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This paper was written as an assignment for Ian Walton's Math G - Math for liberal Arts Students - at Mission College.

To explore other such papers go to the Math G Projects Page.

This paper was submitted by Nomi Goodnight for her Spring 2002 Math G at Mission College.

If you use material from this paper, please acknowledge it.

Nomi Goodnight

Video Report

3/6/02

Dr. Ian Walton

Video #3 Patterns of Nature

As a child, I recall having dreams both wonderful and terrible in which oversized insects chased me into my house and kept me trapped there as they buzzed around the windows, banging up against the glass. Thankfully, these large insects were not clever enough to find their way inside. Thus I was safe, but left wondering when I awoke whether or not such creatures could exist. It took me nearly twenty-two years to stumble across the answer. Although I admit that I did very little active searching as a child, and soon put the question in the back of my mind, as I watched the first segment of the video, I was reminded of that old, unanswered question.

A biologist in the video, by the name of LaBarbara is a fan of those old, camp horror movies in which towns are invaded by such creatures as giant moths and grasshoppers, and an ape the size of a house. He became interested in discovering whether or not the laws of nature would permit such an increase in size. He hearkened back to Galileo’s findings that “Nature is governed by logic. As bones grow, weight increases disproportionately.” In other words, volume increases at a faster rate than area.

According to this principle, it would be impossible for a whopping grasshopper or ape to stand, much less locomote. Its bones would not be strong enough to support its body weight. So, we can all rest that easy that an invasion of automobile sized ants is not forthcoming!

As it is, even ordinary sized creatures put enormous pressure on their bones on a daily basis. According to LaBarbara, by simply walking, humans, and other mammals stress their bones to 25-30% of the breaking point. The reason why the bones don’t break is because of the body’s ability to switch posture. It is an absolute wonder that our bodies are designed in such a manner. Imperfect, yet miraculously functional. We are surely more fragile and fallible than many of us may be willing to believe.

I must pause here to say that since the beginning of this semester I have been consistently amazed by the degree to which mathematics feature in the world. This video has been but one eye opener in a string of similar realizations which have helped me come to the conclusion that we most certainly live in a world of numbers, powered by mathematics. I am quickly developing an entirely new appreciation for the necessity of learning about math.

Years ago, my mother used to read me The Just So Stories by Rudyard Kipling. One of the stories, “How the Leopard Got His Spots” was the basis for a scientific enquiry by Mathematician and Biologist James Murray. In the story, Kipling says that the leopard’s spots were made by an African, who used the dye from his dark skin to paint the spots on the leopard with his fingertips. Murray read the story to his daughter, who wanted to know how the leopard really got his spots. Upon researching the subject and performing many experiments, Murray discovered that the spots are a product of a chemical reaction! This is just the sort of valuable information that can be used to spark a student’s interest in math and science at an early age. What kid doesn’t like animals? Not to mention the thought that if a chemical reaction is the cause, would it not be possible for people to perhaps have spots and stripes like those crazy characters in science fiction movies? That information alone would have sparked my imagination as a child. If only facts like this were incorporated into the classroom when I was younger, perhaps I would have developed a healthy interest in math, rather than a phobic dread! I have to admit that I find this as well as all of the other information in the video quite mind boggling. The very fact that mathematicians, scientists and biologists have the wherewithal to make such discoveries is almost too much for me to comprehend! At this point in my learning experience I am just grateful to have the opportunity to be exposed to this kind of knowledge. The closest I can come to adequately describing how I feel is to say that it is very much like coming across an endless array of dominos, all set up one before the other in such a manner that should you touch one of the dominos, causing it to fall, it would set off a chain reaction that would travel eternally through all the dominos, causing each one to fall in rapid succession. In this case, each domino represents a way in which mathematics touch my life, or a way in which they are used in the world. Consequently, the pleasure that I felt at learning each new and wondrous fact is akin to the elation I once felt as a child, as I watched a row of dominos fall in the physical world.

One of the amazing properties of mathematics is that sometimes a discovery is made and expounded upon, and thought to have been fully explored, then hundreds of years down the road, it proves to be the key to unlocking a new discovery! Such is the case with knot theory. Knot theory is being used by scientists to try and untangle the mysteries of viruses and how they manipulate DNA. When a virus enters the body it forces the DNA to split. The split ends then re-attach themselves to form a knot. These knots are now being closely examined in the hope that they will provide clues to how we may one day stop the spread of deadly viruses such as HIV and Ebola. My head is spinning! Dare I say that all things can be connected by math?!

Undoubtedly, math governs more than I ever thought possible. Even the place most beloved to me since childhood, the great outdoors is touched by math. Many patterns can be found in nature. One need only look closely at a flower to see living proof of the existence of such patterns. What may not be as obvious is that theses patterns can be described mathematically through the use of L systems. L systems are repeating rules. In the video, Dr. P uses L systems to build an accurate replica of a flower on his computer. These systems also pertain to the mysteriously beautiful patterns known as fractals, which I am still a bit mystified by and look forward to exploring further in the future.

In fact, this video has sparked my interest in a variety of new subjects. It has provided a foundation on which to build further knowledge. I actually watched two of the videos in the series. I found them both quite enjoyable because each one took a different approach to conveying the information to the viewer. Video # 3 took a “sight seeing” approach to mathematics. Rather than spend an entire hour explaining one topic, it allows the viewer to spend shorter amounts of time learning significant information about a variety of math/nature related subjects. This approach worked well for me because I am just beginning to learn about some of ways in which math applies to the world. The only shortcoming that I could see was that if I were a more advanced math student, who wanted to hone in on one particular aspect of math and nature, I don’t believe the video would have been as helpful. Although it did serve to spark many ideas about which subjects I might choose to pursue further in the future and that is always useful.

In fact, the information provided by the video was phrased in terms that were easy for a novice such as myself to understand. Consequently, a few days after watching the video, when my husband and I went on a hike at the Fremont-Older Open Space Preserve, I felt compelled to share my newfound knowledge with him. I found myself explaining the concept that it would be impossible for the giant creatures of yesteryear’s horror movies to exist. He kept shaking his head in disbelief as I tried to make clear the concept that mass and volume increase at different rates. He just didn’t understand! He kept insisting that all parts of an oversized insect or mammal must grow proportionately. Interestingly, I now found myself in the position of teacher, searching my mind to come up with a way to illustrate the idea in terms that he could agree with. (This was good practice for me, as I am working toward getting my teaching credentials.) After a few minutes of silence, I asked him to imagine a thin plastic container, filled with water. I told him that the container represented mass and the water represented volume. Next I proposed that both the mass and volume be doubled. The thin container would become only slightly thicker, whereas the water would become much too heavy for the container to bear. And wonder of wonders, my explanation hit home!

As we continued our hike, I shared more of what I learned from the video. I explained about L systems and used one of the examples from the video to show him what these systems are. I pointed to a tree and told him how the branches’ patterns repeat themselves on a smaller and smaller scale. I felt that the math facts served to enhance our experience, rather than to dampen it, as I once would have expected.

As a direct result of my introduction to the Life By The Numbers series, I was able to expand my knowledge of mathematics in nature, biology and science. I have long been a fan of PBS, I remember watching the station as a child. Therefore, it comes as no surprise that this video would provide a quality learning experience. What did come as a shock was how much I actually enjoyed the presentation as well as the fact that I actually retained the knowledge with very little effort. This, as far as I am concerned, is a major breakthrough as it pertains to mathematics! Any medium that transmits mathematical knowledge in an interesting and absorbing way is certainly worth sharing. My only regret is that I grew to be an adult before realizing the absolute importance of mathematics.

As a future teacher, I am now gathering the skills that I will need in order to spark a new generation’s interest in math. I plan to earn a multiple subject credential, which means that I will be teaching math. There are plenty of “real” world math applications that tie into everyday life. Whether one is an adult or a child, math need not be boring. With the right teaching methods and media backup, such as the PBS videos, math can open up a whole new world. Those who are willing to pursue the answers to questions both common and obscure may find that mathematics hold the answers.

This paper was submitted by Nomi Goodnight for her Spring 2002 Math G at Mission College.

If you use material from this paper, please acknowledge it.