In the most basic way, the visible light is special because it is visible. Human eyes can see it, so we called it “light”. Once we figured out ways to change near-visible light into something we could interpret (IR/UV cameras, certain types of fluorescence, etc.) we realized that there was more to light than just what we can see, so we renamed the part that was special to our eyes “light we can see” which shortens to “visible light”.
Why do our eyes interpret visible light while other frequencies on the electromagnetic spectrum are ignored? The evolutionary answer is because there was no reason for humans to see a broader spectrum; most animals that do see a broader spectrum have specialized needs. Bees use it to recognize certain types of flowers, and sea creatures need to see even when the water filters out visible light as two examples. Humans don’t have those needs.
Why don’t our eyes see a broader spectrum anyway? Because evolution is a lazy way to design a creature and it stops trying to be better the moment it is good enough to survive for a little while.
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