(On Screen): Chaos theory is fascinating to me. As a systems engineer, I'm well aware of how complex they can be, and how difficult it can be to understand how a complex system will respond to a particular change in the operating environment. I also know that such systems are everywhere, and that they profoundly affect every aspects of our lives.
Indeed, "our lives" are themselves complex systems. The biological processes involved in life, and the neural processes involved in thought, are extraordinarily complex. So one reason I am fascinated by chaos theory is that it has real, day-to-day significance. But it isn't the only reason why complex systems are, well, "challenging."
The way even a moderately complex system responds to changes in environment is often totally counterintuitive. It's certainly something that doctors run into all the time. Take, for example, hormone replacement therapy. The adrenal glands produce both estrogen and testosterone in small quantities in all healthy humans, including boys and girls and women. But at puberty in males, the testicles begin to produce testosterone at a much higher rate, and the blood level of testosterone in men is much higher. It is not, however, stable.
For one thing, it varies quite a lot over the course of each day. In most men it peaks in the morning and is at its lowest in the early evening, and can vary as much as 2:1. It also varies over the course of a year, peaking in late summer. As a man ages, the average level tends to drop, and in general young men have higher blood levels than older men do.
But disease or injury or poor nutrition or a variety of other insults can make the level drop significantly, and that affects a man's mental and physical health in a lot of ways. Pharmaceutical companies learned to synthesize testosterone and developed ways to administer it to men whose testosterone levels were too low. (It was a tough problem, because like most hormones it is metabolized quite rapidly by the liver. There were a number of approaches eventually found to deal with this, which I won't go into.)
Suppose you're a doctor, and you have a male patient whose blood testosterone level seems to be about two thirds what you think it ought to be. Suppose that you think this is negatively affecting his health. So you write a prescription for one of the forms of testosterone at a dosage level which you estimate will result in absorption of a quantity of testosterone equal to the apparent deficit. In other words, you try to supply the testosterone which isn't being produced naturally, in hopes of increasing the overall blood testosterone level in that patient by about 50% to bring him back into the normal range. What will you actually see, clinically?
The surprising answer is that in the majority of patients, there will be no significant long-term change in blood testosterone level at all. That's because you've run into a regulation mechanism.
One region of the human brain is called the hypothalamus. It monitors and regulates a lot of things such as body temperature. "Regulate" doesn't mean "hold constant"; our body temperature drops considerably when we're asleep, for instance. It often rises when we're sick. "Sleep" is controlled by a hormone, and the hypothalamus responds to that hormone by turning down the temperature. "Sick" also turns out to be a hormone, and this one is released by certain white blood cells. The hypothalamus reacts by turning up the temperature.
In men, the hypothalamus monitors blood testosterone level, and regulates it. It releases Gonadotropin Releasing Hormone (GnRH), and increases the GnRH if the testosterone level is too low, while decreasing the GnRH if it is too high. The pituitary responds to GnRH by producing two hormones called Leutinizing Hormone (LH) and Follicle Stimulation Hormone (FSH), with their levels proportional to the detected level of GnRH. The blood level of FSH controls the rate of sperm production in the testicles, and the blood level of LH controls production of testosterone, also in the testicles.
This turns out to be a classic negative feedback control loop. When you, the doctor, introduce synthetic testosterone into the male patient's system at a rate of about 50% of his natural production rate, his hypothalamus decides that the blood testosterone level is "too high" and responds by producing less GnRH, which causes the pituitary to produce less LH, meaning that the testicles produce less testosterone. You hoped you'd raise the blood level of testosterone by 50%, but what you actually did was to reduce natural production of testosterone by 50%, for a net gain of zero. To actually increase the blood level, you first have to "rail" the feedback loop.
This feedback loop also functions in women between menarche and menopause, but the behavior is radically different. Where in men it's incremental/proportional negative feedback, in women the blood level of these three hormones are step functions with relatively slow transition slew rates, uneven duty cycles and a overall cycle period we call "a period". During part of a woman's period, blood level of GnRH/LH/FSH is quite high, and during other parts it's negligible. That's also true for the blood level of estrogen, except that its curve is approximately the inverse of the other one. (And during pregnancy, progesterone produced by the placenta dominates, and the other four are all shut off.)