If radio waves and X-rays are light too, why can't we see them?

Because our eyes are tuned to one narrow band of a much bigger family. Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays are all electromagnetic waves, and what separates them is their wavelength. Radio waves can stretch for kilometres; gamma rays are smaller than an atomic nucleus. A typical human eye responds only to waves between about 380 and 750 nanometres, millionths of a millimetre, and we call that slice light.

That slice isn't random. The Sun puts out its peak power in the visible band, and visible wavelengths slip almost undimmed through the air, a gap scientists call the optical window. Most animals' eyes evolved to match that window. The edges also differ between species: bees and many insects see ultraviolet, which helps them find nectar in flowers. We miss it largely because the cornea and lens of our eyes absorb it before it reaches the retina.

The rest of the family was found one surprise at a time. In 1800 the astronomer William Herschel moved a thermometer through sunlight split by a prism and found the hottest spot just beyond the red, where nothing could be seen: infrared. A year later Johann Ritter found invisible rays beyond the violet that darkened silver chloride paper even faster than violet light: ultraviolet. In the 1860s James Clerk Maxwell realised that the waves predicted by his equations of electricity and magnetism travel at the speed of light, and concluded that light is one of them.

In 1886 Heinrich Hertz made radio waves in his lab and showed they too move at the speed of light. Hertz himself said his discovery was of no use whatsoever. Within six years, Marconi was building wireless telegraphy.