The Math Behind Spring Beauty

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Chris Cunningham, Math Instructor

As we finally approach spring, we look forward to the return of brilliantly colorful spring flowers. But even more interesting than the beautiful colors we will see, are the beautiful colors we cannot see.

The strength and beauty of mathematics is that it gives us the right perspective to think about confusing statements like the one above. Many people see mathematics as a morass of formulas and calculations, but if you advance far enough, you get to learn things like “linear algebra.” Don’t stop reading there, because I am about to tell you the many ways linear algebra impacts your everyday life.

Netflix uses linear algebra to predict what movie or TV series you will enjoy. Google uses linear algebra to predict what website you are looking for. The Math and Engineering Club at Waubonsee Community College uses linear algebra to predict who will win the NCAA basketball tournament. And we can use linear algebra to describe how color really works.

Human eyesight is based on three types of cones in our eyes. Using linear algebra, we know to think of this as seeing three "dimensions" of color. Look at a computer screen with a magnifying glass to see that the colors are generated by three types of pixels: red, green, and blue. Look inside your inkjet printer to see that the colors are generated using three types of ink: cyan, magenta, and yellow. Look at an image in a computer graphics program to see the color described in terms of three quantities: hue, saturation, and value. There are many ways to describe color, but for most humans, color is always built out of three dimensions.

If someone is born with only two types of cone cell, the person is colorblind. The mathematical perspective though, is that their color vision is reduced to only two dimensions. Many people (and actually most mammals) are colorblind this way. In its most common form, colorblindness means you can perceive the difference between blue and yellow, but a pattern of red and green stripes or a football game between teams with red and green jerseys is impossible to distinguish.

The surprising thing is that many birds and insects have four -- or even five -- types of cones, allowing them to see an even more vibrant spectrum of colors than any person has seen. From the insects' point of view, we humans are hopelessly colorblind. With only three dimensions of color vision, we are unable to see the radiant ultraviolet bulls-eye pattern on the black-eyed susan. We see the daffodil as a flat yellow, oblivious to the shocking alternating stripes that appear on every daffodil blossom.

Imagine what the world would look like if you had 16 types of cones, like the mantis shrimp?

Enjoy the many hues of spring, no matter how many dimensions of color you can see. And enjoy the mystery of it all a little bit more, knowing there’s even more beauty that we cannot see.

Chris Cunningham is a Math Instructor at Waubonsee Community College.