MATHEMATICAL THINKING

We come now to the special case of mathematics, which stands alone as a deliberate attempt to increase our thinking skill by means of artificial aids. Mathematics is concerned with active thinking since it used to bring about results rather than a contemplative mood. Mathematics deals with processes and relationships and the new attitude in mathematics (new maths, etc.) is more concerned with "thinking" than with symbol manipulation.

Though we have developed mathematics to a high degree the application is still rather limited outside specialized areas. Most situations cannot be parcelled up into neat packages with clearly defined pure relationships.

Vietnam was an example of how precise mathematical methods used in the operations research under McNamara left out such vague imponderables as home reaction to casualty figures or the morals of the war.

Mathematics is not a complete thinking because it only operates after the important perceptual stage of thinking has taken place. This is not to say that there is no such thing as mathematical perception but that mathematics as a tool cannot be used to direct perceptions into concepts. Mathematics as a thinking system tends to be crystalline and mechanical. In contrast, practical thinking tends to be amorphous and biological. The development of mathematics is from within. In business terms this is called "technology push" development for it is the available technology that puts a product into service. This is in contrast to "market pull" development for it is the available technology that puts a product is the result of market demand. The proposed subject of thinking would be market-pull development.

But there is no doubt that mathematicians themselves with their "active thinking" attitudes and understanding of processes will have a significant contribution to make to the new subject which should nevertheless remain separate.