HS #30 2018.1.2
Nature’s Patterns
What’s happening around you? Perhaps people walking,
talking, a clock pendulum swinging, icicles growing. Surprisingly, much of it
can be described with just four mathematical relationships.
The simplest is linear: as one thing changes, another
changes in proportion. Crickets provide
one interesting example. As the temperature rises, so does the rate of cricket
chirps. Count the chirps in 15 seconds
and add 37, and you’ve got the approximate temperature. Neat.
Edwin Hubble noticed a linear relationship between the
distance of galaxies from earth and the speed they are moving away from us. Since
there is no scientific reason to think that our galaxy (the Milky Way) is the
center of the universe, that means that all galaxies in the universe are moving
away from each other (similar to how ink spots on a rubber band all move away
from each other as the band is stretched). Extending that linear relationship
into the past, he was the first to posit that the universe began at a
particular point in time - now known to be about 13.8 billion years ago. All of
this from understanding simple linear relationships.
The second is parabolic. Throw a ball into the air (actually
works best if you remove the air) and you’ll produce a parabola. Ever see those
streams of water at the Holland 8th Street fountain (or the fountain
at the Detroit Airport)? Those are parabolas. When I first learned about them
in high school, I ran into physics class one day after using the rest room and
excitedly announced that I had just created a parabola. My physics teacher
wasn’t amused. The beautiful arcs made by the cables of the Mackinac Bridge are
parabolas.
The third is the exponential. Whereas linear growth comes
from repeatedly ADDING the same number, exponential growth happens when
repeatedly MULTIPLYING by the same number. Example: Suppose two technicians are hired for 5
weeks. The first requests $1
million/day. The second asks for a penny
the first day, two cents the second, doubling each day. Who makes out better? The second earns almost
ten times more. Three more weeks would dwarf the national debt. That’s the
power of exponential growth.
Savings accounts and investments grow exponentially (over
the long run) which is why I advise students to start saving and investing
early in life. Exponential growth gives
atomic explosions their power. When a neutron hits an atom, a couple more
neutrons are released which in turn hit other atoms. Something that simple
could destroy all human life.
That’s three, what’s the fourth? What pattern is missing? Hint:
It is the one most central to who you are.
The fourth relationship is periodic. Mathematics uses the trigonometric
relationships (sine and cosine) to describe periodicity. A periodic pattern is
one that, as the name suggests, repeats itself over and over.
Why are periodic patterns so important? Because many
processes in the natural world are periodic. We live our lives by them. Just
think: daily rotation of the earth, the work week, lunar/monthly cycles, tides,
annual seasons, generational cycles, menstrual and reproductive cycles, musical
vibrations, heart beats, election periods. We measure time itself by the cycles/vibrations
of a cesium atom. The regularity of Old Faithful and the other geysers has
intrigued people for generations.
Haley’s Comet comes periodically every 75 years. Mark Twain was born in
a Haley year and predicted that he’d die when it came again – and he did.
In our modern world, we are much less tied to the cycles of
nature than our ancestors. Nature’s cycles were so central to the ancient
Hebrews that they thought of time itself as being cyclical. The interest in
biorhythms is a modern counterpart.
These cycles are likely built into our DNA as with other
living creatures that periodically migrate, lose leaves, bloom, hibernate, and
reproduce. Cicadas mysteriously appear
regularly every seventeen years.
Owners of parrots are told not to put them in cylindrical
cages. Parrots need corners – points of reference - for their psychological
health. Similarly, cycles provide periodic reference points that serve as
reassuring anchors. Birthdays, New Years
Day, new academic year and (my favorite) annual time changes all provide
pivotal occasions for reflection and starting afresh.
Soren Kierkegaard observed, “Life can only be understood
backwards; but it must be lived forwards.” Cycles allow us to do both by
periodically pausing, assessing and then improving the next time around. As 2018 begins, we thus have opportunity to
glance backwards to learn from the past, and then charge headlong into the
future.
