You don't have to look too closely to see math at work in everyday life. From calculating transaction change and sale prices, to looking at the percentage of probability on a weather forecast, to setting timers so that your Christmas lights will turn on at a measured level of darkness, math is arguably irremovable from every experience on Earth. Even nature falls into patterns, routines and life cycles, down to the most micro ecological organizations.
But what about the Earth, high in the air? Birds and other flying creatures have long been making use of Mother Nature’s carefully attuned laws of physics to carry themselves from Point A to Point B. It turns out that the airline industry is also a great borrower of such universal mathematical and physical principles, and given the high economic and human stakes associated with flying, aviation is arguably one of the industries for which reliance on mathematics is the most critical.
It is easy to see how critical it is that a pilot is capable behind the controls. With thousands of pounds of metal and flammable fuel careening through the atmosphere at extremely high velocities, carrying human or economic cargo over invaluable infrastructure, civilizations, and natural environments, the stakes for safe airline operation are extremely high. Airline pilots are rigorously trained in countless formulas, models, and principles of physics. On the other side of airline training, students are equipped to see the world as a series of grids and graphs, and to understand how a whole host of calculable variables interact with each other in three-dimensional space.
Pilots must be proficient in formulaic calculation and must have a keen mind for deviation. They must be able to account for routine and circumstantial factors as well as safety buffers, to calculate fuel requirements and to know the mathematical limits of their resources in case they need to make emergency adjustments to their plans. Pilots have to know how different levels of cargo weight will affect their instruments and handling. Altitude, velocity, and pitch will have significant impacts on how the vehicle operates and where it ultimately goes. It’s the pilot’s responsibility to make sure that from a numerical standpoint, everything is in tip-top shape before taking off or landing.
From Creation to Transportation
Every single component of an airplane is optimized for maximum performance in the air. Decades of research and experience have gone into curating every bolt, every panel, every cavity, and every instrument to deliver the safest flying experience possible. Deviations of fractions can have detrimental consequences, which is why mathematicians and engineers are part of every stage of the development process.
Moreover, maintenance schedules need to be designed and followed meticulously for assurance that the vehicle is operating within its safety margins. These need to be mathematically optimized to calculate the exact amount of variation that can still provide a safe experience. Maintenance operators need to understand how to measure these variables and metrics in order to properly mark an aircraft as safe or unsafe.
And once in the air, safety is not just the responsibility of the cockpit, but it is also critically in the hands of air traffic control. Air traffic control operators manage a series of complex geometric representations of their air spaces. They must have a vivid understanding of flight trajectories, velocities, and geometry, and be able to extrapolate that information to prevent disasters in the air. Pilots and air traffic controllers operate on universal principles to measure and curate safety, and those principles are based on mathematics.
The Fabric of Space
Fixed mathematical principles define and explain how the world works. Math does not change, though our understanding of how to operate within its principles allows us to advance higher than was ever possible before. A constant reliance on math governs our travel in the air, allowing us to catapult forward in our understanding of how humans can move around this planet―and even unlock the potential we are currently exploring for traveling beyond it. Without an insatiable curiosity to explore physics and math when engineering rocket ships and space travel missions, international space travel efforts would simply fall flat.
These principles have helped us optimize all kinds of transportation on the ground, too. Cars and vehicles have gotten safer since we’re better able to mathematically measure risk and adjust accordingly. Roads have been optimized for traffic flow and stoplights have been timed for pedestrian safety. This is math at work, getting us from our everyday Point A to Point B. As we continue to dive into what math has to offer, and how we can creatively apply that to our insatiable desire to explore, perhaps math will one day get us all the way to Point Z, as well.