Math is Beautiful--Don't Give it Up!

Lately I’ve seen a lot of blogs and articles claiming that the teaching of Algebra is holding our kids back. Many students are failing the subject and it’s often listed as the number one academic reason for high-school drop-out. Considered the gatekeeper for students’ careers, many are beginning to call for it to be removed from our curriculum. Roger C. Shank, a cognitive scientist and education reformer makes a simple argument for this in his Washington Post op-ed piece. While I agree that our educational system leaves much to be desired when it comes to truly preparing our students for the future, removing higher mathematics and related sciences from our studies will move the subjects once more into the realm of mastery and the elites, and this will significantly limit us as a society.

The study of the natural world, and mathematics, the language to describe these systems, were actually developed within the structure of mystery schools. Only those with the qualifications were allowed entry. They followed strict rules about how they lived their lives and in return worked together to solve some of the greatest mysteries of that time.The famous Greek mathematician, Pythagoras' school is a perfect example of this. Their science was treated like a religion and entry into their cult was incredibly difficult. Their information was tightly guarded, shared only with initiates, yet all they were really doing was satisfying their curiosity. Like the research labs of our universities, these men were looking out at the world around them and studying it, learning from nature and then trying to describe it and prove it with their equations. While the rest of the world toiled with everyday living, the masters and elites understood how life really worked, how it was created and how we ourselves are a part of this greater mystery.

Mathematics is so much more than simple arithmetic. We can all agree that sixth grade math is something we use, from balancing our bank accounts to building a garden bed. But higher mathematics gives us a peek at something bigger—the construction of the universe itself. Geometry shows us the basic forms of matter. Spheres, squares, rhomboids and cones. Each of these govern how life appears in its physical shape. Understanding Pi, or 3.14159…, allows the student to begin to see that while everything has order, things are also irrational. When we open our eyes to the beauty of these shapes, we begin to appreciate life on Earth and the harmony in which matter exists.

Higher mathematics also teaches us about the unknown. Solving the quadratic equation is not something I’ve done since college, I agree. Yet learning how to take variables and solve for them, to look for data and search for balance in my equations, made me a much better software engineer. A typical software application deals with the mundane, but how you code it, how much memory it takes, the speed in which it runs, and what sort of functions you will call, are all unknowns that you must make manifest. Years studying higher level mathematics enabled me to do just that. Once you’ve studied vector spaces, everything else looks easy.

I hear you. You’re not going to be an engineer so enough of the STEM stuff. Well, there are the practicalities that go with this. Algebra I and II as well as geometry are required to get into most colleges. However, a recent study also found that algebra isn’t just for the college bound. Most careers such as an electrician, plumber or upholsterer--jobs that will pay you enough to feed your family but don’t require a college degree--still require freshman college level math skills to succeed. But that’s not reason enough to study the subject. Life itself follows patterns, it grows and replicates according to mathematical principles and knowing these patterns makes you a better citizen of Earth.

Take the pine cone, whose growth pattern follows the Fibonacci sequence. As a matter of fact, most plants do. This leads us to the Golden Mean, a proportion after which even the human body is modeled. Knowing how you’re built, how a seed germinates, how a tree grows its branches shouldn’t be left to those who are the smartest. These aren’t elite subjects, for each of us is a part of nature and has every right to learn about it. And it’s beautiful. Check out Vi Hart’s work on these subjects, Doodling in Math Class. These videos alone show how amazing math is and it’s relation to our lives.
                I believe that the issue here isn’t that we can’t learn algebra and geometry, it’s that our schools have killed the curriculum. It was a gift when our country decided to teach as many as possible the subjects of reading, writing and arithmetic. There is power in all three of these things and their study leads to a more open society. However forcing kindergarteners to read and learn their multiplication tables isn’t the solution. Five year old children weren’t admitted to Pythagoras’ school. A person had to learn to live in the world physically before they were shown the mental mysteries of the universe. As a result of our pushing early academics and standardizing our teaching methods, we’ve removed the awe and wonder that is natural to the study of math and science, and as a result, many kids are failing these very important subjects.

Rather than remove Algebra from our lives, why not change the way we teach it? Inspire children to learn about the world around them, rather than scare them into learning a subject. Show them how the pine cone grows and how the ancients used the chord functions of a circle to figure out how tall the Great Pyramid was. Without ladders and precision equipment we’re able to know these things because matter follows mathematical principles. We shouldn’t give up simply because we’ve forgotten how to teach others how to learn. It isn’t just the “smart kids” who benefit from these subjects. We all do.

Practicing Discipline in Scientific Endeavor

In 518 BC, the Greek mathematician, Pythagoras, founded a school in which the topics of mathematics, music and philosophy were studied with great discipline and secrecy. Men and women were welcome to live in community and study together, and eventually this group of individuals would contribute much to the subject of mathematics, including:

1. The sum of the angles of a triangle is equal to two right angles.
2. The theorem of Pythagoras - for a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. The Babylonians understood this 1000 years earlier, but Pythagoras proved it.
3. Constructing figures of a given area and geometrical algebra. For example they solved various equations by geometrical means.
4. The discovery of irrational numbers is attributed to the Pythagoreans, but seems unlikely to have been the idea of Pythagoras because it does not align with his philosophy the all things are numbers, since number to him meant the ratio of two whole numbers.
5. The five regular solids (tetrahedron, cube, octahedron, icosahedron, dodecahedron). It is believed that Pythagoras knew how to construct the first three but not last two.
6. Pythagoras taught that Earth was a sphere in the center of the Cosmos (Universe), that the planets, stars, and the universe were spherical because the sphere was the most perfect solid figure. He also taught that the paths of the planets were circular. Pythagoras recognized that the morning star was the same as the evening star, Venus.  (Source)

Most mathematicians would agree that the work of Pythagoras and his followers changed the subject forever. When looking at his school and the pedagogy, it’s obvious that the schooling was about more than math. Music and art, especially geometry in art, were very important. Pythagoras felt that these subjects were intimately linked to mathematics, and to study one meant to study all three.

Most peculiar were the philosophical aspects to this training. The School maintained that every human had a soul and that through math and music, the soul could be purified. In addition, strict procedures were in place to facilitate the growth of each person’s soul, from giving up their possessions to being vegetarian, to regular meditative practices. All of these things were part of the curriculum.

Of course, this spiritual aspect of the school’s training is often seen as religious, and rightly so. For the ancients, God and Science were one. This remained up through the Reformation and Enlightenment, when Science finally broke free from superstition and set about to conquer the world and take it from God. Overall, we have countless reasons to give thanks for this—from the Inquisition, to the discrediting of Galileo, to the burning of libraries, to the witch hunts—religious dogma has proven itself dangerous, not only to science, but humanity in general.

Yet here we are, about three hundred years into Science without God, and I sense that we might have thrown the baby out with the bathwater. While superstitious beliefs often stand in the way of progress, the “spiritual” discipline that religion brought to the scientist was not without its merits. We may teach that we are just a bunch of atoms and molecules randomly bopping around in the universe, but it doesn’t take a PhD to see that something else exists within us—call it consciousness if we must. Or the observer. That part of our system that decides what to do. That part of humanity, and many other animals as well, that lives and is obviously not there at death. This could just be energy, but it’s a force none-the-less and when left unchecked, can wreak havoc on those around it.

Angry children are annoying. Angry adults are terrifying. When we maintain that our physical bodies are the only real part of us, we run the risk of letting that emotional, conscious part of us, run amok. The “soulful” practices in Pythagoras’ curriculum made sure that each scientist took the time to understand themselves, their deepest selves. To know their weaknesses, to see their instincts of fear and domination, and overcome them. Discipline is the way towards “knowing thyself” and in many ways the lack of this practice in our scientific pedagogy is partially to blame for the various negative ways we’ve used technology over the centuries. It’s easy to use our inventions to dominate others if we have no control over our own greed, anger, fear and frustration.

I believe that the heart of Pythagoras’ curriculum was to first see yourself for who you really are, identify your threat to others, and overcome that, all while studying the wonders of mathematics, astronomy, architecture and music. He believed that studying these subjects, when coupled with fasting, the giving up of belongings and living in community, would create the ideal school from which new innovation and ideas would come forth. Ideas that would change the world for the better.

We now hold in the palm of our hand the ability to modify our genes, create super-children in labs, nuke an entire city and blow a hole in the atmosphere. We also hold the keys to solving global hunger, sheltering every human being, and extending life while curing most disease. When our scientific training is devoid of any hint at truly knowing thyself, and actually denies the importance of practices such as meditation, exercise, eating well and serving others as key to any good pedagogy, what sort of direction will our scientific innovation take?

We don’t have to go to church, or believe in Jesus, Allah or God to know that within us lies a power beyond mere atoms. Call it what you will—consciousness, soul, spirit or, for those of you who have read my eHuman novels, the Lux—there’s a part of each human making decisions. It’s the part we hope to download into computers someday. That part of us is every bit as important as our memory or ability to learn advanced technological concepts. Modern practices such as learning a new instrument, meditating every day, exercising, and serving in the community at large helps to discipline our nature and get us in touch with who we really are. Life is more than getting a good degree at our top universities. As scientists, we owe it to the world to take the time to invest in getting to know our deeper nature, and ask the questions that are so hard for science to answer.

“Who am I?”

“Why am I here?”

“What is my purpose?”

“How might I serve?”