Page 180 - A Mind For Numbers: How to Excel at Math and Science

evidenced in modern animated movie-making magic. Coulton’s poetry also
alludes to the idea, embedded in Mandelbrot’s work, that tiny, subtle shifts in
one part of the universe ultimately affect everything else.
The more you examine Coulton’s words, the more ways you can see it
applied to various aspects of life—these meanings become clearer the more you
know and understand Mandelbrot’s work.
There are hidden meanings in equations, just as there are in poetry. If

you are a novice looking at an equation in physics, and you’re not taught how to
see the life underlying the symbols, the lines will look dead to you. It is when
you begin to learn and supply the hidden text that the meaning slips, slides, then
finally leaps to life.
In a classic paper, physicist Jeffrey Prentis compares how a brand-new
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student of physics and a mature physicist look at equations. The equation is
seen by the novice as just one more thing to memorize in a vast collection of
unrelated equations. More advanced students and physicists, however, see with
their mind’s eye the meaning beneath the equation, including how it fits into the
big picture, and even a sense of how the parts of the equation feel.

“A mathematician who is not at the same time something of a poet will never be a full
mathematician.”
—German mathematician Karl Weierstrass

When you see the letter a, for acceleration, you might feel a sense of pressing on
the accelerator in a car. Zounds! Feel the car’s acceleration pressing you back
against the seat.
Do you need to bring these feelings to mind every time you look at the letter
a? Of course not; you don’t want to drive yourself crazy remembering every

little detail underlying your learning. But that sense of pressing acceleration
should hover as a chunk in the back of your mind, ready to slip into working
memory if you’re trying to analyze the meaning of a when you see it roaming
around in an equation.
Similarly, when you see m, for mass, you might feel the inertial laziness of a
fifty-pound boulder—it takes a lot to get it moving. When you see the letter f, for
force, you might see with your mind’s eye what lies underneath force—that it

depends on both mass and acceleration: m·a, as in the equation f = m·a. Perhaps