Page 181 - A Mind For Numbers: How to Excel at Math and Science

you can feel what’s behind the f as well. Force has built into it a heaving oomph
(acceleration), against the lazy mass of the boulder.
Let’s build on that just a wee bit more. The term work in physics means
energy. We do work (that is, we supply energy) when we push (force) something
through a distance. We can encrypt that with poetic simplicity: w = f×d. Once
we see w for work, then we can imagine with our mind’s eye, and even our
body’s feelings, what’s behind it. Ultimately, we can distill a line of equation

poetry that looks like this:

w
w = f·d
w = (ma)·d

Symbols and equations, in other words, have a hidden text that lies beneath
them—a meaning that becomes clear once you are more familiar with the ideas.

Although they may not phrase it this way, scientists often see equations as a form
of poetry, a shorthand way to symbolize what they are trying to see and
understand. Observant people recognize the depth of a piece of poetry—it can
have many possible meanings. In just the same way, maturing students gradually
learn to see the hidden meaning of an equation with their mind’s eye and even to

intuit different interpretations. It’s no surprise to learn that graphs, tables, and
other visuals also contain hidden meaning—meaning that can be even more
richly represented in the mind’s eye than on the page.

Simplify and Personalize Whatever You Are Studying

We’ve alluded to this before, but it’s worth revisiting now that we’ve got better
insight into how to imagine the ideas that underlie equations. One of the most
important things we can do when we are trying to learn math and science is

to bring the abstract ideas to life in our minds. Santiago Ramón y Cajal, for
example, treated the microscopic scenes before him as if they were inhabited by
7
living creatures that hoped and dreamed just as people themselves do. Cajal’s
colleague and friend, Sir Charles Sherrington, who coined the word synapse, told
friends that he had never met another scientist who had this intense ability to
breathe life into his work. Sherrington wondered whether this might have been a

key contributing factor to Cajal’s level of success.