Relation to mathematics and the other sciences
Relation to mathematics and the other sciences
In the Assayer (1622), Galileo noted that mathematics is the language in which Nature expresses its laws. Most experimental results in physics are numerical measurements, and theories in physics use mathematics to give numerical results to match these measurements.
Physics relies upon mathematics to provide the logical framework in which physical laws may be precisely formulated and predictions quantified. Whenever analytic solutions of equations are not feasible, numerical analysis and simulations may be utilized. Thus, scientific computation is an integral part of physics, and the field of computational physics is an active area of research.
A key difference between physics and mathematics is that since physics is ultimately concerned with descriptions of the material world, it tests its theories by comparing the predictions of its theories with data procured from observations and experimentation, whereas mathematics is concerned with abstract patterns, not limited by those observed in the real world. The distinction, however, is not always clear-cut. There is a large area of research intermediate between physics and mathematics, known as mathematical physics.
Physics is also intimately related to many other sciences, as well as applied fields like engineering and medicine. The principles of physics find applications throughout the other natural sciences as some phenomena studied in physics, such as the conservation of energy, are common toall material systems. Other phenomena, such as superconductivity, stem from these laws, but are not laws themselves because they only appear in some systems.
Physics is often said to be the "fundamental science" (chemistry is sometimes included), because each of the other disciplines (biology,chemistry, geology, material science, engineering, medicine etc.) deals with particular types of material systems that obey the laws of physics. For example, chemistry is the science of collections of matter (such as gases and liquids formed of atoms and molecules) and the processes known as chemical reactions that result in the change of chemical substances.
The structure, reactivity, and properties of a chemical compound are determined by the properties of the underlying molecules, which may be well-described by areas of physics such as quantum mechanics, or quantum chemistry, thermodynamics, and electromagnetism.
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