The second half of the 20th century brought many scientific developments to us, including what many people consider to be the revolutionary movement of Chaos Theory. Chaos is a complex, rich and diverse theory encompassing nearly every field of science. In order to stay on track I’ll only be discussing one aspect of Chaos, and it’s implications on human anatomy, physiology and medicine.
In the 1970’s a Polish mathematician named Benoit Mandelbrot looked at the shapes of nature and concluded that the geometry we learn in mathematics is severely lacking when it comes to describing nature: clouds aren’t spheres, mountains aren’t cones. Nature seemingly works in random, chaotic patterns the likes of which science and mathematics could not explain. So like all great geniuses he decided to revolutionize the field in order to better account for and describe the geometry of nature.
In many ways it started when he tried to address the problem of scale when measuring a coastline. How long is the coastline of Britain? For Mandelbrot the answer is that any coastline is infinitely long. Whaaaa? Well it all depends on the scale with which you use to measure.
Let’s say we paid someone to take a yard stick and walk along the entire coast of Britain taking measurements in the unit of 1 yard; the answer is just going to be an approximation because it’s really hard to measure all of those nooks and cranny’s with a yard stick and therefore we have to leave them out. So let’s say we do it again, except the unit of measurement will be 1 foot. The end number will be greater than the yard measurement because the foot is able to capture more detail than the cumbersome yard stick. But even then it’s just an approximation because we still can’t measure all of the bends and cracks and coves along the coastline with a ruler. The person measures the entire coastline AGAIN but using 6 inches as the unit of measurement. This number will be greater than the yard figures and greater than the foot results, but it still won’t be anywhere near accurate enough to say with certainty “The coast of Britain is X units long.” The theme this problem is trying to demonstrate is that of scale. Satellite measurements are going to be significantly different from a person walking the entire coast with a ruler. However, our common sense is going to tell us that no matter how different the numbers are from various scales of measurement, all of the numbers will converge to what the actual length is. But will they? If the coastline was a straight line then perhaps, but since nature is at work here Mandelbrot discovered that the smaller the scale, the more infinite space becomes revealed. The shapes of nature couldn’t be accounted for in Euclidean geometry and this coastline quandary proved it. Nature operates in shapes of roughness, brokenness. He used the word ‘Fractal’ to describe these shapes. The coastline problem also brought up an important point that defied all mathematics: how can a finite shape like Britain have an infinite surface area? That doesn’t make any sense! The answer was found in the self repeating nature of fractal geometry, and this is where things get really trippy.
Take a triangle, in the middle of each side add an identical triangle 1/3 the size of the original and repeat infinitely. The surface area becomes more complex and the shape becomes that of a snowflake. This shape was first described in 1904 by the Swedish scientist Helge von Koch and is known as a Koch Curve, and it presents the answer to the coastline problem: infinite surface area in a finite space. If you draw a perfect circle around the Koch Curve you’ll find that it will never cross the line. Infinity contained in a self-similar repeating structure based on scale, and it absolutely blows my mind. I can go on and on about fractals and how amazing they are, but I’m sure you’re wondering when I’ll get to the point and here comes the medicine.
Mandelbrot highlighted the importance of scale and this perspective changed how many scientists in a variety of different fields view processes and phenomena. The coastline of Britain or the slope of a mountain looks the same at every scale of examination, as do clouds. Geologists discovered that smaller earthquakes behaved exactly like large earthquakes, small storms acted like large ones. The economic trend of a year looked the same as a month, as a week, as a day; it all came down to the scale with which they were examined.
Your circulatory system, from the aorta to arteries to arterioles to capillaries and back up the venous side form a similar continuum. They start off massive and branch and branch again, becoming smaller with each branching until they become so narrow in your capillaries that the red blood cells slowly flow through them single file just in order to fit. The mechanism of how your blood vessels branch is fractal in nature. Physiologically speaking your cells depend on oxygen, without it they die and if enough of them die, you die. In order to effectively oxygenate your tissues your circulatory system has to perform an impressive feat of dimensional architecture. Like the Koch Curve, packing infinite surface area into a finite space, your circulatory system utilizes fractal geometry through branching so that no cell in your body is never more than 3 or 4 cells away from a blood cell. And the amazing thing about this feat is that your blood vessels and blood take up very little space: no more than around 5% of your body!
It doesn’t stop there, fractal geometry is found everywhere in the human body. Your digestive tract is filled with waves of tissue called villi. Then there are microvilli on the villi, etc. It’s the Koch Curve once again, increasing the surface area of your digestive tract to allow for more absorption of nutrients.
Your lungs need to pack a vast amount of surface area (about the size of a tennis court) into your thoracic cavity. This is really important to note because the amount of surface area in your lungs that permit perfusion of oxygen and diffusion of carbon dioxide is the subject of pulmonary pathology. Like the circulatory system, your lungs use fractal branching (not exponential branching, as previously thought) from your bronchus to your alveoli.
The urinary collecting system is fractal, the biliary duct of the liver is fractal. The network of fibers in your heart carrying electrical signals to cause muscle contraction are fractal.
Our bodies are Chaotic systems; what was once considered random and unmeasurable was found to be orderly and precise by these newly observed laws of nature.