Monday, March 21, 2005

The Null Solution

Perhaps you have been following the Terri Schiavo case lately, in which her husband, claiming she is a vegetable, seeks to kill her by having her feeding tube removed. The U.S. Senate recently debated the issue:

Mr. WYDEN. Mr. President, the Senate is now addressing probably the most gut-wrenching decision that an American family can ever face. Without even a single hearing, without any debate whatever, the Senate is tackling an extraordinarily sensitive concern that involves morals and ethics and religious principles, and this troubles me greatly. (Congressional Record, March 17, 2005)

The life of a woman unable to speak for herself has become a "decision" instead of an inalienable right.

The idea of death as a solution has gained wide acceptance in our self-indulgent culture that finds no meaning to life outside momentary enjoyment. Michael Medved wrote a great column in USA Today last week, in which he asks "Has suicide become the pop culture flavor of the month?" and enumerates recent instances of the zeitgeist's promotion of suicide as "brave."

The idea of "solving" life's problems by refusing to live reminded me of the most underrated field of mathematics, linear algebra. (The name is boring, you say. I know: "linear" sounds soporifically straightforward and "algebra" reminds you of your nightmare high-school class.) Trust me: next to geometry, this is the most insightful field of mathematics requiring only limited mathematical abstraction.

There are a number of useful insights in linear algebra that provide a wonderful basis for better understanding how the world works. (I'll leave a neat example to the comments and get back to the point of this post.)

There is a common solution for every* set of linear equations, called The Null Solution, which consists of setting every parameter to zero. The Null Solution is also known as the trivial solution because it is uninteresting: any moron can slap it down.

Death is the Null Solution to all of life's problems. What is the one sure way to rid the world of hunger, poverty, illiteracy, anxiety, terrorism and bad manners and bad breath? Global suicide.

A professor will very rightly flunk a student who enters the null solution for every problem of an exam. As in linear algebra, life's null solution is "trivial" and no solution at all.

Choosing death is not brave. It's cynical and selfish.

*Homogeneous equations, the most common form.

1 comment:

Lawrence Gage said...

Linear algebra allows one to find the values of a number of unknown parameters that satisfy a number of (linear) algebraic equations. Solving a set of linear equations is equivalent to finding the intersection of the lines that the equations describe (the number of variables is the "dimension" of the space in which the lines live).

An example: the shower. Every shower has to control two parameters, temperature and flow-rate, but there are number of different designs that allow the bather to specify the two parameters in different ways.

Imagine the two parameters to describe a two-dimensional space, a plane, like the monitor in front of you. Let's say the vertical direction specifies temperature and the horizontal direction specifies flow. The easiest showers to use (and understand) have a single knob to control temperature and flow-rate, a bit like a using your mouse to the right to increase the flow and upward to increase the temperature.

(One could also have an "etch-a-sketch" arrangement, in which one knob controls flow and the other temperature.)

Other showers have separate knobs to control hot and cold flow. One can increase the temperature without changing flow by increasing hot-water flow while correspondingly decreasing cold-water flow. One can increase flow without changing temperature by increasing the volume of both hot and cold by the same amount.

The showers that I hate the most have only one valve that controls both volume and temperature. These are the ones you find in locker-rooms and cheap hotels: turning the knob past a certain mark starts the water flow cold; continuing to turn the valve increases the water temperature. (I call them single-degree-of-freedom showers.) It's that initial and unavoidable cold spurt that annoys me.

You can apply similar reasoning to the controls of any device, for example, a radio or a stereo.