MGTutoring.com. A Rational Perspective on Education.

Mathematics allows us to grasp and understand things outside of the realm of perception — things like radio waves and microwaves:

Radio broadcasts use the low-frequency, long-wavelength portion of the electromagnetic spectrum. Commercial AM radio is at frequencies of 550 kHz to 1600 kHz (wavelengths of 545 m to 187 m) and commercial FM radio is at frequencies of 88 MHz to 108 MHz (wavelengths of 3.4 m to 2.8 m). Because these waves have wavelengths longer than 1 m, they are called radio waves. But the electromagnetic waves used in microwave ovens have wavelengths shorter than 1 m and are called microwaves. Microwaves extend from wavelengths of 1 m (3.3 ft) down to 1 mm (0.04 inches).

p. 433 , How Things Work (3rd ed.) by Louis A. Bloomfield, John Wiley & Sons, Inc., (c) 2006, ISBN-13: 978-0-471-46886-8.

Such waves are things we never see, touch, taste or smell. But because of concepts and mathematics, we can identify and control electromagnetic waves, as if they were things we could actually see or touch. Math and conceptual thought make possible all devices and inventions based on electricity and electromagnetic waves: radio, live365.com, the iPod, the iPhone, cell phones in general, GPS, the Internet, microwave ovens, AC, the automobile and more. People who say that math is useless are saying, by implication, by logical necessity, that all things logically and causally dependent on mathematics — such as those just enumerated — are useless and can and should be done away with.

But mathematics is implicit in most all the technology we use in most aspects of our lives. (That so many people don’t see this is, sadly, an indictment of the anti-conceptual nature of our culture. How I wish it were otherwise…) Mathematics and measurement are implicit in signage along the roadside and on buildings, in all recorded or amplified music we hear and enjoy, in the medical treatment we receive and depend on, in the cell phones we use to call family or friend or business associate, in the Internet we use to read news or keep up with friends, in the automobile we drive on vacation or in which we are driven to the hospital. The modern life we live is dependent on mathematics — what’s more, I’d argue that mathematics and measurement are essential to human consciousness and experience and thus to human life, and fundamentally differentiate us from all other animals.