Cairns of H.O.P.E. #29
Beginning of the Long Days, 2002

The mission of H.O.P.E. is to turn the prow of our entropyship, the Earth, back upstream so that Earthís evolving consciousness may explore the headwaters of the Universe for billions of years to come.
The work of H.O.P.E. is to make visible the larger relationships we live within - relationships that inspire visions of wonder and works of hope.

Achieving a Life Goal
In late March, I achieved a life goal: I snowshoed solo around Mt. Lassen. It was a great four day trip. It snowed heavily during days two and three as I was moving over the highest part of the circuit (between 7500-8500 feet). Ah, to see the trees in the high forests piled with the maximum snow that can remain poised on each branch is an ethereal experience. Someday I might focus my mind and memories enough to describe what I find so beautiful about mountains in the winter. But I wonít talk about the specifics of the trip here. Instead,, I want to share the effect it had on Chrysalis students.

The week before the trip, I told them I would try achieving a life goal that had eluded me on three earlier attempts. When I returned, I was surprised at how many of the kids asked,  ìDid you make it?î And when I said ìyesî, I was deeply, deeply moved by the pure spontaneous joy they felt in response to my accomplishment. It wasnít just joy for me. It was like a victory for the human spirit which included them. Their pure delight expressed how it should be. Someoneís rising higher elevates us all. We should delight in each accomplishment. The kidsí responses made me realize I had lost contact with that. Maybe that is a consequence of living in a culture focused on zero sum games in which every winner requires a loser, in which a person is compared with others rather than with how theyíve grown. The simple beauty of my studentsí joy brought me back to the realm of simple delight.

The second effect was that several of the kids became intrigued by the idea of a life goal. It was a new and fascinating idea. What is a life goal? How do you get them? Where do they come from? What will your next one be?

Prisonerís Dilemma
I wrote about the Prisonerís Dilemma in Cairns #3.  I created the following game to introduce the idea to Chrysalisís junior high students. I turned it into a Rock, Paper, Scissors game without the Scissors. And rather than calling it Rock, Paper, I called the options Fist and Open Hand. I put the following chart up on the wall; players used it to determine their score for each round. The chart could be a bit confusing because each player reads it for themself. You have to shift to the other playerís point of view to determine what they would score. Kids play 20 rounds and then add up their points.
 

Several interesting things happened. Several kids, when looking at the chart said,  ìOh, this game is so easy. You should always make a fist because you get 5 or a 1 whereas if you make an Open Hand, the same situations gives you only  a 3 or a 1.îAfter they played a couple of games, I asked for their scores (for 20 rounds). Most of the results averaged around 30 points per person. By this time, kids were starting to realize that the strategy of always making a fist was giving both players lots of scores of 1 apiece.

Then I told them that I hadnít mentioned (and nobody had asked) how you win the game. Everybody assumed winning meant scoring the most points for yourself. (Thatís a lesson in itself.) So I put in a new definition of winning: the team that together scored the most points. The results this time fell into 3 categories. One group of kids agreed to have one person always make a fist, one always made an open hand. Their scores were then 100 and 0 for a total of 100. A second group, also fixated on that big 5 score in the chart, agreed to alternate who threw a fist and who threw an open hand so that both players ended with a score of 50 for a total of 100. And the third group realized that by both making open palm they would end up with 3 points apiece for a total of 6 points a round. This leads to scores of 60 and 60 for a total of 120 points. Fascinatingly, when individuals pursue the highest group score, their individual scores are about twice as high (60 points) as when they concentrated on trying to achieve the highest individual score (20-30 points). A paradoxical way to state this is that trying to win causes one to lose.

One shouldnít push the game too far because it is a simple mathematical model. Point structures could be changed to lead to different conclusions. However, the Prisonerís Dilemma has remained essential to game theory because it does model a classic human dilemma that repeats over and over again in a variety of settings. The  ìTragedy of the Commonsî is an example. It helps us wrestle with the real world underpinnings of ethics. Why the need for self-restraint? In the case of our students, it was fun watching their understanding of the scoring table grow from the limited ìwhat should I do?î to the more realistic ìwhat should we do?î In fact, during lunch after the game, I heard a discussion about whether one should burn music CDs. I pointed out how burning CDs is like you throwing a fist when the recording artist threw an open hand. Once the student understood the connection, it led to a wonderful, wide-ranging discussion on ethics.

(An aside: One can see Enron as a corporation that learned how to manipulate accounting so it could be seen as playing ìOpen Handî every time (encouraging others to play ìOpen Handî along with it) when, in fact, it was playing ìFistîand screwing others every time.)

Systems Thinking
Part of Chrysalisís promise for me was a school where kids would learn systems thinking. This year our junior high class made tremendous growth in this area--and many of the students are 7th graders with another year to go at Chrysalis. Acknowledging this growth got Jeff (my co-teacher) and I discussing what elements of their schooling this year contributed to this progress. Thanks to our different perspectives, we championed different elements that probably combined for the success. The main element I contributed was teaching concepts of systems thinking so that students developed a language and a familiarity with the important patterns that tend to be found over and over again. Examples are feedback loops, flows, cycles, and frames of reference.

Elements that Jeff felt were important included a teaching pedagogy that kept all the topics and concepts ìin suspensionî. A dominant teaching pedagogy is to teach a certain unit, have a test, and then let it drop-- hardly to be referenced again. Jeff feels it is important to not let that happen, to keep circling back to previous topics to make connections. That leads to his second point--the teacher (and ideally the students also) need to be constantly drawing connections between various aspects of the world. In many schools this is difficult to achieve because different teachers teach different subjects in different rooms and so different subjects progress independently with no cross-referencing or reinforcement. This leads to a final thought/assumption. Jeff and I have no doubt, watching the electricity when kids make connections, that the mind/spirit ìlivesî for these connections.  There is something perverse in a system of ìeducationî that is structured in a way that interferes with connection-making. How we came to such a system and why we are so accepting of it are topics worthy of deep contemplation.

While editing this, Alysia added another element: ìchild-centered view where kid connections are valued, not teacher lectures where the teacher makes connections and has all the fun.î
 

Moving Shadows
There is a very simple activity I do with younger classes. There is a streetlight pole near the school that casts its shadow over the schoolís lawn. We go to the shadow at the beginning of our walk and I stick a pencil into the ground at the top end of the poleís shadow. When we return to the shadow 40 minutes later, we discover that the top of the poleís shadow is now 10-20 feet from the pencil. Something has moved. A good discussion ensues. Lots of interest. What I have learned NOT to tell the kids is that the shadow moved because the earth moved. That answer does not make sense to them. I simply say ìsomething has movedî. With 3rd and 4th graders, I might hold my hand open with a pencil rising up between my fingers - a model of the lamp pole and show how by rotating my hand from west to east, I can make the shadow on my hand move the same way the lightpole shadow moved. But I donít give them the phrase ìthe shadow moved because the earth moved.î The idea, especially for a child, is bigger than that phrase.

The last time I did this activity, the first grade teacher I was with really wanted me to give an explanation to bring ìclosureî to the ìlessonî. Instead, all I would say is ìsomething is moving and it took people thousands of years to figure out what it is that is moving. Itís a hard question to figure out, but maybe as you grow older, you will be able to figure it out.î For me, such an open-ended experience is what learning should be full of. For the other teacher, however, her training shaped her to be uncomfortable with a lesson that did not end with the statement of a fact that would serve as the answer to a test question.(Why do shadows move? Because the earth is turning.) A teacher-guided experience that ends with an unresolved question is ìincompleteî, is not a lesson.

She really wanted either her or me at some point to say, ìThe shadow is moving because the Earth is turning.îThis--even if kids would not understand the phrase, or more likely would misunderstand it in a way that would move them further from learning. Nevertheless saying ìthe truthî at some point in the lesson becomes sort of like saying ìAmenî at the end of a prayer. Itís expected. It signals that the lesson can now be considered complete.

P.S. As the teacher asked the kids to line up and walk back to school, one boy was off by himself holding his hands up, moving them about while gazing at what was happening to his shadow on the ground. Eventually he trailed back to school with a friend. The friend said, ìThat is a hard question.î And the boy answered, ìI want to grow up to be a scientist so I can find out the answer to that question.î

As I reflect on this experience, I realize that our current emphasis on standardized testing will shape classrooms into places where students will rarely commune with the unknown. Any question raised will be either officially answered by the end of the lesson or else seen as a time-consuming detour. Curiousity will not thrive in such a setting.

Seeing Space
I'm excited. I have my next H.O.P.E. project,  a second book, possibly called Seeing Space. The project has been kicking around in the back of my mind for several years, both as a book or a video project. What suddenly made this book exciting to me developed out of a teaching interaction I had at Chrysalis. I set up a big model of the Solar System and put junior high kids on the orbits so they could see how Mercury and Venus, whose orbits are nearer the Sun than ours, will always appear near the Sun (which is why we call Venus the Evening Star and Morning Star) while planets whose orbits are farther out can possibly be seen at any time of night.

I had hopes for the model, but it didnít work. Something confused the kids, preventing them from seeing what I wanted them to understand. Three mornings afterwards as I lay in bed, I suddenly realized what their confusion was. Let me try explaining (as an excuse for starting the first draft of the new book).

As I mentioned in last issue about point of view, ìLots of the conceptual breakthroughs in the early history of astronomy depended on changing oneís point of view. For example, realizing that the Earth was rotating rather than the stars revolving around required shifting your point of view from the surface of the Earth to an explanation that is best visualized from somewhere out in space looking back at a spinning Earth. ì What I realized lying in bed, however, is that what we need to do now is to take all these ìbeyond the Earthî models and shift them back to the point of view of an observer on Earth. Then we see the universe as astronomy has revealed it. Without that transition, we are left where I think the vast majority of us are - with a divorce between our visual perception and our intellectual models. There is poor fit between the universe as we understand it and the universe as we see it. Furthermore, the lack of fit keeps us from ìgetting itî, keeps us from experiencing the culture-changing revelatory power contained within this human-pioneered process called science.

The universe as we see it and the universe as we understand it should fit perfectly together. When they do, the eyes and mind resonate. This is the aesthetic experience many scientists report. Helping people experience this aesthetic resonance between eyes and mind is why I want to write this book.

So let me try teaching why Venus (and Mercury) can be seen only in the evening and morning by starting with the astronomical model and consciously moving through the transitions needed to move us to the view we have of the model from the surface of the Earth. It will help if you imagine the following diagrams as a series of pictures taken from a rocket ship far out in space as it comes in for a landing where you live.

We start with the following, widely accepted representation of part of the solar system. (The planets arenít drawn to scale and Iíve left out the orbits of the outer planets.) Our rocket is somewhere between Earth and Mars and high above the orbits of the planets.

This model represents our conceptual understanding, what weíve been taught by astronomy. This model is such an intellectual triumph. The story of how people developed and proved this viewpoint from the restricted view from Earth is marvelous. But that story is not our focus. Our focus, instead, is ìridingî this model back to the surface of the Earth. Our ride back to Earth begins by circling around until the Earth is almost lined up with the Sun.

One of the understated features of this model is that the solar system is approximately ìflatî. The planets do not orbit like the diagram below:

Instead their orbits lie close to the same plane and revolve in the same direction. Presumably, this constraint has to do with the origin of the solar system: that all the material from which the planets formed was revolving in the same general direction.

The next part of the rocket ride is to drop ìdownî towards the orbital planes of the planets. As we drop, the appearance of the orbits progressively flatten, changing to this:
 

And then eventually to this:

Two things to point out at this stage: First, the lines representing the orbits exist only in the mind. When we look around Space, we do not see orbital lines. So eventually these lines will have to drop out of our model. But they are still serving a purpose so we will keep them in for awhile. The second point is that the position of the planets in their orbits is arbitrary. The planets could be in other positions such as this:

Because of the constraints of each of their orbits, Mercury and Venus must always appear within a certain range around the Sun.

Mercury, for example, could never be in this position:

Once weíve dropped into the orbital plane of the planets, our rocket starts its approach towards Earth. As we draw closer, the Earth will appear larger in our view. The orbital plane of our Earth extends so far to the left and right of our visual field that Iíve dropped it in the next diagram. Iíve separated the orbits of Mercury and Venus to help us stay oriented. We are now close enough to the Earth to notice its rotation; its direction is shown by the arrow which also marks the Equator.(The axis of this rotation which we call the North Pole and South Pole are also shown.)

Visually, now comes the most important move. Which direction is up? In space, ìupî is extremely relative. However, for us whose eyes are almost one with our brain, having things oriented up and down is very important for making sense of what we see. In all the models so far, right and left have been defined by the solar systemís orbital plane and ìupî rises out of that plane.  But at our mid-latitude rocket landing site stands a person (represented by the red line) whose definition of ìupî is defined by the direction his/her head is pointing. So before we make our final approach, our rocket revolves so that the rocket shipís sense of up and down matches the Earthlingís. The whole model appears tilted.

Now we start our final rocket approach. We move straight ahead and ìlandî on our present position on Earth. As we move closer,  the Earth grows larger and larger until, upon landing, it fills half of our visual field. Only when we look out over the horizon can we see beyond this planet.

Because Venus and Mercury will always appear close to the Sun, it is extremely difficult to see them during the day. Therefore, we will let the Earth rotate underfoot until the Sun ìsetsîand its glare diminishes. Now we will also let the symbolic orbital paths fade away. Finally we have arrived at what we actually see here on the Earth. But can you now see it as part of something greater?

We began with the traditional astronomical model - as seen from a perspective far out in space - and moved back to what we actually see here on the Earth. The history of astronomy was the conceptual movement in the other direction; people carefully observing and measuring how they actually saw the planets moving until they came to the understanding embodied in the model. Moving back and forth between the two perspectives helps the eyes and mind resonate.

Realize that the model we just worked through was for when both Mercury and Venus are in the ìeveningî position as they are right now. Sometimes either of these planets can be orbiting in front of or behind the Sun and so be invisible. Other times they can be on the ìrightî side of the Sun and only be seen in the dawn sky. To help deepen your understanding of this entire example, try the following exercise: The following diagram is what our model would look like if we approached the Earth a half year later in late December. Now the axis of roation tips the Northern Hemisphere away from the Sun. What difference will this create in our view of Mercury and Venus?

Calling all naturalists contest
Last issue I mentioned how life has made possible steeper slopes. A week after sending that out, I thought, ìI can push that thought further. What consequences would a steeper world create?î Steeper slopes would mean steeper streams which would probably have more turbulence which would lead to more dissolved oxygen in the streams which would allow higher rates of metabolism in the streams. There would also be more pronounced slope effects (shaded north slope, hot south slopes) which would create a greater diversity of habitats. As I thought about these consequences, I thought of having a ìcontestî and open myself to help from you, the readers. So, can you think of other consequences that would arise from land becoming steeper, thanks to lifeís ability to hold soil at a steeper angle? Send your ideas; help me think.

And while you are thinking of that fun question, here is another question I need help with. From years of walking in them, I have images of what a healthy, stable drainage and an eroding drainage look like.

Drainages have different cross-sections. An eroding drainage (left - lines added) has a gully gashing the bottom. A stable drainage (right) has a gentle curve. Only in the last few months have I started wondering about that shape. Why should it be a gentle curve? I could understand a flat bottom (like the braided stream downstream of a glacier) or a slightly convex curve like the cross section of an alluvial fan. Both these deposition-created shapes spread the water out over a broader area. A gentle curve does not do this. It concentrates runoff into a narrow cross-section. However, erosion does not occur. What maintains that curve? What keeps it from not eroding into a gully but also not filling in to form a flat bottom? I donít think vegetation is a factor because I have seen the same gentle curve in forests with scant groundcover.

Perhaps what is happening is that near the head of a drainage, most of the rainfall moves as subsurface percolation rather than runoff. This subsurface flow dissolves soluble minerals and carries them out of the drainage. Rather than material being carried away above ground - which would create a gully - perhaps the material is carried away in solution beneath the surface, allowing the land to gently ìcollapseî into gentle curves.

Can anybody out there help me move to a deeper understanding of these beautiful curves?

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My book, Seeing Nature: Deliberate Encounters with the Visible World, may be ordered from me. Prices are $16 for one book, $29 for two books, $64 for 5 books, or $112 for 10 copies. All prices are postpaid and include any sales tax. Mail orders to Paul Krafel, P.O. Box 609, Cottonwood, CA  96022-0609

Cairns is free for anyone receiving it by e-mail. My e-mail address: paul@krafel.net

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© 2002, Paul Krafel, P.O. Box 609, Cottonwood, CA 96022-0609
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