If I remember well, 5 + 1 = 2 x 3, is it right? You may wonder what it represents. Well, it is an equality or mathematical equation, where the key word is ‘mathematical’. Now, what is the difference with the following equations?
Maxwell’s equations: there is not a single day when I don’t write them somewhere just for fun (Note. For practical reasons, the point means the same as the x, that is a product, in the first case it is a scalar product and in the second a vector product, but for us, now it doesn’t matter.
They are a bit scary, aren’t they?
Let’s do the following, if in the equation 5 + 1 = 2 x 3, we replace 5 by the an A, 1 by a B, 2 by a C and 3 by a D, we can write as
A x B = C + D
Let’s go back to the Maxwell’s equations and pay attention to the last one. Is there any difference? Apart from the arrows over the symbols, the inverted triangle and the quotient involving something similar to a 6 reflected on a mirror, if we look at it carefully, It is similar to our something multiplied by another something which equals to another something times something and as we said that the product and addition of something was 5 + 1 = 2 x 3, we come to the conclusion (at least me) that the Maxwell’s equations are not so scary as we may think at the beginning, they are just additions and products that we know since we were children.
Actually, Maxwell’s equations, apart from being beautiful, are a bit scary, specially when one has to solve them in an exam with limited time taking into account that you has not studied too much.
There is a generalised terror between different people towards Maths, and it can be heard very often that they are difficult (in fact, they are), that they are useless (a lie!) and why should I learn Maths when the only thing I need is to know how to add and multiply the prices in supermarkets (if you know add and substract, you can already read Maxwell’s equations, and yes they are really useful)
Although in many cases Maths are difficult, it is not truth to affirm that they are useless. Maxwell’s equations (remember, 4 equations that are additions and products), are in fact an explanation of everything we see! They explain why the light is as it is, they explain all the electricity we use every day from the moment we wake up until we go to sleep, they explain why when we are sit, despite of the gravity force that pull us towards the floor, we don’t pass through the chair and fall down, they explain why magnets are attracted and why the engines of our fridges and our washing machines work, they explain… well, I will not keep on giving examples, otherwise I will not finish this post.
Even If I put Maxwell’s equations as an example (only because they are my favourite equations), the usefulness is not only limited to them. I could have started with something easier such as the famous Einstein’s equation E =mc2 and make a comparison with the equation 1.53×1016 = 0,51 x (3×108)2 and say that 1.53×1016 is E, 0,51 is m and 3×108 is c, where they represent the rest energy of the electron in MeV (Megaelectronvolts), the rest mass of the electron in MeV and the speed of light in meters per second respectively, but I have already written about this equation here and don’t want to repeat myself.
In any case, Maths are fundamental in any moment of our lives. For instance the following equations
Equations of the geostrophic wind approximation
represent the geostrophic wind approximation, that explain the anticlockwise turn of high pressure systems in the atmosphere and the clockwise turn of low pressure systems (in the northern hemisphere) as well as how meteorologists are able of establish the wind direction by looking at the isobar maps (it is easy, the rule is that the wind always moves in the direction where the low pressures are left to the left)
But this is not the end, there are much more examples outside the world of Physics and Natural Sciences. For example, in Economics, the equation
Equation of the change in the value of money
represents the change in the value of money when the price index at the beginning and at the end of an specific period are known.
Even in Medicine, the equations
SIR Model for the development of a disease along time
represent the SIR model, which indicates how a disease evolves along time
And there are much more examples that we don’t pay attention to and that give practical results we use everyday.
Maths is extremely useful, without Maths we would probably still live in caves (Egyptians used Maths already to build pyramids and even for agricultural purposes and since then a long time has passed). And yes, they are difficult. If you don’t believe me, just look at the Standard Model Lagrangian (nice word!) of Particle Physics which explains all the forces or nature we feel, except for gravitation (electromagnetic force which includes Maxwell’s equations, weak force which explains nuclear decays and radioactivity and strong force which explains why atomic nucleus are as they are) and basically it explains how the world that surround us is. Let’s see how many additions and products like those at the beginning of the post you are able to see…
Standard Model Lagrangian of Particle Physics
How to write Maxwell’s Equations on a T-Shirt
Luis E. Rivero. La medición del valor del dinero
The Standard Higgs. Richard Ruiz. Quantum Diaries. http://www.quantumdiaries.org/author/richard-ruiz/