Nature's Patterns

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 8^th 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.