This is the "Mandelbrot Fractal". It is the graphical representation of the infinite iteration of the complex numbers of the simple equation f(x)=x^2+C
Earlier this summer Tom Donovan blogged about the teaching of STEM (Science, Technology, Engineering, and Math) courses in our schools and how imperative it is to do so if we as a country are going to continue to grow. This is absolutely true, but the answer often proposed—introducing these ideas earlier or more often in school—I believe is inadequate. For STEM culture to grow in our society, we need a complete shift in the way our information is presented. Children start to develop their interests and define themselves at a very young age; this makes it so much more critical that the way these courses are taught is changed.
For example, let’s take a look at this from the perspective of a first grade student. This child can walk into his art class and see Van Gogh, Modigliani, Manet, or into his music class and hear Mozart. Even if he cannot fully appreciate or comprehend the complexities, he instantly gets a glimpse into this form. The art teacher then tells him to ‘paint the fence’ and the student does not mind how rudimentary the task is and does it happily because he can aspire to be like the greats. After forty minutes or so, the art class ends and now this student has to go sit in the class he dreads all day… math. In this class, the teacher requires him to sit in his chair and repetitiously perform basic operations (the math equivalent of painting the fence). He hates this class and, as a result, he forms the opinion that math is not for him. The student’s perspective on this never changes because not unless he goes on to study higher applications of mathematics does he understand that math can be more than just ‘painting the fence’. This is in no way the instructor’s fault (and I am certainly not an expert in pedagogy), but it stems from the very nature of the two; art is interpreted emotionally while STEM fields are interpreted cerebrally and, as such, require more development before they can be appreciated.
My life is a prime example of this. Through my high school career, I was never so much a student as I was an athlete. I tolerated school and attended every day because I had to in order to attend practice later that day. I never liked math and certainly did not look forward to attending any classes. This all changed when I started studying engineering. As I delved deeper in mathematics, I started to see math less as a tool and more as a language. I was introduced to some of the revolutionary theories and began appreciating them as most people would Van Gogh’s “Sunflowers”.
One of the most beautiful things is when breakthroughs in math beget breakthroughs in science, or, conversely, when breakthroughs in science beget breakthroughs in math. For example, the quantum physics idea of supersymmetry is in existence because of the development of a new branch of mathematics called group theory—essentially physicists said ‘if group theory exists, then so must supersymmetry’ (which is just one of the examples that ushers in the question if math was invented or discovered). Another example of the pervasiveness of mathematics can be seen in the fractal geometry found in nature that is echoed in African community structures. These ideas are absolutely fascinating and only a select few ever have the chance of seeing them.
I do not know how it would be possible to present this information to a younger crowd in a way that they would be able to appreciate, but a transition like that could put STEM on par with art in the eyes of the majority which would have a great impact on our society.
Until next time,