Man's physical universe







While mathematics has often provided tools far beyond the needs of

the Science of the time, on the other hand, many data have not been

capable of interpretation until many years after they were obtained

because the mathematical tools had not yet been invented.

A great deal of the time required for the preparation for work in the

physical sciences must be devoted to the mastery of such tools as algebra,

plane geometry, descriptive geometry, solid geometry, trigonometry,

and differential and integral calculus. This training in the use of the

mathematical tools of Science is just as important to the elimination of

errors in organizing, classifying, and interpreting data as is training in

the use of the senses in obtaining reliable data.

There Is No Ultimate Form of Mathematical Reasoning.

Mathematics provides methods of arriving at general conclusions

based upon certain arbitrarily chosen definitions.

It is very important

that these definitions be so clearly and concisely stated that every

scientist will use the same definition. The chief reason for the multiplicity

of technical terms in Science is that they are necessary to provide

precise definitions. If new postulates are introduced or old terms are

redefined, the mathematical treatment has to be revised accordingly.

Thus Newton's assumption that time and space are independent gave

rise to a system of mathematics differing considerably from that based

on Einstein's postulate that time and space are related. There is no

ultimate form of mathematical reasoning any more than there is any

ultimate form for an automobile or airplane. The forms in each case

change as old faults are eradicated and new improvements are added.

Inasmuch as all scientific generalizations are obtained by mathematical

reasoning based on arbitrarily chosen assumptions, it is quite evident

that there is

no absolute generalization in Science and that any tentative

generalization or even law is subject to change when new data

indicate that certain original assumptions were not justified.


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