Saturday, November 16, 2013
Spirals and Turkey and Phi
Oh my! Taking Brianna's lead, let's explore Fibonacci, via Vi Hart and her Math class doodles. Please watch all three parts (links to parts 2 and 3 are underneath the Subscribe button, and appear in the video at the end). Please do not say "Mr. Bogel told me to" when your Math teacher asks why you're doodling during class. Please do doodle during class. After you watch these videos, think and write about the relationship between patterns, design, and necessity. We talked about this in class while wearing Einstein's glasses, you'll remember, and were led by Cathy to read and think from right to left. Can you identify another pattern in your world that seems designed but is in fact a necessary result of circumstance and process? Are there times when this distinction is a matter of perspective, and thus open for debate? These are the questions I'd like you to address in your post. Please complete your thinking and writing by Sunday, 12/1, at 6 pm. Then read one another's work before class on Tuesday 12/3. On Thursday 11/28, before you eat, please watch this holiday eating guide. Your fellow celebrants will be impressed. As they stare, awe-struck, at your plate, you might regale them with a recitation of this ode to the spiral.
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Religion is a subject or a concept or something like Maths, which seems designed but actually a necessary result of circumstance and process.
ReplyDeleteReligion is a symbol of civilization. Over long periods of time, people came up with different kinds of beliefs, then created hundreds of religions we have these days. Religions are designed by human being because they are just ways of life that people see beneficial or reasonable.
On the other hand, religion is also a necessary result of human civilization. As human beings became more and more aware of the world they live in, they encounter more unknowns and confusions. Religions provide confusing human beings with guides for life. In the process of human development, things like religions that explain and guide human beings are necessary and unavoidable because these are answers to the questions in life. Humans never stop looking for answers. Even if religions are not necessarily trustworthy and scientific, they are the answers and unavoidable results in the process of human development.
Like Maths, religion can be seen as the origin of human life or originated from life. Although I am not familiar with religion and do not practice any religions, I know that in almost every religion, there is a god. The god creates everything so life is originated from religion. From another perspective，religions are understanding of life after all, so religion is originated from life.
Yes, different perspectives bring different understanding towards things. In my opinion, everything has different meaning to different people. Everyone is raised in different ways so distinctive perspectives are formed, which eventually lead to the first question. Additionally, I believe that everything has more than one side. When people's distinctive perspectives times the different sides of things, there forms countless possibilities in our life.
After staring, awestruck, at Vi Hart’s videos, I realized that through her series of three videos, Vi Hart led the viewer on an exploration from looking at Fibonacci numbers on the surface, to the reason for their existence. It’s so much more than two consecutive integers adding up to produce the third, and it has changed my perspective of Fibonacci numbers, because now I know that there is more reason for its existence. The pattern is existent because of a common necessity in the natural world. It’s how plants grow. I remember myself looking at how Vi Hart marked up the pineapple with colored tape, and marveling at how unbelievable it is that these things were all related to Fibonacci numbers. At the end of the third video, I realized that it really is believable that plants grow in Fibonacci or Lucas numbers, because it is a necessity for them to acquire growth hormones. So because of the necessity for growth, the plant forms a design, and repetition of that design creates a pattern, because many plants have the same necessity, so there is the same repetition and same patterns.
ReplyDeleteEnough about Phi, another pattern in my world that seems designed is the concept of Pi, it is the constant that applies to all circles, it is the fundamental piece in finding the area or circumference of a circle using the radius/diameter. It’s just as easily to say that every theorem in math is something that seems designed but is in fact something that is inspired by a naturally occurring phenomenon, and it is to people’s choices whether to use/believe it or not. Going back to the Phi thing, different perspectives would offer interpretations of a mathematical pattern, a person who is deeply religious would certainly not accept the role of Fibonacci numbers in the way that plants grow, they would not have it that there are spirals in a plant because of plant bits and growth hormones. They would argue that God made the plants the way that they are. Side tracking a little bit, but I find it funny that we tend to think immediately about where we hold our faith when it comes to difference in perspective. Back tracking to Pi, the ambiguity of Pi is contributed to by the many many ways to find it, the simplest of which is to divide a circle’s circumference by its diameter, but sometimes, depending on the circle, the result of the operation varies from the standard value of Pi, but it shouldn’t because it is supposedly the constant in calculations involving circles. Another way to find Pi is by using two polygons, one inside and one outside of an imaginary circles to advance closer to more exact values of Pi, but that method can only provide a closely estimated value of Pi, so the methods with which to find Pi are like the different perspectives. There is also a lot of debate over the validity of the concept of Pi, because in radians, the full 360 degrees of a circle is really not Pi, it’s 2 Pi, so the value of Pi should really be 2Pi instead of Pi, many people believe that using another constant Tau that would embody the value of 2Pi would make everything concerning Pi (Tau) so much less confusing.
The thing that makes Pi so unreasonable (to me) is not that it’s an irrational number, it’s that Pi is so important in everything concerning a circle, it’s used to define a circle, it’s circumference, and area, yet, Pi itself is undefined, it goes on forever. It’s also involved in many other mathematical formulas, which also makes the result of those formulas undefined as well.
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ReplyDeleteAccording to me, science is the nature of living and non living things. Unlike Math, we can also create designs and patterns that can be related to some real life situations. This means that science also has its own trends. A good way that I can use to describe the trends in science is through photosynthesis. I believe that photosynthesis occurs in real life and if I’m not mistaken, I know that most of us have seen its visual demonstration in the biology class. Photosynthesis can also be described through its equation, “C6H12O6 + 6O2 --> 6CO2 + 6H2O” (faculty.clintoncc.suny.edu).
ReplyDeleteIf science is the nature of living and non living things, then living things and non living things describe science. For science can never exist if there were no living and non living things. This means that science originates from living and non living things. But if science describes living and non living things, then we can also say that they can never exist without science. This also means that science is described from living and non living things. Science is highly related to living and non living thing, for there has to be science in order for living things to exist and vice versa.
The science of something or science in general, can be understood differently by different people. I believe that there is always a right answer to a science problem even though people may create different answers that agree with their perspectives. For example, scientists come up with many theories like the Big Bang, Steady State theory… that all explain the same thing. In this case, people are open to choose the theory they agree with, according to what they find is more reasonable to them.
Evolution is a pattern that is highly debated and this debate of whether evolution is true or not forces people to believe that it occurs through design or if it is a necessary result of circumstance and process. Some believe, as I do, that evolution is true and all creatures have evolved through many centuries into what we are today. Some, however, believe that everything was created by some higher power and everything was designed to be the way it is today. Their argument that all living things were designed to what they are today may be proven by the idea of cross breeding to create a new species. Evolution argues that every living thing evolved from the same molecule, but creating a new species would prove that evolution is not necessarily true. Conservationist, Jeff Corwin, studied a new species of fish off the coast of Hawaii. He found that this fish had not evolved from another, but was a species created due to two different species of fish mating. This case, as well as other cross breeding cases, may prove that evolution does not explain why every living species is the way it is today. Rather, it proves that living things today may be the way they are due to design, whether the design that people force in breeding a new species of dog, or the design of fish choosing a different species to mate with on their own.
ReplyDeleteOn the other hand, the theory of evolution proves to those who believe it, that every living thing is the way it is because of the necessity of circumstance and process. The process of animals adapting to the environments they live in to survive shaped them into what they are today. The circumstances in which they lived changed the way they had to live and the qualities they needed to survive. This theory is clearly a pattern that is a necessity of circumstance and process. However it is just that— a theory. While the pattern may be a necessity of circumstance and process, the debate about it questions whether life today is a result of this pattern or of design.
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ReplyDeletePatterns, Design and necessity have a similar relationship in that they provide order, structure and organization to something. In Vi Harts videos she showed that the pinecones had Fibonacci sequences or numbers. Because the pinecones have this it is easy to see how the plants grow. This sequence provides a structured patterned way for the plant to grow so that it grows most efficiently. Fortunately Fibonacci numbers help the plant grow in a way that it will survive. Examples: Plant leaves that grow in a spiral or vertically, depending on plant species. It is interesting to see how plants know to allow their leaves to do this.
ReplyDeleteWhen I was watching Vi Harts videos on the Fibonacci Theory and spirals it got me to think about the seasons (winter, spring, fall and summer) and how they are definite patterns. The seasons change every year with global warming or not and have been doing this for thousands of years. This could be because of science or because of faith. For the aspect of science, the year starts on January 1st every year. During this time the season is winter, because of this one could argue that the world started with the season winter. However in the Bible it says that God created the world with blooming flowers and living organisms, so the season of winter would not make sense because that is the seasons that organisms die. Spring would be a better fit for the faith aspect of the changing seasons because this is the seasons that everything is reborn, thriving and alive. This ideas (put into both perspectives) can be up to the individual and how the individual sees it. However, I think that both sides can agree that the change of seasons is a necessity. If the season summer was all year round organism would die because the weather would scorch everything. Plants would dry up and water would evaporate. Spring would be no better either because organisms would continue to reproduce and there would be over population of organisms. Having the seasons guarantees that these problems and others will not arise.
Happy late thanksgiving !
ReplyDeletePatterns are designed as a way of giving logical evidence behind a particular situation. The pattern designed will emerge from the output gained and give logical reasoning behind it. In the video that was viewed the Fibonacci pattern theory came out of the output of how a hurricane turns and was used to give logical explanation for it's spirals by using a mathematic pattern. This pattern was then used to logically explain the formation of several other spiral shaped objects. The output of how the hurricane turned help to pilot different knowers such as Fibonacci to develop a pattern as evidence to prove the growing shape of it's spirals as it rotated. This then leads to the relationship between patterns, design and necessity. Patterns are designed based on the necessity of it in a particular situation.I watched Catching fire this thanksgiving and the situation was that where the hunger games was kept was designed in the pattern of a clock and every time the clock struck the hour a disaster happened . The design of this pattern came out of the necessity to kill almost all tributes in The hunger games until one was left standing as the winner. As the same with the Fibonacci theory pattern, the necessity to generate how hurricanes turn brought about the design of this particular pattern.
One pattern I thought was randomly designed was a popular childhood game , hopscotch. In hopscotch it is designed in such a way that starts out with one square , then two , then three then back to one repeating the process with the last square at the other end being one. This particular design is as a result under the circumstance that if one should fail to maintain their balance while swiftly transitioning from hopping on one leg to both depending on the size of each square they will lose. I never quite took this particular pattern design based on it's necessity to the game of hopscotch into consideration until learning about this topic. Also hopscotch is a game enjoyed in many countries so the structure and purpose of it may vary depending on the players. A pattern will always be involved in hopscotch but the reason the pattern was created can be debated. Based on what the result of the game is desired to bring forth, one may view it as just a design to a game for fun and others may design it to suit a purpose or circumstance to bring forth a winner and loser.
The three-part video on YouTube we watched was fascinating. It clearly showed the relationship between necessity in design and patterns. These videos, besides the thanksgiving “mathpotatoes”, all took a closer look into the designs in plants. Spiraled plants often have Fibonacci number sequence patterns and are, on the most part, consistent. A few plants do have a difference sequence, but this is very similar to Fibonacci’s. The narrator described how plants grew leaves based on the fact that they all needed sunlight. As this is seen as a design, it was purely designed for necessity. The plant strives to survive by using a specific equation so that leaves and petals don’t overlap. The design and pattern is striking and incredible.
ReplyDeleteAfter thinking about this topic for a while, I finally settled on the respiratory system as a pattern that seems designed but in fact is a necessary result of circumstances and process. In biology, I learned that the first cells were prokaryotic and anaerobic. Due to a lack in oxygen, there was no way these cells could rely on it. Ironically, these cells produced this oxygen, eventually filling our world with it. Once the world had a surplus of oxygen, aerobic cells emerged, purely to take advantage of this new resource. In other words, aerobic activity was driven out of necessity. Fast-forwarded to current times, the lung evolved. The lung serves a purpose to take in a steady amount of oxygen to carry through the human body, sustaining life. Lungs are such advanced organs, almost seeming to be created by modern scientist, but in reality they are simplified evolutionary needs. The rhythmic function of breathing keeps us alive. Arguing the function of a lung would be difficult to do, but I do think that the evolution of lungs leads to many topics and discussions.
There are a few patterns in life that are considered to be a result of design but are actually the results of circumstances and processes. The main example I can think of is the development of an embryo. It sometimes seems that this process is of design and parents often make predictions of what there developing child would look like depending on the phenotypes of both parents. While true predictions can be made, the entire development process is dependent on circumstance. The first circumstance that it depends on is what type of sperm will get to fertilize the egg. This will ultimately determine the sex of the baby. The baby's physical attributes will also be based on circumstances similar to that of rolling a dice. The process is not designed but the circumstances predict the outcome of the new life. While persons with strong religious beliefs or believers in fate will reason that God or nature had designed for the life of an individual to be a certain way. They might think that it was destiny for a boy with long limbs and athletic attributes to bless the world with his skills in basketball. This is quite contrary from the belief that it was all a matter of circumstances, temperature, time or place that allowed a a famous basketballer to enter the world rather than a ballerina. In essence, I'm saying that the entire process of a developing child is dependent on many factors of circumstances rather than design.
ReplyDeleteThis line of thinking can be linked to the debates about fate, where things are destined to be the way they are or wether it was a matter of circumstances or luck. Do humans walk on two legs because God designed them to walk in such manner? Or do they walk on two legs because during devolution the circumstances pushed for us to move on two legs. Some might even compare this topic to evolution and creation. While these topics and debate are quite similar the answers are all dependent on how one perceives it.
After barely surviving the three doodling videos with my jaw dropped and the faint but noticeable "uhhh...woah" coming from my mouth, I came to two conclusions: Number one being that this girl has far too much time on her hands, and number two being that math is a constant mind boggling and ever-enveloping concept that explains, well, everything. Anyways, I'm sitting in my living room next to a Nantucket basket lamp, and, looking closer I realized that if it was broken down to its basic structural tools, the basket is actually comprised of one long line and a circle. Basically, the basket is made with a series of lines that splay out in two dimensions as a circle. This circle is then joined by the continuous weaving of the single line, as I mentioned before, in an in-and-out AND in-between pattern. The goal of this pattern is to create a three dimensional shape with depth, that can later be attached to a light fixture or otherwise be filled with Easter goodies in the spring time.
ReplyDeleteThe function of such a thing has been around for many years, so the concept of adding lines to create circles and later, objects with depth (a mathematical concept, really) is definitely the answer to the simplification of any object. If you look to the very basic tools or ingredients of a thing, then you can see the pattern which that particular thing, came from.
I'm not fully understanding of what I just attempted to explain, but perceiving with simplicity, math can be much more easily explained and understood.
Another pattern in the world that seems designed but is in fact necessary is the rate of growth of each individual being. Brain studies have shown that babies go through this enormous period of growth, and than as adolescents we go through another huge period of growth. Than, teenagers start changing and becoming more independent. They start questioning themselves and arguing with their parents, as well as defying authority and questioning all they ever knew. What I found pretty amazing, if not really obvious, is how all of this correlates to the rest of nature as well. Its our way of starting off in the world, and I suppose we just take it for granted that at age 18 we (generally) leave home and start our own lives, but long before that our brains begin programming us and teaching us so that we are incredibly relieved to get out of the house when the time comes! Its a necessary part of life that I'm sure is explained by some brain chemistry mixed with mathematics mixed with biology, but its pretty amazing how our brains use puberty along with vast amounts of hormone changes and neurological sparks that may be mathematically predictable (maybe?) to make it happen.
ReplyDeleteI think that this topic could be open for debate, but only because of the massive differences in the way we all grow and learn at different rates. If you take a girl who has been boarding at Stoneleigh Burnham since she was in seventh grade and then a guy who hasn't left his parents house by age thirty two, than I think we can conclude that perhaps the brain synapses fire away differently in both cases. The argument could be that this supposedly "necessary" growth that happens during the childhood years is based on nurture rather than nature. This common argument (I honestly believe that both nature and nurture affect it) is based on perspective. Its an interesting question though. I'd be curious as to how others would perceive this topic.
After watching the Doodling in Math Class: Spirals, Fibonacci, and Being a Plant series, I began to seriously think about spirals being one of the bases for this earth’s architecture and natural form. The first thing that came to mind was the Milky Way, the galaxy where our solar system is. It is in the form of a barred SPIRAL. Overall, it makes sense that many objects and life forms our solar system contain that same spiral shape, because the spiral shape seems to be integral in the stability of the whole galaxy. The spiral shape may also be the most efficient design of things, and that may also be a reason why it is reoccurring in nature. If you analyze the spiral, it enables growth (the rings get bigger), yet it also provides some sort of stability (the round shape).
ReplyDeleteOne pattern in this world that seems designed but is in face a necessary result of circumstance and process is the finger print. Every human being has a different finger print which is unique to them. It is arguable that this is not necessary, because humans have so many different traits and characteristics that decipher them apart already, so it may not be needed for every person to have a different fingerprint. A person who believes this may look at finger prints just as a design. An opposing person will say that finger prints are not just a design, they fulfill a much needed purpose, and we can see this in real life-through crime scenes when finger prints are taken to detect a thief for example. The matter of whether finger prints are necessary is a matter of perspective and open for debate. However, there is no argument over the idea that differing finger prints are a result of the different DNA in each human being. Coincidentally, finger prints also take the general shape of a spiral. This left me thinking about why that is and how spirals are seemingly so essential to everything.
When I first began watching Vi’s video’s I thought for once in my life math might actually be something I could enjoy and maybe even involve doodling. But then the doodles involved math…and then it just got really confusing. However, Vi really did open my eyes to see how significant math and patterns are outside our, well lets face it, boring classroom. The video about the leaf petals made this idea very clear. The hard part was to find something in my world that was an example of patterns that are results of circumstance and process. Of course, me being a crazy horse person, I choose to analyze the gaits of a horse.
ReplyDeleteIn horseback riding there are four gates: walk, trot, canter, and gallop. Each gait has a certain number of beats. The walk has 4 beats, the trot has two, the canter has three (sometimes four depending on the horse), and the gallop has four (however, it seems like one). Each gait is a different speed. I have spent a very good deal of my life naturally riding these gaits and having a very limited sense of how interesting they really were. The walk is the slowest, each leg is placed on the ground at a regular interval: left front leg, right hind leg, right front leg, left hind leg. Boom boom boom boom (four beats). The second gate, the trot, has two beats. The diagonal legs move simultaneously (at the same time). It goes: left front with right hind (making a triangle shape) and then the right front with the left hind (also making a triangle shape). Boom boom (two beats). The third gait, the canter, has three beats. It is when one front leg leads while the other front leg and its diagonal hind leg move together, while the other hind leg moves independently. The footfall depends on the lead you would like (since the front legs leads). Boom boom boom (three beats). In the gallop the speed of the horse is increased so the legs that were working diagonally are unable to do so, thus, it becomes a four beat gate. Boom boom boom boom.
All these gates, to me, produce a pattern. This pattern shows how something that seems very natural is actually a process of how a horse moves. These gates are demonstrated in different ways, not just naturally (when a horse is born or wild). For example, dressage uses these gates to preform movements that involve the horse moving sideways, diagonally, and in place. In show jumping, the canter allows the horse to meet the jumps in a specific number of strides. And racehorses use the gallop to race. Each gate provides the horse with a center of balance with the each number of beats. For example, the trot: when both front and hind legs meet they make a triangle shape, allowing the horse to be balance when preforming the trot.
I was so amazed by Vi Hart's doodling video. She connects the pattern on the plants and math. It is just so amazing to see math formula applied on the plants. People usually found the pattern from the nature; then operated in math formula; after that, they designed; finally, they invented and produced new things.
ReplyDeleteVortex is always a fantastic figure for me. I remember that my friends used to shake the diaphaneity bottles with full of water together in order to see the tornado figures. Now, I look up online, and figured out that vortex has two different situations; rational vortex, and irrotational vortex. They have different pattern and design even though both of them are called vortex. I believe scientists found the formula in tornado first. Now these days, they applied it to the juicer.
ReplyDeleteOne pattern that I find incredibly interesting is ocean tides. I knew that they were related to the moon, but other than that my I had no other knowledge about them. Tides seem like something that just happen about twice a day, and bring water to and from the shore. After researching this, I found out about something called Tidal Potential: how tides could be made. I discovered that because the earth is elastic and rotates, the gradient of the gravity field of the moon and sun directly affect the hydrodynamic equations of a self-gravitating ocean. I’m not quite sure what that technically means, but I think I can understand it like this: because the earth rotates and gravity is present, the ocean tides are effected by the gravity gradient of the moon and sun in relation to the earth. Upon further reading, I discovered that “the tidal potential is symmetric about the Earth-moon line, and it produces symmetric bulges.” Therefore, instead of being random, tides are intricately connected to where the sun and moon are. The bulges produced by the earth in relation to the moon continue to be symmetric and rotate as the earth rotates. I think that’s totally cool, because not only is something happening on our earth, it’s happening outside of our earth in the Milky Way. The sun, a whopping 92,960,000 miles (149,600,000 km) away from the earth, and the moon, 238,900 miles (384,400 km) away all intertwine to create a pattern on earth. Therefor tides are a result of circumstance and process. Because ever the moon and sun and earth are in relation to each other, tides are a necessary product.
I don’t know if you can have a different perspective on the necessary patterns. I don’t believe that you can if the pattern natural occurs in nature, seeing as it was created by the earth and solar system and therefor you have no business questioning it seeing as it is simply as scientific fact that would exist even if you didn’t. As of right now I cannot find an example of a time when this would be a matter of perspective, but I hope that as I keep thinking about this I find an example.
Link to the ocean Tides website : http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_04.htm
While and after watching the three videos, I was confused, overwhelmed, and amazed. I was so surprised by how deeply connected patterns and math and design and necessity are. It reminded me a lot of the “putting on Einstein’s glasses” video; I thought of the necessity of something as kind of like the use of it or the everyday look at it (not sure if this is right) and how that is like looking at something from the surface, and then there is the design which is like the diagram, and then there are the patterns and the math the foundation of it all. I realized that things can be way more complex than they seem. I was amazed by how a simple flower that I would just look at and say ‘wow that is so pretty’, connects to fibonacci’s theory. I was mind blown by the different layers of complexity of one seemingly simple thing.
ReplyDeleteFor something that is a pattern in my world that seems designed but is in fact a necessary result of circumstance and process, I was at first very confused and had no idea, but then I thought of birth or the beginning of one’s life. The human body is extremely complex and so is the creation of life. In one persons opinion or from a scientific view a woman’s body was designed to carry a child for nine months. Each woman that is capable of carrying a child, has the necessities in her body to do this, it is sort of like a pattern. There is a pattern of women with the same bodily characteristics needed in order to produce a child that have been having children over a very long period of time in order to maintain the population. One perspective is that overtime through evolution and whatnot the human race evolved and the women body was designed to be able to carry a child because it was necessary for the species; this was through a process and due to certain circumstances. Another perspective is men and women were put on this earth with their specific design and the creation of life can not be explained through science, it is something beautiful and amazing. Basically what I am trying to get at here, is that patterns are very complex and you can choose what you want to make of them. With women and their ability to carry a child, one can look at it from the surface as an amazing wonder, or one could dig deeper into the design and math and science of it all. I don’t think one perspective is wrong, but it’s more of a matter of how much one wants to get into a topic and what it is connected to.
Similarly to everyone else's ideas, these videos were definitely intriguing and eye-opening. Though I understood that math was in close relation to patterns, the extent of this connection surprised me. It was in a way mind blowing as the video we watched in class, to think about the necessary, sophisticated and percise patterns that allow for what we see as everyday simple tasks to be completed. Though it is still hard for me to comprehend and wrap my mind around, it is so interesting to know how fibonacci's theory is so common and important to our lives and the things in it.
ReplyDeleteLooking at the human body, we undergo many processes everyday that can be considered patterns. One may say that these processes and patterns for example the pattern of digestion , is in fact designed because humans are designed to be able to do that, but another perspective may be thatthis pattern only occurs because of its constant use and development over the course of human evolution. The current advancement and sophistication of our digestion process can arguably be a product of the manu years that humans have been digesting. How are we to know that this is a designed function rather than one created by cirucmstances and processes. There is no wrong or right perspective to this in my case, as I am sure both sides have supportive proof. However I think it is interesting to debate since it is a subconcious process we go through several times a day.