Math - The Language of the Universe

Many immature students frequently ask why math is important. They do this with the implication that math is unnecessary in what they call “real life” and therefore they should not have to waste their time studying it. And in their ignorance they may genuinely feel that they are right and actually possess an argument that should be listened to. However it doesn’t take long for anybody with half-a-brain to realize that real life is not only full of math, but that real life is governed by it.

History is full of these people who had more than half-a-brain, these smart people who came along and discovered the manner in which math is involved with our daily lives. One of these individuals was James Clerk Maxwell, a Scottish scientist in the field of mathematical physics who –with his math formulas- revolutionized the concept of electrodynamics.

James Clerk Maxwell’s math formulas brought together –for the first time- electricity, magnetism, and light. In order to formulate the theories he did, Maxwell developed math equations to measure the frequency and wavelength of radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. What’s so fascinating is that all of these forces are very powerful in the manner in which they affect our daily lives, and they are also ‘very invisible’; and yet Maxwell used math formulas to study their natural laws of behavior and to prove their existence. The math Maxwell used has been called the “second great unification in physics”; as he has been regarded as the third greatest physicists of all time -third only to Albert Einstein and Isaac Newton. Sure Maxwell may have always had a sense of intuition which led him to believe that these forces existed in nature, and a sense of intuition to lead him in the right direction in studying these forces of nature; but without math, Maxwell never would’ve been able to grasp the characteristics of these forces and actually prove their existence. And without math, Maxwell would’ve never been able to establish a better mass understanding of how these forces work together to affect our daily lives.

Maxwell’s math equations form the foundation of what is termed classical electrodynamics, classic optics, and electric circuits; all of which involve aspects of our modern electrical systems and forms of communications. Without the use of math it would have been impossible for Maxwell to describe how electric and magnetic fields arise from the arrangement of electrical charges and currents and how these fields change in time. His equations are the accumulation of decades of working with math to formulate equations that would prove to be both accurate and applicable. For example, the addition of Maxwell’s new term –called the displacement current- to the math formulas of Michael Faraday and Andre-Marie Ampere in Ampere’s Law, revolutionized our understanding of electrodynamics; yes it came on the tail end of Faraday’s and Ampere’s math formulas, but it suggested and made evident for the first time that varying electric and magnetic fields could feed off each other and could thereby propagate indefinitely through space, far from the varying charges and currents where they had originated. Prior to this, it was believed that these fields had been tethered to the charges and currents from where they had originated and thus subject to them. But Maxwell’s math freed them to move through space in a self-sustaining and independent fashion –and his formulas even predicted the velocity in which they move, which happens to be the speed of light. The more information like this that you are exposed to as a student, the more it seems to become superfluous to mention that such achievements could not have been made without the use of math; but of course, for this paper I must come back and reinforce that point. It’s connections such as these made by the student –one after the other- which leads a student to realize –again and again- that real life is not only full of math, but that the very laws of nature are governed by it. Yes individuals like James Clerk Maxwell and Michael Faraday may have been blessed with a profound intuition which had a strong tendency to point them in the right direction, but without math they would have been dead-in-the-water; full of great ideas but unable to prove them. It’s very hard to call a philosopher or scientist crazy when they have mathematical proof of whatever it is that they are proposing. And without the math formulas that these gentleman generated, tested and proved, the world would have probably dismissed their ideas of electromagnetic radiation –for example- as pure speculation at best. If this had happened, we wouldn’t have had the evidence and courage to follow Maxwell’s predictions enough to actually utilize the existence of radio waves, for example, like we do with our cell phones today! It was Maxwell’s mathematical theory –now called Maxwell’s equations- that described the existence of light waves and radio waves as electromagnetism that travel in space, radiated by a charged particle as it undergoes acceleration. Heinrich Hertz then demonstrated the existence of these waves by producing them in his laboratory twenty years later, and then Guglielmo Marconi developed the first practical radio transmitters and receivers; my point being that nobody would have gone on to demonstrate and then utilize Maxwell’s predictions if they were dismissed as pure speculation at best, for it was the use of Maxwell’s mathematical use of his equations which pushed this technology forward enough to be made real and utilized. Can you imagine what life would be like without a cell phone? It wasn’t that long ago. My point being of course that each discovery leads us to the next one with technology always improving because of the many steps we take as a society; but without math, like Maxwell would have been with his wild ideas and radical theories, we as a species would be dead-in-the-water.

Dead-in-the-water is a term used to describe something that is unable to move. Life in Nature is most certainly not dead-in-the-water; it is constantly moving and changing. Although it is doing such, it follows certain laws that never change. A cup of coffee left on a table will always become cool. Gravity always remains steady, it never fluctuates. Our planet Earth rotates continuously on its axis once every 24 hours on the dot. This has been going on for billions of years, throughout the history of time itself. A modern cosmologist by the name of Sean Carroll comments “A law of physics is a pattern that nature obeys without exception.” Life as we know it is constantly moving and in order to stay alive and prosper, as a species, it is imperative that we move with it. We can’t do this properly if we can’t understand those laws, or at least, understand those laws better. And we can’t do this without math.

The laws of nature that we discover here and now and anywhere on this planet for that matter are also true anywhere in the universe, and this has been the case since the beginning of time. It’s easy to take this fact for granted. Coming to a better understanding of how these laws operate involves countless experiments over time. And these include measurements and recordings. All of this documentation doesn’t necessarily happen with words and paragraphs, it happens with numbers. Math is the language through which the universe speaks. If you were to move to a different country for the rest of your life and they only spoke one language there and that language was not your own, you would think it not only wise but necessary to learn everything there is to know about that one language in order to not only survive, but enjoy everything that country had to offer. Well the universe only speaks one language and that language is math. This is the primary reason why it is so important to study it, to know it, and to use it.

Although the examples I have provided are a good starting point in presenting the argument behind why a student of Electrical Engineering needs to study math in order to thrive in his career, they are only that, a starting point. The list goes on-and-on. But for the sake of this paper, I think it necessary to make a few other brief points regarding computers, future employers, and the well-rounded individual.

Yes we have invented computers to make a lot of things easier but computers do not make traditional math analysis obsolete –not in the least! Computer programs contain mathematical relations and understanding these relations is still necessary. For example, debugging computer programs can be a difficult art. But one of the best ways to test a program in order to find the problem is to compare a computer simulation to the analytical solution for the same situation, and you need to possess a good understanding of how to use math in order to do so. Also, when brute-force computer code is used to write a computer program that has a long runtime, for example, the presence of error will accumulate as that program runs due to the limited resolution of code written without the use of math; but when a writer includes these math formulas, analytical solutions, and appropriate algorithms into the writing of the code, great increases in both speed and accuracy are the direct result. There is simply no avoiding math, especially when it comes to computers.

Employers are well aware of the relationship between math and computers and are going to be looking for candidates to possess a solid understanding of this truth. It’s a vast spectrum of employers, including: scientific research and development services, navigation, measuring, electro-medical, control instrument manufacturing, electric power generation, transmission and distribution, architecture, and of course engineering.

When it comes to the assimilation of math into one’s life, as the Borg would say in Star Trek the Next Generation, “Resistance is Futile”. Math is the language which governs the forces of nature and if you don’t speak it, you will be dead-in-the-water. You may have many great ideas but without math you will not see those great ideas come to fruition; whether it is you or someone else you pay to do the math, the math must get done. No matter your field, math will always be necessary somewhere along the line of progress because math is the language of the Universe.