1. Knowledge is Rediscovered: Things we presumptuously think we have “discovered” such as the golden ratio and the Fibonacci sequence are actually very old designs created through evolution, and appear in things as ancient as nautilus shells sunflowers and pinecones, as well as very old architecture. When I learned that sunflowers grow in a pattern that relates to the golden ratio, I began to see the pattern everywhere, like in artichokes and lots of other flowers. The pattern has clockwise and counter clockwise tilting spirals that all converge in the middle, and the golden ratio is represented both in the ratio of counter-clockwise to clockwise rows, as well as in the order in which the petals or seeds emerge, which I find amazing. Here’s one description of the pattern: “In the head of a sunflower, the tiny florets that turn into seeds are typically arranged in two intersecting families of spirals, one winding clockwise and the other winding counterclockwise. Count the number of florets along a spiral and you are likely to find 21, 34, 55, 89, or 144. Indeed, if 34 floret (or seed) rows curve in one direction, there will be either 21 or 55 rows curving in the other direction” (Peterson). They are Fibonacci numbers, and if you divide one set of spirals by the other it will usually turn out close to phi. I realize that this pattern must have come about in evolution and must be the most efficient way for plants to grow evenly, and photosynthesize. I’m not sure why that would be but perhaps it’s the best architecture for them to capture sunlight. I searched around but people don’t really understand it: “But why would leaves and seeds strive for the Golden Ratio? There still is no consensus on the answer. It's one of the riddles of what biologists call phyllotaxis” (The Pacific Institute for the Mathematical Sciences).
2. Materialism is Harmful. I learned in this class when we read A Whole New Mind and also when we were watching The Secret that I really believe that focusing on material wealth is unethical and harmful to the self and to others. We all need to start focusing on experiences rather than things. Lao Tzu says “He disregards himself, and his self is increased. He gives himself away, and his self is preserved. Is it not thus: because he desires nothing as his own, his own is completed?” Here I think he is saying that only when we stop desiring possessions will we be happy. I will quote him a little more because he seems to have a lot to say on being non materialistic . “to be rich and titled and arrogant into the bargain: this in itself attracts misfortune. When the work is done it is time to withdraw…”
“Generating and nourishing generating and not possessing being effective and not retaining, increasing and not dominating: this is the secret Life.”
I feel he is saying that nourishing and possessing are opposing forces, so the more we are working towards possessing things the less we are capable of nourishing. During the discussion of The Secret, Dani, you said you did not pass judgment on a man who had accumulated so much wealth as to have a million dollar home. I do pass judgment, I do think that man lives an unethical life in some respect. It is difficult because I know there are some things in my life to which I devote affection, and I do occasionally want more things, like clothes, or an iPod. But I also know that the desire to focus on material things can get out of hand, can be unhealthy, and if I began to submit to all my material desires my life would become less meaningful. I also know I would be focusing purely on myself, rather than committing myself to nourishing, sharing, and helping those around me, and that is not the road that I want to go down. And so I compromise between living in a materialist culture and wanting to keep my life vibrant without relying on material wealth, two opposing forces. We talked at the beginning of the year about how in the English language we use the word “no-thing” to mean that something is of no importance. Lao Tzu believes that nothingness is of utmost importance. He explains what “effectiveness” is, and that it is where there is non-existence that real purpose lies, which I find really beautiful.
“One hollows the clay and shapes it into pots: In its nothingness consists the pot’s effectiveness. One cuts out doors and windows to make a chamber: In their nothingness consists the chamber’s effectiveness. Therefore: what exists serves for possession. What does not exist serves for effectiveness.”
I do not presume to understand his book, Tao Te Ching. I only began reading it but I thought that it really helped me understand more of why I found some of the messages in The Secret so wrong, intuitively they felt wrong to me, and since then I have begun to understand why I see materialism as such a dangerous thing, and one that erodes the better traits of human beings, making us selfish and blind to some powerful things, or I should say powerful non-things. So, although I found only a few people in class agreed with me, the discussions did help me understand my own set of beliefs better.
3. Everything is Vibrations and Waves. Everything we experience can be understood in terms of vibrations as all things which hold and burn energy are in constant motion. And vibrations create shapes, forms and patterns. An article exploring this concept questions whether the claim –“ that the whole universe, from the smallest cell to the biggest nebulae, is formed and maintained by only vibrations” is in fact true (Bindu Magazine). Here is an amazing picture of the shapes and patterns created by matter settling and responding to vibrations:
Caption reads: “Spores of moss (lycopodium) form a galaxy of small globelike piles. See the picture above. Each pile rotates on its own axis and also rotates as a single body in relation to the other piles, like the elements of our solar system.” Another experiment this article mentioned briefly: “ a cyclical sequence appears in a mixture of salt and water. The salt collects itself in round formations - only to change and break up again. At an unchanged frequency and amplitude these regular cycles repeat themselves. They build up, last for some time and then dissolve again at the same constant tone.” So this sort of does support the idea that the universe was created and sustains in its particular design as a response to vibrations… meaning vibrations are the architect of all of the universe in all of it’s geometry and symmetry and patterns. If you believe this claim, then it is not difficult to also believe that everything in the universe can be expressed mathematically. Colors are created in wavelengths, which are all made possible by light, which has various wavelengths as well. Light actually has all of the wavelengths, and whatever color we might see at a given moment is created by certain wavelengths bouncing off the object (while others are being absorbed by the object, concealing those colors from us). So all colors are reactions to light, or relationships to light, and colors do not exist without light. All energy derives from sunlight so it’s hard to imagine the things we perceive existing without sunlight. Sound also, can be explained in terms of different wavelengths, as can thoughts apparently, according to the secret. Here are some interesting snippets of other connections between our existence and vibration:
“All living cells, including but not limited to human beings, as described by George Lakhovsky,2 Dr. Cyril,3 and Ivan G. McDaniel,4 give off vibratory waves somewhat similar to those transmitted by a radio station…. these human emanations can even affect various forms of plant life, thereby causing plants to react productively toward emotions of love and encouragement and protectively toward those of hate and anger” (One Flesh).
I think plants are tuned into things that we are not, and why shouldn’t they be, when they are nourished directly from the sun while we are disconnected from the energy of the sun by one step in the food chain, when we eat plants, or sometimes two or three if we choose to eat meat.
“Most stars, including the Sun, pulse continuously due to the violent mixing of gases in their outer layers, says Professor Bedding. He has described the how a nearby star in our galaxy pulsates by studying the Doppler shift of light waves coming off the star's surface. And he has developed computer models to show how complex the pulsation is. ‘It doesn't just vibrate simply in and out. It vibrates in lots of different modes simultaneously,’ he says” (Salleh).
Two things which correspond, even if they are in two separate bodies, often share visual and structural characteristics. Our lungs, the orgasn which breathe in what plants breath out is shaped like trees. Our trachea are built with the same branching patters as trees, and both have evolved to exchange CO2 with oxygen in this symbiotic relationship which we’ve maintained for so long. So here we have stars pulsating, and sending out their energy, then we have our bodies which rely on star light (the sun is a star after all), and while it is our digestive tracts which actually take energy into our bodies, it is our hearts which keep energy, blood with oxygen and nutrients flowing throughout our bodies, and hearts pulsate. So hearts are like the stars of our bodies, they distribute energy, they pulse. They are distributing oxygen, which is created in photosynthesis, and nutrients, which usually come from photosynthesizing plants, then hearts are distributing light (though it is in an altered form), throughout our bodies. They are stars inside of us.
Hi Dani, Hope your holiday is going well, and you are feeling better. I want you to remember that life is not bleak although at times it may seem to be that way. The future can be very scary, but is important that we keep our mind and body in the present. We don't know what lies ahead of us, and all we an do is enjoy and utilize the day. Whether that means enjoying the company of friends or family, or appreciating what we have around us. Taking a walk with a camera is a nice way to do this as it forces you to notice al the beautiful and wonderful things that we may let pass by us. Life is beautiful and God loves us. From this class, besides patterns (which i found fascinating, especially the golden ratio), I learned that the one thing that the universe is always striving for is balance. An equilibrium so to speak. Because of this the universe will always be working itself out and although it may seem hopeless we are all in the same boat. We need to lean to balance our life and once that happens and we can realize this, I believe we can open the doors to true happiness. Anyways here is my paper, feel free to post your favorite parts on the blog. Enjoy your break and your health. Remember sunshine wouldn't be so special if it wasn't for rain.
Coming into What is Math this year I did not really know what to expect. I could tell coming in that it was not going to be a traditional math class by any means. What I didn’t realize though was how much spirituality was involved in the class. In my opinion this is what made the class for me. I also don’t think that there was any topic that was debated more in our class then after we watched The Secret.
Up until then we had had serious discussions about Math as well as spirituality, but there was always a sense of agreement in the class. However after we viewed The Secret I don’t think I have heard more passion in the ideas of others combined throughout the year.
The Secret is a relatively new film, which was made in 2006 and deals with the “Law of Attraction.” This principle suggests that people’s feelings and thoughts attract real events in the world based on positive and objective thinking.
The problem that many people had with the movie though was not only in the message, but also in the way that it was presented. During the start of the movie they talk up the secret like it is this ancient idea that was passed down through the decades, being used by many successful people along the way, and now it is being passed onto us. At the start of the movie they have a lot of good information on positive thinking, but towards the end of the movie it sort of drifts into the realm of self-help. There were a lot of superficial ideas in the movie, like the person who imagined themselves in a nice car, and soon that is what they got. Also there was this kid who all he wanted was a bike, but he never did anything himself to earn it. He though about it all the time and even put pictures up on the wall of the bike as well as drew pictures of himself with the bike and how cool it was going to be when he got it. Then miraculously some random elderly gentleman (possibly his grandfather) shows up at the door of his house caring the exact same bike that he was picturing.
I think that this was the problem that most people had with the movie were how they were portraying this. The movie made it seem at parts that through positive thinking you can get what you want or rich. Obviously this is not the case for everyone. There are certain environmental and social problems that hinder many people from their dreams and no matter how hard some people try, they might never succeed. Also another problem people had is that you can get whatever you ant just by good thinking and not going out and doing something about it. The way it was presented might have thrown people out as well. With statements coming from Reverends as well as self help authors people though it was a crock.
I believe though that many people were looking at this film in the wrong light. People were looking at the surface of things and not paying attention to the underlying concepts of the film, which I find quite fascinating. If everything affects everything else at the most basic level, then the universe would be completely different if say I wasn’t here. It wouldn’t be a dramatic difference on the grand scheme, but there are definitely people’s lives that I have affected. Now let’s take that and look at it on a smaller scale. We know now through modern science and technology that the brain does in fact emit brain waves when thoughts are being produced. If everything affects everything then that means that the universe needs to readjust itself around your thoughts, and with positive and objective thinking, it is possible to make your thoughts a reality. Now this does not have to be some out of reach though like marrying a certain movie star and living in Bermuda, but it still can be applied to your life. If you want something bad enough, regardless of what it might be, it is better to think positively about it, then send out negative thoughts.
As long as we have a brain we are going to be constructing thoughts as well as actively constructed others and ours universes. To go through life thinking that you don’t have an impact on anything or everyone is silly. In the long run the real secret is to be the best, most sincere person that you can, set some goals, and the world will work out in your favor.
I wasn’t sure what I wanted to writer this paper on – it’s amazing how college has conditioned us to look for prompts rather than simply using our imaginations. I thought about everything we’ve done this semester and the class as a whole, and came to the title of the course. What is math? Is that really what I expected to learn when I signed myself up for this course? Of course I didn’t believe that the class would answer this very immense question, but I think I did get an answer. I got many answers. The combination of everything we’ve done, the activities, the movies the discussion are all an equation in themselves. Added together, they are math. The contents of the class itself form one of the answers to this question. Really what this class has reinforced in me is the idea that there is often not one answer to any one question. Each component of life is vast and contains multitudes within it. Math, like a human being or an ocean, is an infinite subject without limits or boundaries. It is a part of everything and everything is a part of it, all under the same roof, all participating and existing in the same universe. I would be lying if I said that this class was not frustrating for me. It was. Often times I felt as if our class were a miniature model of the world. People talked over one another, points got lost, arguments were formed. I would become overwhelmed by the chaos of the class which seemed to so closely resemble a larger chaos in a larger community: the living community, all of it. Despite my frustrations, I tried to be patient. I tried to distinguish voices and decode discussions. I silently engaged myself in others in an attempt to understand. What are they really saying? What do the really mean? This was a new experiment for me. For a long time I rested on a belief that there was no use trying to understand one another. The mind is so bottomless, there are so many things to consider. Anything anyone says could mean something completely different to you and something else to you friend etc etc. And there is no way to know. No way to ever enter the psyche of another person. So what use is there? We will never be wholly understood by anyone else. I decided that this was reason to keep all thoughts to myself and focus entirely on the self. Being the only thing I have remotely any control over, the self was something I could work with, mold and make better. Improve. I set out to improve myself, rid myself of bothersome faults, excommunicate myself from anything social. Excommunication gets rather lonely however, and the self is perhaps even more difficult to a stranger. As I came out of this phase, a little bummed that I still had not found a comfortable place between myself and other people, I set out to find a new explanation for myself. This is one thing about myself that is really good I think: in general, I am always seeking. Not always finding, as in the case of the example I just gave, but always seeking. I think it is important to never be satisfied with knowledge; to always want a little more. What is math? came just around this time and I incorporated it into my current dilemma right away. What is math? An unanswerable question! I became even more convinced of our inability as humans to understand anything fully. I felt as I often do, that I was only skimming the surface. I wanted more than just bits and pieces. So I searched for meaning in every class. Ruthlessly scoured conversations and expressions and video clips. Read into everything entirely too much and, of course, always came up unsatisfied. Was I missing something? Absolutely. Things are always in the last place you think you’ll find them. What I’ve found after letting go a little bit, relaxing and carefully considering this course, is the answer to the question asked its title. Math is understanding. There is a connection between all things which I tried to deny, but can no longer ignore. Perhaps I will never fully understand another being or myself, but perhaps that is because there are no “other” beings to begin with, no “self”. There can not be any further understanding, until its been understood that everything is connected and is one. So just as we all are a part of one meaning and one understanding, math is a part of one meaning and one understanding. It is a fraction of the whole and the whole would be incomplete without it.
Chuck Lines 12/21/2007 What is Math? Dani Novak Final Paper
From Beginning to End: A Semester in “What Is Math?” How do I begin to summarize everything that I’ve learned this semester in “What is Math?” I’ve learned more than I expected to in this class; about math, about life, and about myself. I scheduled this class as an easy way to fulfill my major’s math distribution requirement, but it became a class that invited me to think outside the box, expanded my horizons, and opened my eyes to the multitude of ways math is related to life and spirituality. I’ve always had difficulty with math. I now attribute that to always having been taught mathematics in an almost entirely left brained manner. I personally respond better to a more holistic and right brained learning style. This was the first math related class I have ever taken that strove to teach holistically and brought right brained understanding together with the left brained understanding to bring students to a higher level of comprehension and to develop a feeling for numbers. As I wrote in my midterm paper, focusing only on one side of the brain is fatal. I learned from the book Randomness that even the right brained thinking that I favored was flawed in some ways. Where the left brained teaching turns students off to math, strictly right brained teaching would open the floodgate for errors and misinterpretation of data and statistics. It is only by allowing the two sides and their individual aspects to work together that we are presented with the whole picture. By utilizing all the aspects of both sides of our brains we can get a feel for the bigger picture in the numbers and be sure our conclusions make sense logically. I admit I was nervous about the class when we began and didn’t always immediately see the relevance of everything we did, but by the end of our time together I was beginning to grasp the bigger picture. I learned that math isn’t the frightening dragon I’d always perceived it to be. It’s fun! It’s captivating! It’s a beautiful queen; the crystal only visible when we face the things we fear. Another idea we talked about in class struck me particularly hard. While discussing in class the relationship between Pi and Phi, we began to talk more and more about higher dimensions. It occurred to me that a large number of and maybe even most mathematical principles can be applied numerous times all the way to infinity. For example, we talked about the Fibonacci sequence and how any part blown up sufficiently would resemble a picture of the whole only in miniature. The same is true of equations, as my group demonstrated at our final. An equation will yield a certain y for each x that is input. This is a first dimension equation such as the equation for how many triangles will be formed by inscribing squares within themselves, with x being the number of inscribed squares and y being the number of triangles created after each inscription. The first dimension finds the pattern in what y’s are yielded by what x’s; how many triangles will be formed by inscribing the squares within themselves any given number of times. A second dimension equation takes things a step further. It strives to find a higher pattern; to find the pattern that governs the pattern of the equation in the first dimension. It looks for the “master pattern”. To continue with the earlier example, a second dimension equation would introduce another variable. Looking at squares, triangles, and other shapes individually in the first dimension would yield the pattern for how many triangles are produced with each successive inscription for only that shape. To take that to a higher dimension would be to find the equation that will tell you how many triangles will be formed by inscribing any shape with more than three sides any number of times. This can be done by adding a variable z representing the number of sides of the shape you choose to inscribe within itself. This higher dimension equation would produce the same pattern as in the first dimension if z was kept at four for each successive x, but would also produce the pattern for triangles if z were kept consistently at 3. As Jeff and Allison related in the scene from Arcadia that they presented, everything is governed by a mathematical equations and all of these are in turn governed by equations in the second dimension. This trend continues to the third and fourth dimensions, the equations governing each becoming more complex with each step, and continues all the way to infinity. If we could see the patterns in the patterns these equations create, we could derive the true master pattern; the equation that governs the answers that all other equations must give. Perhaps we as a people are a very long way from unlocking the keys to the true master pattern, but, as we learned when we briefly studied the akashic records, that understanding is already within each of us. Life itself is governed by this master pattern, so math is a part of us that cannot be ignored. It has been my sincerest pleasure to be a part of this class. I’m no longer afraid to bring math into my life and I truly appreciate being given the opportunity to do it. I am determined to share my newfound love of math and the many crystals that it hides. Thank you for helping me to find this part of myself. Bibliography Bennett, Deborah J. Randomness. 1998. 2nd ed. Cambridge, Massachusetts: Harvard UP, 1999.
Pink, Daniel H. A Whole New Mind. 2005. 2nd ed. New York, New York: Penguin Group (USA), 2006.
4 comments:
Lessons from Math Class
Audrey Gray
1. Knowledge is Rediscovered: Things we presumptuously think we have “discovered” such as the golden ratio and the Fibonacci sequence are actually very old designs created through evolution, and appear in things as ancient as nautilus shells sunflowers and pinecones, as well as very old architecture. When I learned that sunflowers grow in a pattern that relates to the golden ratio, I began to see the pattern everywhere, like in artichokes and lots of other flowers. The pattern has clockwise and counter clockwise tilting spirals that all converge in the middle, and the golden ratio is represented both in the ratio of counter-clockwise to clockwise rows, as well as in the order in which the petals or seeds emerge, which I find amazing. Here’s one description of the pattern: “In the head of a sunflower, the tiny florets that turn into seeds are typically arranged in two intersecting families of spirals, one winding clockwise and the other winding counterclockwise. Count the number of florets along a spiral and you are likely to find 21, 34, 55, 89, or 144. Indeed, if 34 floret (or seed) rows curve in one direction, there will be either 21 or 55 rows curving in the other direction” (Peterson). They are Fibonacci numbers, and if you divide one set of spirals by the other it will usually turn out close to phi. I realize that this pattern must have come about in evolution and must be the most efficient way for plants to grow evenly, and photosynthesize. I’m not sure why that would be but perhaps it’s the best architecture for them to capture sunlight. I searched around but people don’t really understand it: “But why would leaves and seeds strive for the Golden Ratio? There still is no consensus on the answer. It's one of the riddles of what biologists call phyllotaxis” (The Pacific Institute for the Mathematical Sciences).
2. Materialism is Harmful. I learned in this class when we read A Whole New Mind and also when we were watching The Secret that I really believe that focusing on material wealth is unethical and harmful to the self and to others. We all need to start focusing on experiences rather than things. Lao Tzu says “He disregards himself, and his self is increased. He gives himself away, and his self is preserved. Is it not thus: because he desires nothing as his own, his own is completed?” Here I think he is saying that only when we stop desiring possessions will we be happy. I will quote him a little more because he seems to have a lot to say on being non materialistic
.
“to be rich and titled and arrogant into the bargain:
this in itself attracts misfortune.
When the work is done it is time to withdraw…”
“Generating and nourishing
generating and not possessing
being effective and not retaining,
increasing and not dominating: this is the secret Life.”
I feel he is saying that nourishing and possessing are opposing forces, so the more we are working towards possessing things the less we are capable of nourishing. During the discussion of The Secret, Dani, you said you did not pass judgment on a man who had accumulated so much wealth as to have a million dollar home. I do pass judgment, I do think that man lives an unethical life in some respect. It is difficult because I know there are some things in my life to which I devote affection, and I do occasionally want more things, like clothes, or an iPod. But I also know that the desire to focus on material things can get out of hand, can be unhealthy, and if I began to submit to all my material desires my life would become less meaningful. I also know I would be focusing purely on myself, rather than committing myself to nourishing, sharing, and helping those around me, and that is not the road that I want to go down. And so I compromise between living in a materialist culture and wanting to keep my life vibrant without relying on material wealth, two opposing forces. We talked at the beginning of the year about how in the English language we use the word “no-thing” to mean that something is of no importance. Lao Tzu believes that nothingness is of utmost importance. He explains what “effectiveness” is, and that it is where there is non-existence that real purpose lies, which I find really beautiful.
“One hollows the clay and shapes it into pots:
In its nothingness consists the pot’s effectiveness.
One cuts out doors and windows to make a chamber:
In their nothingness consists the chamber’s effectiveness.
Therefore: what exists serves for possession.
What does not exist serves for effectiveness.”
I do not presume to understand his book, Tao Te Ching. I only began reading it but I thought that it really helped me understand more of why I found some of the messages in The Secret so wrong, intuitively they felt wrong to me, and since then I have begun to understand why I see materialism as such a dangerous thing, and one that erodes the better traits of human beings, making us selfish and blind to some powerful things, or I should say powerful non-things. So, although I found only a few people in class agreed with me, the discussions did help me understand my own set of beliefs better.
3. Everything is Vibrations and Waves. Everything we experience can be understood in terms of vibrations as all things which hold and burn energy are in constant motion. And vibrations create shapes, forms and patterns. An article exploring this concept questions whether the claim –“ that the whole universe, from the smallest cell to the biggest nebulae, is formed and maintained by only vibrations” is in fact true (Bindu Magazine). Here is an amazing picture of the shapes and patterns created by matter settling and responding to vibrations:
Caption reads: “Spores of moss (lycopodium) form a galaxy of small globelike piles. See the picture above. Each pile rotates on its own axis and also rotates as a single body in relation to the other piles, like the elements of our solar system.” Another experiment this article mentioned briefly: “ a cyclical sequence appears in a mixture of salt and water. The salt collects itself in round formations - only to change and break up again. At an unchanged frequency and amplitude these regular cycles repeat themselves. They build up, last for some time and then dissolve again at the same constant tone.” So this sort of does support the idea that the universe was created and sustains in its particular design as a response to vibrations… meaning vibrations are the architect of all of the universe in all of it’s geometry and symmetry and patterns. If you believe this claim, then it is not difficult to also believe that everything in the universe can be expressed mathematically.
Colors are created in wavelengths, which are all made possible by light, which has various wavelengths as well. Light actually has all of the wavelengths, and whatever color we might see at a given moment is created by certain wavelengths bouncing off the object (while others are being absorbed by the object, concealing those colors from us). So all colors are reactions to light, or relationships to light, and colors do not exist without light. All energy derives from sunlight so it’s hard to imagine the things we perceive existing without sunlight. Sound also, can be explained in terms of different wavelengths, as can thoughts apparently, according to the secret. Here are some interesting snippets of other connections between our existence and vibration:
“All living cells, including but not limited to human beings, as described by George Lakhovsky,2 Dr. Cyril,3 and Ivan G. McDaniel,4 give off vibratory waves somewhat similar to those transmitted by a radio station…. these human emanations can even affect various forms of plant life, thereby causing plants to react productively toward emotions of love and encouragement and protectively toward those of hate and anger” (One Flesh).
I think plants are tuned into things that we are not, and why shouldn’t they be, when they are nourished directly from the sun while we are disconnected from the energy of the sun by one step in the food chain, when we eat plants, or sometimes two or three if we choose to eat meat.
“Most stars, including the Sun, pulse continuously due to the violent mixing of gases in their outer layers, says Professor Bedding.
He has described the how a nearby star in our galaxy pulsates by studying the Doppler shift of light waves coming off the star's surface.
And he has developed computer models to show how complex the pulsation is.
‘It doesn't just vibrate simply in and out. It vibrates in lots of different modes simultaneously,’ he says” (Salleh).
Two things which correspond, even if they are in two separate bodies, often share visual and structural characteristics. Our lungs, the orgasn which breathe in what plants breath out is shaped like trees. Our trachea are built with the same branching patters as trees, and both have evolved to exchange CO2 with oxygen in this symbiotic relationship which we’ve maintained for so long. So here we have stars pulsating, and sending out their energy, then we have our bodies which rely on star light (the sun is a star after all), and while it is our digestive tracts which actually take energy into our bodies, it is our hearts which keep energy, blood with oxygen and nutrients flowing throughout our bodies, and hearts pulsate. So hearts are like the stars of our bodies, they distribute energy, they pulse. They are distributing oxygen, which is created in photosynthesis, and nutrients, which usually come from photosynthesizing plants, then hearts are distributing light (though it is in an altered form), throughout our bodies. They are stars inside of us.
“Vibrations Create forms” Bindu Magazine
http://www.yogameditation.com/articles/issues_of_bindu/bindu_10/vibrations_create_forms
Salleh, Anna. ABC Science Online. Vibrations reveal stars' inner secrets. May 15, 2006. ABC News Online: www.abc.net.au/news/newsitems/200605/s1638704.htm
One Flesh Chapter Four: Emotional Influences on the One Flesh Union. www.healing.org/OF-Chap%204.html
The Pacific Institute for the Mathematical Sciences http://www.pims.math.ca/education/2000/bus00/sunflower/
Ivars Peterson. Ivars peterson’s MathTrek. http://www.maa.org/mathland/mathtrek_09_02_02.html
Hi Dani,
Hope your holiday is going well, and you are feeling better. I want you to
remember that life is not bleak although at times it may seem to be that
way. The future can be very scary, but is important that we keep our mind
and body in the present. We don't know what lies ahead of us, and all we
an do is enjoy and utilize the day. Whether that means enjoying the
company of friends or family, or appreciating what we have around us.
Taking a walk with a camera is a nice way to do this as it forces you to
notice al the beautiful and wonderful things that we may let pass by us.
Life is beautiful and God loves us. From this class, besides patterns
(which i found fascinating, especially the golden ratio), I learned that
the one thing that the universe is always striving for is balance. An
equilibrium so to speak. Because of this the universe will always be
working itself out and although it may seem hopeless we are all in the
same boat. We need to lean to balance our life and once that happens and
we can realize this, I believe we can open the doors to true happiness.
Anyways here is my paper, feel free to post your favorite parts on the
blog. Enjoy your break and your health. Remember sunshine wouldn't be so
special if it wasn't for rain.
Coming into What is Math this year I did not really know what to
expect. I could tell coming in that it was not going to be a
traditional math class by any means. What I didn’t realize though was
how much spirituality was involved in the class. In my opinion this
is what made the class for me. I also don’t think that there was any
topic that was debated more in our class then after we watched The
Secret.
Up until then we had had serious discussions about Math as well as
spirituality, but there was always a sense of agreement in the class.
However after we viewed The Secret I don’t think I have heard more
passion in the ideas of others combined throughout the year.
The Secret is a relatively new film, which was made in 2006 and deals
with the “Law of Attraction.” This principle suggests that people’s
feelings and thoughts attract real events in the world based on
positive and objective thinking.
The problem that many people had with the movie though was not only
in the message, but also in the way that it was presented. During the
start of the movie they talk up the secret like it is this ancient
idea that was passed down through the decades, being used by many
successful people along the way, and now it is being passed onto us.
At the start of the movie they have a lot of good information on
positive thinking, but towards the end of the movie it sort of drifts
into the realm of self-help. There were a lot of superficial ideas in
the movie, like the person who imagined themselves in a nice car, and
soon that is what they got. Also there was this kid who all he wanted
was a bike, but he never did anything himself to earn it. He though
about it all the time and even put pictures up on the wall of the
bike as well as drew pictures of himself with the bike and how cool
it was going to be when he got it. Then miraculously some random
elderly gentleman (possibly his grandfather) shows up at the door of
his house caring the exact same bike that he was picturing.
I think that this was the problem that most people had with the movie
were how they were portraying this. The movie made it seem at parts
that through positive thinking you can get what you want or rich.
Obviously this is not the case for everyone. There are certain
environmental and social problems that hinder many people from their
dreams and no matter how hard some people try, they might never
succeed. Also another problem people had is that you can get whatever
you ant just by good thinking and not going out and doing something
about it. The way it was presented might have thrown people out as
well. With statements coming from Reverends as well as self help
authors people though it was a crock.
I believe though that many people were looking at this film in the
wrong light. People were looking at the surface of things and not
paying attention to the underlying concepts of the film, which I find
quite fascinating. If everything affects everything else at the most
basic level, then the universe would be completely different if say I
wasn’t here. It wouldn’t be a dramatic difference on the grand
scheme, but there are definitely people’s lives that I have affected.
Now let’s take that and look at it on a smaller scale. We know now
through modern science and technology that the brain does in fact
emit brain waves when thoughts are being produced. If everything
affects everything then that means that the universe needs to
readjust itself around your thoughts, and with positive and objective
thinking, it is possible to make your thoughts a reality. Now this
does not have to be some out of reach though like marrying a certain
movie star and living in Bermuda, but it still can be applied to your
life. If you want something bad enough, regardless of what it might
be, it is better to think positively about it, then send out negative
thoughts.
As long as we have a brain we are going to be constructing thoughts
as well as actively constructed others and ours universes. To go
through life thinking that you don’t have an impact on anything or
everyone is silly. In the long run the real secret is to be the best,
most sincere person that you can, set some goals, and the world will
work out in your favor.
Zach
1Hannah
What is Math? MWF 3pm
Dani Novak
Final Paper
I wasn’t sure what I wanted to writer this paper on – it’s amazing how college has conditioned us to look for prompts rather than simply using our imaginations. I thought about everything we’ve done this semester and the class as a whole, and came to the title of the course. What is math? Is that really what I expected to learn when I signed myself up for this course? Of course I didn’t believe that the class would answer this very immense question, but I think I did get an answer. I got many answers. The combination of everything we’ve done, the activities, the movies the discussion are all an equation in themselves. Added together, they are math. The contents of the class itself form one of the answers to this question. Really what this class has reinforced in me is the idea that there is often not one answer to any one question. Each component of life is vast and contains multitudes within it. Math, like a human being or an ocean, is an infinite subject without limits or boundaries. It is a part of everything and everything is a part of it, all under the same roof, all participating and existing in the same universe.
I would be lying if I said that this class was not frustrating for me. It was. Often times I felt as if our class were a miniature model of the world. People talked over one another, points got lost, arguments were formed. I would become overwhelmed by the chaos of the class which seemed to so closely resemble a larger chaos in a larger community: the living community, all of it. Despite my frustrations, I tried to be patient. I tried to distinguish voices and decode discussions. I silently engaged myself in others in an attempt to understand. What are they really saying? What do the really mean? This was a new experiment for me. For a long time I rested on a belief that there was no use trying to understand one another. The mind is so bottomless, there are so many things to consider. Anything anyone says could mean something completely different to you and something else to you friend etc etc. And there is no way to know. No way to ever enter the psyche of another person. So what use is there? We will never be wholly understood by anyone else. I decided that this was reason to keep all thoughts to myself and focus entirely on the self. Being the only thing I have remotely any control over, the self was something I could work with, mold and make better. Improve. I set out to improve myself, rid myself of bothersome faults, excommunicate myself from anything social. Excommunication gets rather lonely however, and the self is perhaps even more difficult to a stranger.
As I came out of this phase, a little bummed that I still had not found a comfortable place between myself and other people, I set out to find a new explanation for myself. This is one thing about myself that is really good I think: in general, I am always seeking. Not always finding, as in the case of the example I just gave, but always seeking. I think it is important to never be satisfied with knowledge; to always want a little more. What is math? came just around this time and I incorporated it into my current dilemma right away. What is math? An unanswerable question! I became even more convinced of our inability as humans to understand anything fully. I felt as I often do, that I was only skimming the surface. I wanted more than just bits and pieces. So I searched for meaning in every class. Ruthlessly scoured conversations and expressions and video clips. Read into everything entirely too much and, of course, always came up unsatisfied. Was I missing something? Absolutely. Things are always in the last place you think you’ll find them.
What I’ve found after letting go a little bit, relaxing and carefully considering this course, is the answer to the question asked its title. Math is understanding. There is a connection between all things which I tried to deny, but can no longer ignore. Perhaps I will never fully understand another being or myself, but perhaps that is because there are no “other” beings to begin with, no “self”. There can not be any further understanding, until its been understood that everything is connected and is one. So just as we all are a part of one meaning and one understanding, math is a part of one meaning and one understanding. It is a fraction of the whole and the whole would be incomplete without it.
Chuck Lines
12/21/2007
What is Math?
Dani Novak
Final Paper
From Beginning to End: A Semester in “What Is Math?”
How do I begin to summarize everything that I’ve learned this semester in “What is Math?” I’ve learned more than I expected to in this class; about math, about life, and about myself. I scheduled this class as an easy way to fulfill my major’s math distribution requirement, but it became a class that invited me to think outside the box, expanded my horizons, and opened my eyes to the multitude of ways math is related to life and spirituality.
I’ve always had difficulty with math. I now attribute that to always having been taught mathematics in an almost entirely left brained manner. I personally respond better to a more holistic and right brained learning style. This was the first math related class I have ever taken that strove to teach holistically and brought right brained understanding together with the left brained understanding to bring students to a higher level of comprehension and to develop a feeling for numbers.
As I wrote in my midterm paper, focusing only on one side of the brain is fatal. I learned from the book Randomness that even the right brained thinking that I favored was flawed in some ways. Where the left brained teaching turns students off to math, strictly right brained teaching would open the floodgate for errors and misinterpretation of data and statistics. It is only by allowing the two sides and their individual aspects to work together that we are presented with the whole picture. By utilizing all the aspects of both sides of our brains we can get a feel for the bigger picture in the numbers and be sure our conclusions make sense logically.
I admit I was nervous about the class when we began and didn’t always immediately see the relevance of everything we did, but by the end of our time together I was beginning to grasp the bigger picture. I learned that math isn’t the frightening dragon I’d always perceived it to be. It’s fun! It’s captivating! It’s a beautiful queen; the crystal only visible when we face the things we fear.
Another idea we talked about in class struck me particularly hard. While discussing in class the relationship between Pi and Phi, we began to talk more and more about higher dimensions. It occurred to me that a large number of and maybe even most mathematical principles can be applied numerous times all the way to infinity. For example, we talked about the Fibonacci sequence and how any part blown up sufficiently would resemble a picture of the whole only in miniature.
The same is true of equations, as my group demonstrated at our final. An equation will yield a certain y for each x that is input. This is a first dimension equation such as the equation for how many triangles will be formed by inscribing squares within themselves, with x being the number of inscribed squares and y being the number of triangles created after each inscription. The first dimension finds the pattern in what y’s are yielded by what x’s; how many triangles will be formed by inscribing the squares within themselves any given number of times.
A second dimension equation takes things a step further. It strives to find a higher pattern; to find the pattern that governs the pattern of the equation in the first dimension. It looks for the “master pattern”. To continue with the earlier example, a second dimension equation would introduce another variable. Looking at squares, triangles, and other shapes individually in the first dimension would yield the pattern for how many triangles are produced with each successive inscription for only that shape.
To take that to a higher dimension would be to find the equation that will tell you how many triangles will be formed by inscribing any shape with more than three sides any number of times. This can be done by adding a variable z representing the number of sides of the shape you choose to inscribe within itself. This higher dimension equation would produce the same pattern as in the first dimension if z was kept at four for each successive x, but would also produce the pattern for triangles if z were kept consistently at 3.
As Jeff and Allison related in the scene from Arcadia that they presented, everything is governed by a mathematical equations and all of these are in turn governed by equations in the second dimension. This trend continues to the third and fourth dimensions, the equations governing each becoming more complex with each step, and continues all the way to infinity. If we could see the patterns in the patterns these equations create, we could derive the true master pattern; the equation that governs the answers that all other equations must give.
Perhaps we as a people are a very long way from unlocking the keys to the true master pattern, but, as we learned when we briefly studied the akashic records, that understanding is already within each of us. Life itself is governed by this master pattern, so math is a part of us that cannot be ignored.
It has been my sincerest pleasure to be a part of this class. I’m no longer afraid to bring math into my life and I truly appreciate being given the opportunity to do it. I am determined to share my newfound love of math and the many crystals that it hides. Thank you for helping me to find this part of myself.
Bibliography
Bennett, Deborah J. Randomness. 1998. 2nd ed. Cambridge, Massachusetts: Harvard UP, 1999.
Pink, Daniel H. A Whole New Mind. 2005. 2nd ed. New York, New York: Penguin Group (USA), 2006.
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