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| Mathematics and Science |
Mathematics and Science
The rules and procedures of mathematics are based on logical deduction, a process that occurs totally in the minds of humans. At the same time, the procedures of science are based on systematic observations of the external world. If that is the case, how is it possible for mathematics to be so useful in describing the behaviour of the universe as discovered by science? For instance, how was it possible for Isaac Newton (1643 – 1727) and Gottfried Leibniz (1646 – 1716) to invent calculus in the 17th century, and that same calculus was able to describe the motion of moon rockets in the twentieth century?
The answer lies in the feedback that occurs between deductive and inductive thinking, and between mathematics and science. No humans, including mathematicians, are isolated from the real physical world. Everyday experience becomes an integral part of even the most abstract thinker’s mental processes.
Newton created his methods for dealing with infinitesimals and anti-differentiation specifically to deal with calculations related to the motions of planets. An essential part of his genius was his skill in selecting the most appropriate definitions and postulates from which the rest of calculus could be derived.
When searching for the best mathematical equations to represent scientific observations, there are always many possibilities. Making the best choice involves a combination of ‘curve fitting’, and selecting the simplest equations that work over the widest range. It also helps if the selected equations have interesting features with implications for additional research.
The rules and procedures of mathematics are based on logical deduction, a process that occurs totally in the minds of humans. At the same time, the procedures of science are based on systematic observations of the external world. If that is the case, how is it possible for mathematics to be so useful in describing the behaviour of the universe as discovered by science? For instance, how was it possible for Isaac Newton (1643 – 1727) and Gottfried Leibniz (1646 – 1716) to invent calculus in the 17th century, and that same calculus was able to describe the motion of moon rockets in the twentieth century?
The answer lies in the feedback that occurs between deductive and inductive thinking, and between mathematics and science. No humans, including mathematicians, are isolated from the real physical world. Everyday experience becomes an integral part of even the most abstract thinker’s mental processes.
Newton created his methods for dealing with infinitesimals and anti-differentiation specifically to deal with calculations related to the motions of planets. An essential part of his genius was his skill in selecting the most appropriate definitions and postulates from which the rest of calculus could be derived.
When searching for the best mathematical equations to represent scientific observations, there are always many possibilities. Making the best choice involves a combination of ‘curve fitting’, and selecting the simplest equations that work over the widest range. It also helps if the selected equations have interesting features with implications for additional research.
