What is Visual Mathematics?

First of all, what is “math”?

For many people, “math” means equations, numbers, symbols, theorems and proofs, scrawled on pieces of paper. About ten inches above these scrawls is a wrinkled forehead, and just below that: two glazed eyes.

Because of my terrible grades in math, never getting beyond Algebra II, and then failing the lowest possible math class in college, I concluded that I was a complete math failure.

But I now know that mathematics encompasses a much broader set of activities than what most of us have been lead to believe. The curriculum is what failed. Thanks to my skills in visual thinking, drawing, and spatial logic (talents often associated with dyslexia) I was able to leap over that crufty heap of equations and explore mathematical concepts with my visual brain. And I didn’t even know I was doing math…until I got accepted into MIT, all expenses paid, to earn a master’s degree. MIT doesn’t pay full tuition and stipend to math flunkies. So, how do you explain this?

The purpose of bringing this up is to tell all you math flunkies out there that math (Real Math) may not be what you think it is. If you have a knack for music, puzzles, perspective drawing, a love of architecture, or are good at building things, you may have a natural talent or mathematical concepts, even if you can’t stand to look at symbols piled onto each other. You are a bundle of potential. The science and engineering industries NEED you. Too bad they’ll probably never find you.

Brett Victor takes the extreme view in Kill Math, claiming that we think of math as “assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules.” And therein lies the main culprit – the thing that used to snag me all throughout school:

RULES (without explanation)

I used to constantly ask my teachers, Why? Why? Why? The response from my teachers can be best summed up by a quote, apparently from the poet W. H. Auden:

“Minus times minus equals plus. The reason for this we need not discuss.”

Exploring animated patterns using simple computer programming can open the minds (not just the eyes) of young visual thinkers (or anyone who is turned off by equations). The reason is that the “why” is built-in to the activity. My own personal trajectory towards understanding and appreciating mathematical equations came only after years of programming computer animations, at first only for the sake of aesthetics. I came up with my own distilled bits, which often expressed a concept in an elegant way.

The point is: only after having had the experience of creation did these distilled bits mean anything to me. That is what math is about.

And THAT is the philosophical basis for the revolution in math that needs to take place in our schools. Ken Fan, who founded a math club for girls in Cambridge Mass, says: “I am concerned that the way math is typically taught in school in the US often fails to acknowledge the extraordinary differences in the way we think – too often, schools demand that students solve their assignments in very specific, overly rigid ways.”

I would even go a step further and ask, why must we always “solve” something? Why must there always be a “problem”? Is that the essence of mathematical activity? Can’t math be based upon a paradigm of creation?

This is a new blog and this my first blog post! I am planning on touching upon many topics. I am a Math Flunky who discovered Real Math despite my education. I have a story to tell. And I have reason to believe that my story is not at all original.

Stay tuned for posts about fractals, Buffon’s Needle, the golden ratio, locusts, the geometry of sex, multihomuncularity, and why we love trees.

But mostly, I’ll just be showing you a bunch of pictures.

-Jeffrey

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3 thoughts on “What is Visual Mathematics?

  1. Hi Jeffrey! Exciting stuff! I share your views on math, and I’ve been a math education professional for over 20 years. I am also a digital artist. I’d be careful saying you hate rules — you really don’t. I think you hate rules without reason or purpose! Every picture you make is according to rules. And every you picture you create is a solution to a problem you created. In fact, every step of your process is a series of small problems that you’re finding solutions for! I don’t think we should hate on rules and solutions — rules produce amazing artwork and are the structure for math. Rules are toys to play with!

    Looking forward to reading more and seeing more of your stuff!

    Mike

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