MathDepartment, Mission College, Santa Clara, California
Go to Math Dept Main Page |Go to Mission College Main Page
This paper was written as an assignment for Ian Walton's Math G - Mathfor liberal Arts Students - at Mission College.
To explore other such papers go to theMath G Projects Page.
Nomi Goodnight
Video Report
3/6/02
Dr. Ian Walton
Video #3 Patterns of Nature
Asa child, I recall having dreams both wonderful and terrible in which oversizedinsects chased me into my house and kept me trapped there as they buzzed aroundthe windows, banging up against the glass. Thankfully, these large insects werenot clever enough to find their way inside. Thus I was safe, but left wonderingwhen I awoke whether or not such creatures could exist. It took me nearlytwenty-two years to stumble across the answer. Although I admit that I did verylittle active searching as a child, and soon put the question in the back of mymind, as I watched the first segment of the video, I was reminded of that old,unanswered question.
Abiologist in the video, by the name of LaBarbara is a fan of those old, camphorror movies in which towns are invaded by such creatures as giant moths andgrasshoppers, and an ape the size of a house. He became interested indiscovering whether or not the laws of nature would permit such an increase insize. He hearkened back to Galileo’s findings that “Nature isgoverned 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 awhopping grasshopper or ape to stand, much less locomote. Its bones would notbe strong enough to support its body weight. So, we can all rest that easy thatan invasion of automobile sized ants is not forthcoming!
Asit is, even ordinary sized creatures put enormous pressure on their bones on adaily basis. According to LaBarbara, by simply walking, humans, and othermammals stress their bones to 25-30% of the breaking point. The reason why thebones don’t break is because of the body’s ability to switchposture. It is an absolute wonder that our bodies are designed in such amanner. Imperfect, yet miraculously functional. We are surely more fragile andfallible than many of us may be willing to believe.
Imust pause here to say that since the beginning of this semester I have beenconsistently amazed by the degree to which mathematics feature in the world.This video has been but one eye opener in a string of similar realizationswhich have helped me come to the conclusion that we most certainly live in aworld of numbers, powered by mathematics. I am quickly developing an entirelynew appreciation for the necessity of learning about math.
Yearsago, 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 basisfor a scientific enquiry by Mathematician and Biologist James Murray. In thestory, Kipling says that the leopard’s spots were made by an African, whoused the dye from his dark skin to paint the spots on the leopard with hisfingertips. Murray read the story to his daughter, who wanted to know how theleopard really got his spots. Uponresearching the subject and performing many experiments, Murray discovered thatthe spots are a product of a chemical reaction! This is just the sort of valuable information that can beused 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 achemical reaction is the cause, would it not be possible for people to perhapshave spots and stripes like those crazy characters in science fiction movies?That information alone would have sparked my imagination as a child. If onlyfacts like this were incorporated into the classroom when I was younger,perhaps I would have developed a healthy interest in math, rather than a phobicdread! I have to admit that I find this as well as all of the other informationin the video quite mind boggling. The very fact that mathematicians, scientistsand biologists have the wherewithal to make such discoveries is almost too muchfor me to comprehend! At this point in my learning experience I am justgrateful to have the opportunity to be exposed to this kind of knowledge. Theclosest I can come to adequately describing how I feel is to say that it isvery much like coming across an endless array of dominos, all set up one beforethe other in such a manner that should you touch one of the dominos, causing itto fall, it would set off a chain reaction that would travel eternally throughall 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 inwhich they are used in the world. Consequently, the pleasure that I felt atlearning each new and wondrous fact is akin to the elation I once felt as achild, as I watched a row of dominos fall in the physical world.
Oneof the amazing properties of mathematics is that sometimes a discovery is madeand expounded upon, and thought to have been fully explored, then hundreds ofyears down the road, it proves to be the key to unlocking a new discovery! Suchis the case with knot theory. Knot theory is being used by scientists to tryand untangle the mysteries of viruses and how they manipulate DNA. When a virusenters the body it forces the DNA to split. The split ends then re-attachthemselves to form a knot. These knots are now being closely examined in thehope that they will provide clues to how we may one day stop the spread ofdeadly viruses such as HIV and Ebola. My head is spinning! Dare I say that allthings can be connected by math?!
Undoubtedly,math governs more than I ever thought possible. Even the place most beloved tome since childhood, the great outdoors is touched by math. Many patterns can befound in nature. One need only look closely at a flower to see living proof ofthe existence of such patterns. What may not be as obvious is that thesespatterns can be described mathematically through the use of L systems. Lsystems are repeating rules. In the video, Dr. P uses L systems to build anaccurate replica of a flower on his computer. These systems also pertain to themysteriously beautiful patterns known as fractals, which I am still a bitmystified by and look forward to exploring further in the future.
Infact, this video has sparked my interest in a variety of new subjects. It hasprovided a foundation on which to build further knowledge. I actually watchedtwo of the videos in the series. I found them both quite enjoyable because eachone took a different approach to conveying the information to the viewer.
Infact, the information provided by the video was phrased in terms that were easyfor a novice such as myself to understand. Consequently, a few days afterwatching the video, when my husband and I went on a hike at the Fremont-OlderOpen 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 giantcreatures of yesteryear’s horror movies to exist. He kept shaking hishead in disbelief as I tried to make clear the concept that mass and volumeincrease at different rates. He just didn’t understand! He kept insistingthat all parts of an oversized insect or mammal must
Aswe continued our hike, I shared more of what I learned from the video. Iexplained about L systems and used one of the examples from the video to showhim what these systems are. I pointed to a tree and told him how thebranches’ patterns repeat themselves on a smaller and smaller scale. Ifelt that the math facts served to enhance our experience, rather than to dampenit, as I once would have expected.
Asa direct result of my introduction to the Life By The Numbers series, Iwas 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 qualitylearning experience. What did come as a shock was how much I actually enjoyedthe presentation as well as the fact that I actually retained the knowledgewith very little effort. This, as far as I am concerned, is a majorbreakthrough as it pertains to mathematics! Any medium that transmitsmathematical knowledge in an interesting and absorbing way is certainly worthsharing. My only regret is that I grew to be an adult before realizing theabsolute importance of mathematics.
As a future teacher, I am nowgathering the skills that I will need in order to spark a newgeneration’s interest in math. I plan to earn a multiple subjectcredential, which means that I will be teaching math. There are plenty of