Academic Portfolio – 2011Erin Collier-Zans

Portfolio Index

1. Index2. 2011 Five-Year Plan (pg 3-8)3. College Course Work:

1. Title Page/Intro (9)2. Geography: Glacial Isostasy (10-19)3. History/Environmental Studies: Greens: The Role of

Diversity in the Formation of the German Green Party,2970s-80s (20-25)

a. ENV207 Final Question Response (26-28)4. Peace Studies: A Critique of Hannah Arendt’s On

Violence (29-32)4. High School Course Work:

1. Title Page/Intro (33)2. Science: Crayfish Dissection (Lab Write-up) (34-44)3. Science: Climate Change in China/Colorado (45-53)

a. Rubric (54)4. Maths: Population v. the Planet (55-70)

a. Rubric (71-72)5. Maths: Orchard Hideout (73-86)

a. Rubric (87-88)6. Humanities: The Freedoms That Be (89-99)

a. Rubric (100)7. Spanish: Un Barco Se Hundio (101)

a. Rubric (102)8. Copper Canyon Reflection (103-106)

a. Rubric (107)5. Small selection of artwork (’08)

1. Intro (108)2. Art:

a. Mask (109)b. Gawain and The Green Knight (110)c. Gateway (111)d. Crab (RMSEL Yearbook cover ’08) (112)e. Figure study sketches (113-17)

Collier-Zans, Erin, *6520 1

01/2011

Five-Year Plan, 2011

In one year’s time, I foresee myself at a new college or university. I will be well on

my way to completing all core/liberal-arts mandated course work and degree prerequisites. I

will be in regular contact with my advisor, and will have elicited their assistance in planning

out my schedules for the following semesters (with enough detail that I can create a

flowchart, so that there can be no confusion when class registration rolls around). I will also

be in contact with department heads/chairs and/or instructors from the majors in which I’m

interested in pursuing, so that I can be sure that I’m prepared for all coursework, and

understand before going in what exactly the focus’ of these programs are. By the end of the

year, my major will have been declared and I will have begun junior/senior level work

therein.

I will have settled into a calm living situation, conducive for learning and my own

mental and physical health. If I’m in a dorm, I will understand all rules and policies, and be

able to plan ahead for the coming year(s). If in an apartment, I hope to have found some place

small, quiet and in a good neighborhood, with good access to bus and/or pedestrian routes. I

will either have a work-study (hopefully) or have found a part-time job in something I’m

interested in (book/art store, etc) and be able to pay for my own living expenses, and

hopefully some of my monthly tuition payments.

In two year’s time, I will have declared my major and be well into prescribed course

work. I will have already finished the planning and begun some of the preliminary work for

my senior thesis/capstone project – I will have likely sources, and have pinned down

fieldwork contacts and opportunities, hopefully with the assistance of instructors who’ve

done work in the field. Ideally, I will already have begun my fieldwork, and be keeping up

with the academic work associated with it. I will also have done a semester abroad, an

internship, or something of the kind, both for fun and hopefully relating to said final product.

I will already have done research on post-graduation options, and have some idea by middle

of my second year what my next steps will be. I hope to have a strong feeling, either of

engagement in a particular area (in which case application to a graduate program will be well

in the works) or of ambivalence (in which case I will already have applied to an internship or

to the Peace Corps – something non-academic that will get me working and help me clear my

head).

Collier-Zans, Erin, *6520 2

In three year’s time, if I haven’t already graduated with a single major, I will be

graduating with a major/minor or a double major. Much of the above applies, if I’ve just

finished my bachelor’s at the three-year mark, but if I’ve already been out for a year, then I

hope to have a good idea of what field I would like to start my first career in. I will either

have finished an internship and be working/attending graduate school, be in the middle or in

between internships, be in the middle of my first masters degree, or in the middle of a Peace

Corps tour. Any of the above should be able to help me refine my focus, if it still needs

refining at the age of twenty-three, and by the end of the third year I should have tentative

plans for my next steps in mind.

At four years, I will either be working, or be pursuing an even higher level of

education – either finishing a Graduate degree, or attending medical school. I will be on my

way to financial security, with some idea of what my average income will be, and should be

able to handle tuition/loan payments, etc. I have begun taking leases on my residences, and be

able to plan my movements and plans at least six months in advance. I will be able to handle

any familial eventuality.

In five years time, I will either have finished my graduate degree and be employed in

the field, hopefully doing research and working on my first scholarly publications, or I will

be finishing medical school and beginning my internship as a general surgeon. I will have a

firm idea at this point of what my basic moral coda is (and hopefully be able to articulate it),

and understand fully why I am doing whatever it is I am doing; I want there to be no doubt in

my mind that the work I am doing is good and important, and valuable to the (global)

community.

I will be handling loan payments and living expenses well and be living simply, with

a healthy short-term savings account and be making (even small) monthly deposits to a

retirement fund. By twenty-five I will have made exercise a much bigger priority in my life,

be able to run a 10K at least once a month, and be on my way to training for a full marathon.

At this point I should start making health decisions that will effect the rest of my life –

corrective surgery on my feet and allergy shots may be considered at this time (if they

haven’t been already). I will be able to play guitar, will be proficient in more media and be

doing art at least once weekly, and will have begun to pursue other interests and hobbies, i.e.

learning a new language or instrument, etc. I will have completed the manuscript of at least

one book (hopefully a trilogy) and be well into the editing process. I will be able to ride a

bike by this point, as well. Finally, at twenty-five I will be able to draft a tentative five-year

plan to carry me through to thirty, with opportunity to reassess at that point.

Collier-Zans, Erin, *6520 3

1. Financial:a. In school:

i. Find job (preferably work-study), plan out time to balance school/work ii. Create an honest monthly budget – review transactions at the end of

the month, have self-planning sessions to set reasonable goals for thenext month

iii. Split all extra earnings and deposit in short-term/retirement accounts –plan to save at least of total earnings 10% monthly.

iv. Speak to financial advisor (use parent’s?), do research and understandbasics of the financial system.

v. Make periodic purchases of stocks/bonds etc when funds allow, begincreating a portfolio, get help on this.

vi. Get parents’ help learning how to fill out/file taxes – become fluentwith the various tools available.

vii. Assess living situation; are dorms more practical, with cookinglimitations, noise, etc than an apartment/lease, which may be moreexpensive but save money in terms of grades, time, etc? Consider thisaccording to budget, time constraints, personal preference, housingavailability – all possible factors.

viii. Assess loans – will I be able to pay them off after school? Take onlywhat I am sure of being able to handle.

b. Three years (out of school) i. Re-asses portfolio, savings accounts, assets, investments. Do whatever

periodic maintenance is necessary on this. ii. Assess next steps – am I financially secure enough at this point to drop

everything and do a Peace Corps/similar tour? iii. Re-asses loans – create new monthly budgets, set up automatic

payments near the beginning of the month, keep to the budget andreassess monthly.

iv. Write-out monthly/bi-monthly goals, plan ahead for recreationalspending, don’t touch savings accounts – set up third savings for short-term spending money, re-allocate other moneys to emergency savings,continue making deposits in retirement fund.

c. Five years (beginning career) i. Assess goals. Make sure that next steps will not set me back

financially, but hopefully continue to carry me forward, or that I can atleast maintain at healthy level. Options:

1. Graduate school.2. Begin career, put off masters/doctorate a few years (this would

be for loan purposes, if earnings will not be high enoughduring/after graduate school to handle additional loans/cost ofliving during school time – health of savings account and otherassets may be a factor)

3. Medical school (same concerns as for graduate school)2. Career:

a. Three years: i. Best option: take time to continue education, either graduate or

medical school. ii. Other options: assess whether I have any strong feelings on the matter.

If not, take time to travel, join Peace Corps, live in another country,

Collier-Zans, Erin, *6520 4

work in wilderness – find some way to jump-start myself, take space,create the sense if not the reality of freedom so that I don’t get boggeddown in no-where jobs, feeling like I’m stuck.

iii. If yes, take action. See options, above.b. Five years:

i. Best option: if it hasn’t happened already, make additional schooling areality – graduate/medical.

ii. If time was taken off, assess if I now have any strong feelings. If yes,take steps, if no, seriously consider my sanity.

3. Physical:a. One year:

i. Learn to ride a bike. ASAP. ii. Assess health/life insurance ASAP: what do I do w/o Cover Colorado?

School-provided insurance? Assess options, fit various into budget,then take a plan.

iii. Be able to run three miles comfortably. Continually assess footsituation – do they still feel healthy, safe? If not, speak with parentsabout surgical options.

iv. Keep track of body/fat%/calories – make sure that I am maintainingmyself, keeping myself healthy.

v. Begin doing 5Ks on weekends. Look for sponsors? vi. Stop biting my nails. Do whatever it takes. Find alternate means to

relieve stress. vii. Continue to work on posture – improve on what I already have, work

on holding head up and back, consciously work on making attitude ofassertive confidence a constant.

b. Next three years: i. Be doing five miles in three years, three times a week. Continue to

monitor status of my feet. ii. Consider getting shots for cat allergies.

4. Relationships:a. Next five years:

i. Work through anger with my father – neutrality is better thanresentment. If necessary, decide not to care and stick to it.

ii. Continue being supportive of my mother – don’t let my feelings get inthe way, honestly assess what will be healthiest for her, keep control ofmy tongue so that I am not being hurtful.

iii. Spend time with grandmother. iv. Look people firmly in the eyes while talking to them, work on

projecting confidence, even if I’m not feeling it. v. Work on keeping calm, self-contained when interacting with others.

Work on being self-aware, even in engrossing situations – this willgive me the ability to be more aware of what others are doing, whichwill enable me to respond appropriately, in a way that will be moreappreciative of and kind to others.

5. Spiritual:a. Next five years:

i. Reassess my spirituality. Purge as much indoctrination as possible,find out what I really believe using my thoughts, actions, and reactionsas reference points.

Collier-Zans, Erin, *6520 5

ii. Re-discover the loving, spiritual connection I have with non-humanworld and reality.

iii. Re-learn to cultivate silence – God is in the silence.6. Educational:

a. By three years from now: i. Have graduated college, with a double-major or major/minor in

biology and anthropology. ii. Begin paying off loans iii. Make plans for masters/doctorate/medical school – now, or later? iv. Learn to read music. v. Be relatively fluent on guitar. Be proficient enough to start learning

classical Spanish pieces. vi. Start working on violin – get great-granddaddy’s repaired, if need be,

or buy a used student’s model, get a book, and start learning. vii. Know how to quickly, cheaply and efficiently retrofit an apartment to

be more environmentally conservative/secure – caulking, heater fixes,window wrapping, etc.

b. Next five years: i. Start working with kids again – work at a daycare, volunteer,

something. They have so much to teach! ii. Keep an eye out for a cheap-ish copy of Rosetta Stone, start working

through languages. Priorities: Spanish (Spain), French, Irish, Swedish,Arabic, Hindi, Portuguese.

iii. Get a Wacom tablet, work on my digital art skills iv. Practice with acrylic/oil paints, improve my still-life/portrait skills. v. Get into a figure drawing class, work on figure studies – keep a

journal, in order to track progress. vi. Keep subscriptions to a couple of journals pertinent to my majors, keep

up to date wit the new research. vii. Keep reading – go through bibliographies and keep up a rolling book

list (but find ways to avoid buying new books)1. Keep notes – write a short essay after each chapter/book, in

order to better absorb what I’m reading.7. Fun:

a. Next five years: i. Research for and write books: the two publishable books I have plans

for, also keep notes on ideas for more & get started outlining. Shoot forhaving at least one in one series done in five years – preferably awhole trilogy.

ii. Write short stories as they come to me – try to get them published, andif they don’t catch, then put them on a blog or something.

iii. Work on art – take ref photos, draw from them, write down/quick-sketch ideas, get to the point where drawing digitally is fun, rather thantedious – start posting on dA, consider taking small commissions onthe side, as time allows.

iv. Plan graduation trip, for my mom? Something that would be fun forher – start saving for this ASAP.

v. Take a sailing trip, or something. Something to be on/near the sea.Semester at sea, during school, maybe? Anyway, learn how to sail.

Collier-Zans, Erin, *6520 6

vi. Track down trails and hike as many of them as possible – keep a hikingjournal, with photos and pressed samples, to keep track of this.

vii. Go to a film festival somewhere. viii. Go to a Broadway show – maybe Ave Q, S Pacific, something like

that. ix. Continue going to Cirque shows – take mom! x. Keep up with things my mum wants – what sorts of things is she

interested in doing/seeing? Maybe plan another Santa Barbara trip fortwo-five years from now.

Introduction to College Course Work2008-2010

What follows is a small selection of my academic work from the past two years,including teacher comments when available. I believe that these three pieces exemplify my workat Naropa, and though I have some issues with their quality and content looking back, I believethat they are at least a fair demonstration of my capabilities at this point.

The first is the final paper I wrote for ENV100: ‘Physical Geography – Beholding theBody of the Earth’ – the only geography class required for the Environmental Studies major atNaropa. My topic of research, as you may have guessed, was the phenomenon of glacial isostasy.In writing this piece I learned to navigate the online world of scholarly journal publications, andthe experience of reading researched, scientific articles was like a breath of fresh air. I trulyenjoyed writing the resulting paper.

The second is the final piece for ENV207: ‘History of the Environmental Movement’, forwhich I did a cursory study of the history of the German Green Party, or Die Grünen, from the1960s through 80s. In addition, I have left my response to the final question assigned by theinstructor attached to the end of the document; it contains my most recent thoughts on theenvironmental movement and my place, or possible lack thereof, in it.

‘On Hannah Arendt’ is a short paper I wrote in response to said author’s On Violence, anilluminating work on the nature of power, violence, and the present world order. This piece waswritten in 2008; my opinions have changed somewhat and I have developed as a writer, but it isa good example of the sort of texts I grappled with in my Peace Studies classes.

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Erin Collier-Zans

Anne Parker

ENV100 Physical Geography

2/12/10

Glacial isostasy is directly related to the planet’s climate and hydrological cycle, and

possibly even to the movement of tectonic plates and the planetary gravity field. Because we

in the present day are living in an interglacial warming period we are clearly able to detect

natural isostatic effects, but it is now clear that anthropogenic global warming has

exacerbated the natural rate of glacial melt creating these effects. Similarly exacerbated

isostatic response is to be expected, and may already be occurring. This may instigate a

greater occurrence of tectonic plate-related natural disasters, such as earthquakes, tsunamis,

and volcanic events.

The purpose of this paper is to investigate and summarize currant understanding of

the phenomenon of glacial isostasy, and then give a brief overview of what research has been

done on the isostatic-related effects of glacial melt and sea-level rise in the present, warming

climate.

“Isostasy,” in the broadest sense, is the “general equilibrium in the earth’s crust

maintained by a yielding flow of rock material beneath the surface under gravitative stress”

(Mirriam-Webster). An important term to understand here is ‘lithosphere,’ which is “the

surface shell of the earth, [capable of] sustaining long-enduring stress differences without

significant flow,” or the “[that] which comprises the crust, which is relatively cold and brittle,

and the uppermost part of the mantle that is relatively cool, strong, and elastic” (Wolf 96;

Gornitz 374). When pressure is applied to an elastic surface floating on top of a viscous or

liquid substratum, the part of the surface absorbing this imposed pressure will sink or be

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depressed into the liquid below. When seen on a planetary scale, this phenomenon is an

example of ‘isostasy.’

The term isostasy was first coined by Dutton in 1889 to “describe the apparently

‘compensated’ state of Earths surface topography… [though] the idea that such compensation

must occur dates from the studies performed by both Airy (1855) and Pratt (1855) based

upon the observations of plumb line deflections made during the original geodetic survey of

India” (Peltier 111). A more detailed description is given by Nansen (c.1928):

“The earth’s crust may… be considered as a slowly flexible sheet of solid rock

floating on a viscous substratum. If loaded in one place this sheet will bend slowly

under the load, and the plastic matter underneath will be displaced to the sides… if

unloaded in one place the sheet will rise slowly in that area; there will be an inward

flow in the substratum underneath, and a slight subsidence of the sheet in the

surrounding area” (qtd in Wolf 99).

The concept of isostasy was originally developed in relation to mountains (which are an

external load simultaneously integrated into the crust) (Peltier 111; Gornitz 374), but it

applies equally well to the compensation of the Earth’s surface to superimposed mass, like

transient glaciers or the more permanent ice sheets present at the poles.

The above phenomenon is called “glacial isostasy.” The first use of this term was

made during the second half of the nineteenth century (Wolf 95), and in the broadest sense it

refers to “the response of the solid Earth to any changes in the planet’s ice sheets” (Gornitz,

374). More specifically, it is “the process of lithospheric depression beneath the weight of an

ice sheet and subsequent rebound when the ice mass is reduced or removed” (“Glacial

Isostasy and Eustasy,” Aber). A more detailed description of the process of glacial isostasy is

given by Aber:

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“Lithospheric depress of [hundreds] of [meters] takes place beneath large ice sheets

due to the static weight of the ice mass. This excess loading causes elastic and plastic

deformation in the lithosphere and underlying asthenosphere. Crustal rock is displaced

as the mantle sinks. Given ice density of 0.9 g/cm3 and mantle rock density of about

3.3 g/cm3, the potential depression beneath an ice sheet 1000 m thick could be as

much as 275 m.”

When mass, like a great volume of ice, is added to the planet’s surface, the initial

response will be an “elastic deformation of the entire lithosphere-mantle followed by a

viscous creep as the mantle stresses relax and the load is increasingly supported by the

lithosphere. The local isostatic limit will be attained as a limit” (Gornitz 375). Conversely,

“when the ice sheet is removed, the initial response is elastic followed by a viscous rebound”

(375). This would seem to imply that, hypothetically, if a glacier were to suddenly be

dropped onto a section of continental crust, a broad area of the surface would be depressed to

a lesser initial degree, with the localized severity of the depression increasing as the total

extent of the depression gradually decreased over time, until the isostatic limit was achieved,

which according to Aber rarely if ever occurs since “several [thousands of] years are required

for complete isostatic adjustment to take place, by which time ice thickness has often

changed” (“Glacial Isostasy and Eustasy”).

Related to the above is the phenomenon of “bulging” in relation to isostatic depress,

where, “in order to compensate for lithospheric depression beneath a crustal load, the

surrounding area may [rise,] creating a forebulge. These principles are demonstrated by the

Amazon delta, where huge sediment loading has created a central depression that is

surrounded by peripheral uplifts… in like manner… the glacial forebulge subsides when the

ice mass is reduced or removed” (Aber).

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The two above phenomena paint a clear picture: as a glacier forms it gradually settles

farther and farther into the lithosphere, and a bulge is formed around it to compensate for the

matter it displaces beneath. When the ice is removed through melting, the land beneath the

ice rebounds swiftly (i.e. elastically) to a certain comfortable point, and then it gradually

creeps up to its natural position of equilibrium (that is, unless more ice forms over it before it

can accomplish this). As the edges of an ice sheet melt, then, the land rebounds and the bulge

moves inward, and presumably as the ice’s total mass decreases the lithosphere beneath the

remaining sheet rebounds slowly in a more viscous fashion as the weight forcing it

downwards diminished.

In beds created by stationary, intraplate bodies of ice during glacial periods in the

planet’s Quaternary cycle, thee bulges would gradually erode into the two bordering troughs

(the glacial valley and the land directly outside of the bulge), possibly causing the crust to

once again equalize when viewed in relief. However, this sedimentation would increase the

mass of the crust in the two troughs, thereby increasing their weight even without

significantly increasing their vertical depth, which would further exacerbate the isostatic

effect, i.e. the glacier with its surrounding container of packed sediment would continue to

sink to the maximum limit allowed by the rigidity of the crust, as would the land beyond the

bulge, which would cause the crust forming said bulge to continue to rise and be eroded, just

as before. As the bulge continued to lift, the asthenosphere would follow and harden as it

neared the surface. This is the same balance struck by mountains, whose roots extend far into

the mantle, and which may remain at a constant height for 100 kyr’s despite the forces of

weathering and erosion (Peltier 111). This seems to imply that when there is weight

superimposed on the planet’s surface, creating an isostatic effect, it is the forces of erosion

and sedimentation, rather than the forces of lithospheric rigidity v. elasticity, that create the

illusion of equilibrium (i.e., land around a glacier appearing to be level). True equalization of

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the crust is not restored in such a case until the mass is removed, as happens eventually to

mountains due to erosion and to glaciers as they melt.

Water in it’s liquid form is just as dense as ice, so there is an isostatic adjustment

involved in the melting and freezing of water on a global scale and the oscillation of sea level

that follows, which is called ‘eustasy’. The two are inextricably tied, but the finer interplay

between ocean loading/basin size and glacial mass/isostasy is unclear.

Data on their synchronicity feeds directly into the field of paleoclimatology, however,

demonstrating the interrelationship between global phenomena. Data on glacial isostasy has

been used to facilitate the research and support the conclusions of innumerable researchers in

many other fields considered to be ‘unrelated’ to glaciology. One such realm is the study of

Global Isostatic Adjustment (GIA), which is “the global process… whereby the Earth’s shape

and gravitational field are modified in response to the large scale changes in surface mass

load that have attended the glaciation and deglaciation of the planetary surface” (“Glacial

Isostatic Adjustment; A Survey of Recent Studies”). It is unclear how exactly the shifting of

mass affects the planet’s gravitational field, and what further affect this would have on the

location of ice mass, the behavior tectonic plates, the distribution of ecosystems, etc., but all

of these phenomena are obviously part of an incredibly complex chain of feedback loops.

Isostatic data can also be used in models depicting other aspects of global history.

With said data and additional information on the planet’s viscosity, and as well as parameters

for prehistoric ice sheets, models can be developed that describe “the deformation of the of

the entire planet, that distribute the meltwater in a self-consistent way into time-dependent

and realistic ocean basins, and that include the effects of the changing water load as well as

ice load” (Gornitz 375). In fact, scientists have only arrived at their present understanding of

the earth’s viscosity thanks to the observable deformation of the planet’s surface due to

glacial isostasy: “one of the primary motivations for studying the uplift of formerly glaciated

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regions such as North America is to deduce a radial structure and viscosity profile of the

inner earth. The disappearance of ice and subsequent isostatic response recorded as changes

in relative sea level at coastal locations is one of a limited set of phenomena that allow

investigation of the earth at depth” (Zweck 321). Glacial isostasy is particularly suited for

scrutiny since it acts on a scale of thousands, rather than tens or hundreds of thousands of

years. There is, however, no model that can include the world’s complexities, so models must

be assumed to give skewed or uncertain results.

This component of uncertainty, and the inability of models to predict the future or

even accurately portray the past, has made understanding the effect anthropogenic global

warming will have on the glaciers in terms of isostasy even more difficult. It is known that

inter-intraglacial cycles run in spans of approximately 100kyr, that the “Last Glacial

Maximum” occurred between 19-30kyr years ago, and that since that time approximately

50x166 km3 of ice has melted, “leading to a rise in global sea level of ~130m” (Shum, Kuo,

and Guo (?) 149).

Whatever the cause of the present intraglacial period, it is clear that anthropogenic

factors are behind the present “global warming” phenomenon, which is raising both

atmospheric and oceanic temperatures. This has exacerbated the melting of both the Antarctic

and Greenland ice sheets, contributing to an estimated rise of average sea levels by between

1.5 and 2.0 mm/year (Shum et al). Since global warming is not likely to abate, it is likely that

glacial melt will also continue, at a continuously accelerating rate.

This acceleration has already been observed. In 2008 an international team of

scientists “estimated changes in Antartica’s ice mass between 1996 and 2006 and mapped

patterns of ice loss on a glacier by glacier basis. They detected a sharp jump in Antarctica’s

ice loss, from enough ice to raise sea level by 0.3 millimeters (.01 inches) a year in 1996, to

0.5 millimeters (.02 inches) a year in 2006” (“Antarctica Ice Loss Speeds Up”). Also in 2006,

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a team of researchers at UC-Boulder “used data from a pair of NASA satellites orbiting earth

in tandem to determine that the Antarctic ice sheet… is loosing up to 36 cubic miles of ice, or

152 [km3]” (“Antarctic Ice Sheet Loosing Mass”) out of it’s 14 million km2 total, on an

annual basis. In terms of eustatic change, the complete melting of the Antarctic sheet, which

as of 2008 contained about 90% of the world’s ice and 70% of it’s fresh water, would raise

the global sea-level by 56.6 m, while complete melting of the Greenland sheet would raise

the global sea level by 7.3 m (Shum et al). This is theoretically within the realm of

possibility, at least for the Greenland sheet during the summer months, but it is not yet known

whether the Antarctic sheet could ever melt completely.

Neither is it known what sort of effect the tectonic rebound following such a severe

melting of the remaining polar ice would have, how severe it would be, or how soon the

effects would be seen. This uncertainty is largely due to the fact that: a. the future severity of

global warming is difficult, if not impossible, to predict; b. the thickness of the crust beneath

the remaining glaciers and ice sheets is not well documented; and c. that even the viscosity of

the mantle beneath is not yet completely understood. These three factors, in addition to a

plethora of others, make modeling future isostasy difficult.

There are, however, a few researchers doing work related to the subject. In 2000 Wu

and Johnston studied the likelihood of rebound-related earthquakes in the North American

continent, after they noticed that despite the fact that the area “east of the Rocky Mountain

Cordillera is supposedly a stable continental region… it experiences intraplate earthquakes

with magnitude as high as M8” (Wu and Johnston 323). They site a previous study done by

researchers in 1996 which found that “intraplate earthquakes in Eastern Canada,” again, a

supposedly tectonically stable region, “may be a consequence of tectonic forces and

postglacial rebound stress,” largely due to “past tectonic processes [which] created weakened

zones where faults, brought close to failure by the current tectonic stresses, may be

Luthien

Typewritten Text

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Works Cited

Aber, James S. "Glacial Isostasy and Eustasy." Emporia.edu. Emporia State University, 2008.

Web. 28 Nov. 2010. <http://academic.emporia.edu/aberjame/ice/lec09/lec9.htm>.

"Antarctic Ice Loss Speeds Up, Nearly Matches Greenland Loss." Nasa.gov. National

Aeronautics and Space Administration, 23 Jan. 08. Web. 1 Dec. 2010.

"Antarctic Ice Sheet Losing Mass, Says University of Colorado Study." ScienceDaily.com. 2

Mar. 2006. Web. 2 Dec. 2010.

Detlef, Wolf. "The Changing Role of the Lithosphere in Models of Glacial Isostasy: a

Historical Review." Global and Planetary Change 8 (1993): 95-106. Print.

"Glacial Isostatic Adjustment; A Survey of Recent Studies." Nasa.gov. IERS/GGFC Special

Bureau for Mantle, 10 Apr. 2000. Web. 27 Nov. 2010.

<http://bowie.gsfc.nasa.gov/ggfc/sbm_gla.html>

Gornitz, Vivien, ed. Encyclopedia of Paleoclimatology and Ancient Environments. New

York: Springer-Verlag, LLC, 2008. Print.

"Iceland Volcano Eruption Triggers Fears for Glacier." Telegraph.co.uk. The Telegraph, 21

Mar. 2010. Web. 2 Dec. 2010.

"Isostasy - Definition." Dictionary and Thesaurus - Merriam-Webster Online. Web. 04 Dec.

2010. <http://www.merriam-webster.com/dictionary/isostasy>.

Peltier, W.R. "Global Glacial Isostasy and the Surface of the Ice-Age Earth: The ICE-5G

(VM2) Model and GRACE." Annual Review of Earth and Planetary Sciences 32

(2004): 111-49. Print.

Shum, C.K., Chung-yen Kuo, and Jun-yi Guo. "Role of Antarctic Ice Mass Balance in

Present Sea-level Change." Polar Science 2 (2008): 149-61. Elsevier.com. National

Institute of Polar Research, 12 June 2008. Web. 1 Dec. 2010.

Wu, Patrick, and Paul Johnston. "Can Deglaciation Trigger Earthquakes in N. America?"

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Geophysical Research Letters 27.9 (2000): 1323-326. Print.

Zweck, C. "Glacial Isostasy and the Crustal Structure of Antarctica." Annals of Glaciology 27

(1998): 321-326. Print.

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Erin Collier-Zans

Douglas Duper

ENV207

13/12/10

Greens:

The Role of Diversity in the Formation of the German Green Party, 1970s-80s

In many movements, there has been a strong dynamic between people of different age

groups and worldviews. In many cases, this dynamic is antagonistic and counterproductive.

The young demographic is often more radical and craves sweeping reform, while the older

demographic is usually more inclined to try to work within the existing, familiar system to

create less drastic changes than those craved by the young. Within any movement, it follows

that there will also be disagreement about what the focus should be. Should a so-called

“Environmental” movement focus solely on issues of environmental health and preservation,

or should it be flexible enough to include clean energy, citizen health, women’s and

minority’s rights, anti-nuclear, peace and social reform movements among others, in addition

to environmental concerns. Is seeking to accommodate a diverse electorate with an array of

ideals and agendas ‘unacceptable compromise’ on the issues, or is it a success in its own

right?

In Germany, the modern Alliance ‘90/The Greens has gained significant support,

winning almost 11% of the votes in Germany’s last election cycle. But how did a series of

small, diverse groups and movements in Germany coalesce to form the modern Green Party,

and how did this group manage to gain such a foothold in national and even EU-level politics

when many other nations’ Green Parties struggle to gain even municipal-level success?

The diversity of the German Greens, the party’s historic acceptance of diverse

viewpoints and outspokenness on a wide range of issues, all under the banner of “The

Greens,” has been a major contributor to its success. It has gained popular support thanks to

the fact that it does not radicalize its membership and voter base into “Environmentalists” and

“Non-environmentalists,” remaining unspecialized and inclusive of many ‘alternative’ issues

and agendas.

The evolution of the German Green Party, or die Grünen, is considered to have really

begun in the early 1970s with the formation of as many as several thousand “‘citizen

initiatives’,” which were fragmented and entirely local movements seeking to address very

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specific issues, like the establishment of a particular nuclear power plant or the need for

greater democracy in a workplace (Longguth 6). Soon, however, initiatives with common

goals began looking for support in the greater community and many became part of one of

many umbrella associations, such as the Federal Association of Citizen Initiatives for the

Protection of the Environment, to which over 300,000 people and over 1000 local citizen

initiatives were affiliated by 1977 (7).

According to Longguth, this was the ‘first phase’ of the Greens’ development. The

backbone of environmental initiatives in this period was confronting the proliferation of

nuclear power stations after the Cold War rather than the severe environmental degradation

driving movements in the United States and even other parts of Europe(clarify/split up).

Germany did not have as great an issue with environmental safety concerns prevalent in other

nations due to the fact that, according to Shull, “Germany had had a fairly enlightened policy

toward the environment as early as the nineteenth century, when preunification German

Lander and private business associations regulated water and air pollution… After [WWII], a

premium on strict adherence to legal principles set by the institutions of the Federal Republic

[had] fostered precautionary and preventative attitudes toward potential environmental

hazards” (12). This is in stark contrast to the policies of the United States in the 20th century

onward, which focused on remediation and cleanup after severe damage to the land had

already been committed and the danger recognized, rather than focusing on avoiding such

damage in the first place. (good point)

Thus began the second ‘phase,’ with the above-mentioned consolidation of many

fragmented movements and ideologies into voter initiatives. These manifested in the form of

‘Green’, i.e. ecologically-minded, and ‘Rainbow’, i.e. social-reformist ‘Lists’, which

proceeded to run in various elections, but which failed to gain the requisite 5% of the national

vote in order to send deputies to the Bundestag, or German parliament (Longguth 9). These

collaborative organizations continued to gain support, but it was those such as the “Rainbow

List/Defend Yourself!” and “Alternative List for Democracy and Environmental Protection”

which gained more traction than more conservative, single-issue groups such as the strictly

ecological GLU (Green List for the Protection of the Environment) and later the GAZ (Green

Action Future). These unaccommodating groups were especially unappealing to the younger

portion of the populace, and in 1977 the GLU received only 2.4% of the 18-24 demographics

vote, which conversely gave a large portion of their support (18.2% nationally) to Rainbow

List in that same year (9). It has been suggested that blue-collar workers and others were the

most important and therefore target demographics for alternative parties, including the early

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Greens, in 20th century Germany (Shull 26-27), but at least in this country the importance of

the younger voters is easy to see, and for a party to have any staying power it must have some

way to continue to capture the imagination, hopes, and loyalties of students and young

professionals if it is to remain viable in the long-term(split up long sentences).

These consolidated second-phase groups brought together a wide range of interests

and issues, from the perceived failings of the democratic system, to the oil shocks of the 70s

and the waning appeal and gradual collapse of a ‘progress’-model economy, to women’s,

worker’s, and gay rights, and anti-nuclear/anti-war protest initiatives (Shull 31). The most

successful managed to maintain this diversity into the late 1970s-early 80s, when the ‘third

phase’ began with the founding of SPV-The Greens, in 1979. This group was specifically

aimed at carrying the ideals of the early protest movements forward into the established

political arena, something that has been viewed alternatively as a wise and effective choice

and as a betrayal of the group’s own ideals. SPV-tG was composed of both conservative

ecological groups like the GLU and the GAZ (‘the Greens’) and a variety of other initiatives

of vital importance to many, more liberally-minded social reformists (‘SPV’ – Other Political

Associations).

The fourth phase of the German Greens’ development arrived with this group’s first

convention, held in 1980, when their first platform was drafted, addressing everything from

abortion and women’s rights, to economic reform and the alleviation of unemployment, to

issues regarding the environment and its protection. The Greens achieved several regional

successes, but national success would not come until the ‘fifth phase’ when, in 1983, the

Greens received more than the requisite 5% of the national vote and were able to send 27

delegates to the Bundestag and 7 to the European Parliament. Their message was clearly

stated: they promised to represent “the interests of all who are affected by the policies of the

European Community but not represented in it” (qtd in Longguth 16). Several like-minded

groups in the EU parliament soon banded together to form the ‘Rainbow Faction’, with the

obvious intention of carrying forward the established precedent among ‘Green’ groups of

advocating for many issues not commonly addressed by their more conservative political

counterparts.

The ‘fifth phase’ of the 1980s, the end of our review of the Greens’ historical

background, was marked by “increasing skepticism… by a portion of [SPV-The Greens’]

voter membership due to and about increasing parliamentary participation, with both

established governments and radical groups feeling the party [had] been compromised by

‘extremists’,” with a major point of contention being their past and possible future

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involvement with the socialist SPD (Social Democratic Party of Germany), and other similar

organizations. This led to fragmentation within the party between liberals (mostly younger,

more radical) and conservatives (mostly older, wealthier, strictly ecologically-minded), and

also along the lines of major philosophical affiliations, largely among the “(i) eco-

libertarians”, who believed that market forces were the answer, “(ii) realists”, or those

encouraging political alliance and negotiation, “(iii) fundamentalists,” the eco-conservatives

mentioned above, and the “(iv) eco-socialists”, or those who “insisted on the interrelationship

of social and ecological questions and the need to oppose the capitalist state” (Weisenthal

11).

Some of the more conservative members of the party left to form the ÖDP

(Democratic Ecological Party), but like its predecessors the GLU and GAZ, it failed to

achieve much traction and as of the late 1980s had not managed to gain official party status

by claiming the requisite 5% of the vote. The Greens struggled for a while in this period, but

managed to stay intact and after another trying couple of decades, is now taking between 8

and 12% of the German vote in each of the most recent years’ election cycles.

The Green party emerged from and rode the wave of post-industrial/Cold War

disillusionment and subsequent strife prevalent in 1970s Germany, which sparked a national

movement seeking generally to create a ‘new’ civilization out of the old. The Green Party

arrived on the scene as a distillation of these various movements, first into “Lists” or national

electorates sharing the same general interests and goals for the future, and then into its own

self-identifying ‘Party’. (if you are paraphrasing, be sure to include sources)

It was supported by a vast array of peoples rather than by a small, single-minded,

issue-centric and loyal demographic. Internal conflicts in the party really only became a

problem not after unification, but after their initial success in 1983 when, as a natural step

towards ‘partydom’, various representatives sat down and tried to finalize the groups’

platform and thereby define what exactly the focus and main issues of the party would be.

They were trying to honor the ‘roots’ of this party, but there was disagreement over

what exactly this meant. Would they side with their supporters in workers unions seeking

economic reform? Would they side with radical anti-nuclear activists seeking energy reform

and greater self-dependence for Germany as a nation? Or would they focus solely on issues

of the environment, and thereby further disenfranchise those of their supporters most keen on

addressing other issues?

There is, in any political party, a choice to be made between ‘efficacy’ and ‘identity’,

or diversity v. focus. On the one side, a party may “press intense, often nonnegotiable

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demands for change,” which with their specific goals have a chancge of achieving great

success, but which also “[conflict] with the guarantee of diversity… or the continuation of the

organization itself” if it fails to capture a significant proportion of its target electorate. The

obvious alternative, then, is a strategy of diversity, which means “articulating the demands of

a range of social movements… By expanding the scope of issues addressed, the aim is to

rally the broadest possible base of supporters” (Shull 45).

If the former path is taken, the “electoral support may be deep (that is, reliable), but

not wide (that is, extensive in members)… [and] to maintain credibility with its base, the

party has to keep up the intensity and momentum of demands for change” (46). This focus on

one issue and on appealing to a single worldview “often implies deferring actual movement –

that is, obtaining tangible gains – in the name of guaranteeing the authenticity and purity of

the mobilizing ideals of the supporting social movement” (46).

This dynamic was clearly seen with the Green Party throughout the 70s and 80s.

Critics of SPV-The Greens often claimed that they had made just such a sacrifice of ‘purity’,

that they were ‘betraying’ the ideals even of those who had rallied to create and support it by

associating with other groups and especially with the SPD and FDP. On the other side,

however, were those groups such as the ÖDP and GAZ which sought to maintain

‘authenticity’ by focusing only on ecological issues, and which summarily failed to gain any

quantifiable success.

Some may believe that taking on social and other issues in tandem with problems of

environmental endangerment is somehow compromising the effectiveness and inherent worth

of the ‘Environmental Movement’. By this logic, the Rainbow List/Defend Yourself!, its

descendent SPV-The Greens, as well as the ‘Rainbow Faction’ of the 1980s EU Parliament

were all failures, despite all evidence to the contrary. They may have made accomplishments

on the ecological and related anti-nuclear fronts, but these accomplishments were already

‘tainted’ due to their simultaneous outspokenness on problems of social inequality, etc,

because their focus was diluted.

But which is better: effectiveness, or ‘purity’? When considering the downright

failure of dedicated environmental groups in 20th century Germany to achieve any lasting,

national-level changes, would it not be better for environmental reform to arrive even as a

footnote of more conservative policies continuing the established, ‘corrupt’ system, than to

have this reform not arrive at all due to the over-dependence on over-identified political

parties such as many of the modern-day “Greens”.

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It is better to achieve widespread, diluted change by garnering support from

widespread, diverse interest groups than to fetter the movement from the start by remaining

singularly focused on any one issue.. Who is to say that peace movements, women’s and

minorities rights movements, democratic labor movements, etc., have no place in movements

concerned with the ‘environment’. If people and their actions are going to be acknowledged

as being the ‘problem’, then surely people are the answer, and to succeed people, from all

walks of life, seeking a better world through many avenues, must be included in the solution.

If social reform is the goal, then the historic development of die Grünen has a lot to teach us.

The Greens Party of Germany, after all, “might justly be regarded as the finest achievement

of the second wave of environmentalism, referred to by the respectful capital that sets it apart

from its peers and contemporaries: the Greens, as distinct from all other kinds of greens”

(Guha 97).

A solidly presented and researched paper—you do a very good job of tracing the

development of the Greens in Germany. It might be interesting to consider how their

approach could be adapted (or if it could be) to U.S. politics, and if so, what would strategy

look like? Grade: A

Works Cited

Guha, Ramachandra. “The Ecology of Affluence”. Environmentalism: A Global History.

New York: Longman, Inc., 2000.

Longguth, Gerd. The Green Factor in German Politics: From Protest Movement to Political

Party. Boulder: Westview Press, 1984.

Shull, Tad. Redefining Red and Green: Ideology and Strategy in European Political Ecology.

Albany, NY: State University of New York Press, 1999. Print.

Weisenthal, Helmut. John Ferris, ed. Margaret Curran, trans. Realism in Green Politics:

Social Movements and Ecological Reform in Germany. New York: Manchester

University Press, 1993. Print

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Final Question:

Reflect upon the history of the environmental movement since the “second wave,”that began in America about 50 years ago with Silent Spring. Have your ideas aboutenvironmentalism changed or deepened? If so, how? What practices, theories, or peopleof the environmental movement in this time period have resonated with you and why?What do you think are the successes and most effective solutions offered by this waveof environmentalism? What are its failures and weaknesses? Finally, project yourthinking from the past to the future, remembering that “those who don’t understandthe past are destined to repeat it,” as a philosopher once said. What would be effectiveenvironmentalism for the future? Support your answer with plenty of support from thereadings after the midterm.

There were several, very important concepts that stuck with me from this portion of

the semester, but for the sake of time and space, and because many of the readings have been

removed from the e-reserves(I emailed them most likely), I will only speak on one at the risk

of failing miserably at this assignment

This one, strongest issue for me, which has in a way overridden other concerns, is the

involvement of women and minority groups in ‘environmentalism’, and the issues of social

justice that inevitably follow and become incorporated.

It might be good here to look at the ‘environmentalism of the poor’, of which there are

many examples, each soundly disproving the unfortunately yet prevalent misconception that

“environmentalism is a phenomenon peculiar to the rich nations of the North, a product of the

move toward ‘postmaterialist’ values among the populations of North America and Western

Europe” (Guha 98), a presupposition that leads to the horrible conclusion that for

‘environmentalism’ to take hold in the rest of the world, the world’s poor must first be

brought up to first world-identical living standards, something that various countries and

groups have been trying, often unsuccessfully, to accomplish, probably since the end of the

Colonial era.

I suppose that we might need a new word for what is being practiced in the so-called

‘third world’, because it certainly doesn’t look like most environmentalism in this and other

rich countries. The environmentalism of the poor is often, on some level, driven by the

economic deprivation created by local environmental degradation (105). The livelihoods of

communities are routinely threatened by first-world economic ventures like mining and clear-

cutting, and their form of ‘environmentalism’ is driven at least partially by true, human

desperation. Without the forest, how would they live? Without clean streams, what will they

drink?

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Along with any spiritual or cultural associations/factors, these are true needs. They are

immediate, and cannot be forgotten or looked over, unlike the oil spill or Katrina for people

in the US not living on the coast, or strip mining for people not living in the Appalachians,

etc. It seems to me that a significant portion of modern ‘first-world’ environmentalist action,

stemming from any number of complicated and unquantifiable emotional/logical attachments,

tends toward detachment or inefficiency, while the environmentalism of the poor, being

attached as it is to an “often more visible concern for social justice” (105) involves blood,

sweat, and tears because they are true movements of the kind we haven’t seen on a national

level since the 1970s feminist movement, itself growing out of the 70-some year struggle for

civil rights and the 100-odd year struggle for women’s votes.

I feel it might be a good time to bring in the possible ‘death of environmentalism’.

The authors of The Soul of Environmentalism say, “in the ‘90s, the declaration that “poetry is

dead” was an attempt to deny and marginalize a rich array of new anti-establishment forms of

poetry. Back then, the writers ignored rap, performance art, and poetry slams. The debate

over “The Death of Environmentalism” feels like a similar exercise in its omissions” (6).

They go on to point out that “environmentalism and other progressive movements in the

United States are not dead, but they are crippled by denial… [Yet] environmentalism, like

poetry, has a soul deeper and more eternal than the one described by its examiners. It’s a soul

tied deeply to human rights and social justice, and this tie has been nurtured by the

Environmental Justice and Sustainability movements for the past 20 years” (6).(good

supporting quote)

Perhaps the soul of environmentalism can be seen in the paradigms of

‘environmentalism for the poor’. This is not to say that the soul is only here – I at least have

the unfortunate habit of associating soul with ‘one’, and thinking that the soul can only be in

‘one’. But the soul is a web. Soul is a verb. The soul is the network of information, energy,

activism, art, tradition, everything that makes us quintessentially human.

Now, a bit of a jump, to wrap up: Why is this important?, I have been asking myself.

Is the history of the environmental movement and its future important to me as a detached

observer? Is it important to me, as a future activist? I think the latter is truer, but that raises all

sorts of other questions that I have been grappling with for a year now. Is my attempting to

become involved in ‘environmentalism for the poor’ a continuation of the unfortunate White

Knight syndrome, whereby wealthy people feel obligated to get involved not out of a real

sense of purpose or belief, but out of guilt, or out of a mistaken and idealistic perception that

‘other is better’? And how could I possibly get involved without being perceived as an

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ambassador for the Western model of my origin, merely by showing up? Should I even get

involved abroad? If the problems have been largely caused by the actions of first-world

nations, shouldn’t I stay in my own country and spend a significant portion of my life trying

to do something from here?

But then I remembered the early months of the Democratic Movement in China.

Westerners, educators and participants in the civil rights/anti-war protest movements went

there to teach successful models of nonviolence, not because they believed their models were

‘better’ or their audiences ‘ignorant’ but because activists in that country requested that they

come and share information and experience. These educators, then, were serving the common

good and the good of those they were teaching by being there. They were serving, not

enforcing.

So, I guess that my personal model of ‘environmentalism for the future’ is focusing on

preserving human-ecological diversity. If we are animals, and we are not separate, then we

should not be separate and the preservation of unique cultures should go hand in hand with

the preservation of biodiversity. In the end, I’m only going to live a few more decades and I

should do what I feel best about, knowing that whatever change I manage to make happen is

a drop in the ocean, and while not necessarily unimportant, certainly miniscule. Change is for

all generations. Humanity is a work in process, and giving the present a sort of ‘calm before

the storm’ feeling associated with the perception of the future as the coming apocalypse, isn’t

particularly helpful in my mind.

I have no idea what the grand picture of future environmentalism ‘should’ look like. I

can only hope that it is more diverse and vibrant than what we have now, with less emphasis

on individual and personality (unless we find a useful rallying point like Gandhi or MLK),

and that it will be lead by the humble and the sincere. I hope that, if necessary, the world will

leave the US behind and stop waiting for it to lead the way into this more environmentally

friendly future – something that it is quite probably incapable of, at this point. In the end, I

have hope. What else can I do?

A thoughtful response that grounds your study of the class topics with your personal

motives. As one aboriginal elder said, to paraphrase, “only come to help us if you realize that

your liberation is connected with ours.” Grade: Check +

Luthien

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Luthien

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Introduction to High School Course Work2006-2008

For this portfolio I have also provided a selection of my high school work, fromsophomore through senior year.

I have chosen pieces that I believe exemplify my capabilities as a writer during thatperiod, in the core subject areas. Teacher comments have been included where available, andrubrics with final grades are also attached to the end of each document. These rubrics arethemselves valuable, in that they give a clear idea of the standards to which RMSEL held itsstudents; the grades I received for these pieces demonstrate the standards to which I held myself.

I have provided two pieces from Science: one is a write-up for a dissection lab my classdid sophomore year, while the other is the final product for an expedition we did on weatherpatterns (and data sets), global warming, and research skills.

I have also provided two math write-ups. The first relates to our senior-year expedition inexpressing exponential growth; in my own words from 2008, “there were other write-ups thatperhaps demonstrated my capabilities as a math student better, but his piece showcases myability to work in generalizations and abstractions (of which I am very proud), to go above andbeyond the requirements of an assignment, and to connect statistics reality and especially to[the] humanitarian issues we will be facing in the future.” The second, entitled simply ‘OrchardWrite-up,’ I wrote at the conclusion of an expedition on geometry and angles. My favouriteelement in both expeditions was generating generalized formulae to express the entirety of thatsemester’s work – I enjoy working, as mentioned before, in abstractions, and I find formulasboth elegant and beautiful; they are art.

Rather than present yet another investigative piece to exemplify myself as a ‘Humanities’student (Humanities being the subject encompassing sociology, history, mythology, etc), I haveinstead chosen to provide 2008’s best attempt at creative writing – a piece entitled ‘FreedomsThat Be,’ a modern-day interpretation of the myth of Daphne, a nymph. As I said in 2008,

“This subject [i.e. art and myth] is very personal to me; I can paint and draw quite well,and have often been asked, ‘why don’t you want to become an artist?’ I answer thisquestion in my myth by creating a [character] who did become an artist, and suffered forthis choice… Art is very personal [for] me, and I am very proud of this myth; I consider ita work of art unto itself. Perhaps that is why I worked so hard on it, and picked over itagain and again in an attempt to make it perfect, [which] demonstrates another of mypersonality traits: perfectionism and an unwillingness to just let something go. This traitdoesn’t serve me well when I’m making a painting, but I believe that the quality of mymyth benefited greatly from an extensive drafting process.”Finally, ‘Un Barco se Hundio’ is an example from 2007 of the sort of work we often did

in Spanish class. It was a fun, interactive class – we got up on chairs and tables and danced, puton costumes and enacted plays, in order to enact the vocabulary we were learning. We also wrotelittle stories like this one, often with animal characters in silly circumstances, again usingwhatever vocabulary words the teacher opted to require. My study of verb conjugation duringmy time in Quetzaltenango, Guatemala in 2006 helped a great deal with this piece.

Luthien

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-Notice that the main difference between the cephalothorax and the abdomen isthe segmented nature of the former. The thorax bends and is used to move theanimal about, while the cephalathorac is a hard shell, protecting the animals headand many of its internal organs. The crayfish’s exterior is not similar to that of ahuman, as they have exoskeletons, while we have an internal skeleton.

3. Turn the crayfish on its side, and locate the rostrum, which is the pointed extension ofthe carapace at the head of the animal shown in the diagram above. Beneath the rostrumlocate the two eyes. Notice that each eye is at the end of a stalk. Diagram observations onobservation sheet.

4. Locate the five pairs of appendages on the head region. First locate the antennules inthe most anterior segment. Behind them observe the much longer pair of antennae.Diagram observations on a new observation sheet.

-Is is advised that you keep the animal on it’s side for this part of the study,because the appendages of the head are best viewed from this angle.

5. Locate the mouth. Then observe the mandibles, or true jaws, behind the antennae. Nowlocate the two pairs of maxillae, which are the last appendages in the cephalic region.Diagram observations.

--The appendages related to the eating of food are the maxillipeds, of which thereare three pairs. They all hold food, tear it up, and pass it into the mouth, where themandibles crush it. The second pair of maxillipeds are also used for passing waterover the gills. They operate in a similar fashion as our hands, or fingers, tearingfood up and passing it to our own mouths, however our arms are also similar tothe chelipeds, or claws.

6. On the thoracic portion of the cephalothorax, observe the three pointed maxillipeds.Diagram.

7. Next observe the largest prominent pair of appendages, the chelipeds, or claws. Behindthe chelipeds locate the four pairs of walking legs, one pair on each segment. Diagram.

8. Now use the walking legs to determine the sex of your specimen. Locate the base segment of each pair of walking legs. The base segment is where the leg attaches to thebody. Use a magnifying glass to study the inside surface of the base segment of the thirdpair of walking legs. If you observe a crescent-shaped slit, you have located a genitalpore of a female. In a male, the sperm duct openings are on the base segment of thefourth pair of walking legs. Use a magnifying glass to observe the opening of a genitalpore. Diagram.

-This specemin was a male. The external reproductive organs of the crayfish arenot similar to humans, as male humans have a protruding reproductive organ,while both sexes of the crayfish have ducts used to transport eggs and sperm tothe outside.

Exchange your specimen with a nearby classmate who has a crayfish of the opposite sex.Then study its genital pores. Diagram!

9. On the abdomen, observe the six distinct segments. On each of the first five segments,observe a pair of swimmerets. Diagram.

10. On the last abdominal segment, observe a pair of pointed appendages modified into apair of uropods. In the middle of the uropods, locate the triangular-shaped telson.Diagram.

11. Now turn the crayfish ventral side up. Observe the location of each pair ofappendages from the ventral side. Diagram

-Notice that the appendages can be better viewed from the ventral side, as whenthe animal is on its dorsal side, the area where the limbs are attached to the bodyis hidden, as are the swimmerets.

12. Next you will study the internal anatomy of a crayfish. If you must store yourspecimen until the next lab period, cover it with a dampened paper towel. Then place thespecimen on the tray in a plastic bag. Close the bag with a twist tie. Write your name onthe bag with a felt-tip marking pen, and give your specimen to your teacher.

13. Clean up your work area and wash your hands before leaving the lab.

Consult with a member from an earthworm dissection group, and create a table ofsimilarities and differences between your two specimens:

Similarities DifferencesBoth segmented animals Worms reproduce using the clitellum

Both have appendages used in movement Crayfish have true limbs, i.e. pincersNeither have true lungs Worms breath through pores on their skin,

crayfish using gillsShare same basic organs, heart, stomach,etc.

Crayfish are aquatic, while worms areterrestrial

Both have regenerative capabilities Crayfish have exoskeletonsBoth in kingdom animalia Worms have 5 hearts, crayfish has only oneBoth have genders Phylum: Worm-Annelida, Crayfish-

ArthropodaCrayfish fertilize eggs internally, after themale passes sperm to the female usingmodified swimmerets. Earthworms fertilizeeggs externally.

Crayfish are more advanced because they have a more developed respiratory system.Oxygen, in worms, in transferred directly to the circulatory system by its soft skin, whilethe Crayfish passes water over its gills, taking the oxygen from the water, and thentransferring it to the circulatory system (?). The pores on the exterior of the earthwormabsorb oxygen but if the animal is put into water, it will drown. However, when thecrayfish is put on land for an extended period of time, it suffocates, as its gills cannotfunction as lungs do, and it must be in water to breath. Therefor, each animal has evolvedto function in specific environments. The earthworm thrives in loam, and other nutrientrich soil. The crayfish inhabits most freshwater bodies, though it seems to be common instreams, rivers, and ponds. Its relative, the lobster, lives in saltwater.

Part 2- Internal Dissection:

14. Put on a lab apron and gloves.

15. Using one hand to hold the crayfish dorsal side up in the dissecting tray, use scissorsto carefully cut through the back of the carapace along dissection cut line 1 as shown inthe diagram below. Cut along the indentations that separate the thoracic portion of thecarapace into three regions. Start the cut at the posterior edges of the carapace, andextend it along both sides in the cephalic region.

16. Use forceps to carefully lift away the carapace. Be careful not to pull the carapaceaway too quickly. Such action would disturb or tear the underlying structures.

17. Place the specimen on its side, with the head facing left, as shown in the diagrambelow. Using scissors, start cutting at the base of cut line 1. Cut along the side of thecrayfish, as illustrated by cut line 2. Extend the cut line forward toward the rostrum (atthe top of the head).

18. Use forceps to carefully lift away the remaining parts of the carapace, exposing theunderlying gills and other organs.

19. Use the diagram below to locate and identify the organs of the digestive system.Locate the maxillae that pass the pieces of food into the mouth. The food travels downthe short esophagus into the stomach. Locate the digestive gland, which producesdigestive substances and from which the absorption of nutrients occurs. Undigestedmaterial passes into the intestine. Observe that the intestine is attached to the lobedstomach. The undigested material is eliminated from the anus.

-The teeth on the inside of the stomach are used in grinding up the food, after it istorn up and passed to the mouth by the maxillipeds. Muscles on either side of thestomach are used to contract and move the stomach about.

20. Use the diagram below to locate and identify the organs of the respiratory system.Locate the gills, which are featherlike structures found underneath the carapace andattached to the chelipeds and walking legs. A constant flow of blood to the gills releasescarbon dioxide and picks up oxygen.

-The gills have a very large surface area for greater oxygen absorption. This issimilar to human lungs. A person with larger lungs will absorb more oxygen thatsomeone with smaller lungs.

21. Use the diagram of the internal anatomy of the crayfish to locate and identify theorgans of the circulatory system. Locate the dorsal tubular heart and several arteries. Thecrayfish has an open circulatory system in which the blood flows from arteries intosinuses, or spaces, in tissues. The blood flows over the gills before returning to the heart.

22. Use the same diagram to locate and identify the organs of the nervous system. Findthe ventral nerve cord. Locate a ganglion, one of the enlargements of the ventral nervecord. Locate the dorsal brain, which is located just behind the compound eyes. Note thetwo large nerves that lead from the brain, around the esophagus, and join the ventralnerve cord.

-Many nerves leave from the ganglion, and are used to activate the swimmerets.

23. Use the same diagram to locate and identify the organs of the excretory system. Theblood carries cellular wastes to the disk-like green glands. Locate these organs just infront of the stomach. The green glands excrete waste through pores at the base of eachantenna.

-The green glands secrete excess water and ammonia. In this, they are similar tothe bladder, storing wastes, and then removing them from the body.

24. Use the diagram once again to locate and identify the organs of the reproductivesystem. The animal shown in the diagram is a male crayfish. If your specimen is a male,locate the testis. The testis is the long, white organ under the heart and a bit forward. Thesperm ducts that carry sperm from the testis open at the fifth walking leg. If yourspecimen is a female, locate the bi-lobed ovary. It is in the same relative position as thetestis, but the ovary appears as a large, reddish mass under the heart. Then locate theshort oviducts that extend from near the center of each side of the ovary and open at the

third walking leg. Exchange your specimen with a nearby classmate who has a crayfishof the opposite sex. Then study its reproductive system.

25. Dispose of your materials according to the directions from your teacher.

26. Clean up your work area and wash your hands before leaving the lab.

Conclusion:

The hypothesis proved to be true. Humans and crayfish are both motile animals, andshare many of the same internal structures, such as: organs used for breathing (thoughboth are adapted to their environment, lungs vs. gills), stomach, intestine (and a similarway of absorbing nutrients, breaking down the food in the stomach, then absorbingnutrients through the intestine, into the bloodstream). Both have appendages capable ofgrasping things, in humans, it is the opposable thumb, in crayfish, the chellipeds.However, the skeletons of these two creatures are very different. The crayfish has anexoskeleton, which it must shed periodically in order to grow, while the human has aninternal skeleton, and stops growing after a certain point. There are other dissimilarsystems, such as the maxillipeds. There are no similar structures in humans. Humans usetheir fingers to grasp food while it is put in the mouth, then teeth to grind and tear it intodigestible pieces. In conclusion, excepting a few differences, crayfish and humans areincredibly similar.

Diagrams:

Observations Inferences

Rostrum/Eyes

Antennae

Mandibles andMaxillae

Maxillipeds

Chellipeds andWalking Legs

Sperms/Egg Ducts,Modified Swimmerets(if male)

AbdominalSegments/Swimmerets

Uropods/Telson

Gills

Heart

Ventral Nerve Cord/Green Glands

Erin Collier-Zans2007

Global Warming and Disease Outbreaks in Colorado and China

Is the climate changing? Few scientists would deny that something drastic is going on.

This century has seen a global increase in average temperatures by between .7 and 1.5° F. The

burning of fossil fuels has released aerosols into the atmosphere, which capture and retain heat,

hence the greenhouse effect. The sea ice is retreating, causing the sea levels to rise. Sea-surface

temperature warming is causing more severe and frequent hurricanes, cyclones, and typhoons.

Desertification and floods plague non-coastal areas. Is global warming to blame? Are we to

blame? Does global warming really affect us, and what can we do to make positive changes?

Hypothesis:

The average temperature and precipitation for the month of August, collected by weather

stations around Colorado, and the RMSEL weather station, will show a general warming/rising

trend, for the period between 1950 and the present day.

Data from Colorado weather stations:

Average High Temperature for the State of Colorado In the Month of August By Year

6262.5

6363.5

6464.5

6565.5

6666.5

6767.5

6868.5

6969.5

70

195019

5219

5419

5619

5819

6019

6219

6419

6619

6819

7019

7219

7419

7619

7819

8019

8219

8419

8619

8819

9019

9219

9419

9619

9820

0020

0220

0420

06

Year

Tem

pera

ture

(°F

)

Average High Temp.Expon. (Average High Temp.)

2

This chart shows the average monthly temperature (from the month of August), for the periodbetween 1950 and the present day. You can clearly see the rising trend line. This trend lineshows a raise in the average temperature by approximately .7°F. Below is the dataset:

Year °F Year °F Year °F1950 63.3 1969 68.1 1988 671951 65.7 1970 68.1 1989 64.31952 66.8 1971 66 1990 64.81953 65.4 1972 64.4 1991 65.51954 66.5 1973 65.8 1992 63.51955 67.8 1974 63 1993 63.91956 64.3 1975 64.8 1994 67.61957 66.4 1976 64.2 1995 68.71958 68.1 1977 65.7 1996 66.21959 67.1 1978 64.3 1997 65.21960 67.2 1979 64.4 1998 66.51961 66.7 1980 66.4 1999 65.81962 66.1 1981 65.3 2000 69.41963 64.3 1982 67.3 2001 67.31964 63.5 1983 69.1 2002 67.11965 64.6 1984 66.6 2003 69.11966 64.6 1985 66.3 2004 63.61967 63.7 1986 66.2 2005 65.71968 62.6 1987 64.3 2006 65.8

Precipitation for the Month of August from the Grand Junction Weather Station

0

10

20

30

40

50

60

70

80

197019721974197619781980198219841986198819901992199419961998200020022004

Year

Millim

ete

rs precipitation inmillimeters

Linear (precipitation inmillimeters)

This is the precipitation in millimeters from Grand Junction. The trend line shows a definite

increase as the year’s progress, and the variation year to year becomes more extreme. In the raw

data set shown below, you can see that the precipitation in 2003 was 56 millimeters, the highest

3

since 1999. It should also be noted that the three highest rainfalls during the 1970-2004 period

fall in the last 8 years of data.

Year mm Year mm Year mm1970 12 1982 24 1994 131971 27 1983 18 1995 121972 8 1984 46 1996 51973 16 1985 7 1997 701974 12 1986 25 1998 141975 3 1987 25 1999 56.41976 9 1988 35 2000 15.21977 15 1989 26 2001 381978 14 1990 12 2002 211979 16 1991 14 2003 561980 36 1992 20 2004 51981 17 1993 36

Hypothesis:

Global warming causes higher average temperatures and average precipitation. This

higher humidity and temperature in turn causes the outbreak of deadly tropical diseases, like

malaria and West Nile Encephalitis, which pose a serious threat to human health both locally and

globally.

In the summer of 1998, China suffered a massive flooding of the Yangtze River, the

worst in 44 years.1 It had been an unusually wet rainy season, leading to extremely high water

levels in lakes and rivers. This resulted in 7 consecutive flood surges, 3 of which occurred within

a span of 3 days.

It was suggested to the Chinese government that the flood might be diverted, but instead

of paying heed to this suggestion, the government decided that the bank of the river should be

secured instead. To aid in the accomplishment of this, the government “instructed that authorities

at all levels increase material and manpower to secure the bank at all costs. According to the

Ministry of Water Resources data, materials and supplies worth more than 10 billion Yuan

(US$1.2 billion) were expended on the situation.”2

1 http://edition.cnn.com/WORLD/asiapcf/9808/25/china.floods.01/2 http://www.theepochtimes.com/news/4-12-27/25263.html

4

A soldier helps an elderly flood victim

The first levee to collapse was in Waijiang, Hezhen of Jiayu County. It collapsed on

August 1, after which soldiers and rural workers from the area worked nonstop for five days and

nights, attempting to block the hole. Finally, the strategy of sinking of ships and trucks and

fixing wooden boards succeeded.

On August 5th, the levees in Paizhou, Jiujiang, and Jiangxin area of Jiayu County

collapsed. This area was densely populated, mostly around the Paizhou area, which was

inhabited by some 500,000 people. Almost all the able bodied were out working, trying

desperately to block the flow of the river, but to no avail. The levee collapsed completely at

midnight, engulfing about 100 soldiers, locals, and policemen who were working on the dam.

The river swept into the villages all along the riverbanks, flooding homes, schools, and

farmlands. The sleeping children, women, and elderly didn’t stand a chance. They had received

no forewarning, and 11,000 died. A further 1,000 laborers were declared missing, presumably

swept away by the flood crest.

During the rest of the day, the lower reaches of the river flooded, collapsing more levees

in Jiujiang and Jiangxinzhou. The main Yangtze levee collapsed on the 7th, at which point the

government grew desperate, and ordered that any and everything that would pack down be

thrown into the river, to block the hole. 5 million tons of rice, soybeans and other grains were

thrown in, along with some 50 trucks and 18 ships.

A unit of 200 soldiers specially trained to handle flood disasters was dispatched from

Zhangjiakou, who filled the hole with concrete and boards, finally blocking the hole and

stopping the flood. 12,000 people were

claimed by the river upstream, around 6,000

people died in the rivers’ lower reaches, and

the series of levee collapses amounted to some

58 billion yuan, or around 7 billion US dollars

in damages.On top of that, around 14 million

people were displaced. Many had no homes toreturn to, once the floodwaters had subsided.

The Yangtze River area contains a boomingeconomy, and people were quickly moving into the river basin. The fertile lands around the rivercontain about 3% of the countries total farm land, the erosion and inaccessibility of which

5

drastically affected the health of the countries economy since China at the time contained 1/5 ofthe worlds human population and only 7% of its arable land.

The hardships faced by the survivors continued, without relief. Many remained shelter-

less. Those who returned to the flooded areas were plagued by a multitude of diseases spread by

insects and aided by unsanitary conditions. Many of the flooded areas remained so for months,

preventing people from picking up their lives. Many have wondered if this tragedy could have

been avoided.

The floodwaters could, for instance, have been diverted to some of the rivers smaller

tributaries, minimizing the loss of human life and the damage to property. The severity of the

flood was only exacerbated by the construction of various dams and levees, which inhibited the

rivers ability to regulate itself. This situation was exacerbated by the clear cutting the riverbanks

and the building of roads and mines, which raised the silt levels of the river leading to

abnormally higher water levels: “Zhuang Guotai of the State Environmental Protection Agency

Ecological Section told Worker Daily in early August that for every 70,000 hectares of forest

that is lost, a natural reservoir that can store one million cubic meters of water is lost. Zhuang

said that the peak flow rate of the Yangtze at Yichang this year is below historic highs. Twenty-

three years have had higher flow rates. But the destruction of forests resulted in natural water

storage loss and silting of rivers and lakes and raised the level of the river further. The

encroachment of land-hungry farmers on lakes reduced the capacity of the environment to absorb

floodwaters. Dongting Lake, a major regulator of Yangtze floods, shrunk from 6000 square

kilometers in 1700 to 4350 square kilometers in 1949 and by another third to just 2820 square

kilometers by 1980.”3

The incredible damage that the flood caused was also in large part due to poor resource

management on the part of the Chinese government. “Farmers faced with a declining amount of

arable land- available per capita are increasingly encroaching on lakes and riverbeds. Balancing

the interests of land hungry farmers with the need to protect against flooding is a difficult

question of land use policy formulation, regional coordination and enforcement.”4 As more and

more ‘land-hungry farmers’ flock to flood-prone areas, the amount of damage the floods cause

increases along with the number of people in harms way.

3 http://www.usembassy-china.org.cn/sandt/fldrpt.htm4 -

6

The strength of the country’s defenses against floods also need to be strengthened:

“Chinese river dikes are designed to withstand the largest flood that might be expected to occur

over a ten to twenty year period while in Europe, Japan and the United States, a 100 - 200 year

flood standard applies to large rivers and a 50 - 100 year standard might apply to other rivers.

The Chinese standard is calculated by comparing the cost of avoiding flood losses versus that

cost of building massive dikes and reservoir areas to control floodwaters. This formula…does

not adequately reflect losses to the national economy and to the people of the region.”5

Perhaps the flood was in fact due, in some way, to global warming. Scientists predicted

that a severe flooding of the Yangtze river was likely due to “the strongest El Nino on record in

Spring 1997 continuing into the Summer of 1998, the most serious snow disaster of the century

on the Qinghai - Tibet plateau from November 1997 - February 1998,” and the fact that the

“rainfall along the Yangtze River from November 1997 to April 1998 was the highest ever

recorded” as illustrated by the chart below:

Average Precipitation for the Months of April-August in China

0

20

40

60

80

100

120

140

160

180

1960196219641966196819701972197419761978198019821984198619881990199219941996199820002002

Year

Millim

ete

rs mm

Poly.(mm)

This chart shows the average precipitation in millimeters of the months between April

and August, which are the rainiest months in China. A trend line has been included, which shows

a gradual decrease in precipitation. You can see a number of high peaks and rapid falls. In

1995, the average precipitation during this period was 73.4 millimeters, but in 1996, the average

precipitation was 124 millimeters. In 1997, the precipitation was 63.6 millimeters, and in 1998,

5 -

7

it jumped up to 123 millimeters. This combination of drought years and extremely wet years led

to flash flood conditions. Below is the raw data;

Year mm Year mm Year mm1960 84.6 1974 80.8 1989 67.41961 86.2 1975 73.4 1990 112.81962 65 1976 117.4 1991 126.41963 149 1977 122.4 1992 85.61964 134.8 1978 110.2 1993 861965 43.4 1979 133.6 1994 1531966 94.8 1980 58.8 1995 73.41967 105.4 1981 63.6 1996 1241968 46.8 1982 103.4 1997 63.61969 149.2 1983 86.2 1998 1231970 106.4 1984 85.2 1999 43.21971 80.8 1985 131.8 2000 63.21972 48 1986 103 2001 48.81973 111.6 1987 115.2 2002 56.6

1988 118 2003 40.4

Scientists have also reached the conclusion that the abnormally high average temperaturefor the year of 1998 in China made the weather patterns in the area less predictable and moresevere, and therefore contributed to the variability in average rainfall.

Average Temperature for the Month of August (in °C)

22.5

23

23.5

24

24.5

25

25.5

26

26.5

27

27.5

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

Year

°C

°CLinear (°C)

This chart shows the average temperatures for the month of August. As you can see, 1998 isamong the highest recorded. This data is only for the weather station in Beijing, and does notinclude data from other weather stations in China, or from elsewhere in the world. Below is theraw data represented in the graph:

8

Year °C Year °C Year °C1950 25 1969 24.2 1988 24.41951 25.8 1970 23.8 1989 25.11952 24.3 1971 23.8 1990 25.41953 23.6 1972 23.8 1991 27.11954 24.3 1973 24.4 1992 24.61955 25.4 1974 24.5 1993 25.21956 23.8 1975 25 1994 26.51957 24.2 1976 23 1995 25.41958 23.9 1977 24 1996 23.91959 24.6 1978 23.9 1997 26.61960 25.4 1979 23.6 1998 25.11961 24.8 1980 23.7 1999 25.61962 25.9 1981 24.8 2000 25.71963 25.5 1982 25.8 2001 25.81964 24.4 1983 25 2002 25.71965 24.8 1984 25.4 2003 26.21966 25 1985 25 2004 24.91967 25.2 1986 24.51968 24.2 1987 24.8

Many Chinese Scientists agree that the 1997 - 1998 El Nino ocean warming and La Nina

ocean cooling phenomena is a likely contributor to the heavy rains of the Yangtze basin in1998

as well as an indicator of a global short term climate abnormality. Former Chinese lead

researcher on the international Tropical Oceans and Global Atmosphere (TOGA) project Chao

Jiping said, “just because there is more rain doesn’t necessarily mean that there will be a flood.”

Other important contributors to the likelihood and severity of flooding are those related to

environmental degradation, like the soil loss and inadequate flood prevention capacity along the

Yangtze.

The combination of heavy snowfall in Tibet, torrential rains in the Yangtze area, and

record high temperatures were the cause of the flood, but poor management was to blame for the

incredible human suffering that occurred after the floodwaters had passed.

9

Conclusion:

The climate is indeed changing. The temperature is increasing, both in the state of

Colorado and in the country of China. A reasonable assumption is that the global temperature is

warming also. The average precipitation in China is not increasing, but rather decreasing. The

precipitation in Colorado for the month of August shows a definite increasing trend. So the

original hypothesis did not prove to be entirely true, but facets of it are accurate. The

precipitation is not increasing globally, but rather is changing. It is becoming less consistent, and

some places are in fact experiencing droughts, where they were much less frequent before.

Temperature is increasing, and seems to be doing so in a uniform manner. This would be

confirmed if a global average was shown, but as it is, both of the data depicting average

temperature for the two regions show an increase of between .7-1° F. This increase in

temperature and the variability of precipitation do pose risks to human health. In China,

unexpected droughts and torrential rains caused a flash flood of epic proportions, deadly diseases

spread in the wake of this disaster, worsening the situation.

What can be done? The solution to global warming is a subject of constant debate in the

scientific community. There are no definitive, easy answers to the situation. Surprisingly there is

still debate about whether the climate is indeed warming because of human influences, or if this

is merely another natural warming phase, like the ones our planet has experienced throughout its

history.

As to the issue of human health and the problems posed by global warming, we can only

seek to minimize the damage. Natural disasters have always occurred, and the damage they cause

only seems to be worsening as people flock to disaster prone areas, for lack of space. It does

however seem likely that the warming of the planet is causing some of the deadliest natural

disasters to become yet more severe. All that we can do is try to manage our own growth.

Population must be controlled, and the use of land must be monitored. Countries should attempt

to grapple with their poverty problems, and find better solutions to land shortages than clear-

cutting forests along riverbanks and in areas prone to landslides and floods. If these things were

accomplished, along with the reduction of our emissions to slow the progress of global warming,

then perhaps the threat disease and disasters pose to human health and safety could be

minimized.

Luthien

Typewritten Text

Erin Collier-Zans2007

Population V. The Planet

We have been studying the relationships between average and instant rates of change to

better understand human population growth. In this paper I will illustrate my understanding of

these concepts.

In part one, I will describe average rates of change in the context of human population

growth. Then I will describe “instantaneous speed”, or the concept of derivatives. I will then tie

these two concepts together, and analyze the formulae developed in the earlier parts of the paper

from an algebraic and calculative perspective with the purpose of developing a formula to find

the derivative of any quadratic equation. Then I will examine several varieties of formulae, and

explain the relationship between these functions and their related derivatives. I will then

generalize finding an equation for the derivatives of each of these functions.

An average rate of change is the average amount something is growing over a specific

period of time. Observe the chart below, which demonstrates approximations of human

populations by year. Notice how the line is curved. The fact that it is so tells us that human

population grows at an exponential rate, growing faster and faster as time goes on. The black line

across the curve of the blue line is called a “secant line”. A secant line is a representation of

average rate of change. If the human population of the world grew at the same rate every year for

the whole of it’s existence, then the line representing this growth would look like the black one.

Lines like this one could be drawn between any of the periods of time shown on the graph, and

could be used to tell us the average rate of growth for that time period.

An average, in this case, may also be described by the concept of “rise over run”, which

is the increase in the y value divided by the increase in the value of x. Rise over run can be

represented graphically by a triangle, where the run is the bottom of the triangle and the rise is

the vertical side of the triangle.

In the case of this write-up, the average rate of change will be represented by the phrase

“∆y/∆x”, or “delta (change in) y over delta (change in) x”.

2

340,000,000545,000,000

907,000,000

1,610,000,000

2,509,000,000

3,650,000,000

5,300,000,000

Estimated Population

Estimated Population 340,000,000 545,000,000 907,000,000 1,610,000,000 2,509,000,000 3,650,000,000 5,300,000,0001 2 3 4 5 6 7

An example of ∆y/∆x can be seen in the graph above. It is illustrated by the red triangle.

Below, one may see a table of the data represented in the graph above:

Year Population

1000 340,000,000

1650 545,000,000

1800 907,000,000

1900 1,610,000,000

(x1) 1950(y1) 2,509,000,000

(x2) 1970(y2) 3,650,000,000

1990 5,300,000,000

The legs of the red triangle hit the blue line at two points, 2,509,000,000 in 1950 and

3,650,000,000 in 1970. The legs of the triangles represent the change in time (horizontal leg) and

the change in population (vertical). To find the slope, one can set up the numbers like so:

y2-y1

x2-x1

This gives one the ‘lengths’ of the two legs, horizontal and vertical. Below is the

expression with values from the table above:

3

y2-y1 3,650,000,000-2,509,000,000 1,141,000,000

x2-x1 1970-1950 20

57,050,000 is the slope of the hypotenuse of the triangle, but the important thing to

understand is that it is also the average increase in population each year for the 20 years between

1950 and 1970.

Below, this procedure is represented in triangles, like the one seen in red on the graph on

the previous page:

A derivative is an instantaneous rate of change. Where an average rate of change takes

into account all of the data and the period of time the data describes, an instantaneous rate of

change takes into account only a millisecond or an instant, and the data that corresponds with

that intant only.

While a secant line represents an average rate of change, a “tangent” line represents an

instantaneous rate of change, or a derivative. This line goes through only one part of the graph. It

takes into account the slope of the curve on a graph, but it does not depend on two points to

determine its angle. Notice the graph below:

= = = 57,050,000

1970-1950

3.65E9-2.51E9

20

1.14E9

4

The black line is a tangent line, and the red line represents the secant line. You will notice

that it only touches one part of the curve. At that one point, the slope of the tangent line is equal

to the value of whatever the curve represents, at the one moment in time when the line touches

the curve of data.

In class we used a problem titled “Speedy’s Speed” to understand the numerical approach

to average rate of change in a quadratic formula. Speedy is a runner who completes a 400-meter

section of a relay race in 50 seconds. The formula is m(t)=0.1t2+3t, where t represents time. You

will recall that an average in this case can also be represented by the phrase ∆y/∆x.

We learned that one may find an approximation of an instantaneous speed by finding the

speed at any given time and at a time a fraction of a second before, and taking an average of

them. I will start by measuring the speed at half a second to go to 20 seconds. By progressively

getting closer to 20 (i.e. 19.999…etc.), one approaches ‘limit’, and can reasonably estimate the

instantaneous speed.

5

∆y 0.1(20)2+3(20) - 0.1(19.5)2+3(19.5) 100 – 96.525∆x 20-19.5 .5

∆y 0.1(20)2+3(20) - 0.1(19.99)2+3(19.99) 100 - 99.93001∆x 20-19.99 .01

6.999 is close to a whole number, which implies that the real instantaneous speed is

probably 7. We can be sure by continuing to make the fraction of time progressively smaller

until we reach the “limit”, or until the result will not change any more.

∆y 0.1(20)2+3(20) - 0.1(19.9999)2+3(19.9999) 100 - 99.9993∆x 20-19.9999 .0001

∆y/∆x is also distance/time, and as you may remember, this can also be represented

graphically by a triangle where the horizontal leg represents time and the vertical leg represents

distance. The ∆y is the change in the value of y. As you can see, we changed the value of y, or

her distance at 20 seconds, by .0001. We subtracted the distance she had gone at 20 seconds from

the distance at 19.9999 seconds. We then divided this by the time, or 20-19.9999. What we are

left with now is 7. We can safely assume that at exactly 20 seconds, she was traveling at

precisealy 7 meters/second.

The standard, general quadratic expression is ax2+bx+c. We can take the idea of ∆y/∆x

and generalize it using these exponents.

∆y 0.1(20)2+3(20) - 0.1(19.9999)2+3(19.9999) ∆x 20-19.9999

Becomes

∆y ax2+bx - a(x-∆x)2+b(x-∆x) ∆x x-(x-∆x)

∆x is some small change in the value of x, in this case a microsecond (i.e. .0001, .000001,

etc.). Here is a table depicting the expression above:

X y

1 X ax2+bx

= = = 7

= = = 6.999

=

=

= = 6.95=

6

2 x-∆x a(x-∆x)2+b(x-∆x)

Point one is the time (value of x) before we change it. It’s the actual value, i.e. 20

seconds, 30 seconds, etc. point 2 is when we introduce the small change to the time, by

subtracting an infinitesimal millisecond from the first value.

We will now look at an algebraic method of determining the derivative, or formula forinstantaneous speed at a single point in time.

∆y ax2+bx - a(x-∆x)2+b(x-∆x)∆x x-(x-∆x)

We will now distribute to remove the parenthesis.

First we will look at the expression a(x-∆x)2. (x-∆x)2 is the same thing as (x-∆x) · (x-∆x):

x - ∆x

x x2 -x∆x

-∆x -x∆x ∆x2

The expression a(x-∆x)2 becomes a(x2-2x∆x+∆x2). When we remove the parenthesis by

multiplying everything inside them by a, the expression becomes ax2-2ax·∆x+a∆x2.

b(x-∆x) becomes bx-b∆x, and x-(x-∆x) becomes x-x+∆x, because a negative outside a set of

parenthesis will reverse the “charge”, if you will, of what’s contained inside them.

The expression, put back together, becomes

ax2+bx - ax2-2ax·∆x+a∆x2 + bx-b∆x x-x+∆x

Here is a graph of the expression as it is so far, returning to the triangle imagery:

=

7

We will now get rid of all values that cancel out.

ax2+bx - ax2-2ax·∆x+a∆x2 + bx-b∆x x-x+∆xThe expression becomes

2ax·∆x+a∆x2-b∆x ∆x

We will now divide the expression on the top by ∆x.

2ax·∆x+a∆x2-b∆x ∆x

∆x cancels out only one of a∆x2, so we are left with a∆x. We are left with 2ax+a∆x-bWe now will introduce the concept of limit to simplify the equation even further. With λ,

∆xα0 (i.e. the value of ∆x becomes infinitely tiny, and then becomes nothing). The idea of limit

can be seen in the graph below. Limit is forcing the two points you see below to become one.

This is the essence of instantaneous speed.

x x+∆x

∆x

-2ax·∆x+a∆x2 + bx-b∆x

a(x-∆x)2+b(x-∆x)

ax2+bx

8

When we remove ∆x, the equation becomes 2ax+b, a formula to find the derivative at

any given time.

Now, we will briefly revisit “Speedy’s Speed”. I will use the same example, that of

Speedy’s speed at the instant she had been running for 20 seconds. The general quadratic

formula is ax2+bx+c. The formula for Speedy’s speed is m(t)=0.1t2+3t (there is no ‘c’ value). The

formula for finding a derivative of an equation is 2ax+b. This in terms of Speedy’s speed is

2(.1x)+3. When x=20, the formula is 2(.1·20)+3. 2(.1 · 20) + 3 = 7.

We will now look at a selection of formulae. You will see the value of x and y, but also

that of y1, or the derivative. The next sets of columns are the differences between the derivatives.

First we will look at the function x2:

x y y1

0 0 01 1 22 4 4

x x+∆x

∆x

-2ax·∆x+a∆x2 + bx-b∆x

a(x-∆x)2+b(x-∆x)

ax2+bx

2222222222

9

3 9 64 16 85 25 106 36 127 49 148 64 169 81 1810 100 20

You will notice that the value of y1 is the same as x·2, or 2x. So, the value of the

derivative when x=8 is 16, the derivative when x=10 is 20, and so on. Therefore, the function for

the derivative of x2 is 2x. This is a graph for the function x2:

10

Now we will examine the function x3. This

This is a table of the function:

x y y1

0 0 01 1 32 8 123 27 274 64 485 125 756 216 1087 343 1478 512 1929 729 24310 1000 300

This time it takes two tiers to reach a point where the difference between the derivatives

is the same. In this case, it’s 6. First, I will examine x2. One may look at the table on the previous

page for the values of y. Now, 22 is 4. Y1 of 2 is 12. 12/4 is 3. 32 is 9. y1 of 3 is 27. 27/9 is 3. So,

the pattern is 3·x2, or 3x2. 3x2 is the function for the derivative of x3.

This is a graph for the function x2. Theshape made above is called a‘parabola’. It’s an up-turned bellshape.

This is a graph for thefunction 2x, which is alinear function.

11

This is a graph comparing the functions x2 and 3x2:

The sharper bell-curve is 3x2, and the wider is x2.

Above is the graph for x3,which is a cubic function.

Above is a graph for thederivative of x3, 3x2.

12

Finally, we will examine the function x4. This is a table for the function:

x y y1

0 0 01 1 42 16 323 81 1084 256 2565 625 5006 1296 8647 2401 13728 4096 20489 6561 291610 10,000 4000

You will notice that this time it takes 3 tiers for the differences in y1 to equalize, and that

when they do, the result is 24. We will use x3 to solve for a function for the derivative of this

equation. One may observe the table on a previous page. 23 is 8. 32/8 is 4. 33 is 27. 108/27 is 4.

This pattern continues. So, the function for the derivative of x4 is 4·x3, or 4x3.

Below one may observe a table of the function x4 and 4x3:

We have now found functions for the derivatives of x2, x3, and x4. Here is a table:

428761482443645086768681804

24487296120144168192936

24242424242424…

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x2 2xx3 3x2

x4 4x3

We will now generalize so that we may find a formula that will allow us to find a

function for the derivative of any equation…

x2, x3, and x4 all become xn. In the table above, one may notice a pattern. The pattern is

that the value of n, or the exponent, is no longer an exponent and may be found in front of the x

in the formulae to find the derivative. The value of the exponent in the derivative formulae is n-

1, as in x3. The derivative formula for x3 is 3x2. x3 generally is xn, and 3x2 is nx(n-1), or 3x(3-1).

Here is a table:

Generalized Expression: Function to find the derivative:

xn nx(n-1)

So far we have only dealt with equations of the xn type. We well now take a brief look at

equations of the ax variety. Below is a table of the expression 2X and it’s derivatives.

x y y1

0 1 .693151 2 1.38632 4 2.07943 8 2.7726

The original expression is f(x)=2X. The formula for the derivative is f1(x)=.693•2X

because .693 is the derivative of the original formula what x=0.

Next we will look at the expression f(x)=10X, the derivative of which is f1(x)=2.302•10X.

x y y1

0 1 2.30261 10 4.60522 100 6.90783 1000 9.2103

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We noticed that the derivative for both of these functions is the value at 0 times the

original equation. We then noticed that the derivative at 0 is equal to the natural log of the value

of a in the generalization aX. So, the generalization of a formula of the aX type is Ln(a • aX):

Derivative:aX Ln(a • aX)

Conclusion:

Now that we know what derivatives are and how to find them, we will return to the

original idea of human race. The approximate population of the human race at various points in

time is as follows:

Year Estimated Population1950 2,510,000,0001960 3,030,000,0001970 3,680,000,0001980 4,480,000,0001985 4,870,000,0001990 5,290,000,0001995 5,370,000,000

To create an exponential formula for population growth, we need to first find the rate of

change. The problem is, the increments of x, the years, are not equal between all data points, and

move from 10 to 5 years. We need to take this into account in our calculations.

For example, there has to be some growth rate for the 10 years that lie between 1950 and 1960.

2,510,000,000 • k10 = 3,030,000,000

To solve for the growth rate, we will divide both sides of the expression by the starting

population value, or 2,510,000,000:

2,510,000,000 • k10 = 3,030,000,000 = k10 = 1.2071

2.51E9 2.51E9

To find our growth rate, we must get rid of the ^10. We will square both sides of the

expression to the 10th:

10√ k10 = 10√ 1.2071 = 1.019

Here is a table of all the growth rates:

15

1950-1960 1.01900031960-1970 1.019621970-1980 1.019851980-1985 1.016831985-1990 1.0166821990-1995 1.016107

We then take an average of the growth rates, which equals 1.018014883. Now we can use

this in an exponential equation, which in it’s general form is abX, where a is the starting amount

and b is the growth rate. Our equation therefore will equal 2,510,000,000 • 1.018X.

e is commonly used as the growth rate. We learned that to convert any base to e, one

simply has to replace bX with e raised to the power of the natural log of b • x. So, with e as the

growth rate, the equation becomes 2,510,000,000 • e(ln1.018)x.

Discussion/Conclusion:

• When will everyone on earth have on average only one square foot of land to live on?

Mathematically speaking, this will occur in year 2698. It seems extremely unlikely that

the human race will be able to survive and continue to reproduce at an exponential rate for that

long, however

• When will the instantaneous population growth be 1/2 billion a year? 1 billion a year?

We noticed that the derivative of eX is in fact eX. Therefore, the equation for the

derivative, or instantaneous speed of the human population equation with a growth rate of e is

2,510,000,000 • e(ln1.018014)x. Using this equation, we find that in 2085 the annual growth rate

will be .5 billion, or 500,000,000 people a year, and in 2124 the annual growth rate will be 1

billion people per year. 2085 is only 77 years away. In 2085, I will be 94 years old. Our species

will be growing at a rate of 500,000,000 per year within my lifetime.

• If the world were split up evenly, how much land would each person have to live on?

Each person would have about 8.646 square miles to live on.

8.6 miles is enough for a person to live on, but that is merely surface area. There is very

little arable land compared to the amount of inhospitable land. In reality, if arable land were

divided equally among the people of the world, each person would have about .0018 square

miles to live on, or about 1.15 square acres. In the year 1 A.D, there were 31.44 square acres of

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arable land per person. In 2050, there will be approximately 14,964,000,000 people, if

population growth continues at about 1.8%. So, in 2050, each person will have only .5 acres to

live on. At current soil fertility levels, it takes about 1/4 or .25 acres to produce food for one

person for an entire year. In 2090, each person will have only .25 acres, and in 2092 only .24

acres, at which point our planet will literally be completely incapable of sustaining our

population even if all arable land is shared equally, and all 31 billion people will begin starving

to death. In 2131, each person will only have .1 acre, and in 2278, there will only be 1/10 or .01

acres of land per person. In 2610, each person will only have 1 square foot of arable land.

The fertility of the world’s farmlands is decreasing, and studies have shown that basic

raw food products (raw grains, fruits, vegetables, seeds, etc.) have become 38% less nutritious

than they were at the dawn of the agricultural age, despite and perhaps aided by the use of

synthesized fertilizers. It could likely be proven that there are too many people already, and that

the earth soon will simply not be able to feed us, thanks to erosion and desertification of topsoil.

On the bright side, for an inexplicable reason, population growth seems to be tapering off. After

the 1980s, the growth rate went from about 1.9% to about 1.6%. If population growth ceases or

even becomes a negative value, there will perhaps be hope for the future.

Orchard HideoutErin Collier-Zans

This is a tale of the exploits of the infamous criminals Bonnie and Clyde. Theirmathematical exploits, of course. One day, Bonnie decided that city hideouts were far too easy todiscover, and she was quite tired of jumping out of windows to escape the cops. So she came upwith a brilliant and fantastical idea. Why not make a hideout out in the countryside, in the middleof an orchard? She presented this idea to Clyde, and after much debate, he agreed to her plan. Sothey bought a plot of land, jumped in a car, and began their work.

Bonnie decided that what they really needed to do was figure out exactly how long itwould take for them to create an orchard hideout. She needed to know how fast and how bigtheir trees would need to grow.

The problem was, they couldn’t decide how big to make their orchard. They had decidedthat though their plot of land was quite large, and rectangular in shape, they would designate asmaller, circular orchard to be their hideout. Clyde wanted their smaller orchard to be 100 treeswide, but Bonnie had decided that a much smaller orchard would suffice, mostly since she didnot quite know how to create a 100 tree wide orchard so that no one should be able to see intotheir hideout. A 2, 4, or 6 tree wide orchard seemed much simpler.

2 Unit Orchard:

This is a picture of an orchard if it were to have a 1-unit radius. The black circles at theboundaries represent trees, and the arrow represents the line of sight. The trees need to grow tomeet at this point to prevent anyone from seeing into the hideout.

1

1

As you can see, the lines radiating from the center point to the tree trunks are 1 unit long,and a right triangle can be formed between 2 of these lines. Because of this, we can use thePythagorean theory to find the ideal radius of the tree trunk:

12+12=2. The square root of 2 is 1.11. This is the hypotenuse of the triangle.1.11/2=.707, or the radius of one of the trees when it reaches the line of sight.

4 Unit Orchard:

As you can see, the radius of this orchard is now 2 trees. Again, the arrow represents theline of sight. The line of sight will always pass through an imaginary tree outside the boundary(in this case, the grey tree shown outside the circle). The red dots are the trees we are going tofocus our attention on. Notice how both of them have a vertical line connecting them. You mightthink that this is the radius, but in fact, the second line radiating from each of them is our radius.

2 Units

1

AB

We discovered that two trees do not actually need to touch to block the line of sight, but they doneed to touch the line at some point.

We are going to use triangles again to solve for the radius. The bigger triangle shown(triangle B) has legs 1 and 2 units long. We are also focusing our attention on the palest of thethree teal triangles. The hypotenuse of this triangle is 1 unit long. We can use right triangletrigonometry to solve for the radius, if we know the angle created by the horizontal line on thegrid and the line of sight.Finding the angle:

We are going to use inverse tan (tan is opposite over adjacent) and the larger triangle.Inverse tan uses the ratio between two sides to find an angle. The two sides we are using are 1and 2 units long, so:

Tan-1(1/2) = 26.6º.This is the angle at the point of the larger and smaller triangles. Now we are going to use trig tofind then length of the unknown leg of the small pale triangle, or triangle A. We know thehypotenuse, and we need to know the side opposite the 26.6 degree angle, so we are going to usesin (opposite over hypotenuse).

Sin(26.6=.448 units.This is the radius both trees would need to reach to block the line of sight.

6 Unit Orchard:

This is a picture of an orchard with a radius of 3 trees. Again, the line of sight passesthrough an imaginary tree outside of the boundary. The radius of the red trees do not radiatevertically, but instead at an angle to meet the line of sight.

The large triangle has legs 1 and 3 units long. We are going to use right triangletrigonometry to solve for the radius again, beginning with finding the angle created by thehorizontal line of trees and the line of sight:

Tan-1(1/3=18.4º. We used inverse tan because tan represents the ratio between oppositeand adjacent, the two sides of the triangle that we know. Now that we know the necessary angle,we can find the radius of one of the trees:

We are using the dark blue triangle, or triangle a. It’s smallest side is the radius of a tree.So, sin (18.4º=.316. We used sin because it represents the ratio between opposite andhypotenuse.

3 units

1

118.4º

a

Bonnie noticed that the procedures for finding the radius stayed much the same. She alsonoticed that whatever the radius of your orchard, the line of sight always went out radius/1. So,for instance, if she tried making an orchard with a radius of 4, the line of sight would go out 4and up 1, to meet an imaginary tree outside the boundary. She decided that she should create aformula for finding the radius of a tree in an orchard of any size. This is what she came up with:

Sin ( tan-1 ( a/b)), where a represents the length of the smallest leg of the triangle, or they coordinate on an x, y coordinate graph (“a” is always going to be 1), and b represents the xcoordinate, or the length of the larger leg. She tested this on all of the orchards that she haddrawn out so far:

Sin ( tan-1 ( 1/1)) = .707Sin ( tan-1 ( 1/2)) = .448Sin ( tan-1 ( 1/3)) = .316

She then found the radius of a tree in an orchard with a radius of 50:

Sin (tan-1 (1/50)) = .019996, or .02 units.

Bonnie noticed that her drawings seemed to be laid out on an x,y coordinate plane. She alsowondered if putting an orchard somewhere besides the center of the graph would make any kindof difference in any of her calculations. So she began drawing out circles with varying radii, andvarying center coordinates:

These were the two circles she decided to work with. She also created triangles inside ofthem, and decided to work out how to decide if the points of the triangles were inside or outsideof the boundaries of the orchard, or the edge of the circle. This is the information for the twocircles:

The larger circle:Radius: 7Center: 5,3Points:18,915,1213,14

The smaller circle:Radius: 3Center: 4,6Points:5,86,87,7

She noticed that a triangle could be made from a line that connected with the radius. Shealso noticed that the Pythagorean theory could be used to find the length of such a line:a2+b2=r2, where r is the radius.

She realized that if a2+b2 > r2 then the line ended outside of the circle, and that theopposite of this was true for lines ending inside of the circle. Then she noticed that this processwould not for circles which centers were not at the 0,0 point on the x,y graph.She made the inference that perhaps the center point of the circle might have something to dowith this equation. After much pondering, she figured out that subtraction would give her asolution. In all of the equations below, the variables and what they represent are as follows:

“a”= the x coordinate at the center of the circle“b”= the y coordinate at the center of the circle“x”= the x coordinate at the end of a line, or in this case, the point of the triangle“y”= the y coordinate at the point of the triangle

The equation for a line that ends on the circle:(x-a)2+(y-b)2=r2

Outside of the circle:(x-a)2+(y-b)2>r2

example:(7-4) 2+(7-6) 2=10. The square root of 10 is 3.16, which is outside the radius of 3.

Inside the circle:(x-a)2+(y-b)2<r2

Example: (5-4)2+(8-6)2=5. The square root of 5 is 2.32, which is well inside the circle with a radius of 3.

Bonnie began to wonder what the area and circumference of her orchard was. She didn’thave a way to measure it, but knew that if you measured the diameter of a circle, and wrapped inaround the outside, that you would be able to measure out the length of the string a little morethan 3 times, like this:

As you can probably guess, the little bit is .14, so, the diameter wraps around thecircumference of a circle 3.14 times, or π.

She then noticed that she could create a mini square orchard around her circular orchard,and measure the area of the square. This gave her a general idea about how big her circularorchard was, but it just wasn’t precise enough. She made another small drawing of thiscircumscribed square and it’s enclosed circle, this time with a radius of 10, figuring that smallernumbers would be easier to work with:

10’

20’

20’

That line is the radius of the circle. Because the radius of the circle is 10, each of thesides of the square is 20 feet long.

Area:The area of the square is base x height, or 20 x 20, which equals 400. Finding one side of

the square can be represented by the expression 2r, where “r” is the radius. So, finding the areaof the square boils down to 2r x 2r, or 4r2. Bonnie had already discovered that the ratio betweenthe area of a circle, or AO, to the area of a square, or A�, was .8205. The ratios lined up like this:

AO = x = .8205A� 4r2

To find the area of the circle, one needs to multiply the area of the square by the ratio. So,20 x 20 = 400. X/400 = .8205, therefore 400 x .8205 = the area, or 328.2.

Circumference:To find the perimeter, or “p”, of the square, we take the lengths of the sides and multiply

that by 4, or the number of sides. 20 x 4 = 80. Bonnie, on top of figuring out the ratio betweenthe area of a circle and the area of a square, had also discovered one for the perimeter of a squareand the circumference of a circle. The ratio looks like this, if “P”, or perimeter, equals 80: C = C =.8175 P 80

The circumference of the circle is the perimeter of the square, times the ratio. So, 80 x.8175 = 65.4.

Bonnie then realized that it would be necessary to know exactly how fast her trees wouldgrow. The arborist that she bought her trees from said that the saplings would gain about 1.5square inches per year. She went back to the orchard and found that the trees had acircumference of 2.5 inches.

She then found the radius of the trees by reversing the formula for finding thecircumference of a circle (2πr):

2.5/π/rThis equaled .397, or approximately .4 inches. Because the area of the tree goes up by 1.5

square inches per year, she developed a formula for finding the radius of her saplings at anygiven time during their growth:

R=√ (.397+(1.5 x year))/πOr, in the general form:

R=√ (a+(1.5(n))/πSo, in the first year, the trees would have an area of π.3972, or .495.

She then wondered if it might be possible to combine these two formulas, and create arelatively easy to work with super formula, which would tell her the number of years it wouldtake for any tree to grow to block the line of sight in any orchard. She first lined up the twoformulas she had created earlier:

10 x (sin (tan-1 (1/ro)))=√ (1.5y+.495)/π

10= the feet per unit (Bonnies trees are planted 10 feet apart)ro= the radius of the orchard1.5= the growth factory= years.495= the starting area of the sapling trunks.

After solving for “y”, she was left with:((π (12 (10 (sin (tan-1(1/50)))))2-.495) /1.5)This was the formula for finding the years it would take a tree in any orchard to grow to

block the line of sight. She discovered that in her orchard with a radius of 50, and with trees thatgrew 1.5 sq inches per year, it would take her trees 11.72 years to grow large enough to block thelast line of sight, and create a true orchard hideout.

Appendix:

Finding the area of a polygon:The internal angles of a polygon will always equal 360º. It is possible to split up polygons

into separate triangles, and use right triangle trigonometry to find the area of any polygon. Forthe sake of this practice, the apothem of the right triangles will be 10. At the end of this section, ageneralization will be given for this.

Pentagon:This shape is split up into 5 triangles, as it has 5 sides.

We will take one of these triangles, and split it into two right triangles, like so:

360º is then split up into 5ths, so 360º/5 = 72º. This is the angle of the point of thetriangle that faces the center of the polygon, or the top of the triangle. This is then split up intotwo, for the point of one of the right triangles. 72º/2 = 36º.

We will now use trig to find the length of the base of the triangle (one of the sides of thepentagon). We will use tangent, because we know the length of the side that is adjacent to the36º angle, and we need to know the length of the side opposite of it.

Tan ( 36º = .7265. We multiply this by 10, or the length of the known side, for the lengthof the desired side. .7265 x 10 = 7.265. To find the area of any rectangle you simply do base xheight. This works for the two right triangles, lined up as they are. Simply imagine disconnectingone of the right triangles, and flipping it up and over. Their hypotenuses would touch, and theywould become a rectangle. So, we will do base x height to find the area of these triangles. 10 x7.265 = 72.65. We will then multiply this by 5 to find the area of the figure, as there are 5triangles. 5 x 72.65 = 363.271.

Hexagon:

360º/6 = 60º60º/2 = 30ºtan ( 30 = .5773.577 x 10 = 5.7735.772 x 10 = 57.7357.73 x 6 = 346.38

Octagon:

360º/8 = 45º45º/2 = 22.5ºtan ( 22.5º = .4142.4142 x 10 = 4.1424.142 x 10 = 41.4241.42 x 8 = 331.37.

This is a table that shows the area of polygons:

# of sides Area5 363.2716 346.4017 337.1028 331.37

10 324.91920 316.76850 314.573

100 314.261000 314.1602

100,000 314.159

The area of the polygons get closer and closer to 314.159. You may notice that if youmove the decimal point over, the area of the last polygon becomes 3.14159, which is π. The areaof a polygon will ever approach π, but will never meet it exactly.

You may notice that the procedure for finding the area of a polygon is the same eachtime. There were two formula’s or generalizations discovered for finding an area in an expediantmanner:

area = (tan ((360º / n / 2)))(r 2 (n))

“n” is the number of sides, and “r” is the apothem of the created right triangle.

(r (tan (360º / (2 (n)) r)

Again, “r” is the apothem, and “n” is the number of sides.

The Freedoms That Be

Erin Collier-Zans

The girl was petty. A sniveling toddler in the face of real art. All photographers are like

that. They’re either clinging onto the cuffs of celebrities, or trying to market themselves as

artists. “Artists”. Michelangelo was an artist. Da’Vinci and Picasso and Renoir and Matisse were

artists, but a brat meandering aimlessly around with an overlarge piece of noisy machinery in her

hands? I think not. Artists take what they see and filter it with their own essences to create

something that resembles reality, but that transcends it in beauty, making all of life seem

transfused with light. The cameraman-turned-(self proclaimed) artists uses a box hooked up to a

light bulb to capture life directly. If they change the scene they aim to capture, they change it in

the real world, in the mundane world, and therefore do nothing to transport their viewers to other

worlds. They are limited by the physical. There is no way to overcome the limitations of their

precious cameras. The artist can transcend himself with long, hard practice, with drugs, with

fasting, with any manner of tools. He changes himself within himself, without the assistance of

others. The artist is alone, and glorious. The cameraman depends on the whims and reactions of

others to capture anything that even remotely resembles the moods created by artists with hard

work and suffering.

The girl was obnoxious in the extreme. She wanted to do an article of some sort on me.

Well, not on me, on what I used to be. And she was going to commingle me together with an

entire posse of petty posers claiming to have skill. Skill... Bah. They haven’t the genes for it, not

one. They haven’t the schooling for it. She told me about some of them. They sound as if they all

have the same basic character flaws as she herself does. Sincere, caring, idealistic. Naïve.

Infantile. It charms others, like my sister, but I think they’re pathetic. Deluding themselves with

the belief that they can change the world by starving and making art, or worse, piles of

photographs.

I must admit, however, that it would be difficult to photograph something beautiful and

original when there’s so little beauty and originality to go around. The originality is spread quite

unevenly, after all. A few people get the creativity, and the rest of the populace simply has to

struggle along, longing for something but knowing not what it is they are missing. Holes in the

heart, holes in the soul, and beauty just filters straight through them. Poor things. The few get the

2

ability to see things differently. Or perhaps we simply see. Actually see, not just see that which

we want to see. We see suffering and squalor, and see the beauty in it. We don’t need waterfalls

and rainbows and puppies and feel-good novels and wives in perfectly pressed dresses and

children with little lunch pails and fathers who look satisfied to be trapped in their suits. We see

hylic settings and we want to improve them, because of course mundanity means pain, and you

either want to remove all the pain and create a vision such as one might see in the garden of

Eden, or you create something that causes people even more pain than anything they could see in

the world they live in. The human soul longs to express, and it longs for beauty and connection.

The few are given the ability to find these things within themselves, and the rest are so

entrenched in their mundanity that they don’t know any better than to be happy, or unhappy, as

their nature demands. Perhaps they don’t feel at all. Perhaps the feelings they experience are

fleeting compared to the emotions of the artist, so that they cannot feel the pulling pain that I feel

when I witness the world’s splendor.

And the new day did dawn. And I did open my eyes, and my two eyes did see

My sister hates looking at my paintings. She always has, even when we both loved

horses, and that was all I could draw. I decided when I was twelve that she was simply jealous of

me. She was the younger, but our parents had great love for her. They loved it when I would give

them drawings, however. That must have driven her simply batty.

I tried to save her, really I did. I tried to save her from her mundanity. She is steadfast in

her determination to see no beauty in the world, to feel nothing. She’ll ooh and ah over a puppy,

of course, but she thinks that those atrocious smoosh-faced beasts are the most attractive dogs

ever created by the perverted minds of men. That simple preference states more clearly than ever

I could how twisted a woman she has become. I mentioned before happy wives in perfectly

pressed dresses? I was referring to my sister, I must have been. She married when she was

nineteen, had her first brat at twenty, and has been popping them out ever since. She has four

children now, three boys and a girl. None of them show any of the talent that usually manifests

itself in our family. My aunts are artists, many of my cousins are artists, and my mother was an

artist until she had my sister. I should be able to nurture talent in my nieces and nephews, by

right. But their father won’t have it, and my sister believes that art is unnecessary in life. She

3

wants the little beasts to grow up and become dentists and lawyers and politicians. When she told

me that her oldest son was already talking about his dreams to become president, and that his

father was encouraging him to go into politics after graduation from whatever-ivy-league-

college, I shuddered to think of the depths of her depravity, and the pitiful nature of her spouse.

And she thinks that I should breed! We had one of our many conversations on the subject this

morning…

The phone did ring. I went over to my nightstand, and did pick it up. Low and

behold, it was my sibling.

“Hello, Kate?”No, it isn’t. It’s the bloody president of Citizens For Katydid Extermination, you stuck up

tar….

“Oh darling, I was just calling to see how you were. We’ve been so worried about you,

you know, and dear Mister Masterson tells me you haven’t been taking the medications

he’s given you, and you haven’t been going into sessions, which is of course how he

knows you haven’t been watching that you take those pills, because you haven’t needed

to go in and ask for refills, and darling, it’s been weeks since you got them, and he only

gave you enough to try them for a few days dear.”I don’t want Mister Masterson's bloody medications. I wasn’t even invited to the session

that day he prescribed them to me. I run my own life, and that makes you just furious….

“I haven’t been taking them, you’re right. I’ll start trying to watch that I do, don’t you worryabout it. You have enough to worry about anyway, don’t you, you with your innumerable brats

and witless husband… Get of the line already, leave me be, and I never want to speak with you again…”“What was that Dear? I couldn’t hear you…. Nothing? Oh, well, I’m sorry I didn’t catch

that; it’s just that when you mumble along like that, no one can rightly understand what

you say. Anyway… What was I saying? Ah well. We’ve just met the Pemberly’s lovely

son. He’s only thirty, you know, and already he’s set up as a partner for life at that firm

he works for…. What was it? Ah well, I don’t remember, but anyway dear, he’s the

loveliest boy, and I really do think that you should meet! Little Janie keeps asking me

when the angels are going to bring Aunty Kate a little baby of her own, it’s the most

darling thing, and I have to tell her ‘Well, when the angels bring Aunty Kate a nice

husband, just like your father’, and she says the darlingest thing, you know, she says

4

‘Well, I’m gonna ask the angels mommy, and God will send a nice husband down from

heaven and bring a baby with him and they will all go on uh-hun-ee-moon’. Walter thinks

she’s just darling too, isn’t that lovely? Anyway, but seriously Kate, when are you going

to marry? I’m sure that there are many nice men amongst your nice artist friends who

have galleries or whatever who would be only ecstatic to marry a lovely artsy girl like

you once he got to know you!”

“I’m not going to marry, Carol. I’m an adult, I’m six years older than you, and do not needyour help organizing my life in any way. I told you this on Monday. Mother didn’t even meetfather until she was thirty-two, and didn’t marry him until she was thirty-four. Not all of us are

baby machines, after all… What? Didn’t catch that? So sorry… Dear. As I was saying, I’m notgoing to marry in this life, and you’ll just have to tell ‘Little Janie’ that ‘Aunty Kate’ is afeminist, believes that no, girls don’t have to be less intelligent than their brothers andhusbands, and that no, real women don’t need husbands to feel like women.”

I tried to picture her face pursing up as I said this. It was hard, like everything else having

to do with imagination these days, but it was an amusing exercise nonetheless. I could see her

newly-gained double chin wobbling beneath that fat, round face of hers, her over-trimmed

eyebrows sinking in, covering her eyes in folds of skin, her upper lip pulling up and underneath

her nose, so that it looked as if her face had been turned to clay and that someone had taken their

fist and punched all of her features into the back of her too-small skull. There was a click, and a

tone, and the woman I have to call a sister was gone. She’ll be calling back tomorrow, she’ll tell

me how much my words hurt her, how she too feels that educating women outside of the home is

a very valuable thing, that she only wants to know that I’m being taken care of in my fragile

state, and that she does have thoughts that having a husband would do me immeasurable good in

that regard.

Sometimes I truly hate that woman. I know that we are not supposed to feel an emotion

like that towards our siblings, but sometimes, she truly deserves it. She thinks I’m crazy.

Wouldn’t you be angry? Wouldn’t you wish that she would leave you alone? I am thirty-one

years old, and my brat of a sister is still trying to run my life, despite the great disparity in the

accomplishments we have made during the course of our lives. And she has the temerity to

suggest that I need medication. Medication for what, one might ask? The supposedly boundless

5

powers of science have managed to kill belief in faeries and God, but they have not been able to

return to the artist gifts given to them by these ethereal powers. They can’t give me back the

ability to paint.

And to make matters worse, I still have commission work to complete. The tactless,

talentless imbeciles have no idea of the difference between the vintages of my work. They think

that work I do in the summer looks exactly the same in style and mood as work I do in the

winter. They think that the work I did in my college years looks exactly the same as the work I

do now, and they say to me ‘Well, why can’t you give me one of those? You were so well liked

even then; I don’t know why you’d want to something as radical as what you’ve proposed. Give

me that! I’ll pay whatever you like!’ And at least in that regard, they are true to their word. I was

wildly popular in my early twenties, and have now retired to a comfortable quality of familiarity.

People familiar with the art scene, all those hip cats of the “modern” age have a chance of

recognizing me on the street. My sister’s friends and enemies have no idea who I am. They

sometimes say to me ‘Oh! Aren’t you that girl I heard about a few years back? You made that

statue of… Well, anyway, it was all over the covers of newspapers!’ Yes, that’s right. That statue

a few years back. That’s me.

My sister, when I tried to explain the concept of talent to her, said that the paintings I

made a month ago are practically the same as those I made five years ago. So did the

psychologist she chose for me. And so all I can really do is be angry with my sister, and hope

that feeling an emotion that powerful can

a vast world spread before me. The trees, the streams, they all do sing of the joys they do feel, the joy of being

wild, the joy of being powerful, the joy of being original, the joy of being nurtured and favored by the gods

themselves. No other forest can match this one in power. A place doesn’t have to be impassable to be wild.

This one is full of great evergreens, of ancient hardwoods too, all of which grow up and up, so that they brush

fingers with their creators. The young treelings do not strive to murder their parents with their numbers, but

instead wait patiently and demurely at their feet. When their parents die, they calmly raise themselves up

from the undergrowth, happy simply for the chance to be nearer to our gods. My father does tell me this is

the way of things. My father should know, he has been here through the ages, he saw the parents of the

mightier gods fall, saw the oldest of the trees

6

bring back to me what I have lost.

I try to think, always trying to think, what can bring back to me my powers of creation,

even those powers all artists have to hallucinate. I haven’t come up with anything yet, obviously.

I didn’t know yesterday when my sister and I had that short, painful conversation. I don’t know

today. I won’t know tomorrow. I go on walks. That is all anyone has been able to tell me to do.

Get out of your house and look around. Look at the trees; you always have had great love for the

trees. Look at the parks, look at the ponds, get in your car, go for a drive, look at the parks, look

at the deer, look, look, look, look, look, look, look.

I do what they tell me to. It makes them feel better about what they call my

‘despondency’. But what they don’t know is that I am in fact trying to find some proof of a

higher power. If there is a higher power, then it must have been it that did take away my abilities.

It must have been. There is no other explanation. What can make an artist of great vitality and

health, whose name is practically household, who takes only enough commissions to support

herself, loose her talent? Stress cannot, for I was not stressed. Pain cannot, for I have never had a

truly traumatizing experience.

You see, I believe that talent is given to us by the grace of some higher power. There are

those who have it, and those who don’t. Genes play into this as well. If you are born into a

talented family, then chances are you shall be talented too. But those people who are born with

abilities to express do not have to work for it. I could always create art. There is no way to

explain how, it simply was. I saw something, and I could draw it. I was always aware of the

ways of things. I knew how water ran, I knew how trees grew. It simply was. Then I lost what

Grace had given me, and because I never had to work at anything, I never truly knew anything.. I

was attached to my art. Images of what I could create flowed freely, and I loved what I could see.

When it left me, I had nothing. I lost the instinct to create. I had nothing to build on, nothing to

work with. I have been left destitute.

I have started praying. Not every night, of course, I am not my sister. And I don’t pray to

God directly, no. What if it doesn’t exist? What if it’s dead? No, instead I do direct my thoughts

out towards the cosmos as a whole. I don’t ask it why this has happened to me. I don’t delude

myself into thinking that the cosmos would actually talk to me, or send a sign, or that if it did, I

would be able to interpret “Gods” wishes correctly. The only people who believe that they can

converse with gods or that gods will actually converse with them are those seeking to control

7

other people. No, instead I just wish to be given back my gifts. That, I believe the cosmos could

do. Even if there is no power out there to answer me, if I can trick my own mind so fully into

thinking there is, maybe I can also fool it into believing that it actually answered me. You never

know, after all.

But I don’t think that even my mind

here fall from the hands of their forbearers as mere seeds.

I am on a hunt to-day. I go on a hunt almost everyday, with the blessing of my goddess. She has given me

all of the trappings of the sport, and on some days she does even give me her hounds, her celestial

companions. All I must do to keep her favor is to follow her rules. I must avoid contact with other humans,

most of all those whom she abhors herself. This is not difficult, none but those who search for me deliberately

come to this place, for fear of being found by Her.

It was not always so. There was a time when I did not do her bidding, when I was but a bare-footed

child who roamed along the banks of her father the river. Men came to my father, came into the wood, then.

They came to beseech my hand in marriage. They had the right to beseech, but my father thought none of

them had the right to have me, and he did not have the nerve to give me away. I didn’t mind them then. They

seemed odd to me, tall and ugly, but they spoke to me kindly, most of them, and brought me things, hoping

that I would remember them favorably as I grew older.

Then I was struck. I woke up on that day, and loathed the sight of them, like my mistress. I do not

know if it was her doing, if she chose me among her servants to be most like her and to do her bidding, but

however it came to be, I could not stand them. They seemed to me to be full of nothing but lusts and foul

odors, and I hated them for it. They dabbled their toes in the water as they waited for my father, and I hated

them for polluting the lifeblood of the forest. They chased after me, some for a long ways, even after I said I

did not wish to set sight on them for as long as I live. They spoke loudly and boisterously of their petty

accomplishments, and I hated them for it. Bold-faced simpletons that they were, they thought that I was

desperate to be torn away from my home, and my mistress. The fools could not know, I must allow them,

how she appeared to me in all of her glory, and that I would not leave her for all the riches in the world, nay,

not even if a god came here in pursuit of me.

And so I grew. And I grew into even greater beauty, or so they said. The men became even more

persistent in their advances, and there were many more of them. They came back again and again. And now

huntsmen, those blessed by my mistress, began to hunt me. I could turn them aside from their quarry

8

simply by allowing myself to be seen. This disturbed me greatly. They were dim enough to forsake the gifts

my mistress had given to all men in favor of chasing after me.

It became better after I almost killed a man. He was young, and I suppose a woman of more

mundane origin would have thought him beautiful. He had had the audacity to use the name of my mistress

in a couplet designed to woo me. I did not mean to kill him, only to injure him, but he surprised me. Then he

angered me. So I shot him. He lived, and others learned of his disgrace. The persistent went right on being

so, but the others became afraid, for I had not been punished.

That was until he came. How could I

can save itself. I could not save myself. I’m tired today. Perhaps I’ve accepted my fate.

Perhaps I’m feeling exhausted because I did expend so many of my energies towards being

angry with my sister. Perhaps that is why I do truly have the feels of being despondent today. `

I don’t see there being much I can do about this situation, though. I work, I do work on

commissions, but that is all I do feel up to doing today. Even this is work. I am lying in my bed,

taking rests, and having drinks of tea. The tea does help to calm my mind; it does help to smooth

the waters. But it does not make these feelings go away. There is nothing I can do about them.

Nothing. I have nothing left to me. My mother is dead, my father is ill, my sister is beyond all

hope, and I have lost my soul. I can no longer imagine it. I simply sit here and stare at a charcoal

sketch I did make of it some time ago.

It is of a prune. It is a picture of my heart. It is having the shape of a diamond, roughly.

There are deep wrinkles in it, and I did mark these wrinkles with streaks of red paint. The points

of the wrinkles are painted with streaks of deep green paint. That is how the spot in my heart

where my soul was does feel. Today is the first day I can feel this empty place. It is a great

gaping hole, something deep and red and painful. I feel, when I ponder over it, as if I could

simply fall into it if I do focus too hard upon it.

A year ago, I connected with the whole world. I would see simple things, and the beauty

of it would flood me, and I would feel myself filling up with it, so that my mind hurt, and my

stomach hurt, and my whole body would shiver and grow cold. Then I would feel like

screaming, like singing, and I would throw my consciousness skyward, and let the stars hear my

rage and my love and my joy. I connected to all of existence, and I felt like they connected to

me. I felt like, by transmuting the quintessence of a thing into paint, by channeling it through me

9

onto canvas, that I could make them better. By simply appreciating all that was around me, I

made the world a more exquisite place. Now I am powerless. I don’t feel rage or joy anymore. I

feel like my insides are numb, like I am falling into some dark place. Perhaps it is as books do

call it, and it is ‘the depths of her depression’. I don’t know. I do know that I will not move from

this place. There is no point.

refuse him? He is the brother of my mistress. He is a god. I saw him coming for me from a tree near

the edge of the woods. He looked so certain of his place; he had a quality about him that my mistress and

father do not have. Looking at him makes me understand why so many maidens accept his father. If all the

gods have this aura, it is a wonder there are not more godlings roaming the earth.

I will not accept him. Artemis will accept the hand of no god, and I will not accept the advances of

her brother. Nothing will sway me from this. But now I fear it is too late, for he has seen me. He stands at

the bottom of this tree and calls to me. He calls quietly and calmly. He gives me no promises of wealth and

riches, he recites no poetry, he does not call upon any gods. He merely calls my name. He can’t see me in the

tree, it has closed its branches around me and hidden me, but he knows I am here. He is a god, after all, and

I don’t know how I will be able to refuse him, if he should decide to climb. But he doesn’t move; he merely sits

there amongst the great roots.

I decide to try to outsmart him. If all the tales of his father are true, then it shouldn’t be difficult.

He will be confident that I am too cowardly to come down and flee from him, and he will be convinced that I

will not want to. So I slip around through the branches along another great limb, and slide silently down the

other side.

I begin to move quietly through the moss and young grasses away from him. I get not twenty paces

when I hear him rise from where he sat. He calls my name again. He comes around the tree, and speaks to

me. He can hear my breathing, I’m sure of it. How else would he have been able to know I intended to get

away? He professes his love for me. He says that he has loved me since I was but a child. He says that it was

the arrow of Eros that struck him as punishment for his arrogance, and he has suffered this love for me ever

since.

I tell him to be off. He does not leave, but calls my name yet again. I know he won’t leave, if this is

Eros’, and by extension, Aphrodite’s doing. Aphrodite has no love for my mistress, and therefore will have no

pity for me. I decide to run.

Living my entire life in this wood, reveling in the joys of the hunt, pursuing the most perfect of the

beasts of the earth has made my legs strong. I am the daughter of a god, I remind myself. No man has been

10

able to catch me yet, and no man will. I will run circles around this continent; I will flee into the sky itself if

he does not leave off. I can hear him running behind me. His feet slip over the stones, he stubs his toes on the

roots.

I can hear him yelling behind me, I can hear him calling to me in my mind. He says he does not

wish to harm me, but I believe him not. His is like every other man that servants of my mistress have

encountered, and they run along side me now naiads and draiads, warning me, giving me strength. They too

remind me of my father, and remind me of the merciless nature of our mistress. The stags tell me I must

run, the birds and the wolves tell my I must run. This is the way of all hunted creatures. I know this now.

But he is a god, and he can run faster than any mere mortal on this earth, regardless of whom they

serve. I can hear him breathing behind me, and for the first time in my life, I experience the emotion of fear.

Breath catches in my lungs, they bubble and groan like overworked bellows. My eyes flow with tears, my

legs burn. My father calls out to me, and I call back.

“Peneus, help me!”

I am accepting now. I do regret the loss of what I have, and have spent all of my long,

empty days pondering the works I have done in the past. It comforts me, this contemplation. I

still cast my thoughts upwards, to the stars, but now I simply wish to be heard by them. I’m sure

I will be.

My sister called today. She said that she’s going to get doctors to look at me tomorrow.

She’ll come by to pick me up and take me there, wherever there is. I don’t mind. I have decided

that agreeing with her is the best way to get her to leave me be. I’ve decided to drop these absurd

commissions, as well. I don’t need them, I can’t complete them.

I’m trying to keep a certain amount of peacefulness about me these days. It’s working. I

don’t mind anything anymore. My sister is coming to pick me up tomorrow, and I don’t mind. I

don’t mind. I’m trying to keep a certain amount of peacefulness about me, after all. It’s working.

I have been stopped. It happened just as I reached the banks of my father’s river. I can see Apollo

approaching, and now I can see fear and anger in his eyes. Then there is shock. I can feel a tingling and

itching sensation creeping up my calves, then up my belly, then up my raised arms. I can feel the extension

of all of my limbs, and I can feel a pushing behind my shoulder blades. My arms give, and lengthen,

swirling upward above me. There are flashes of green, and I turn my eyes upwards to find that I have

sprouted a canopy. My hair is pulled upward, and becomes a new collection of branches, joining my arms

11

high above me. My toes lengthen and dig into the loam, fixing me more firmly in place. Bark has wrapped

itself around my body like a great bodice or cocoon, inflexible and immobile.

Apollo has caught up with me now. He stands below my eyes, and looks up at me, projecting great

hurt and sadness. I do feel sorry for him. If the merciless arrows of Eros began this love, then he was not

himself. And he is the twin of my mistress; I cannot hate him, him who so resembles her in facial features

and strength of presence.

He steps slowly forward, still looking upward. He runs his hand up my torso, now encased in rough

bark. I cannot feel his touch, and am grateful for this blessing. He lays a kiss near to his hand, and this I

also cannot feel. He then speaks to me, saying that since I will not be his wife, he shall make me his tree, a

sign of his might. He shall decorate his brow and the brows of his warriors in wreaths of me, his harp shall

wear me whenever he does play it, his huntsmen shall adorn their bows with me. Since I am his love, and his

tree, and since he will never age, I too shall remain young, and be always green. I feel grateful for this as

well, and strive to bow, to demonstrate my gratitude towards him. He nods, and departs, taking a sprig of

me with him, holding it near to his heart.

The days pass, and I grow into being a tree. I learn of the joys of my new form. I feel closer to my

father, now that his lifeblood is also mine, I know the joy of feeling no cold, feeling no heat, but feeling

always the wind running over my leaves and the coolness of it. I feel the sun nourishing me, feel a tingling in

my hands whenever he does shine. I speak to my brother trees, now, and they can answer me, in their quiet,

whispering way. I am accepting now.

But I long for the joys of the hunt. My mistress visited me, with her hounds and a number of the

mighty stags that reside in the forest. She said nothing, but I could feel her regret, and her sadness at my

predicament. Many a day we did hunt together, and this was my greatest joy. Now I must remain here,

fixed to this spot, giant and ageless. I traded my life for my chastity. If I had chosen otherwise, however,

Artemis certainly would have killed me, and I would not die at her hand only to leave her alone. So I stand

quietly, and learn the ways of trees. My father says that my treehood is not a permanent thing. He did bless

me with this state, when I asked it of him. He can remove it, when it is safe to do so. When Apollo, the

brother of my mistress, does fall in love with another maiden, then Eros’ curse will be broken, and I will

again roam the forests with my mistress, ageless, and I will again find myself able to enjoy all of the

freedoms that this world offers.

So here I will stand, and I here I will wait.

Modern Myth Rubric - 11th/12th HumanitiesFinal Draft

Karen Armstrong says, “There is never a single, orthodox, version of a myth. As our circumstances change, we need to tell our stories differently in order tobring out their timeless truth… [E]very time men and women took a major step forward, they reviewed their mythology and made it speak to new conditions.But…human nature does not change much.

Students will write a modern myth (based on creation, destruction, or the hero’s journey) that illuminates what their society holds dear (meaning of life, value oflife, etc.), the importance of ritual, and the dichotomy of the sacred and the profane.

Learning Target Accomplished Looks Like Final Assessments and commentsA. I can write a myth that illuminates

what my contemporary society holdsdear.

• The tension between art, madness, medicine,and the best intentions of misguided family aresurely an illustration of what our society holdsdear.

Exemplary

B. I can write a myth that includes boththe sacred and the profane.

• This occurs in your creation of two worlds, andthe pontifications on the nature of art and talent.

Exemplary

C. I can write a myth that both explicitlyacknowledges what came before(alludes to pre-existing mythology)and conveys a modern perspective onsociety's values and rituals.

• Allusions to Daphne and Aphrodite are weavedwell into the story so that the artist herselfgrapples with what came before and how itrelates to modern society’s values.

Exemplary

D. I can craft myth with a voice that isengaging and compelling andappropriate for a modern audience.

• Your performance/reading of your textdemonstrated clearly the strength of yourcharacters’ voices.

Exemplary

E. I can craft a myth that shows a freshand original take on a "classic" idea.(A good artist borrows, a great artiststeals.)

• See comments above Exemplary

F. I can craft a myth that utilizes thestructure and flow of a mytharchetype. The details fit where theyare placed and the sequencing islogical and effective.

• Although the hero doesn’t physically journeyanywhere, she grapples with her foes andtravels within her mind. This is an excellentstretching out of a relatively minor myth.

Exemplary

Final Assessment: Exemplary

Erin Collier-Zans

Un Barco se Hundio

Yo soy un gato, llamado Fiddlesticks. Un dia, yo fue a pescar. Cada dia yo

pescaba. Yo tenía un barco pequeño. Me gustaba mi barco, porque mi barco era azul. Una

ola grande vino, y pegó mi pobre barco. La ola hizo mas hoyos pequeños. Yo vi una isla

en el lago. En la isla un millonario vivia, llamado Bill. Otra ola vino, y pegó my barco.

La ola hizo un hoyo grande. Mi barco pobre se hundió. Yo dije:

- Adios mi barco!

Mis zapatos estaban lleno de agua. Yo tuve un problema… yo no sabía nadar! Bill

me rescató. Ambos nos gustabamos golf. Bull tenia diez pelotas de golf, pero Bill

necesitaba mas pelotas. Yo tenia mas pelotas de golf, pero habia un problema… yo no

sabia nadar. Bill me enseñó como nadar. Yo nadé en el lago, y encontré mis pelotas de

golf. Bill tenia bastante dinero, y Bill me pagó por mis pelotas. Bill me dio mucho dinero

(mil dolares). Bill tambien compró barco vacio para mí, y me lo dio como un regalo. Bill

tenía una botella de vino, que casualidad! Bailamos y abrimos la botella. Ambos

estábamos felices.

Erin Collier-Zans2007

Copper Canyon Reflection

The Tara live in direct contact with nature all the time. When they wake up, they don’t

lounge around in their houses all day, they go outside to perform daily tasks. Their homes are

basically, from our cultural point of view, out in the middle of nowhere, so they live in nature,

and have for their entire existence as a people. According to Rolf, Eulalia is perfectly

comfortable when she’s just sitting outside. When we were in the copper canyon, she may have

had us to watch, but the rest of the time she was just silent, seemingly content to just tune in to

her surroundings. They instinctively “tune in”. They don’t have thoughts going through their

minds all the time. They aren’t constantly worrying when they’re moving about or resting in

their world.

Something that I feel is very important to mention about how I see the world as a human

being and as a member of a very distinct culture is how hard it is for me to comprehend that the

Tara simply do not understand certain things. They understand that certain things just are, and

that they can’t change them. They most likely wouldn’t understand our fighting or trying to

change things. I see things as constantly changing. I have to keep up with the change to survive. I

cannot simply be, or I would fall behind, lose my grasp on the goings on, lose my thoughts. I

have thoughts running at all times. They keep me awake, they persist no matter what I do to try

to quiet them. I worry about what is going to happen, recall embarrassing situations, wonder

what I could have done differently. I have vague memories of my early childhood, of basic

emotions, but after that, it is all stored thought. Sometimes I do not know what to do with myself

because I am frozen by the fear of the possible outcomes of a situation.

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I believe, from what Rolf has said about them, that the Tara have not lost the ability to

quiet their minds. They do it naturally, by practicing something called “deer meditation”, which

is perhaps the first form of meditation. During deer meditation, you simply clear your mind. You

can be doing things with your hands, performing daily tasks, but you go about them in a

disconnected way, with a clear mind. For centuries, the philosophers and practitioners of the

eastern religions have sought to return to this meditation, but with intention and control. It seems

likely that all religions have also made the attempt. In Christianity, praying directs the focus of

the mind in one direction: towards God.

In a monastic situation, at least in regions like Tibet, the world is something that we must

adapt ourselves to. You do not attempt to control nature, other people, or what occurs during the

course of the day. It is common knowledge that trying to do this is futile, and impossible. You

try to fit yourself around the needs of the world and the people around you. You try to help solve

the problems of others, because you know that this is the way to enlightenment, and in the

immediate sense, contentment.

The Tara, in a very direct, almost unintentional way, have this concept present in their

culture as well. They live in some of the most rugged territory in the world. In the areas they live

in, a crop may fail at any time, due to innumerable and uncontrollable reasons. There is no way

to control what nature is going to give you tomorrow. If your crop fails, you have no way to feed

your family. If it wasn’t for your neighbor and the rest of your community, you would die of

starvation. So, as a whole, they practice a collective sharing. If a crop fails, and you have more

than you need to survive the year, or the immediate future, you give that excess to support your

neighbor, in the understanding that for all you know, yours could be the next crop to fail. It is

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simply understood that withholding food, or wealth, is the wrong thing to do. You are not a very

good person if you do not help people who need it.

In this way, they have come to expect the unexpected. They have no way to predict what

is going to happen, and no way to protect themselves. In western society, we do everything we

possibly can to defend ourselves from inevitable disaster. Happiness to us is protection from the

unforeseeable. We buy insurance for our homes, our cars, and our bodies. We do everything

within our power to protect our children from the world. To protect our families, and ourselves,

we have to be the best. We have to surpass everyone around us. We have to win that promotion,

and make sure that the guy in the next cubicle doesn’t get that raise instead of us. So, in our push

towards dominance, we will disrespect and dehumanize the people around us. It is too hard for us

to keep the happiness of strangers in mind when we are so focused on ourselves.

Nature is just one of the many things that we must be wary of. It causes our homes to

flood, to burn down, costing us many thousands of our hard-earned dollars. So, we have fallen

into a circle of self-destruction. We tear down the rainforests, to build houses, which are then

destroyed. We separate ourselves from the natural world with our cities and our suburbs, and

subsequently destroy entire ecosystems for the materials to build our densely developed utopias.

The human machine drives ever onward, upward, always striving for what we believe to be

“better”. And better, it seems, is almost always bigger. But we never stop to think about where

the resources for this push towards happiness are going to come from. We decimate the

rainforests, one of our major sources of oxygen, to burn and build cities, which produce CO2,

which the rainforests can no longer absorb.

This utter disregard for the rest of the world seems to be one of the major symptoms of

our inherent lack of disrespect. In this society, we must teach our children to respect other

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children, perhaps by doing so creating the understanding that respect is conditional. We may

choose to demonstrate it, or not, depending on our opinion of whoever we are interacting with.

This disrespect only extends to nature. We simply do not think about the ramifications our

actions may have.

We are able to dehumanize and disrespect other people because we are simply

disconnected. Disconnection and dehumanization seem to go hand in hand with the spread of

western civilization. Connection is one of the most inherent human qualities. Finding a

connection to another human being is the most natural thing to do. In western society, however,

we have ceased to see humans as humans, as our equals in intelligence and in their possession of

a soul. And again, nature takes the brunt of our disregard. It does not occur to us that every

object that we hold dear, all of our little comforts in life, are the result of our deliberate

destruction of the natural world.

Being in copper canyon afforded me the space to attempt to connect. I was far away from

the constant, external noise, and so, through deliberation, I was able to silence the constant

internal noise. I entered into a state of deer meditation without intending to. I stopped thinking

and started feeling. I could sit on the edge of a cliff, surrounded by an expanse of grass, and look

down at the river far below me, clouded by distance. A vulture would fly below me, and I got the

rare pleasure of seeing a bird soaring from above. I wasn’t thinking, and I wasn’t regretting

anything. I was surrounded by true reality.

Introduction to Artwork: Sketches and Misc. Pieces2007-2008

What follows is a little selection of some of the smaller art pieces I did during my senioryear.

The two blue pieces, both done with coloured pencil in the span of a week, were drawnon a blue folder for Humanities class that I was encouraged to decorate. I’m happy and amusedto say that I was drawing floating islands at 16, while James Cameron didn’t start doodling hisuntil much later. The ocean scene was very muched inspired by a particular view of the oceanfrom the beach in Baja, California, where I spent two weeks of school break counting marineinvertebrates for a population census. And the other piece… Well, I was the only person in theschool with a nude figure openly displayed on a school folder – I’m shocked now by how littlecrap I got for it.

Also inspired by humanities class is a graphite sketch of a scene from Gawain and TheGreen Knight, a myth I studied during the same expedition for which I wrote ‘Freedoms thatBe’.

The crab piece was drawn with pen on a piece of printing paper during my Yearbookelective, second-semester senior year. It was inspired by the art of Varekai, my favourite ofCirque Du Soleil’s productions. A Photoshop-fluent friend inserted the text, and it was used asthe yearbook cover for ’08. The remaining pieces are just little bits of figure study, done fromphotos and books. I hope, in the future, to join art classes that will give me access to live models,so that I can continue to improve my skill.