Energy and Human Ambitions on a Finite Planet, 2021a

A.2 Forget the Rules 361
Americans is roughly 15%. A month is about 8% (0.08) of a year. Six
goes into 100 a little more than 16 times. Four quarters make up a
dollar. π fits into 10 about π times. Each student in a 30-student class
represents about 3% of the class population.
Some students view math <strong>and</strong> numbers as dangerous, unwelcoming
territory—maybe like deep water in which they might drown. But think
about dolphins, who not only are not afraid to immerse themselves in
deep water (numbers), but frolic <strong>and</strong> play on its surface. Numbers can
be that way too: flinging them this way <strong>and</strong> that to see that a calculation
makes sense in lots of different ways. <strong>Human</strong>s are not natural-born
swimmers, but we can learn to be comfortable in water. Likewise, we
can learn to be quantitatively comfortable <strong>and</strong> even have fun messing
around. So get your floaties on <strong>and</strong> jump in!
A.2 Forget the Rules
Math, in some ways, is just an expression of truth—a logic about
relationships between numbers <strong>and</strong> their manipulations. It is easy to
be overwhelmed by all the rules taught to us in math classes through
the years, <strong>and</strong> students 7 can lose sight of the simple <strong>and</strong> verifiable logic
underneath it all. Most math mistakes come from faulty or deteriorating
memorization. The good news is that we can usually do simple tests to
make sure we’re getting it right. The lesson is not to memorize math! Math
makes logical sense, <strong>and</strong> we can create the right rules by underst<strong>and</strong>ing
a few core concepts. This section attempts to teach this skill.
Consider for a moment the concept of language (<strong>and</strong> see Box A.1 for
fun examples). Language is riddled with rules of grammar <strong>and</strong> spelling,
yet we learn to speak without needing to know what adjectives or
prepositions are. We learn the rules later, after speaking is secondnature.
And unlike math, the rules of language can defy logic <strong>and</strong> have
many exceptions. In this sense, math is much easier <strong>and</strong> more natural.
It is the language of the universe. We would likely share no words in
common with an alien species 8 , but we can be sure that we would agree
on the integers, how they add <strong>and</strong> multiply, all the way up through
calculus <strong>and</strong> other advanced mathematical concepts. We can use its
innate nature to expose the rules for ourselves.
7: . . . teachers, too!
8: Except, perhaps we would learn that we
inexplicably share the word “sock.”
Box A.1: Rules of Language
Let’s step aside for a moment to explore how rules of language
are obvious to us without explicit thought. 9 Consider the following
constructions: trlaqtoef; flort; aoipw; squeet; yparumd. None of
these are English words, but only two of them are even worthy of
consideration as viable words. The others violate “unspoken” rules
9: . . . acknowledging that this exercise may
be less intuitively obvious to non-native
English speakers
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.