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Northern Arizona University/Environmental Ethics/Journals/Spencer S's Journal

Music

Mystic Travels

Forest Rain

Flying Above the Mountains

Lord of the Woodland

Wisdom of Animals

Set Free by the Storm

The Wolf and the Crow

Facing Death With a Charging Spirit

Journal

8/31/09 #1

The state of nature doesn’t vanish entirely after submission to the Leviathan. In one sense, it vanishes as the dominant form of interaction within a group of humans, but in another sense, the state of nature remains contained as a secret wish in every individual, struggling to break free. In the state of nature, there is a constant tendency, or rather, an impulse towards action based solely on self-interest. Only as a necessary evil does the agreement of authority arise (to further self-interest in a more reasonable way), but why would the impulse towards self-interest disappear simply because the types of action it tends to produce are now out of the question? When an authority is designated with the ability to give us security in return for freedom, our self-interest tells us to complete the sacrifice, but at the same time our self-interest also tells us to take any subsequent chance possible that will let us get away with a breach of the Leviathan for a taste of the now archaic statue of nature. In other words, the sacrifice of freedom to authority that ‘necessarily’ comes with a true desire to secure increased self-interest does obviously increase our chances of survival in the long run, but the full satisfaction of exerting power over others never comes. This is why, no matter how much we may wish against it, crime will always exist. The Leviathan can never give us everything that the statue of nature offers. Most will feel complete with the new pleasure, convenience, and increased chances of survival they can obtain under the Leviathan (the ones who faired poorly in the statue of nature), but it remains that the urge for total freedom in the state of nature will always exist. The only question is to what degree does this urge override the safety of the Leviathan.

9/14/09 #2

Beauty and ugliness may seem to be a duality, separately existing from one another, but ugliness is more accurately described as already being contained in all beauty; it is the shadow side of beauty that can be noticed by itself, but not completely separated from its larger whole. Every living thing has in it the history of production from a long line of violence (something most would call ugly). Violence in terms of the number of its ancestors that had to die to make its life even possible, and violence in terms of what its ancestors inflicted on others to survive. When we view something typically beautiful, like a tree, everything that is beautiful becomes amplified, but ugliness is still there (in the form of death, decay, disease, etc.). In just the same way, a negative event in life or an ugly occurrence can't help but be brought to the forefront, creating the impression that it is pure ugliness, but it doesn't mean that beauty still isn't there. This isn't to say that ugliness should be appreciated in the same way as beauty, but it's worth noting that any attitude which tries to ignore the immediately unpleasant aspects of life will be unpleasantly surprised eventually. We should at least confront life and nature in all of its aspects in such a way that allows us to cultivate a sense of respect and awe. This way, any ugly parts can be regarded as simply necessary evils to a more beautiful whole. This also isn't to say that once we get rid of notions of beauty and ugliness, everything becomes beautiful, but rather that typically ugly things can be appreciated in a different way. Death, for instance, is not something pleasant by anyone's standard, but it is something inevitable and necessary, something that drives nature at its very core. This is not beautiful in the same way a flower is beautiful, but beautiful in a more grandiose way, commanding of respect and wonder. We can reject death with fear and paranoia, putting it off with some kind of postmortem speculation, or we can accept it in all its unpleasantness and use it to drive our meaning during life.

Think of it this way: in seeing a group of plants or animals, we can set our minds on all the ones that will die, or all the ones that will live. The former seems tragic, but the latter seems inspiring. Picking a different option doesn't change what is actually happening, it just changes our perception of it. Not that beauty is something up to the whim of every person, the point here is that beauty and ugliness interact in a very close way. Nobody is claiming that a decaying corpse stirs the emotions like a vast expanse of forest, just that both exist in the beauty of nature.

9/22/09 #3

"God" in the deistic sense is really just a poetic way of describing nature; in a single word it summarizes all the infinite qualities and unfathomable depths we experience in the natural world. Why not just simply use the word "nature" instead? I never use the word "God" this way, but I can see why someone would. "Nature", for the average person, or in its everyday use, tends to conjure up an image of something typically pretty, like a forest, something that is obviously aesthetically pleasing, but is not asserted to be more than something nice to look at. We use the word "nature" even for something silly and artificially natural, like a park. On the other hand, the word "God" brings much more into play. It conveys a sense of power, transcendence, awe, and beauty in its perfection. When a person says they are on a quest for God, it is automatically a quest of epic proportions, compared to a quest for "nature" or connectedness to nature, which seems trivial. Of course, most people are talking about God in a theistic way, because it makes them feel important. Atheists rarely prefer to take someone's speaking of God with a grain of salt on the off-chance that they are really just talking about nature, choosing to use a word that has more "inspiring" connotations. Speaking about nature as God also gives it a human quality. It implies that everything was made with the clear intention to benefit humanity, or at the very least not be antagonistic to it. In this way, we can find meaning easily. Finding meaning in pure "nature" is entirely more complex. First of all, we have to create it, it can't just be given by some sort of religious text. Second, it opens up the possibility that nature may even be hostile to us, and we may not be sacred...

10/27/09 #4

The cold outside is something that needs submission in order for us to gain any insight from it. Fighting against the natural conditions and grumbling about how uncomfortable they are only serve to make them more of a problem; if we have to be stuck in the cold, we might as well make the best of it. Normally, we spend so much time complaining that aspects of real life which could have something to teach us pass by (namely, the aspects we are complaining about). Giving in to the cold creates an exhilarating feeling, which may not be one entirely pleasant, but one completely life-affirming. It pushes life at us unfiltered by discomfort or hesitation; we are forced to confront life in all its intensity. This experience is something of the sublime, something or sheer power. Recognizing our powerlessness against the cold (outside of technology), we are humbled and allow life to flow through us.

Indoors versus outdoors is no question, even in circumstances such as the cold. The cold is like a jolt that tears through the stagnation that comes from attempting to make life all pleasant all the time. It's a refreshing, awakening feeling, granted the conditions aren't miserable, but mild to moderate cold should be taken stoically and with excitement. How could this experience be anything but enlightening? It is a test of our limits and a demonstration of these limits within the framework of nature's grand system.

11/3/09 #5

Why do Thoreau and Emerson dislike philanthropy so much? How could someone criticize selflessness of all things? Is it not a godly virtue? But, could it not be selfishness in disguise, a cheap substitute for a stable self?

They see through the facade of "altruism" that modern man wears to cover up his true motives in charity. Emerson himself speaks of donations to the poor thought of as a "penance" that modern man pays as an "apology" for living. This kind of attitude is everywhere: donate a dollar here and there to avoid confrontation with those who would denounce you as selfish, donate fifty dollars once in a while to enjoy the privilege of announcing yourself as a good person, clearly in higher moral standing than those you address. There is no real caring involved, just a taxation to avoid being labeled by the people who get their self-esteem from touting moral superiority for all to recognize and affirm. It is blasphemous to even suggest self-improvement as a high goal, even if it is done as a precursor to some kind of work involving the improvement of others. Who has done better moral work, those who continuously siphon their money to the coffers of another or those who teach others a valuable skill that they can use on their own without dependence? One does not have to avoid philanthropy altogether, one should simply re-examine the intentions behind it. Is it used as a surrogate, a means to enhance self-image, an ego booster, a self-esteem generator? When these things cannot be created independently of verification from others, it is time to stabilize oneself as an individual. Only then can charitable work be rewarding.

11/8/09 #6

Emerson's quest for new values isn't as complicated as it first seems. As a starting point, we have all kinds of sources from history detailing what works and what doesn't work in the way of approaches to life (so many years of history has got to be almost entirely exhaustive), and even if we're working to transcend these years of previous experimentation and start from scratch, certain values will be quickly rewarded by life while others become problematic. We can ensure the accuracy of this project as long as we are continually open. To avoid being duped by a false value for years to come, we need to view life as a continual experiment, where continual examination plays the main part. We must notice how each value begins to shape life. If it is of any productive value, we will be able to feel it moving in a positive direction. Of course, we always have truisms and cliches that will just refuse to be bypassed; these can be the framework in which we experiment with new values. Emerson himself speaks in 'History' of the personal value that all history has: we see in the history we read our own lives, the connection is so obvious that we cannot avoid it. Ancient Greek philosophy has dealt with issues that people still fall prey to today; love of money and social status over truth and wisdom. There is no utopia which we are progressing towards...

11/15/09 #7

One form of self-congratulatory philanthropy that is very prominent today is trendy environmentalism: buy these "green" products, and you're automatically an eco-savior, or at least now have the privilege of acting like one. The strange point that gets lost in all this hip rhetoric is the fact that our trendy sort of environmentalism is just narcissistic consumption with novelty green tacked on. It's a false dilemma. Which should you buy, the "regular" version of the product or the "green" version of the product? How about reject both? This option seems to be conveniently ignored. What is really being said when we're told that switching light bulbs and turning off the faucet will thwart global warming? Not that this literal statement is endorsed, but the general line of thought is. Somehow we're supposed to reconcile unrestrained population growth, unrestrained technological advancement, and unrestrained consumption with a healthy planet. Have we not learned what thinking exclusively in the short-term brings us? Now we're just cloaking it with some kind of pseudo long-term thinking, where the short-term impulse to consume is hidden under a new, more safe justification: well at least now we're endlessly consuming with the earth (read: our reputations and status) in mind. Just buy the "eco-friendly" version and all is well. Isn't getting rid of all our plastic crap more of an "eco-friendly" choice? Environmentalism has become a great-sounding slogan to throw on a t-shirt, and all our politicians now must be up to date with "cutting X by Y by the year Z". The real assumption behind this is that as long as something sounds nice, for all intents and purposes, it is. Common sense says that an exponentially increasing population cannot last forever. Eventually, Nature is going to destructively react to an extent that cannot be avoided by human beings. The entire earth has a carrying capacity too, and humans are straining it. When it finally tops out, we'll have plenty of diseases, natural disasters, and infertility to look forward to.

11/16/09 #8

I connect more deeply with animals than with people in nearly all circumstances. What do they offer that humans do not? For starters, they are non-judgmental and they can't hide their true motives. There is nothing deceptive about an animal. Animals simply are; I can just sit down and watch a crow walk around, and something about it feels better than the typical conversation between human beings, where one party does all the talking and there is some kind of unspoken questioning: what does this person really want from me? This is, of course, excluding stronger relationships. Animals are above the level of petty manipulation. A second interesting characteristic is their lack of speech. All too often, words are used as some kind of distraction; most of us feel uncomfortable in silence. Even when wild animals ignore me, in the silence I feel more connection than in a noisy, crowded room. Of course, animals will show no mercy if it is their prerogative to kill you, but it beats hanging out with a bunch of phonies who want to kill you, but won't admit it. If an animal is showing no rage, it can safely be assumed that you are at best, a minor annoyance. Humans go around messing up perfectly stable ecosystems when the animals show no sign of threat. If this kind of behavior causes personal injury, rest assured you probably deserved it. It would be a better idea to take what wisdom we can from animals and learn from their way of life before we are killed off ourselves by idiocy. Animals may be living more dangerous lives while we sit in the glow of a convenient television, but at least they still have excitement. Now any person has the freedom to be as mundane as he wishes, getting rid of that pesky feeling of true living, awash in passivity and overstimulation. It is high time to take some much needed advice from animals. They've been slowly and efficiently moving along, hindered only by moronic humans who have better things to worry about, like contests to see who can get the closest to alcohol poisoning, important discussions of cartoons and politics, and spending half their life striving to make enough money so they can procure the ability to sit around for the other half.

11/24/09 #9

Parks are a pale shadow of nature; wilderness without the wild. I often wonder why so many gravitate towards them. Is it an attempt to connect with nature? Is it about convenience? Is it about safety? None of these can be used coherently as an excuse when our ecosystems are being laid waste to at an exponential rate, yet we still have lands that one can readily traverse to discover a mystical communion with the natural world. There is nothing natural about a big lawn with a sidewalk stuck in the middle, beside a few trees here and there for good taste. The heavy dose of convenience and safety comes at the expense of danger and reality, all the way establishing an entirely boring atmosphere. Of course, fresh air in a park is better than the stale air brought by too much time indoors, but even more fulfilling is the breath of the forest. When we breathe in the breath of the forest, so much more than a pleasant satisfaction is accomplished. The entire living realm can be taken in during a breath. Couple this with the awe-inspiring sight of the seemingly infinite forest, and a profound appreciation cannot be avoided. Could something like this ever happen in a park. At best, we could gain a sense of inner peace and relaxation, but this is minuscule compared to the staggering power of real nature, the kind of experience that is necessary to spur oneself toward a love of nature, one not superficial, but deep and timeless. Until we actually go out into the natural world and breathe it in, we won't know what is at stake.

11/30/09 #10

Emerson's concept of the lenses brings up an interesting point in relation to one of Leopold's ideas. Essentially, when Emerson claims that we can never resolve the imperfections in our lenses, he is claiming that our experience of reality is subjective, while at the same time it remains that objective reality does exist. This is similar to Leopold's claim that we should respect the innerworkings of nature to such a degree as to admit our own deficiency in ever coming to fully understand them. Of course there are real connections and laws operating, but we can only experience these in varying ways. To experience them unfiltered and directly would suggest that the conqueror role is justified, so perhaps this subjective experience of objective reality is necessary to remind us of the fact that our understanding is limited, and even the most advanced theories and experiences cannot completely predict seemingly random surprises. When we can fully admit that a direct experience of reality is impossible and simultaneously admit that this does not mean that reality is up to us, we can begin to approach Leopold's recommendation fully. This admission ought to capture an experience of the sublime, setting us up to realize just how vast the sea of ignorance really is.

12/1/09 #11

The cause of environmental collapse can be narrowed down to an obsession with short-term thinking. As Kaczynski argues, in the course of technological progress, each tiny step can be easily justified by taking it out of context; every aspect can be seen as beneficial, necessary, or harmless, at the very least. When we think "it's just one more tiny step", but then say this every single time as we take hundreds and hundreds of "tiny" steps, each one harmless by itself, but together monumentally harmful, we have sealed our doom. Each passing day seems completely safe because the change is so extremely gradual that it cannot be seen unless our thinking is adjusted toward the long-term. Sure, eating a few donuts "today" is essentially harmless, but when each day becomes "well, it's just today", a monster has been created. This is analogous to our problems with the environment. Of course, on a day-to-day basis, they are not at all obvious. Everything is still running smoothly, and if it becomes slightly more degraded tomorrow, nobody will notice. Thinking in the long-term shuns this fate of a cliched 'frog in the slowly boiling water' and gets us ready for real progress.

This lesson can be applied everywhere. The typical modern approach is to think of every day as "just today" (except in the case of mindless career ladder-climbing), effectively making any choice seem like a great one, or at least minimally harmful. When the long-term effects of cumulative short-term choices begin to pile up and the consequences are obvious, only then will be spurred into change if we can avoid the temptation of changing "tomorrow", which is never here, always in the future.

12/7/09 #12

The snow that came this morning is a great testament to the power of nature. We couldn't help but shut down so many of our typical activities; anything less would have been dangerous, at least, any activity that couldn't be accomplished on foot. It's paradoxical, in a way. A big snowstorm comes and it encourages everyone to stay indoors. If this was combined with a power outage, the options would have been limited even more. Everyone would be forced to reorganize their day, prioritizing often-ignored activities like reading and socializing.

Walking outside in a forest full of snow gives off a completely serene feel at points in the day, like nobody else in the world exists. The landscape seems to stretch on forever and the horizon meets the sky. Wind covers up the usual sounds, or the sounds level out to a pure silence, real, true silence. The snow blankets every tree, making the forest look more like a vast plane with differing shapes, but not in a way that is monotonous. It's more like the size and power of everything is amplified. Go to far and the landmarks will disappear, white as far as the eye can see, no sense of direction. It's cold and death will slowly begin to creep up as soon as it can. This kind of feeling is completely exhilarating, even if the circumstances are only slightly life-threatening. The forest always carries an aura of death, underlying all the plants and geography. It's everywhere, but seems to be nowhere at the same time. It could come up and kill, but there is no way to predict when and where.

12/10/09 #13


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User:Egm6321.f09.team4/HW2

Homework #2: Team 4 (Complete)  Please add 'EDIT' links to each problem so that I can leave feedback one problem at a time. Without these links I have to scroll through your entire page to find each line. This will also assist you in editing your problems. --Egm6321.f09.TA 03:29, 28 September 2009 (UTC)

The way you "add the 'EDIT' link" is to create sections and subsections using the equal signs "=", instead of using the html code H4; see the HW report of Team 1 or my Lecture Plan as examples. Egm6321.f09 13:14, 1 October 2009 (UTC) Problem #1:

(Lecture 7-1)

Given :
 * $$h_xN-h_yM+h(N_x-M_y)=0$$

 Start a line before this, with $$hM+hNy'=0$$ to show where this equation comes from. --Egm6321.f09.TA 03:45, 28 September 2009 (UTC) Find :
 * Solve for h(x,y) given that $$h_xN=0$$

Solution :

 * Substitute $$h_xN=0$$, then move one term to right-hand side of equation:

 * $$ \begin{align}

-h_{y}\left(x,y\right)M\left(x,y\right) + h\left(x,y\right)\left(N_{x}-M_{y}\right) &= 0 \\ h\left(x,y\right)\left(N_{x}-M_{y}\right) &= h_{y}M\left(x,y\right) \end{align} $$

 * Isolate terms involving $$h\left(x,y\right)$$, then simplify using definition of derivative of $$\text{ln}\left(u\right)$$:

 * $$ \begin{align}

\frac{h_{y}\left(x,y\right)}{h\left(x,y\right)} &= \frac{1}{M}\left(N_{x} - M_{y}\right) \\ \frac{\partial}{\partial y}\left\{\text{ln}\left[h\left(x,y\right)\right]\right\} &= \frac{1}{M}\left(N_{x}-M_{y}\right) \end{align} $$

 * Integrate both sides of the equation, then take the exponential function of both sides:

 * $$ \begin{align}

\text{ln}\left[h\left(x,y\right)\right] &= \int\frac{1}{M}\left(N_{x}-M_{y}\right)dy + C\left(x\right) \\ h\left(x,y\right) &= C\left(x\right) \text{exp}\left[ \int\frac{1}{M}\left(N_{x}-M_{y}\right)dy\right] \end{align}$$

Problem #2: (Lecture 8-2)

Given :

 * The non-homogeneous linear 1st Order ODE with Varying Coefficients $$y^{\prime}+\frac{1}{x}y=x^2$$

Find :

 * Verify that the integrating factor necessary to make the ODE exact is $$h(x)=x$$

Solution :

Multiplying through by h(x) yields:

 * $$xy^{\prime}+y=x^3$$

In order to be exact, both exactness conditions for 1st Order ODE's must be satisfied. To satisfy the first condition, the ODE must have the form:
 * $$F(x,y)=M(x,y)+N(x,y)y^{\prime}=0$$

Rearranging terms of our ODE after multiplication by the integration factor gives:

 * $$F(x,y)=\left (x \right )y^{\prime}+\left (y-x^3  \right )=0$$

Where $$N(x,y)=x$$ and $$M(x,y)=y-x^3$$ Therefore the first exactness condition is met. To verify the second exactness condition we must show:

 * $$M_y=N_x$$

We differentiate M and N with respect to y and x,

 * $$M_y(x,y)=1$$

 * $$N_x(x,y)=1$$

Therefore, both exactness conditions are satisfied and the 1st order ODE is exact.  You did not show that the solution is $$y(x)=1/4\cdot x^3 +\frac{1}{x}C$$. You showed that the integrating factor $$x$$ does indeed put the equation in an exact form, but you did not solve it. --Egm6321.f09.TA 03:45, 28 September 2009 (UTC) Problem #3:  (Lecture 9-2)

Given :

 * $$\frac{1}{2}x^2y^{\prime}+[x^4y+10]=0$$

Find :

 * Show that the above linear, 1st Order, ODE-VC is either exact, or exactly integrable by the integrating factors method.

Solution :

First, does this linear, first-order ODE satisfy the conditions for exactness?

 * If $$M$$ and $$N$$ are defined as follows:

 * $$ \begin{align}

M\left(x,y\right) &= x^{4}y + 10 \\ N\left(x,y\right) &= 0.5 x^{2} \end{align} $$

 * Then, can we find some function $$\Psi\left(x,y\right)$$ such that:

 * $$ \begin{align}

\frac{d\Psi\left(x,y\right)}{dx} &= M\left(x,y\right) \\ \frac{d\Psi\left(x,y\right)}{dy} &= N\left(x,y\right) \end{align} $$

 * For each equation, integrate both sides:

 * $$ \begin{align}

\Psi\left(x,y\right) &= \int{M\left(x,y\right)}dx + g_{1}\left(y\right) = \frac{x^5y}{5} + 10x + g_{1}\left(y\right) \\ \Psi\left(x,y\right) &= \int{N\left(x,y\right)}dy + g_{2}\left(x\right) = \frac{x^2y}{2} + g_{2}\left(x\right) \end{align} $$

 * Note that no choice of the arbitrary functions of integration $$g_{1}\left(y\right)$$ and $$g_{2}\left(x\right)$$ will make these two equations equal, due to the different powers of $$x$$ in the first term. So, this equation does not meet the conditions for exactness.

Since this ODE isn't exact, is it exactly integrable by the integrating factors method?

 * The equation under consideration can be rewritten in the following form, by multiplying both sides with $$2x^{-2}$$:

 * $$ \begin{align}

y' + p\left(x\right)&y = g\left(x\right) \\ \text{where} \quad &p\left(x\right) = 2x^{2} \\ &g\left(x\right) = -20x^{-2} \end{align} $$

 * Since this equation is a linear, first-order ODE with this particular structure, it is integrable via the integrating factors method. Let $$\mu\left(x\right)$$ be the integrating factor, then multiply both sides of the equation by it:

 * $$ \begin{align}

\mu\left(x\right)y' + \mu\left(x\right)p\left(x\right)y = \mu\left(x\right)g\left(x\right) \end{align} $$

 * If we then assume that $$\mu\left(x\right)$$ satisfies $$\mu\left(x\right)p\left(x\right) = \mu'\left(x\right)$$, this equation becomes:

 * $$ \begin{align}

\mu\left(x\right)y' + \mu'\left(x\right)y &= \mu\left(x\right)g\left(x\right) \\ \frac{d}{dx}\left[ \mu\left(x\right)y \right] &= \mu\left(x\right)g\left(x\right) \quad \text{(product rule)} \end{align} $$

 * Integrating both sides of the equation, then solving for $$y$$, yields the following solution to the ODE:

y = \frac{\int{\mu\left(x\right)g\left(x\right)dx + c}}{\mu\left(x\right)} $$

 * To find $$\mu\left(x\right)$$, we then use the assumption described above:

 * $$\begin{align}

\mu\left(x\right)p\left(x\right) &= \mu'\left(x\right) \\ p\left(x\right) &= \frac{\mu'\left(x\right)}{\mu\left(x\right)} \\ p\left(x\right) &= \frac{d}{dx}\left[ \text{ln}\left(\mu\right) \right] \\ \int{p\left(x\right)}dx + k &= \text{ln}\left(\mu\right) \quad \text{(choose k=0)}\\ \int{2x^{2}}dx &= \text{ln}\left(\mu\right) \\ \mu\left(x\right) &= \text{exp}\left( \frac{2}{3}x^{3} \right) \end{align}$$

 * Finally, the solution to the equation is obtained by plugging in $$\mu\left(x\right)$$ and $$g\left(x\right)$$:

y = \frac{ -20\int{\text{exp}\left(\frac{2}{3}x^{3}\right)x^{-2}}dx + c }{\text{exp}\left(\frac{2}{3}x^{3}\right)} $$

 * While the solution to this integral is very difficult to obtain, it does exist. Therefore, this equation is exactly integrable via the integrating factors method.

 You were asked to show exactness, not solve for the solution. Calculating $$h(x,y)$$ (or in your case)$$\mu(x,y)$$ and verifying that$$\overline{N}_x=\overline{M}_y$$ would have sufficed. --Egm6321.f09.TA 03:45, 28 September 2009 (UTC)

Problem #4:  (Lecutre 9-3) Lecture 9-3 Given :

 * $$\frac{1}{3}x^3(y^4)y^{\prime}+(5x^3+2)(\frac{1}{5}y^5)=0$$

Find :

 * Show that the above equation is an exact nonlinear 1st Order ODE or integrable by the integrating factors method.

Solution :

To simplify, first divide through by $$y^4$$

 * $$\frac{1}{3}x^3y^{\prime}+(5x^3+2)(\frac{1}{5}y)=0$$

Notice that

 * $$\underset{N}{\underbrace{\frac{1}{3}x^3}}y^{\prime}+\underset{M}{\underbrace{{}(5x^3+2)(\frac{1}{5}y)}}=0$$

For exactness,

 * $$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$$

For our case,

 * $$\frac{\partial }{\partial y}((5x^3+2)(\frac{1}{5}y))=\frac{\partial }{\partial x}(\frac{1}{3}x^3)$$

 * $$\frac{1}{5}(5x^3+2)\neq x^2$$

This equation is therefore not exact. To see if it is integrable, we manipulate the original equation

 * $$\frac{1}{3}x^3y^{\prime}+(5x^3+2)(\frac{1}{5}y)=0$$

 * $$y'+\left (\frac{x^{3}+\frac{2}{5}}{\frac{1}{3}x^3} \right )y=0$$

This equation now has the form of,

 * $$y'+p(x)y=0$$

Multiple by each side of the above by integrating factor, $$h(x)$$

 * $$h(x)y'+h(x)p(x)y=0$$

We shall chose choose $$h(x)$$ such that

 * $$h(x)p(x)=h'(x)$$

 * $$p(x)=\frac{h'(x)}{h(x)}$$

Integrate,

 * $$\int p(x)dx=ln(h(x))$$

 * $$\int \left [\frac{x^{3}+\frac{2}{5}}{\frac{1}{3}x^3} \right ]dx=ln(h(x))$$

 * $$\int \left [3+\frac{6}{5}x^{-3} \right ]dx=ln(h(x))$$

Therefore,

 * $$h(x)=C_{1}e^{3x-\frac{6}{10}x^{-2}}$$

Let $$C_{1}=1$$ because it is arbitrary

Recall that this was selected so that

 * $$h(x)y'+h(x)p(x)y=0$$

 * $$\frac{\partial }{\partial x} \left [h(x)y(x) \right ]=0$$

 * $$\left [h(x)y(x) \right ]=C_{2}$$

 * $$y(x)=\frac{C_{2}}{h(x)}$$

And so,

 * $$y(x)=\frac{C_{2}}{e^{3x-\frac{6}{10}x^{-2}}}$$

This equation is integrable only for intervals where $$x\neq 0$$  Calculate $$h(x,y)$$ and then verify $$\overline{N}_x=\overline{M}_y$$. You were not asked to determine the solution, merely verify an exact form. --Egm6321.f09.TA 03:45, 28 September 2009 (UTC) Problem #5:
 (Lecture 10-3)

Given :

 * $$(xy)y{}''+x(y{}'^{2})+yy{}'=0$$

Find :

 * Determine if the 2nd condition for exactness is satisfied for the above equation.

Solution :

 * First, note that this equation can be rewritten in the following form:

 * $$\begin{align}

f\left(x,y,p\right)y'' + g\left(x,y,p\right) &= 0 \\ \\ \text{where} \quad f\left(x,y,p\right) &= xy \\ g\left(x,y,p\right) &= xp^{2} + yp \\ p &= y' \end{align}$$

 * This means that the first condition of exactness is satsified. For the second condition, two equations involving the partial derivatives of $$f$$ and $$g$$ must be satisfied:

 * $$\begin{align}

\text{(a)} \quad &f_{xx} + 2pf_{xy} +p^{2}f_{yy} = g_{xp} + pg_{yp} - g_{y} \\ \text{(b)} \quad &f_{xp} + pf_{yp} + 2f_{y} = g_{pp} \end{align}$$

 * Values for each of the required partial derivatives are obtained from the definitions of $$f\left(x,y,p\right)$$ and $$g\left(x,y,p\right)$$:

 * $$\begin{align}

&f_{xx}=f_{yy}=f_{xp}=f_{yp}=0, \quad f_{xy}=1, \quad f_{y} = x \\ &g_{xp}=2p,\quad g_{yp}=1,\quad g_{pp}=2x,\quad g_{y}=p \end{align}$$

 * These values are then substituted into the two equations from the second condition:

 * $$\begin{align}

\text{(a)} \quad &\left(0\right) + 2p\left(1\right) +p^{2}\left(0\right) = \left(2p\right) + p\left(1\right) - \left(p\right) \\ \text{(b)} \quad &\left(0\right) + p\left(0\right) + 2\left(x\right) = \left(2x\right) \\ \\

\text{(a)} \quad & 2p = 2p +p - p = 2p \\ \text{(b)} \quad & 2x = 2x \end{align}$$

 * Conditions (a) and (b) are both satisfied. Therefore, this ODE is exact.

 Instead of working two equations simultaneously, show one equation from the second exactness condition and then show the other. Working a.) b.) .... a.) b.)  is confusing to the reader. --Egm6321.f09.TA 03:56, 28 September 2009 (UTC)
Problem #6:
 (Lecture 11-2)

Given : Equation (5) of 10-2,

 * $$f_{xp}+pf_{yp}+2f_{y}=g_{pp}$$

Find :

 * Derive the above equation by differentiating Equation (3) of 10-1, which is,

 * $$g(x,y,p)=\Phi _{x}+\Phi _{y}p$$

 * with respect to $$p=y{}'$$.

Solution :

First find the partial derivative of g(x,y,p) with respect to p:

 * $$g_p=\frac{\partial}{\partial p}\left ( \Phi_x+\Phi_y p \right )$$

 * $$g_p=\Phi_{xp}+p\Phi_{yp}+\Phi_y$$     by the Product rule

The second partial derivative of g with respect to p is similar:

 * $$g_{pp}=\frac{\partial }{\partial p}\left ( \Phi_{xp}+p\Phi_{yp}+\Phi_y \right )=\Phi_{xpp}+\Phi_{yp}+p\Phi_{ypp}+\Phi_{yp}$$    by the Product rule

Because of the nature of the exactness condition, the order of differentiation does not matter, therefore:
 * $$\Phi_{xpp}=\Phi_{pxp}=\frac{\partial^2}{\partial p \partial x}\left ( \frac{\partial \Phi}{\partial p} \right )=\frac{\partial^2}{\partial p \partial x}\left ( f \right)$$
 * where $$f=\frac{\partial \Phi}{\partial p}=\Phi_{p}$$

Making the appropriate substitutions for every term with a partial derivative of $$\Phi$$ with respect to p.

 * $$g_{pp}=\Phi_{xpp}+\Phi_{yp}+p\Phi_{ypp}+\Phi_{yp}$$

 * $$g_{pp}=(\Phi_{p})_{xp}+(\Phi_{p})_{y}+p(\Phi_{p})_{yp}+(\Phi_{p})_{y}$$

 * $$g_{pp}=f_{xp}+f_{y}+pf_{yp}+f_{y}$$

The final result is:

 * $$g_{pp}=f_{xp}+pf_{yp}+2f_y$$

 nice work. --Egm6321.f09.TA 03:56, 28 September 2009 (UTC)

Problem #7:
 (Lecture 12-1)

Given :

 * $$\Phi _{xy}=\Phi _{yx}$$

Find :

 * Use the above relationship to derive the following 1st relationship in exactness (condition 2) for N2, ODEs;

 * $$f_{xx}+2pf_{xy}+p^{2}f_{yy}=g_{xp}+pg_{yp}-g_{y}$$

Solution :

Working from the relations: $$\Phi_{xy}=\Phi_{yx}$$,$$\Phi_{xp}=\Phi_{px}$$,$$\Phi_{py}=\Phi_{yp}$$,

and the expressions: $$f=\Phi_p$$ and $$g=\Phi_x+\Phi_yp$$

We obtain:

$$\Phi_{xy}=\Phi_{yx}\Rightarrow \left ( \Phi_x \right )_y=\left ( \Phi_y \right )_x$$ where $$\Phi_x=g-p\Phi_y$$ and $$\Phi_y=\frac{1}{p}\left ( g-\Phi_x \right )$$

Plugging in and taking the derivative, we obtain: $$\left ( \Phi_x \right )_y=\left ( \Phi_y \right )_x\Rightarrow \left ( g-p\Phi_y \right )_y=\left ( \frac{1}{p}\left [ g-\Phi_x \right ] \right )_x\Rightarrow g_y-p\Phi_{yy}=\frac{1}{p}g_x-\frac{1}{p}\Phi_{xx}$$

From another relation, we can obtain: $$\Phi_{yp}=\Phi_{py}\Rightarrow \left ( \Phi_y \right )_p=\left ( \Phi_p \right )_y\Rightarrow\left (\frac{1}{p}\left [ g-\Phi_x \right ] \right )_p=f_y\Rightarrow -\frac{1}{p^2}\left ( g-\Phi_x \right )+\frac{1}{p}\left ( g_p-\Phi_{xp} \right )=f_y$$

From here we see that $$\Phi_{xp}=\Phi_{px}\Rightarrow\ \left ( \Phi_p \right )_x=f_x$$ and rearranging terms gives:

$$\Phi_x=g-p\left ( g_p-f_x \right )+p^2f_y$$

From the last relation we have: $$\Phi_{xp}=\Phi_{px}\Rightarrow \left ( \Phi_x \right )_p=\left ( \Phi_p \right )_x\Rightarrow \left ( g-p\Phi_y \right )_p=f_x\Rightarrow g_p-\Phi_y-p\Phi_{yp}=f_x$$

Again we see that $$\Phi_{yp}=\Phi_{py}\Rightarrow\ \left ( \Phi_p \right )_y=f_y$$, and rearranging terms gives:

$$\Phi_y=g_p-pf_y-f_x$$

$$\Phi_x$$ and $$\Phi_y$$ are then substituted back into the relation we obtained from $$\Phi _{xy}=\Phi _{yx}$$ as follows:

$$g_y-p\left ( g_p-pf_y-f_x \right )_y=\frac{1}{p}g_x-\frac{1}{p}\left ( g-p(g_p-f_x)+p^2f_y \right )_x$$

Taking the remaining derivatives and simplifying yields:

$$g_y-p\left ( g_{py}-pf_{yy}-f_{xy} \right )=-\frac{1}{p}\left ( g_x-g_x-p(g_{px}-f_{xx})+p^2f_{yx}) \right )$$

$$g_y-pg_{py}+p^2f_{yy}+pf_{xy}=g_{px}-f_{xx}-pf_{yx}$$

$$g_y-pg_{py}-g_{px}=-2pf_{xy}-p^2f_{yy}-f_{xx}$$

Multiplying through by negative one gives the final solution:

$$f_{xx}+2pf_{xy}+p^{2}f_{yy}=g_{xp}+pg_{yp}-g_{y}$$

 You made a great deal of extra work for yourself. Start with $$\Phi_{xy}=\Phi_{yx}$$ and proceed from there, using expressions for $$\Phi_x$$ and $$\Phi_y$$. You do not need to have these $$\frac{1}{p}$$ terms in your solution. --Egm6321.f09.TA 03:56, 28 September 2009 (UTC)

Problem #8:
 (Lecture 12-2)

Given :

 * $$f=8x^{5}p$$

 * $$g=2x^{2}p+20x^{4}p^{2}+4xy$$

Find :

 * Show that equations (4) and (5) on 10-2 for exactness are satisfied for the above equations. Equations (4) and (5) are

 * $$ \begin{align}

\text{(a)} \quad & f_{xx}+2pf_{xy}+p^{2}f_{yy}=g_{xp}+pg_{yp}-g_{y} \\ \text{(b)} \quad & f_{xp}+pf_{yp}+2f_{y}=g_{pp} \end{align} $$

Solution :

 * Values for each of the required partial derivatives are obtained from the definitions of $$f$$ and $$g$$:

 * $$ \begin{align}

&f_{xx} = 160x^{3}p, \quad f_{xp}=40x^{4} \\ &f_{xy} = f_{yy}=f_{yp}=f_{y}=0 \\ &g_{xp} = 4x + 160x^{3}p, \quad g_{pp}=40x^{4} \\ &g_{yp} = 0, \quad g_{y}=4x \end{align}$$

 * These values are then substituted into the two equations from the second condition:

 * $$ \begin{align}

\text{(a)} \quad & 160x^{3}p + 2p\left(0\right) + p^{2}\left(0\right) = \left(4x+160x^{3}p\right) + p\left(0\right) - 4x \\ \text{(b)} \quad & 40x^{4} + p\left(0\right) + 2\left(0\right) = 40x^{4} \\ \\ \text{(a)} \quad & 160x^{3}p - 160x^{3}p = 4x - 4x \\ \text{(b)} \quad & 40x^{4} = 40x^{4} \\ \\ \text{(a)} \quad & 0 = 0 \\ \text{(b)} \quad & 0 = 0 \end{align} $$

 * Both equations (a) and (b) are satisfied.

 Again, work on one equation at a time. Mathematical explanations never evolve two equations simultaneously. --Egm6321.f09.TA 03:56, 28 September 2009 (UTC)
Problem #9:
 (Lecture 12-3)

Given :

 * $$\sqrt{x}y{}''+2xy{}'+3y=0$$

Find :

 * Verify exactness of the above ODE.

Solution :

 * The first condition of exactness is that the equation follows the following expression:

 * $$\begin{align}

f\left(x,y,p\right)y'' + g\left(x,y,p\right) &= 0 \\ \\ \text{where} \quad f\left(x,y,p\right) &= x^{\frac{1}{2}} \\ g\left(x,y,p\right) &= 2xp + 3y \\ p &= y' \end{align}$$

 * The first condition of exactness is satsified. For the second condition, two equations must be satisfied:

 * $$\begin{align}

\text{(a)} \quad &f_{xx} + 2pf_{xy} +p^{2}f_{yy} = g_{xp} + pg_{yp} - g_{y} \\ \text{(b)} \quad &f_{xp} + pf_{yp} + 2f_{y} = g_{pp} \end{align}$$

 * Values for each of the required partial derivatives are obtained from the definitions of $$f\left(x,y,p\right)$$ and $$g\left(x,y,p\right)$$:

 * $$\begin{align}

&f_{xx}=-\frac{1}{4}x^{-\frac{3}{2}} &f_{xy}=f_{yy}=f_{xp}=f_{yp}=f_{y}=0 \\ &g_{xp}=2,\quad g_{yp}=g_{pp}=0,\quad g_{y}=3 \end{align}$$

 * These values are then substituted into the two equations from the second condition:

 * $$\begin{align}

\text{(a)} \quad &\left(-\frac{1}{4}x^{-\frac{3}{2}}\right) + 2p\left(0\right) +p^{2}\left(0\right) = \left(2\right) + p\left(0\right) - \left(3\right) \\ \text{(b)} \quad &\left(0\right) + p\left(0\right) + 2\left(0\right) = \left(0\right) \\ \\

\text{(a)} \quad & -\frac{1}{4}x^{-\frac{3}{2}} = -1 \\ \text{(b)} \quad & 0 = 0 \end{align}$$

 * Only condition (b) is satisfied. Therefore, this ODE is not exact.

 Good. --Egm6321.f09.TA 03:56, 28 September 2009 (UTC)

Contributing Team Members:
 Egm6321.f09.Team4.meyerat 03:33, 23 September 2009 (UTC)

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Northern Arizona University/Environmental Ethics/Journals/Tucker H's Journal

Tucker Herbert Phil 331 Journal Entry #1 Aug. 30, 2009

During the course of his life, Aldo Leopold developed the notion that the human race needed to make a transition. He believed that a change was needed in our relationship to the rest of nature. We can make this transition if we start to see ourselves as citizens and members of a larger biotic community who treat the land as more than just property. There is no denying the need for a land ethic now more than ever. During my lifetime I have witnessed the destruction of earth’s natural resources at an enormous scale in the absence of any real land ethic. My greatest fear is that my generation will have nothing truly natural left to pass on to our children. I grew up in a rural part of Maryland where my brother, sister, and I spent almost every day of our childhood exploring and discovering the natural world. It was my parents who encouraged me to join the Boy Scouts of America where I first learned how to respect and protect the land. I see the children of today becoming alarmingly disconnected from nature at a very young age. Playing capture the flag with the neighborhood kids and family camping trips are being replaced by video games, the internet, and resort vacations. Perhaps the best solution to this problem can be found in education. Respect for the environment and the need to become citizens of a larger biotic community is something children should be taught from the minute they begin their education. It wasn’t until my first year of community college that I took a course involving the environment. For children, the development of ethics and morals begins at a very young age. Why not then expose our future generations to the idea of a land ethic when they first start their educational careers. We need to take our children away from the television and expose them to the natural world as much as possible. I happened to be fortunate enough to have parents who understood how important it was for me to have a connection to nature. We know that communities are built on individuals connecting and cooperating with other individuals. Educating future generations about the land ethic and respect for the natural world will help us to build stronger communities where humans not only look out for the needs of each other, but those of the land as well.

Tucker Herbert Phil 331 Journal Entry #2 Sept. 8, 2009

While camping this weekend with some friends I had an opportunity to really think about some ideas that we have been discussing throughout the semester. Aldo Leopold believed that by viewing ethics from an ecological perspective, we can see that evolution is based on cooperation between species. The last couple days before we headed out into the woods, I spent a good amount of time watching different episodes of Planet Earth. The series is one of my all time favorites because it so vividly illustrates the delicate relationships that every species on earth share. While Darwin’s theory of evolution makes all nature seem violent, destructive, and based on predation, Leopold focused more on the cooperation between species. As I sat on our hillside campsite and looked out towards endless miles of Ponderosa pine stretching all the way to to the horizon, I couldn’t help but think of how important every tree was to the entire biotic community. For each individual tree I imagined a unique ecosystem consisting of plants, insects, squirrels, elk, and various other animals of the forest. Without the trees, what would sustain all of those living creatures?

Living in Flagstaff over the past year has come to be a real blessing for me. I came here to not only receive a degree in environmental studies, but to also surround myself in natural beauty. Back home in Maryland I felt as if I was starting to disconnect from nature, something I had known very well my entire childhood. The busier my schedule became, the less time I found for treks to the forest. Friends began moving away and with them went our camping trips to the Appalachian Mountains. I started feeling that in order to really grasp a degree in environmental studies; I had to reconnect myself with nature. Sitting on that hillside, watching the pines sway back and forth in the wind like the waves of the ocean, I knew I had finally found home. Leopold spoke at length about the importance of communities. Perhaps someone has to feel that they belong to a community before they can fulfill their obligations to it. It’s taken almost a year and a half, but Flagstaff is now a community that I feel a part of. This doesn’t mean that I have been any less of a good citizen in that time. I recycle, I work, I volunteer, and I’ve put a lot of effort into my education. After this weekend, I consider protecting and respecting the land around me as larger part of my moral obligation to this community. This leads me to believe that a land ethic can be found if we can see just how important a role we all can play in the biotic community.

Tucker Herbert Phil 331 Journal Entry #3 Sept. 12, 2009

I have found myself struggling with some of the arguments pertaining to the Romantic Movement in regards to the biotic community. I personally do not believe that beauty has to be a real aspect of the natural world. Why must we see something as beautiful before we begin to respect its worth? I don’t like to think of beauty as some sort of biotic evaluation that in turn gives some organism’s greater worth. Perhaps human society has become so wrapped up in our own perceptions of what is beautiful that we have blurred our perceptions of what is also valuable. An organism in the biotic community should never be seen as more valuable than another simply because it appeals more to our senses. Many of our current economic and environmental problems stem from our culture’s obsessions with material wealth. Our current capitalist market is fueled by marketing forces that lead us to believe that the products we currently own are no longer in style. In order to keep up with the so-called status quo, we are driven to the mall or department store to purchase the latest fashions. The result of this wasteful cycle is a natural resource stock hold that is being depleted at an alarmingly fast rate. I’ve heard many times that American citizens alone are responsible for consuming one-third of the earth’s natural resources. I believe that we have managed to somehow carry these materialistic tendencies over to the biotic community. If something in the natural world is perceived to be ugly in some way, we often find ourselves ignoring it. Qualities like taste, texture, and odor are not found only in our perception. They are in every living organism and as such, they account for every organism having its own inherent worth. It is unfortunate that we must see something as beautiful before it evokes an emotional response in us. An emotional response to an organism is likely to lead to concern for the well-being of that organism. Only by respecting and loving every organism will we ever be able to achieve a true balance within the biotic community. Beauty is in the eye of the beholder, and in this case, the beholder can too often be naïve.

Tucker Herbert Phil 331 Journal Entry #5 Sept. 27, 2009

For anyone who has ever made the trip, it isn’t hard to see why John Muir fell in love with Yosemite. When our class was asked who had been to Yosemite, it didn’t surprise me that half of the class raised their hands. My first visit to Yosemite last summer was an incredible experience. Although I was only able to spend one day in the valley, the place left a lasting impression on me. Being in Yosemite National Park, you get the feeling that you are in a special place that has been blessed by God. It is no wonder that this is the place where John Muir developed his concept of nature as the “sublime.” I understand the sublime in nature as something sacred and beautiful. It is something awe-inspiring and humbling at the same time. In class we described the sublime as an overwhelming awe that makes us feel insignificant because nature is so powerful. We feel so insignificant because our lives seem so finite in comparison to nature. Nature has a sense of continuity to it that doesn’t compare to human lives. In Yosemite, John Muir was able to see that the world we live in was not put together with just us in mind. I think this is such an important idea because we have seen the mistakes that have resulted from our attempts to dominate the land to our benefit. John Muir is known to many as one of the most influential preservationists and environmentalists of his time. He was one of the first at the time to stress the idea that nature and wilderness were good for their own sake and should therefore be protected. This goes back to Leopold’s ideas of the land having inherent worth. What separates Muir and Leopold are the separate platforms they used to express their ideas. Aldo Leopold used the principles of ecology to get his message across while John Muir focused more on the aesthetic qualities of nature, the beautiful and the sublime. Being slightly more arts oriented, I find it easier to connect with John Muirs descriptions of nature. Having visited his beloved Yosemite, I see why the man chose to dedicate his life to protecting the one thing he loved the most, the natural world and every living creature within it.

Tucker Herbert Phil 331 Journal Entry #6 Oct. 4, 2009

I have an older brother named Jay that reminds me a little of Henry David Thoreau. A few years ago, Jay decided he wanted to drop out of college and live on an organic farm in Vermont. The first section of Walden, titled Economy, reminds me of the type of questions my brother was asking when he left society for the peace and quiet of the woods. Why do men toil and slave their lives away in order to buy a bunch of things that they don’t really need? I like how Thoreau states that “the civilized man is a more experienced and wiser savage.” I think it would be safe to say that men like my brother are becoming a rarer breed of individual. He once told me he didn’t need to go into debt trying to pay for a college education because all the knowledge he needed he could get from reading a book. Thoreau points out that, “Those things for which the most money is demanded are never the things which the student most wants.” Jay would most certainly agree because he gets his education from reading, writing, personal reflection, and conversing with his peers. Jay has never had a cell phone, he drove a car for only a couple years of his adult life, and he makes the effort to sew his own clothing and grow his own food. Thoreau wanted to know what makes men need all these seemingly meaningless material goods. When he speaks of rich men and all their material possessions, Thoreau remarks, “the more you have of such things the poorer you are.” There isn’t a day that goes by that I’m not a little envious of the life my brother is living. I go through my days feeling stressed out and constantly rushed. Wouldn’t it be easier just to walk away from it all? I feel that I could live a simple life and still be happy. I think that is one of Thoreau’s main points in Economy, the more you burden yourself with, the less time you have for personal reflection and leisure, the very things that bring about happiness.

In my case, I think I want to stick it out and finish my college education. The daily temptation to walk away from it all will never leave me, but I happen to find my major very interesting and therefore worth pursuing. In the end, I think all humans must find out what things in their life are worth pursuing. For my brother, the path he chose for himself has brought forth a lot of personal growth and satisfaction. Society can be a dangerous hindrance to living a simpler life. It dictates to us what we should be doing with our lives when the real answers are found within ourselves. Tucker Herbert Phil 331 Journal Entry #7 Oct. 11, 2009

An idea we discussed in lecture on Friday reminded me of one of my favorite movies, There Will Be Blood. In Walden, Thoreau is exploring the notion that humans have more than just physical desires. What he finds is that most of us fail to restrain our physical desires. We always want more, even the men and women who have already made it to the top. The main character in the movie is a classic example of one of these men. Throughout the film, he manipulates his peers in order to gain a competitive advantage in America’s oil production. In the end, after he has made himself into one of the richest men in America, he finds himself living an unsatisfied life without any friends or family. In searching for the origin of virtue, Thoreau is accepting the fact that spirituality is necessary for the health of the soul, not just physical desires. Today we have global environmental problems, originating from individuals and nations concerned only with their physical wants and needs. Thoreau sees nature as a refuge for the human soul. It can provide for us a type of spirituality that cannot be found in material possessions.

I sometimes find it hard to stay motivated in college because I’m not so sure about the direction it seems to be leading my life in. Getting a degree and then joining the workforce seems to be the most logical path to satisfying my physical desires. But where then do I go to find my spirituality? Rather than sit in class, should I not be out in nature searching for spirituality? If I understand Thoreau correctly, I should be able to live a virtuous life without all the physical possessions that generally accompany some type of successful life. Thoreau warns us that there are no limits to our desires, but perhaps in nature, we can find a way to balance our physical needs with our spiritual needs.

Tucker Herbert Phil 331 Journal Entry #8 Oct. 20, 2009

In Higher Laws, Thoreau again ponders the question, what is the chief end of man? Thoreau believes that the pursuit of virtue in all endeavors of life should be one’s ultimate goal. In this particular reflection, Thoreau focuses on the virtue of purity and its place in the human spirit. Without purity, man will never be able to live a noble and virtuous life because he will be constantly tempted by sensuality and ignorance. At the same time, Thoreau is also a little skeptical about human beings ever really achieving the type of purity found in nature. He admits that there is never an instant’s truth between virtue and vice in our lives. Nature has an inherent worth in and of itself that doesn’t require the approval of human beings. Thoreau states that we have much to learn about ourselves from nature. If this is true, why then does he remark, “Nature is hard to be overcome, but she must be overcome.” From what I have learned in other classes, this is the exact type of thinking that first set us down the path of environmental destruction at the hands of humans. We now know how irrational this type of thinking can be. Society and Christianity set out hand in hand conquering the American wilderness inspired by an idea I never expected to hear come from Thoreau. We cannot look at nature as something to be conquered because as we have seen, we are successfully conquering nature at an alarming rate. Thoreau does save himself from some criticism regarding that earlier statement because he goes back to the idea that we can improve our lives in relation to nature if we treat our bodies like temples that reflect our personal styles. If we live impure and ignorant, our body will reflect this, and if we chose a virtuous and pure life, we shall be rewarded in our souls. I’m personally going to take some of Thoreau’s words to heart and start treating myself with ever increasing respect.

Tucker Herbert Phil 331 Journal Entry #9 Oct. 25, 2009

After reading Douglas Crase’s introduction to his essays, I have to say I am excited to be reading Emerson for the first time. Having just finished reading Thoreau, I look forward to now learning the philosophy of his mentor. Emerson seems as if he went about his life questioning every social norm and fact that the rest of society took to be truth. At a time in the history of America where everything in society was based around the religious notions of a divine being, Emerson preached of a harmony with nature. A problem that I see with modern society is that we have too many conformist and not enough leaders. We need leaders who aren’t afraid to question the status quo when they believe in something different. Emerson was controversial and it is that exact quality which attracts so many people to his writings. In his time, who else had the courage to stand up in front of his congregation to tell them that they were too inconsiderable to be noticed among the millions of burning suns? In modern times, statements such as the above are commonly accepted by some. Did Emerson knowingly set the stage for the types of arguments beginning to emerge today in the environmental discussion? Perhaps Emerson’s best quality is the optimism he shows for the human race. Just as Thoreau encouraged us to reexamine the true purpose for our lives, Emerson will encourage us to question why the world around us isn’t the way we hoped it would be. Just like the last line of the introduction states, the happiness of the universe depends on us. We now have the words of Emerson and Thoreau to guide us, there can’t be any more excuses.

Tucker Herbert Phil 331 Journal Entry #10 November 1, 2009

So what is it that makes it so hard for humans to be self reliant? Just like Emerson, I believe conformity is the biggest obstacle standing in the way of self reliance. Capitalism breeds materialism, and materialism leads to conformity. It is hard for someone like me to move outside of those forces when I have been raised in a capitalist society. We are taught to believe that we need more than we already have when in reality we really don’t. Emerson urges us to insist on ourselves and never imitate, but how could he have accounted for the effect Hollywood has had on society. American society has become so obsessed with celebrities that we find ourselves obsessively following their lives on Twitter. How are we to become self reliant individuals under the immense pressure of conformity? Personally, I have decided to take Emerson’s advice to heart. I might actually have a shot at becoming more self reliant because I was lucky enough to have an older brother that went against conformity for the majority of his adult life. He showed me the importance of questioning everything that I see and hear in life against what I believe to be true. Needless to say, I have found that there is a whole lot of bull crap flying around out there. Sometimes I think people so easily conform to the rest of society because they lack the courage to be themselves. This isn’t necessarily the individual’s fault because like I stated earlier; capitalism has done a great job training us to be conformists. From what I have read of his work so far, Emerson seemed to be very intuitive when it came to foreseeing the trajectory of human society. We have now come to the point now where as a society; we tend to look down at the nonconformists because they have separated themselves from the rest of us. This viewpoint is the exact opposite of what Emerson urges us to embrace. The individual represents freedom, and without any individuals, we can only watch in desperation as human society slowly deteriorates.

Tucker Herbert Phil 331 Journal Entry #11 November 8, 2009

I love the approach Emerson takes regarding friendship. Too often our view of friendship is shallow and superficial. Emerson encourages us to look within ourselves to find a more noble type of friendship. We cannot claim to know someone else if we haven’t taken the time to get to know ourselves. As Emerson himself so clearly puts it, “We must be our own before we can be another’s.” Too many people I feel rely on friendships as a way of filling a hole in their own souls, instead of the other way around. I would like to think that I am a great friend. I have a great group of friends that I am still connected to back in Maryland, along with an ever-expanding group that I have meet since I moved to Arizona. Yet at times I find myself wishing that I had more solitude. I go to my friends for encouragement and advice when I should be looking within myself. Instead of placing my personal fate in the hands of someone else, I should begin trusting my own thoughts and opinions. As Emerson remarks, “the condition which high friendship demands is ability to do without it.” In this light, maybe I am not the great friend I previously considered myself to be. In regard to this realization, I must challenge myself to bring more truth and tenderness to my friendships. I often find that selfishness pervades even my strongest friendships. The greatest friends that I have ever had were the ones who went out of their way to help me with something when I needed it. Friendship must be reciprocal or it is nothing. As important as my family is to me, I know that most of my spiritual growth in life is attributed to the friendships that I have grown up with. My ultimate goal in life is to make every friendship a great one.

Tucker Herbert Phil 331 Journal Entry #12 Nov. 15, 2009

The idea that Emerson explores in “The Over-Soul” reminds me of one of my favorite books, The Alchemist. Emerson defines the over-soul as a collective soul that governs over all of humanity, helping us to see truth and virtue in the world. Likewise, The Alchemist develops the theme of a universal soul that is carried through history on the wind. In order to benefit from this universal soul, the main character in The Alchemist must attune himself to it. Throughout the book, the main character has many revelations regarding love, friendship, and courage. Emerson refers to revelations as an influx of the divine mind into our mind. This is essentially the same idea that is present in The Alchemist. The Alchemist is one of my favorite books because it inspired me the first time I read it. Before picking it up, I was content to go through most of my daily life accepting everything I heard and saw to be truth. I wasn’t attuned to the over-soul because I had no idea such a concept even existed. As Emerson himself states, “Persons are supplementary to the primary teaching of the soul.” We often think that we hold all the answers to life’s questions when in fact we really don’t. The soul can contain all the truth and wisdom in the world should we choose to acknowledge it. The Alchemist concludes with the main character finding the hidden treasure he had combed the desert looking for. He was successful because he listened to the wind that carried the universal soul with an open heart and mind. Modern man has gotten himself into such a big predicament with the environment because he is no longer attuned to the universal soul. Should we decide to seek it out, the path to a better life is written in the pages of The Alchemist and “The Over-Soul.”

Tucker Herbert Phil 331 Journal Entry #13 Dec. 2, 2009

While I was back in Maryland with my family over Thanksgiving break I had some very interesting discussions with my mother and sister. When she graduates from ASU this spring, my sister has proposed heading out into the wilderness for a few months to do some backpacking. The reason that we all got into such a heated discussion over this proposal is that my sister wants to make this trip all alone. My sister wants to make this trip because she plans on becoming an environmental journalist. After having read Walden this semester, I was in a good position to give some constructive criticism to my sister. I explained to her that I understood why she wanted to do this alone, mostly because she would have freedom and uninterrupted time to write and reflect while she was hiking. However, my mother’s biggest concern was that while Henry David Thoreau went to Walden in a relatively safe period in American history, the United States today has become a very dangerous place for a 22 year old woman to be hiking all by herself. My mother’s main concern was that my sister would get attacked or kidnapped and never be heard from again. I had to admit that this was a very valid concern because I have read numerous stories about this exact type of thing happening on the Appalachian Trail. With all of the safety concerns aside, I still found myself encouraging my sister to make the trip. However, I proposed that she do something similar to what John Muir did when he first came to Yosemite. I suggested she go to a National Park, try to find some type of work in the park, and then spend her free time hiking around by herself. It would be a much safer alternative while still giving her a chance to do what she wants. Ultimately, I hope she takes my advice and does it. When I graduate from NAU next fall, I plan on doing the same type of thing. My sister was absolutely right, I cannot expect to make a difference in the world if I don’t give myself a chance to go out and experience it.

Tucker Herbert Phil 331 Journal Entry #14 Dec. 9, 2009

As the fall semester here at NAU comes to an end, it provides everyone with an opportunity to look back on what they learned over the course of the last 3 months. Personally, I believe college shouldn’t be just about learning new information and taking tests. For most undergraduates, college is an opportunity to mature and learn more about yourself and what your goals in life will be. As an environmental studies major, I took a lot from this environmental ethics course.

Thus far, my biggest realization is that most of my fellow students tend to have a very narrow point of view when it comes to the environment. For having this point of view, the students aren’t always the ones to blame. The American public school system, and in some ways Christianity, is to blame. Throughout their education, most students learn that nature is here to be used and exploited for human means. Now, most teachers don’t come out and say this exact thing, but often the idea is emphasized in what they teach. If we want future generations of Americans to grow up respecting the environment, we must implement more environmental courses in school curriculum.

Environmental ethics is the type of course students should be exposed to by the time they have reached middle school. Not every child was fortunate as me to have parents that instilled in them an ethic of respecting nature. If a student makes it all the way to college without ever having any type of environmental ethic class, their chances of developing a respect for nature diminish significantly.

As we now know, the future of the planet is in serious jeopardy. Greed and irresponsibility have forced the earth to the verge of its capacity to sustain human life. If we don’t start educating our children now on what it means to respect the environment, this discouraging trend will continue until the planet can no longer sustain human life. Ultimately this is a very discouraging scenario, but with the right direction, we can change the outcome of the human race. Please education, wake up and take note, its time to start incorporating the environment into the curriculum, our future, and the future of the planet depends on it.


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User:Egm6321.f09.Team06.sada

user:egm6321.f09.Team06.sada/HW1

user:egm6321.f09.Team06.sada/HW2

user:egm6321.f09.Team06.sada/HW3

user:egm6321.f09.Team06.sada/HW4

user:egm6321.f09.Team06.sada/HW5

user:egm6321.f09.Team06.sada/HW4 make-up

user:egm6321.f09.Team06.sada/HW4 make-up

user:egm6321.f09.Team06.sada/HW6

user:egm6321.f09.Team06.sada/HW7

title: User:Egm6321.f09.Team06.sada


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User:Egm6321.f09.team7/HW1

Homework one: Problem one
Given : fucnctionfunction F is a a function of Y and t where Y is also a function of t  Find : Using normal methods find the first and second total time derivatives of F     Function F $$F = f(Y(t),t)$$ Problem Solution: The first step is to find the first total time derivative for F using the chain rule (Y is implicitly a function of t and will no longer be noted as such): $$\frac{dF}{ds} = (Y,t) * \dot{Y }(t)$$ and, $$\frac{dF}{dt} = (Y,t)$$

This gives a final form for the first time derivative of, $$F,s (Y(t)*\dot{Y } + F,t (Y(t))$$

 Missing a parenthesis here, and subscripts are obtained in math mode using _{}.--Egm6321.f09.TA 03:51, 24 September 2009 (UTC)

The next step is to once again use the chain rule and find the second total time derivitive using the notation first developed in class to specify each of the parts,

$$F,s (Y,t) * \frac d{dt} \dot{Y } = F,s (Y,t)\ddot{Y } $$ $$F,ss (Y,t) * \dot{Y } = (Y,t)\dot{Y }*\dot{Y }\to(\dot{Y })^2 $$ $$F,st (Y,t) * \dot{Y } = (Y,t)\dot{Y } $$ $$F,ts (Y,t) = (Y,t)\dot{Y } $$ $$F,tt (Y,t) = (Y,t) $$

Results :adding all of the terms together gives a final equation for the second total time derivative that has the following form:

$$F,s (Y,t)\ddot{Y } + F,ss(Y,t)*(\dot{Y })^2 +F,st 2 * ((Y,t)\dot{Y }) +F,tt (Y,t)$$

Homework one: Problem two
Problem statement : Derive equation 2 given in class on page 4-2 of notes using integration factor method

Equation 2 given in class page 4-2

$$p(x)=Ae^ +x-1$$

Problem Solution:

Starting with the equations given in class reduce the second order ODE with missing dependent variable by a first order ODE with dependent variable p knowing that:

$$p(x)=y'(x)$$

the second order ODE is

$$y''+y'=x$$

and the new ODE is

$$p'+p=x$$

The method of integration factor requires a first order equation like the one above to be multiply by function u(x).

$$(p'+p)u(x)=xu(x)$$

The above equation becomes:

$$u(x)p'+u(x)p=xu(x)$$

Lets take a look at the derivative of:

$$[\frac{d}{dx}(u(x)*p)]=u(x)* [\frac{d}{dx}( p)] +p*[\frac{d}{dx}(u(x))]$$

This equation is identically to $$u(x)p'+u(x)p=xu(x)$$ as long as $$[\frac{d u(x)}{dx}]/u(x)=1$$ which means that:  Your motivation here is a little off. Multiply the original equation through by $$u(x)$$ and then enforce the exactness criteria for the new $$\overline{M},\overline{N}$$.--Egm6321.f09.TA 03:53, 24 September 2009 (UTC)

$$[\frac{d }{dx}ln|u(x)|]=1$$

After integrating both sides:

$$ln|u(x)|=x+C$$

Using the above method we find the value of u(x).

$$u(x)=Ce^x$$

Since we do not need the most general solution we can set the value of c=1.

$$u(x)=(1)*e^x$$

Now the integration factor u(x) can be replace for its real value:

$$e^x*p'+e^x*p=x*e^x$$

Integrating both sides of the following equation will give us the value of p:

$$[\frac{d}{dx}(u(x)*p)]=x*e^x$$

$$ u(x)*p =(x-1)*e^x+A$$

$$ e^x*p =(x-1)*e^x+A$$

After dividing the expression by e^x we get the value of p:

$$ p = Ae^ +x-1$$

Since we set p equal to the derivative of y, we know already that integrating p will give us the value of y:

$$ y = -Ae^ +x^2/2-x+B$$

Homework one: Problem three
Problem statement : Show that the 1st order ODE below is nonlinear

Equation 1 given in class page 4-3

$$(2*x^2+y^1⁄2)+x^5y^3y' =0$$

Problem Solution:

Starting with the definition of linearity from page 3-3 of the notes:

$$L( \alpha*u+\beta*v ) =\alpha*L(u)+\beta*L(u)$$

Using the above equation we get:

$$(2*x^2+(.)^1⁄2)+x^5(.)^3[\frac{d}{dx}(.)] =0$$

We know the equation is linear if it satisfies the test for linearity previously shown.

$$(2*x^2+(\alpha*u+\beta*v)^1⁄2)+x^5(\alpha*u+\beta*v)^3[\frac{d}{dx}(\alpha*u+\beta*v)] \neq \alpha(2*x^2+(u)^1⁄2+x^5(u)^3u')+ \beta(2*x^2+(v)^1⁄2+x^5(v)^3v') $$

The equation above failed the test because the left hand side is not equal to the right hand side. Equation (1) of page 4-3 failed the test and therefore it is nonlinear.  This is indeed correct, but your solution is difficult to read. You should take both equations and simplify them separately. Then it is clear that they are not equivalent. In their current form it is not readily obvious that they couldn't be made equivalent with some mathematical gymnastics.--Egm6321.f09.TA 03:57, 24 September 2009 (UTC)  You should define your differential operator $$L$$ as you have done, and explicitly state that you are trying to show that $$L(\alpha u+\beta v)\neq L(\alpha u)+L(\beta v)$$--Egm6321.f09.TA 03:57, 24 September 2009 (UTC)

Homework one: Problem four
Problem statement : Using theroems discussed in class show that equation given on Page 4-3 of notes is non-linear Example NonLinear 1st Order ODE $$x^2y^5+6(y')^2=0$$ Problem Solution: Using the method described in meeting 3, Define D(.) as: $$D(.)=x^2(.)^5+6[\frac{d}{dx}(.)]^2$$ then $$D(y)=x^2(y)^5+6[\frac{d}{dx}(y)]^2$$

It is linear If, $$D(\alpha*y_1+\beta*y_2) = \alpha*D(y_1) + \beta*D(y_2)$$ plugging in we see that,

$$x^2(\alpha*y_1+\beta*y_2)^5+6[\frac{d}{dx}(\alpha*y_1+\beta*y_2)]^2 \neq \alpha*(x^2y_1^5+6(y_1')^2) + \beta*(x^2y_2^5+6(y_2')^2)$$

Results : equation is shown to be nonLinear.  Again, simplify the two expressions so that it is clear that they are not equivalent. This problem however is clearer in terms of explanation than problem 3 (see note above).--Egm6321.f09.TA 03:59, 24 September 2009 (UTC)

Homework one: Problem five
Problem statement :(6-1): Generating exact nonlinear 1st order ODEs: Let $$ \Phi(x,y)=6x^{4}+2y^{3/2}$$, then $$ M=\Phi_{x}$$ $$ N=\Phi_{y}$$ Complete the details and invent 3 more examples.

Problem solution Just invent $$\phi$$: Completing details:

$$\phi(x,y)=6x^4+2y^{\frac{3}{2}}$$ $$M=\phi_x$$ $$N=\phi_y$$ $$M+Ny'$$ $$24x^3+3\sqrt{y}y'=0$$ 1st invention $$\phi(x,y)=e^x+e^y$$ $$e^x+e^yy'=0$$ 2nd invention $$\phi(x,y)=\sin(x)+\sin(y)$$ $$\cos(x)+\sin(y)y'=0$$ 3rd invention $$\phi(x,y)=\ln(x)+\ln(y)$$ $$\frac{1}{x}+\frac{y'}{y}=0$$

 Nice work.--Egm6321.f09.TA 04:03, 24 September 2009 (UTC)

title: User:Egm6321.f09.team7/HW1


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Connectivism and Connective Knowledge

 * Description

This page offers editable wiki notes about the Connectivism and Connective Knowledge 2009 course.

You are welcome to contribute: Be bold!

Register by signing up to The Daily or to formally enrol for credit contact George Siemens.

Session 1: Introduction

 * 1) Official wiki description
 * 2) Week 1 official blog post
 * 3) Introduction to course structure and philosophy (elluminate recording)
 * 4) Introductory video
 * 5) Cover It Live
 * 6) What is connectivism?
 * 7) Discussion forum: The most notable thread was about "What is connectivism?"

 * Notes
 * 1) Connect everything via CCK09 tag - many paths
 * 2) What is a lurker? (good or bad?)
 * 3) Discourse/participation/content is distributed - what draws it together are the interconnections (a design philosophy)
 * 4) No strict borders
 * 5) We'd like to see you "create something somewhere" e.g., blog, bookmarks, images, etc.
 * 6) Grasshopper will be used to collate/harvest ""CCK09" RSS feeds in the daily newsletter: Submit feeds here
 * 7) Aggregation key 'way-finder', 'sense-maker' in this process
 * 8) Some connections will get a life of their own
 * 9) Participate in whatever discussion space you like - just share it with others :)

Session 2: What is Connectivism?

 * 1) Thursday, September 17, 4:00 pm CST : Focus: What is Connectivism

 * 1) What is connectivism? (Elluminate recording)

Session 3: Networks

 * 1) Resources
 * 2) Discussion forum
 * 3)  (Elluminate recording)

Week 3: Connectives and collectives

 * 1) Week 3: Connectives and Collectives
 * 2) Introductory video
 * 3)  (Elluminate recording)
 * 4) Provided a recap of the course to date
 * 5) Discussed differences between between groups and networks, and the pedagogical implications

Participants' CCK09 stuff

 * Blog posts
 * 1) Spring is in the air
 * 2) Connectivism and Connected Learning Online Course
 * 3) Connectivism wiki and the creation of knowledge

 * Aggregations
 * 1) http://www.netvibes.com/saandreoli#Connectivism_CCK09
 * 2) http://www.pageflakes.com/dfee/

title: Connectivism and Connective Knowledge