delara news
Delaware Amateur Radio Association, Delaware OH VOL 37 NUMBER 8

2x + 3y = ?
Joe Fischer, AA8TA
I read Michael Gerson’s review of a book called “Origin Story” by David Christian.
The review includes this excerpt:
Christian has achieved something remarkable: an engaging guide to the physics,
chemistry, biology, anthropology, linguistics and sociology that constitute the story of
history itself. The author practices what he calls “Big History”— gathering the Big
Bang, the advent of molecules, plate tectonics, eukaryotes, dinosaurs, Homo
sapiens, climate dynamics and globalization into one sweeping arc. In roughly 300
pages. With no equations.
I emphasized the last sentence, the one that caught my eye – “no equations.” What
is so bad about equations?
My major in college was electrical engineering which led to undergraduate and
graduate degrees in that field. During those years, our heads barely came up out
the equation pond – engineering is all about mathematics and science. So, I have a
bit of familiarity with equations and the fear of them was shaken out of me quickly
when I entered the collegiate academic world.
It is sad that so many people fear math, I think young children hear their parents,
siblings, other family members, people on TV and many other older people say that
math is hard, it is evil, a person has to possess super powers to understand it and
on and on. And if you are a girl, then steer clear – don’t even think about it.
What a disservice, especially the part about girls. It is no wonder that kids reach
high school and assume that any math class that they take is going to lead to a bad
grade and they will not learn anything.
Math is just a language, like any language that is written. It has a structure like the
nouns, verbs and sentence syntax that English has. Printed music is a language
which conveys ideas and ways of playing a song. Math is just a way of concisely
expressing a scientific concept. I never hear children, and especially girls, being
dissuaded from pursuing music because musical scales are impossible to
understand.
Let’s consider this: perhaps we are interested in how long it takes to hit the ground
and what velocity an object achieves if it is dropped from various heights. We could
gather up a variety of objects and drop them from many different heights, measure
how long it takes them to hit the ground and what their final velocity is. Then we
write all that in a big table listing all the parameters and values for each object and
height.
What a complicated mess that would be! What if we wanted to know the velocity of
some object at a height where neither was included in the test? Rather than using a
lot of confusing words and tables of information that does not contain what we have,
let’s just turn to physics and math:
and
That messy table replaced by two simple equations. “g” is the gravitational constant,
“t” is time, “d” is distance and “v” is velocity. We can decide what units we want to
use and look up the appropriate value for “g”, which is a constant.
We can rearrange these equations to suit the data we have and can use any
distance, or other variables, we want. We are not constrained to whatever is in that
messy table from earlier.
We can also quickly form some conclusions by looking at those equations: it does
not matter what kind of object we drop; a marble and a bowling ball lead to the same
results. It might take a while to reach those same conclusions from a page of tables
or complicated test words.
We can also look at that and ask: “where is the air resistance?” Is there an upper
limit on the velocity, in other words, if the distance or time is high enough, could an
object go supersonic? We quickly have the beginnings of more investigation and
more equations that quickly tell an interesting story.
There is nothing to fear from math! It is fun, the things one can do with numbers are
fascinating. How does radio work? Maxwell’s equations are pretty concise and tell
quite a story in just eight equations.
If you are a girl, or a woman, this should be a language that makes you swoon. It
should if you are a boy or man, too.