Math & Physical Sciences

Math & Physics

Physics tries to understand the causes and effects of physical phenomena on the Earth & in the Universe, both at the micro and macro levels. It progresses by observing physical phenomena, collecting data, analysing it, trying to perceive patterns of causes & effects and make hypotheses. Then experiments are set up to verify the hypotheses which again involves collection and analysis of the data generated by the experiment. If the experimental data agrees with the observed data, then many other scientists try to repeat the experiment and verify the results.

We can see that math has provided tools for enable each and every stage of this process.

Math is the language of Physics

Math is said to have become the language of physics. As physics has advanced into atomic levels, the events at that level, called quantum mechanics, can only be described mathematically with equations.

The physics curriculum contains many equations which describe the essence of the physics behind it. Explaining the physics behind the equations in day-to-day language is almost impossible.

Also expressing relations between entities as a mathematical equation, strips away most "excess" data from the relation allowing us to focus on the essence of the relation. It also helps us to manipulate the equation using laws of mathematics and tease out hidden relations!

Take for example the equation that relates temperature readings in centigrade and Fahrenheit scales. By writing it as F = 9/5 C + 32, even a primary school student can find out many related questions. What is the melting point of ice in both scales? What is the boiling point of water in both the scales? What is absolute 0 in both the scales? What is the temperature at with both scales will give the same reading? This is a powerful process which cannot be done verbally without mathematics. This is the power of mathematics.

Problems in physics have also pushed scientists to invent new math to handle them. The invention of calculus was to solve the problem of studying physical entities that keep on changing.

Universal Physical Constants

Mathematics, which is an invention of the human mind, has been found to be very effective in expressing relations in the physical world. Scientists have identified over 20 constants which seem to define the structure of our nature and its constituents from the macro level to the microlevel.

Some of them are the speed of light, the Plank Constant, Newtonian Constant of Gravitation, the Fine Structure Constant, the Cosmological Constant etc.

The Fine Structure Constant determines how stars burn, how chemistry happens and even whether atoms exist at all. Physicist Richard Feynman, who knew a thing or two about it, called it “one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding”.

What is remarkable is that humans have used mathematics to calculate the value of these constants to orders of precision of 10 to the powers in negative two digits! For example Newton’s Gravitational Constant has been calculated as 6.67430 ×10 −11 leaving out the units.

These are what prompted scientist Eugene Wigner to say, in his famous essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", that this is something which we neither deserve or understand!

Chemistry

One of the lasting images that all students would retain is that of balancing equations and the periodic table, both of which are ideas from math! The principle of balancing a equation of a chemical reaction is very similar to that in algebra. The periodic table is the organization of all known elements into a table so that patterns in the properties of elements & their relationships become easy to deduce.

The names of chemical compounds, concepts such as atomic number & atomic weight are mathematical. Physical chemistry is full of measurements and ratios. The representation of the atomic structures is mathematical.

The visual representation of the atomic & molecular structures and molecular bonds uses many geometrical models.

Ideas from "graph theory" are used to represent chemical bonds in complex molecules and their orientations. If you recall, graph theory developed from a puzzle regarding the bridges in the city of Konigsburg,