Theos-Talk Archives (October 1995 Message tl00504)

Leisel:

Glad you enjoyed the article by Dr. Hong:

<about non-linear equations
& I still don't know what they are. Can you explain it to me, who
doesn't know much about higher mathematics?>

Well, considering that one could take many years of formal training in
mathematics, it would be hard to answer your question here, but I can try at
least to give you a simple idea of what is going on.

There are linear equations and nonlinear equations. Simply stated, linear
equations give you a straight line when you make a graph of them. There is
nothing mysterious going on here. It is that simple. Nonlinear equations do
not give a line when they are graphed: the give some kind of curve such as a
sine curve or an exponential curve, to name only two possiblities.

The reason Dr. Hong's statments are significant is that, for most of the history
of science, scientists have only used linear equations. This is because linear
equations are easy to solve. Most nonlinear equations can only be solved by
computers, and seeing as there were no computers for most of science's history,
that meant that there were many equations people just couldn't solve.

So, since these nonlinear equations couldn't be solved, scientists for the most
part ignored anything that could not be described by linear equations (which is
what Dr. Hong sarcastically called "the privilage of reductionism"). And its
been this way pretty much until the 1960s with the wide spread use of
calculators and computers. With computers, the nonlinear equations are very
easy to solve. And since scientists have begun working with nonlinear equations
they have discovered that for many things, the nonlinear equations work better
at describing nature than the linear equations did. As a matter of fact, the
linear equations didn't work very well anyway, but, until the computer, linear
equations were all that people could solve.

So, I've skipped the "what" about nonlinear equations and just went to the
significance and a little history of whats going on here. I hope this helps.

Basically, math is a kind of window on to how nature works. When you use math
expressions, these tell you how things are related. Like Einstein's famous
E=mc2 equation. This equation reads: "energy equals mass multiplied by the
square of the speed of light". So, this equation tells you that energy is
related to mass, and the factor that relates these is the speed of light. Thus,
the math expression gives one insight on how the various parts of nature are
related.

Again, Liesel, I don't have time to write a book about this, but I hope the
little I said here helps put this in perspective for you.

Best wishes,

Don