Analysis in the physical sciences is largely based upon the assumptions that nature can be understood and that nature is well described by the language of mathematics. That this is a fundamentally religious belief is obvious in the statement by Henri Poincare, the French mathematician, “If God speaks to man, he undoubtedly uses the language of mathematics.” We discover many mysterious patterns in nature only because we choose to convert raw observations into numbers. While these patterns may be illusory, they have the general appearance of being meaningful, hence our religious assumption. Thus physical scientists seek mathematical forms to store and interrelate their observations.

Scientists will often claim that science differs from the arts in the sense that scientific concepts, unlike artistic ones, must be supported by reproducible evidence. However, concepts in art are subject to various forms of verification as well. It is not the condition of verification, but rather the reliance upon mathematical forms of verification that distinguishes the physical sciences from the arts. Artists may ask if anything meaningful about the physical world could ever be described in mathematical terms? Science and art are not different hierarchies of truth but equally valid attempts at arriving at truths through differing assumptions. Most educated people believe that it is as much a folly to live without poetry as it is to live without science.

A typical physical science (chemistry, physics) experiment will begin with words, yet even the words have that peculiar scientific quality of referring to measurable entities. We have lots of these so-called variables: length, mass, time, temperature, etc. Are these variables a part of the physical world, and have they been observed or discovered? Or are these variables mental constructs that have been made up, invented, or imagined? It is revealing that the same questions are asked about mathematical systems. The specialized language of science permits that experimental data will generally be in the form of numbers, needle readings read from linear scales (rulers, balances, clocks, thermometers, barometers, etc.). This translation of physical phenomena into needle readings is one of the distinguishing features of the scientific method.

Such numbers may best be understood when organized into a data table. Select some useful variable (sometimes referred to as the independent variable) and order the numbers in sequence according to this variable. Qualitative trends may then be observed. For example, as variable “a” increases, variable “b” also increases.

But with mathematics, we can proceed much further than qualitative trends. A graph of “b” vs. “a” may show a pattern, permitting a best fit line or curve to be drawn. Not only does the graph correct the small experimental errors in the evidence, but it also is useful for making quantitative predictions. A line has an infinite number of points, and each point relates “a” to “b”. We now know the value of “a” for any “b” and v.v. You should be aware, however, that the line, while probably more accurate than the original data table, is far from perfect, and becomes less reliable the further you travel on it from the region in which data were collected.

By converting observations into numbers, then into data tables (where qualitative predictions can be made), and then into graphs ( which permit pattern recognition and quantitative predictions), we have a considerable gain in the quality and quantity of information. But we are not done. While graphs cannot be combined, equations of graphs can. The next step is, if possible, to determine the equation of the line or curve from the graph. Equations are like building blocks. They can be algebraically combined with each other to give more and more complicated, multidimensional models of reality.

Experimenting in the physical sciences, then, involves taking a complex world and identifying or inventing relevant variables. We then attempt to control these variables so that only two may change so that we may easily discover the equation that relates these variables. One by one, we perform new experiments, adding new variables to the equation, in an attempt to rebuild the complex world that we began with, only in mathematical terms.

When scientists invent abstract variables such as pressure, volume, moles, and temperature, as solutions to various measuring instruments, scientists are acting in ways parallel to some modern abstract artists in inventing symbols. And when scientists rebuild nature in the laboratory in the form of the abstract mathematical model, pV = nRT, scientists again parallel the means in which modern artists will take common symbols and relate them in new ways to generate new interpretations of old ideas.

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