963, pp 247-249
