Biology and Chaos

In order to be in good health, every system in the body (including the systems we haven't discovered yet) must be functioning well. Furthermore, the states of each system must be in sync with each other so that they will keep functioning well for a reasonable period of time. If the lungs are working faster than the muscles, the blood will gain too much oxygen and lose too much carbon dioxide, which will soon throw several systems off balance. But if all your systems are working well, and working together well, then your health will be good.

An automobile can be analyzed piece by piece. If the battery is dead, the headlights won't work; the burning gasoline pushes on the piston, which makes the wheels turn; and so on. A biological organism is not so simple. Frequently there is no clear boundary between the parts--one part may have several functions, and the whole system is in constant flux. A simple mechanical analysis will miss subtleties of operation. In fact, there is a whole new branch of mathematics called chaos that had to be invented to deal with systems like this.

You may have heard of the "butterfly effect"--a butterfly flapping its wings in China may create an air current that grows into a hurricane months later. A chaotic system, such as the weather or the human body, is inherently unpredictable: no matter how precisely you know its starting state, you can't tell what it will do in the future. (As we'll see later, most butterflies do not cause hurricanes--the point is that a single butterfly can sometimes make a big difference.) In fact, the body seems to depend on chaos. Normally the timing of the heartbeat is chaotic; if it ever becomes more regular, the person is about to have a heart attack. (References are at the end of this article.)

Suppose you wanted to study the body's response to exercise. You could look at the effect of blood oxygen level on breathing rate by making a graph with oxygen level on one axis and breathing rate on the other. Measure each quantity at one-minute intervals, plot the resulting points on the graph, and draw a line between successive points. If the relationship were perfectly simple, the graph would show a diagonal line: breathing rate would increase when oxygen level went down, and decrease as oxygen level recovered. In fact, because breathing affects oxygen level with some delay, the graph will show a cycle: first the oxygen decreases, then breathing increases, then oxygen increases, then breathing decreases, and around and around it goes. On the graph, this cycle would appear as an oval. Other factors would be deforming the shape. Over time, you would notice that the tracing crossed itself repeatedly. And you'd see something else: there would be more than one oval on the graph, representing states of waking, sleep, and so on, and the lines running from one oval to another would themselves be interestingly complex. If you did the experiment for years, you would find that all the lines stayed within a certain area of the graph: the breathing rate would never be above, say, 120 breaths per minute or below one breath every three minutes.

Now consider all the vast array of bodily mechanisms and substances. You could make a 3-D graph by adding insulin to your list of things to measure. But there are hundreds of hormones in the body, as well as other chemicals, temperature (core and extremity), bacterial counts, and physical conditions including scarring and posture. You would have to make a 300-D graph! If you could do such a thing, the shape on the graph would be vastly more complex than a few ovals. Even if you could make the graph, it's not clear how much you could learn from it--the graph covers so many possibilities, and the line you plot would be so small in comparison, that even several lifetimes of data could only explore a tiny fraction of the possible states. And don't forget that the body is chaotic: even if another body seemed to begin in a similar state, it would inevitably trace a different course through the graph.

If the body is chaotic, how can it keep functioning for years at a time in a changing environment? There is a mechanism called "homeostasis" that tends to pull things back to nominal levels. If the blood sugar gets too high, extra insulin is released. If the core temperature gets too low, blood vessels in the skin contract to save heat. But even with homeostasis, there are things that can go wrong if the body is pushed too far out of whack--vicious cycles the mechanisms of the body may enter. Medicine has named and studied many of them: diabetic coma, toxic shock, fibrillation, epilepsy, Cheyne-Stokes breathing, and death. Happily, many of these conditions are reversible with a big enough push in the right direction; the next section will explore the implications of that.