Hidden in Plain Sight

Tuesday. December 19, 2017 - 4 mins

Math is the language of the nature. It’s all around us. It’s within us. It has a profound effect on our lives. But when we say math, something like this is what usually comes to our mind:

$ \frac{y^{2}}{b^{2}}-\frac{x^{2}}{a^{2}}=z $

Coincidentally, this is the equation of a hyperbolic paraboloid. As scary as the above equation looks, it depicts a 3 dimensional object like this:

Yes! Pringles chips!

Why did they have to undergo so much trouble just to make potato chips? Couldn’t they have just sliced them and fried them random? The design doesn’t look so important, does it? Actually, it does. This design facilitates the chips to be packed closely into the box. The design ensures that they don’t break easily and they remain in shape during transportation.

This is just one example. A few more:

• Every natural change is a differential equation: cooling of water, change in temperature, change in humidity, the rate of curdling of milk, the rate of iron getting rusted, the speed of vehicles.
• Many things are probabilistic in nature. Survival, the occurrence of rainfall, the position of an electron.
• Music is a complex combination of sine and cosine waves.
• The growth of a pine cone, the structure of the DNA, the uncurling of a fern, a simple leaf, sunflower seeds - everything is a wonderful illustration of the Fibonacci sequence.
• Fractals appear in river networks, lightning bolts, snowflakes, bryophyllum leaves, and heartbeat patterns.
• Mathematical analysis of smoke trails, beehives and particle collisions have inspired many wonderful man-made creations today.
• Google’s search engine uses linear algebra. Modern day security systems use mathematical concepts like Chaos Theory for password encryption.

Paul Erdos, a mathematician, once said,

“Why are numbers beautiful? It’s like asking why Beethoven’s Ninth Symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.”

What exactly is the source of mathematical beauty? All appealing responses seem to come from identifying simplicity in complexity, pattern in chaos, structure in stasis. But what about mathematics? Aesthetic responses, as Santayana has argued in ‘The Sense of Beauty (1896)’, require a certain distance:

When we have before us a fine map, in which the line of the coast, now rocky, now sandy, is clearly indicated, together with the winding of the rivers, the elevations of the land, and the distribution of the population, we have the simultaneous suggestion of so many facts, the sense of mastery over so much reality, that we gaze at it with delight, and need no practical motive to keep us studying it, perhaps for hours altogether. A map is not naturally thought of as an aesthetic object…

And yet, let the tints of it be a little subtle, let the lines be a little delicate, and the masses of the land and sea somewhat balanced, and we really have a beautiful thing; a thing the charm of which consists almost entirely in its meaning, but which nevertheless pleases us in the same way as a picture or a graphic symbol might please. Give the symbol a little intrinsic worth of form, line and colour, and it attracts like a magnet all the values of things it is known to symbolize. It becomes beautiful in its expressiveness. This captures the aesthetic in mathematics: balancing form and content, syntax and semantics, utility and autonomy.

Mathematics is scary because we are taught about it in a wrong way. Kids shouldn’t be scared with dozens of arithmetic problems and numerical tables. Calculate this, simplify that, solve this, learn that. Geez, shoot me!

In order to see the simple and beautiful side of math, one usually has to complete an entire high school math curriculum as well as the first year or two of an undergraduate math major’s coursework. And by then, many students are already turned off by the subject, usually due to the emphasis in these earlier years on repetition, standardized testing, and rote learning.

Imagine a musician learning the scales and practicing the same tune for over ten years before he gets to play an actual song? Most musicians would either get scared or just plain bored. We would have hardly had any musicians. It’s a similar case with math. We spend years and years teaching kids nothing but ‘mathematical scales’.

Mathematics is simple. We need to teach kids how natural ‘numbers’ are. We need teachers who can show students the beauty of numbers in nature - from Fibonacci series to Kepler’s laws of planetary motion. We need a system where we can put behind “conventional” education. Math isn’t about solving equations. It’s about learning and appreciating the world. It’s about talking to nature.

But most importantly, we need to acknowledge the simplicity and beauty that mathematics is. Only then can we appreciate the beauty that lies hidden in plain sight.