Volume 16, #26

Spring 2010

David Mitchell. Editor

1158 Quince Avenue
Boulder, CO 80304
davidm@awsna.org
303/541-9244

1
2
 Waldorf Science
Explorations in Phenomenology as Practiced in Waldorf Schools

A Science News Roundletter

Editor: David Mitchell

1158 Quince Ave.

Boulder, CO 80304
Phone and Fax: 303/ 541-9244
E-mail: davidm@awsna.org

© Copyright 2010 by AWSNA Publications

All materials may be reproduced for individual use in Waldorf/Steiner Schools but not published without permission of the editor.

Printed with the Support of the Waldorf Curriculum Fund

____________________________________________________________________________________________________________
VOL. 16, #26 Spring 2010

This edition features the following: “Going through,

FROM THE EDITOR Taking in, Considering: A Three-Phase Process of
Learning as a Method of Teaching in Main Lesson
Indications and quantifiable results1 suggest that Blocks” by Manfred von Mackensen; “The Geometry
the subject of Waldorf science has both improved and of Life” Toward a Science of Form” by Arthur Zajonc;
strengthened in the past decade. More Waldorf graduates “Phenomenology: Husserl’s Philosophy and Goethe’s
report that they selected a science major in college and Approach to Science” by Michael Holdrege; and the
that they felt better prepared than past graduates reported. “First Approach to Mineralogy” by Frederick Hiebel.
We consider this a positive sign and applaud the teachers Also included are instructions for growing salt crystals,
who have made this a reality. as well as articles on the beauty of slime molds and
Our capable co-editor for the past several years, symbiotic mutualism. An interview with Daniel Pink
Bob Amos, has left his teaching position and had to pull gives an outside perspective on Waldorf education and
back as co-editor from the Waldorf Science Newsletter. caps off this edition.
Bob is a valued friend and was a trusted support in The editor would be overjoyed to receive
the production of this effort and I will miss him. A contributions from all teachers. It is hoped that this
replacement for Bob is sought and interested individuals edition will be helpful and informative for teachers,
should contact me with a résumé at the above address. parents, and individuals training to be Waldorf teachers.
The tasks include gathering material, proofreading, and _________________
having an interest in science and phenomenology. 1. Survey of Waldorf Graduates, Phase II, Reseach Institute for
Waldorf Education, 2007.

3
 Books of Interest
The book containes many interesting facts that will
delight the reader such as:

• The orchid, whose blos-

soms are the most ornate
of any flowering plant,
has the smallest seed of
any such plant, just 1/50
of an inch long, a seed
that does not germi-
nate unless an invasive
fungus provides it with
nutrition.

• The sooty albatross can

glide for hours without a
Metamorphosis: Evolution in Action single wing beat, but is
by Andreas Suchantke unable to stand or walk
on flat ground because
Suchantke is a teacher and biological researcher who has of its turned-in feet.
spent his life observing phenomena and the formative prin-
ciples which shape them. Following in Goethe’s footsteps • The marauding columns
he shows how the development and evolution of plants and of the African army
animals can be understoof in terms of metamorphosis. ant, which consume
everything in their path,
can include 20 million
individual ants.

• Members of different
species of butterfly in
the same forest envi-
ronment develop similar coloration based on
the prevailing patterns of color and light and
shadow in the forest.

• One species of squid, Onychotheutis banksi, is

able to leap out of the water and to glide several
hundred yards through the air, carried by sail-
like fins.

This book will find a place on your bookshelf along

Metamorphic sequence in a peony (cultivated with your other prized volumes, that is, if you can stop
double form)— leaf sequence from the upper reading it and resist from leaving it on your table top
leaves via calyx to petals, continuing with where all you friends can admire it.
intermediate forms, part petal and part stamen,
and finishing up with a normal stamen.
ISBN 978-0-932776-39-6 Richly illustrated
Suchantke urges us to observe and then think about nature Pages 324 8.5 x 11.25 inches Hardcover
with fresh eyes. The book covers a wide range of top- Adonis Press $50.00
ics including: plants, mammals, birds, butterflies, insects, Available from AWSNA Publications
molluscs and the human being. Each is examined from the
perspective of metamorphosis, which Suchantke refers to as
“the key to understanding the nature of life.”
4
 Wilderness Survival Handbook
Waldorf Journal Project #14 by Michael Pewtherer
Darwin (and More)
Edited by David Mitchell What a joy it was to find this excellent resource writ-
ten by a Waldorf graduate and part time teacher at the
Contents Hawthorne Valley School in Harlemville, New York.
• What Makes Human Beings Human? by Wolfgang Schad Our Waldorf students crave the knowledge of how to
• Darwin’s Incomplete Knowledge of Death by Wolfgang gain mastery in the wilderness. They seek to learn how
Schad to accurately observe the secrets in nature and survive in
• Darwin Suffered from Darwinism by Wolfgang Schad the wild. The subject of wilderness survival should be an
• Body Movements Are Invisible Thinking, Mathematical adjunct course in every school. Pewtherer covers such
Thinking Is Inner Movements by Erik Marstrander topics as:
• What Is Goetheanism? by Trond Skaftnesmo
• The Hippopotamus and the Eagle by Trond Skaftnesmo • Preparing to survive and making a proper survival kit
• Close Contact with the Earth: Necessary Experiences • Observing the terrain and building a proper shelter
that Provide a Basis for Lessons in Natural Sciences • Locating water, sap gathering and building a solar still
An Interview with Linda Jolly by Eli Tronsmo • Building a proper fire
• Physics Lessons that Start with the Human Being by Geir • How to navigate and deal with medical emergencies
Øyen • Trapping, making hunting weapons, tanning hides,
• The Power of Observation in Literature Lessons by Tom making cordage, building crude containers like bark
Horn canteens, sealing with pitch for waterproofing and so
• Insight into Human Nature as a Basis for Waldorf Edu- forth.
cation: Anthroposophy and Modern Brain Research by
Helge Godager Modern youth in North America increase their self-
• Think Globally and Act Locally: The Ecology Practicum esteem, connect with the fabled pioneers of our continent,
in the 11th Grade by Holger Bauman and gain confidence as they learn these “real” skills. The
• Music: An Endangered “Species”? by Magne Skrede activities can be a turning point for challenged youth and
• Performing Arts versus Degraded Speech by Magne both a boost and balance for capable students caught in
Skrede the confines of the classroom and a one-sided intellectual-
• From Crisis to Cooperation by Sylvia Fuehrer ism.
• Productivity and Receptiveness: How Do We Work To-
gether on the School Organism? by Karl-Martin Dietz ISBN 978-0-07-148467-1
Pages 266 7.25 x 9 inches Softcover
Pages 114 8.5 x 11 inches Price: $19.95 Illustrated
Spiralbound Illustrated McGraw Hill Publication
Available as a spiralbound copy at cost through
AWSNA Publications and gratis Online at >http://
www.waldorflibrary.org/pg/journalFocus/journalFocus.
asp?journalID=15<.

5
 Michael’s Sanctuary in Chonae (From the Greek)
The Sanctuary of Michael on Mount Gargano (Latin)
Mont Saint-Michel (French Legend)
Mont Saint-Michel (Chronicle of the City of Speyer)
The Leper Jew
The Unfulfilled Vow
The Blind Man
The Possessed
Sequence on St. Michael Dedicated to Emperor
Charlemagne (Hymn from the Middle Ages)
The Dragon of Ireland (French Legend)
Michael as Friend of Mankind (Icelandic Legend)
Michael Leads the Army of Barbarossa (German)
Waldorf Journal Project #15 To St. Michael (Latin Hymn, 11th century)
Michaelmas How Henry II Beheld Michael on Monte Gargano and
Edited by David Mitchell How He Was Touched and Lamed by Him (German)
Prayer (From Old Norway, circa 1300)
Contents The Death of St. Elizabeth of Thuringa (German)
Lucifer’s Crown (From the “Singers’ Contest on the
Teacher Study: Wartburg,” 13th century)
Michaelmas and the Soul Forces of the Human Being The Vision of Jeanne d’Arc
The Activity of Michael and the Future of Humanity Michael, the Angel, Speaketh
The Michael-Christ-Experience of Humankind St. Michael on the Crescent Moon (Polish Legend)
The Work of Michael Of Michael, the Archangel (From the Russian)
Why Do Waldorf Schools Celebrate Michaelmas? Why the Sole of Man’s Foot Is not Even
Working with the Festivals through the Twelve Senses Miner’s Song (From Bohemia)
The Devil’s Scythe (French Legend)
Stories and Legends for Teachers to Tell: What the Peasants of Normandy Tell about Michael
Feast of St. Michael (From The Golden Legend) The Twelfth Chapter of the Revelation of St. John
Michael Legends (by Pico Della Mirandola) Concerning the Iron in the Kalewala and the Spiritual
Gothic Hymn unto the Archangel Michael (Greek) Forge in the North
Michael (Greek Hymn from the Middle Ages) Michael Legend from the Philippines
Michael as Indra (Rigveda) The Legend of Mont Saint-Michel by Guy de
The Bhagadvad-Gita as a Reflection of Michael’s Battle in Maupassant
Heaven
Michael as Mithras (From the Avesta) 148 pages 8.5 x 11 inches Spiralbound
Mithras, Revealing the Sacred Names (Mithras Liturgy) Illustrated
Michael as Marduk (After the Babylonian Song of World)
Creation of Adam Available through AWSNA Publications at cost
Michael as Guardian of the Word and Online gratis at >http://www.waldorflibrary.org/pg/
Michael Tests Moses’ Willingness to Sacrifice journalFocus/journalFocus.asp?journalID=15<.
Michael as Savior of Isaac
Moses’ Death
The Four Winds
The Rainbow
The Bowl of the World
The Book of the Seventy-Two Signs
Michael as Guardian of Paradise (Medieval Tale)
Golgotha (Russian Legend)
Michael and the Risen One (Easter Play, 15th century)
Michael and Evil (Ancient Bulgarian Legend)
Michael and the Doubter (German Legend)

6
 The Metamorphosis of Plants
Colloquium on High School Physics by J.W. von Goethe

Organized by the Waldorf High School Research Group This book is a wonderful validation of the scientific worth
through the Research Instititute of Goethe’s pioneering researches on morphology. Here
Goethe “coupled rigorous empiricism with precise imagi-
A group of experienced teachers discuss and explore nation to see particular natural phenomena as concrete
the Waldorf physics curriculum and suggest new ideas symbols of the universal principles, organizing ideas [to
while solving some of the riddles found in the current perceive] the inner laws of nature,” says the editor Gordon
curriculum. Miller. Published by the MIT Press in hardcover with high
quality paper and stunning colored illustrations, this book
AWSNA Publications 8.5 x 11 inches is an absolute treasure.
Pages 98 Spiralbound Illustrated
ISBN 978-0-262-01309-3
Pages 123 6.25 x 8.25 inches Hardcover
Price: $30.00 Illustrated
The MIT Press Available through AWSNA Publications

Growing Patterns
Fibonacci Numbers in Nature
by Sarah C. Campbell

This title holds a lot of promise but the book was a let-
down. The illustrations are lovely but the text is overly
simplistic. Recommended only for those who know Coming in the autumn of 2010
absolutely nothing about the Fibonacci sequence.
Mathematics in the Eleventh Class
ISBN 978-1-59078-752-6
Pages: 32 12.25 x 7.5 Hardcover AWSNA Publications is currently translating this resource
Price: $17.97 Illustrated book for Waldorf high schools in North America. An an-
Boyd Mills Press nouncement will be made when the book is available. The
edition for the 10th grade mathematics is available and can
be ordered Online through Books & More at the AWSNA
website.

7
Research Bulletin Autumn/Winter 2009 Research Bulletin Spring/Summer 2010
Volume XIV, Number 2 Volume XV, Number 1

Editor: Stephen Keith Sagarin, PhD Editor: Stephen Keith Sagarin, PhD

Dedicated to furthering research in education, the Re- • What Can Rudolf Steiner’s Words to the First Waldorf
search Bulletin provides schools with studies and data that Teachers Tell Us Today?
place Waldorf education at the forefront of the educational • Social Emotional Intelligence: The Basis for a New
scene in North America. Key topics in this issue are: Vision of Education in the United States
• Rudolf Steiner’s Research Methods for Teachers
• The Social Mission of Waldorf School Communities • Combined Grades in Waldorf Schools: Creating
• Identity and Governance Classrooms Teachers Can Feel Good About
• Changing Old Habits: Exploring New Models for • Educating Gifted Students in Waldorf Schools
Professional Development • How Do Teachers Learn with Teachers?
• Developing Coherence: Meditative Practice in • Does Our Educational System Contribute to
Waldorf School Colleges of Teachers Attentional and Learning Difficulties in Our Children?
• Teacher’s Self-Development as a Mirror of Children’s • Survey on Waldorf School Trustee Education
Incarnation: Part II
• Social Emotional Education and Waldorf Education Pages: 72 7.5 x 11 inches Price: $12.00
• Television in, and the Worlds of, Today’s Children: A Available from AWSNA Publications
Mounting Cultural Controversy
• Russia’s History, Culture, and the Thrust Toward
High-Stakes Testing: Reflections on a Recent Visit
Phenomenological Organic Chemistry
For the Ninth Grade
• Da, Vadorvskii! Finding an Educational Approach for
by Manfred von Mackensen
Children with Disabilities in a Siberian Village
Through the stellar efforts of
as well as the writings of our Research Fellows. If you
Peter Glasby from Australia, we
have not seen the latest edition, you are encouraged to
now have an English version of
obtain a subscription available from:
Manfred von Mackensen’s Phe-
nomenological Organic Chemistry.
researchinstitute@earthlink.net
Included are experiment descrip-
tions, discussion of deeper themes
80 pages 7.5 x 11 inches Price $12.00
and methodology for carrying
Available from AWSNA Publications
out student laboratory projects.
Contents include: deeper thoughts
on the intent of the curriculum;
Stages of Refinement; Combustion; Fragrances; Petroleum;
Essential Oils; Anasthetis; and much more.

ISBN # 978-1-888365-79-5
Pages 134 8.5 x 11 Softbound
Illustrated Price $25.00
Available from AWSNA Publications
8
Going Through, taking in, Considering
A Three-Phase Process of Learning as a Method of “Teaching Main Lesson Blocks”1

by

Manfred von Mackensen

Curtain Raiser
We would like to elaborate certain phases of teaching by, deliberately,
taking an example from our everyday life. Occurrences which usually
take place in school may, for the time being, be projected onto a private
situation. So let us have a try on three phases and imagine the following:

Phase I A couple is going to a birthday party. Good luck!

– A lot of guests, a lot of confusion.
Phase II On their way home, they exchange their
impressions: a highpoint, a striking character.
Phase III The next morning they debate:
(a) in what way were the guests related to
each other and to the host?
(b) which news about the world did one
learn from them?
(c) how would oneself wish to celebrate a
coming birthday; what do birthdays
really demand, anyway?

Are these really three phases? Let us have a look again at what exactly
happens here.
At the beginning, one just throws oneself into the crowd (Phase I). One
makes acquaintances without thinking much about it and enjoys meeting
with the people who turn up. Any form of investigation or classifying
would be distracting.—Afterwards, all that is resounding in both of them
(Phase II); both are still preoccupied with what they experienced2 and,
while talking it over, their emotions unite the details automatically. The
ups and downs of the party now appear more as a related “whole,” and
less as a mere series of events. Something that was frightening changes
into a deep impression, rejoicing into true interest, a muddle into a
sequence of related scenes. Later on, one dissects that “whole” again into
fragments and discusses their interrelations (Phase III). One examines
___________________
1. This paper was written during the work on the project Phenomenological
Natural Science and Human Didactics. In conferences and courses it has served
as a text for introduction, reflection, and fixation. At the same time it can be
regarded as an example for how to organize teaching lessons (Pädagogische
Forschungsstelle beim Bund der Freien Waldorfschulen Stuttgart, Abt. Kassel,
Brabanterstrasse 30, 34131 Kassel).
2. Perhaps humming softly the refrain of a song, such as “Going through, Sing-
ing about, ….”

9
how this related to that, who has secretly wanted what or who has
suffered, and so on (a). One is digging for insights, for knowledge (b).
Finally, one ponders, asks what consequences will follow, and also, how
oneself could achieve something (c).
In this story, not a word about school lessons appeared. It
demonstrates how the three elements of the elaborated method work
in real life.

An Example

1. Understanding on Your Own (enterprising, joining in,

experiencing) = Phase I

We imagine teaching physics, perhaps in Grade 8, and we are

experimenting. (a.) The pupils stream out of the school building. Soon
they are gathered around a flexible tube of which the end is immediately
lifted up the wall of the house until it reaches a window. There it is held
12 meters above the ground. The tube, about 3 cm diameter and made of
transparent plastic, has a plug at each end and is completely filled with
boiled and slightly colored water; there is no air in it. Air is surrounding
everything. Every two meters it is marked with a line.

Figure 1: A flexible tube, with marks every two meters, is hanging down
a wall. The second mark at the lower end bears a little flag with “2m”
written on it. The bucket is filled to the brim with water.

10
 (b.) The lower end is now dunked into the bucket provided which is
filled to the brim with water, causing an overflow, and another student
puts his hand into it and after counting “1,2,3!” the plug under water
is pulled out. Immediately, several meters of the water in the tube runs
into the bucket. But surprisingly, most of the water remains in the tube.
The water level settles down around the 10-meter mark. Now, from the
top down to approximately 8 meters high, the tube is “squeezed” in the
middle:

Figure 2: Cross-section of the squeezed tube at approximately 9-meter

height, after the water level has fallen to 10 meters.  

After the bucket has been refilled, an assistant in the window draws
the attention to the water level in the tube. The pupils count the meter
marks down to the surface of the water in the filled-up bucket. The
number remains the same, even when the upper end of the tube is moved
downwards or when the bucket is lifted upwards.

(c.) When, just for a short moment, the lower end of the tube is taken
out of the bucket, approximately 1 meter of water runs out. Its space
is replaced by air. This air rises in the tube as a stretched bubble, and,
afterwards, the water level is several meters lower than before.

(d.) If the upper plug is pulled out, the remaining water column shoots
into the bucket, causing again an overflow. The tube is thrown to the
ground. Now it is straight again, that means, no longer squeezed like in
Fig. 2.

2. Common Recollection in Class = Phase II

Back in the classroom, the teacher characterizes the experience,
accompanied by various observations or answers of the pupils, however,
without explaining a thing! He does that by using more personally
colored words, like following the motto: “Gosh! What are we going
through here!” E.g., when recalling the tube lying on the ground, he
evokes a feeling of how everything was at rest, the water being closed
in. Looking back at the tube, hanging in the air, he then creates the
impression that the situation was somehow full of tension, as if the water
would come running out at any moment. Who would have been the
first to get wet? Did the situation seem to be suspicious for somebody,
perhaps, when we built a sort of barrier in the bucket—a barrier for the
tube, water out of water?
After all, it came to stop somehow. Isn’t it amazing what our teacher
is able to achieve? Maybe the air, surrounding everything, was helping?
Later on, what a relief! With just one grip this spooky phenomenon was
gone.
A recollection like this, led by the teacher, should be carried out with
sympathy and benevolence—towards the objects, the occurrences and
also towards the participating humans; no harsh questions, no forced

11
explanations. Everything that gets mentioned is accepted, as you would
do during a good meal in the hut after a tiring alpine tour. A cheerful
common feeling runs through all and everything and should be kept light.
Perhaps somebody writes some key words on the blackboard, so that the
collective experience can be recalled later. The beginning of a sketch
similar to Fig. 1 may also be drawn on the blackboard.
This recollection is not at all a purely subjectively roaming; however
objective judgments of facts, such as cause and effect for example,
are avoided or simply ignored. What arise are collective images, clear
enough for all to remember: this was first and that followed. Through
the teacher calling the attention of the pupils to the closed-in water, the
air and the way the water runs out, as well as to the air surrounding, the
beginning of explanations could be anticipated. It is this anticipation that
should be worked towards.

3. Questioning and Considering the Facts = Phase III

On the next morning, the pupils bring along their completed drawings,
similar to Fig. 1, as well as their personal review of the experiment—
which in no way must resemble an impersonal technical description.
(How to create both, see below.) The ideas and imaginations concerning
the course of the experiment that were called up the day before (see the
above paragraph), have now “settled down.” Particular turning points are
recalled into common awareness (consciousness) with a few repetitive
questions. And now follows the elaboration of the case as such. It begins
with questions about interconnections as well as with explanations and
widening reflections:

• Could the upper plug hold the water column from above—
without any threads between the bottom of the plug and the
surface of the water? If not:
• Could the water in the bucket from downwards up carry the
water column above it; does the size of the bucket play a part
here?
• Could the water in the bucket at least slow down the running out?
• What is it that squeezes the tube; and why isn’t the lower end
squeezed too?
• What is contained in the tube above the water level?
• How strong was the carrying force of the air pressure shown
to us, expressed in meters of water column? How many meters
would it be if we used other fluids (salt water, oil)? Would the
water column have the same height everywhere on earth and at
all times?
• Does the air temperature play a role? Yes, through the pressure
of the steam, at 20° C it is 23 millibar which equals to 23 cm of
water column. But those finer details don’t have to be explained
in Grade 8 yet, nor any of the other questions before.

It is of great importance that individual opinions come up in the class,

as engaged and diverse as possible. The more original and even more
fantastic they are, the more they stimulate. Thus, they will be impressed
if it is revealed that neither the water in the bucket nor the plug above
brings about a force that could hold up the water level, or even draw it

12
back when it swings downwards. Rather there is something invisible
at work here, namely the “endless ocean of air.” And moreover it is
important that the standard aero-mechanical explanation with the help of
the pressure of the outer air upon the water surface in the bucket, should
not be ruling alone here,3 but should be expanded through ‘vaguely’
qualitative elements, like “endless,” “ocean of air” or “horror vacui.”4
These elements direct the attention less to the mechanical facts but
rather lead the pupils to feel, to understand, even to immerse themselves
in a subject. This is the only way to motivate a pupil towards a lasting
striving for knowledge and learning. In addition to the logical subjects
and the pure qualitative aspects, there might arise more widening
questions, like changes of the air pressure, the influence of the weather,
breathing in relation to the flying heights of airplanes, and so on.

Discussing the Method

A. Making Use of the Night

The advantages of a teaching in two-day loops, partly already evident
in the above example, will be obvious especially if the subjects are
taught in blocks, i.e., the teaching of technical subjects occurs in main
lesson blocks, so that the ripening process of the night can be included.
What can we do to activate this process? A part of it was already shown
above (see Chapter 2), where, for a long time that work was done non-
informative but nevertheless systematically theme-oriented, let us say
with the aim: “Getting an impulse to move on instead of receiving
information.” Such an effort pays off immediately causing sympathy
and, in the end, leading to a successful level of education (a well-known
experience in practice). The well prepared process of ripening during
the night is even generally known and nowadays scientifically observed,
but, since cognitive-psychological, never simply deductible. With the
above exemplified model of the three steps in two days, perhaps called
“two-days-three-steps-model of learning in blocks,” we have a practical
method at hand that is proven and certainly an ingenious invention, no
matter by whom. It should just be presented in a form that is ready for
use.
Its core derives from the question: How can it be achieved that the
student not only gains a profit for his mind and behavior, but that he,
with every subject, takes a step forward in his entire existence and his
individual development? A single subject in school has to be more than
a sum of communicable notions and definitions. That means, closer to
life, to reality, and, therefore, also dark. At first the subject has to be
introduced to the class in open and sensitive terms, that warmly flow

______________
3. It is well known that the actual air pressure drives the water against a vacuum
up to a height of about 10 m above the surface of the water upon which the air
presses, no matter whether the tube is sloping or lying in waves. These measures
can be only approximate because the air pressure changes with the weather, often
hours until days in advance; i.e. about +5 or –10%, and also because it generally
decreases along with the height above sea level (in 5.500 m by 50 %).
4. It is the term for an experience; built on the discovery that the world is lacking
the natural, continual vacuum spaces. The “horror vacui” was, during thousands
of years, an important, fundamental force of earth and heaven and was attributed
to the universe, as also was philosophically given its place. Today we see it more
in terms of some continuous pictorial gesture.

13
around the pupil and will become seeds for him to sprout, so that he
won’t get emotionally petrified by being exposed to mere definitions
and final statements. And still, these open terms should provide a basis
for a deeper elaboration of the matter, since everything has to end in
professional knowledge.—How could this, generally, be achieved?

B. The Various Activities of the Teachers

1. Concerning Phase I
First of all, our experiment was intended to provide more than mere
information. It should not convey teachings subjects but, structured by
the teacher, the dark reality of the world (this concept of reality may,
for the time being, remain unexplained). In any case, the pupil should,
at first, save his perceptions as inner pictures (“. . . now he takes that,
there, that is dangling . . . ”), without understanding them technically. For
that, he naturally combines all his recollections with his observations, in
order to identify them somehow as objects. This is a really demanding,
an exhausting process, since all the impressions will hit him shapeless
and hard. Basically, the teacher and the pupils, since they are completely
immersed in the matter, enjoy all that is developing here.
The teacher provides the students with objects and facts as well as
with impulses for his soul by an elaborated experiment (in other school
subjects rather with pictures, narratives, music, sightseeing-tours, and so
forth). He creates a configuration. The students adapt to that. Therefore,
this first step regarding the mental activity of the pupils could be called
deliberate or determined (volitional), for they were fully dependent on all
their physical sense organs. They adapted the situation in an interactive
way—which, indeed, provides a basis for any decisive will to act.

2. Concerning Phase II
Looking merely at information, it is just a repetition of Phase I. In
reality however, everything is different. Nothing at all gets repeated.
Completely different mental powers are devoted to a problem when the
person moves from one inner activity to the next: at the beginning, he
used his will, now his feeling. In Phase I, the pupil struggled to sort out
his own recollected imaginations. Now these imaginations are picked
up in class and the group process helps him to harmonize and confirm
them. The emotions of all group members are flowing together, so that
a cheerful sense of community replaces the preceding silent feeling of
helplessness and captivation. Through this, the unconnected facts of
the initial confrontation are brought on a way towards being embedded
in something greater. In Phase I, the inner pictures of the pupil are
pushed back and forth by the outer occurrences. In Phase II, they will
be mentally refreshed in such a way that they can serve as a seedbed
for something new, mentally as well as intellectually, which ought to
grow during Phase III; even if, superficially, the experimental noises
are, at first, only followed by nice word noises. In any case the students
will begin to look out for the context of it all. Connecting links seem to
emerge. The pupil even gets the impression that he achieved something.
At this stage of Phase II, the teaching may pause.

3. Concerning Phase III

In Phase II, the consolidation of the swirling impressions of Phase I
formed a solid basis for anchoring the questioning now as well as for

14
a new construct of ideas. This was caused, on the one hand, by writing
down a review of the experiments, quite possibly in the style of Phase
II, and by the natural settling-down and the ripening process during the
night.
On the next morning, the gelled imaginations will call for evaluation,
expansion, and categorizing through a joint exchange of ideas in class!
Only thereafter, the time will come to start the necessary general survey,
and for the teacher to deliver broader contemplations, e.g., Why is this
topic so important? What else belongs to it? The history of discoveries
in this field, special tools and measuring devices, technical applications
and/or accidents may come into play, and ecological problems are
to be regarded.5 At the end, during the final lecture of the teacher,
the group process is carried by a sense of community and sympathy.
Before that, however, during the process of questioning and searching,
uncompromising and distance have been prevailing, i.e., antipathy
contracted into mere facts.

4. To all three phases

Only within the third Phase, the first part of the double period on the
second day, a general realization (cognition) arises. It arises out of the
change of experiences, practical knowledge and actions, which took
place in the individual. So, the conventional “aim of the lesson” is first
to come on the second day, but then, larger and deeper than would have
been possible on the day before—provided everything went well. The
aim of knowing the subject is completed with an educational aim, for,
in such a way, its light shines into the world outside as into the personal
power and abilities.6

****

Other scientists, too, are striving for such a way in three phases. Klaus
Schmidt, one of the most famous and successful archaeologists of the
present time, talks about strategies like this when he tries to comprehend
“the oldest monuments of mankind,”7 in this case the context of a
complex structure of an entire excavated temple city.8 This early
metropolis was founded with all its buildings, murals and other objects
of art at the end of the glacier epoch. It is not yet known why, after
several thousands of years, the whole town became completely filled up
again, buried up to the wall copings in the hidden seclusion of Anatolia
up to our time—a phenomenon that seems to be from another world.
________________
5. How to include such aspects within the period on physics of class 8, and also
more about the pressure of the air and so on, one will find in: M. v. Mackensen:
A Phenomena-Based Physics, Vol. 3 for Grade 8, AWSNA Publications.
The problems that airplanes have by the pressure of the air are described in Hof-
berger/Mackensen : Flug, Landung, Absturz; Publ.:Verlag Bildungswerk Kassel,
2009 (in preparation).
6. The author describes how the different judging forces of the soul are active
and at work in all three stages, also how then the logic of the subject opens up to
“over-logical” extensions, in “Urteilstätigkeiten . . . ,” Kassel, 2009.
7. The title of the accompanying book; edited; Badisches Landesmuseum Karl-
sruhe 2007, published; K. Theiss Verlag, Stuttgart.
8. Klaus Schmidt; Sie bauten einen Tempel; dtv München, 2008, p 1909.

15
 And yet, here lies the origin of our culture, upon which followed
the ancient empires and, finally, Europe. “To look at, to describe, to
understand,” that is now the general working plan of the research team at
Göbekli Tepe. Three separate steps! Otherwise, the unexpected would be
overwhelming. We, immediately, see that these steps basically correspond
to our three phases, provided the aim is not only to categorize the
structures of the excavated objects but also to sort out the mental state of
the humans involved.
And indeed, where anyhow would we end up, if teaching would not be
life itself?

Seeing the above as a whole, we elaborate the following

Phase I An attentive observation, The impact of single objects

active in all our senses— and impressions from outside
suffering from the world physically The WILL is challenged.

Phase II Feeling the characteristics Interaction of opinions and

of one’s own experiences– stirring of the mental state
a taking and giving FEELINGS, and EMOTIONS surge up.

Phase III A fierce dividing into pieces, An approach to the spiritual

reconnecting them powers of the world
expanding them—
Moving the thoughts around The THINKING becomes creative.

Phase II works for the short term memory, the efforts in thinking of
Phase III for the long-term one. And if the latter also open up to the mind
to make out the intrinsic character of man and world, the striving for
knowledge becomes education. Then, a stepping through the three phases
will encourage the student to want to remain committed to his world. This
would be an initial exercise for his subsequent freedom, which would
then be not to let oneself be washed over arbitrarily by pleasure, but to
find fulfillment in one’s own awareness and conscious actions so that his
freedom, later in life, exceeds the influence of school.

These three steps should grasp the entire adolescent person: body, soul
and mind. And in his soul: his thinking, his feeling and his will (Steiner).9
And always all the three simultaneously, just different combined. That
should needs to be elaborated more deeply. Not only concepts and logic
should be troubled. We did point out in the above paragraph (Section A of
this Chapter): a progression from a mere transfer of information to a step
forward in life, i.e. from abstract learning towards a real development,
transformation instead of information.

__________________
9. Rudolf Steiner, 1919 and 1921, GA 293 and 302, especially lecture III.

16
 The Geometry of Life
Toward a Science of Form

by Arthur Zajonc

Amidst nature’s ever changing raiment, we descry

what may be her greatest miracle—her constancy. Each
year, fresh, new soil, water, and light weave to form
the familiar shapes of leaf and flower. The memory of
last year’s forms silently lives through a wintery night
to unfold under warmer skies into the foliage of spring.
Nature remembers the maple’s leaf just as we do. The
miracle deepens as we turn from the kingdom of plants to
that of animals. For while leaf and stem die each fall into
the earth, the life of beast and bird is not so completely
bound to the seasons. They—and we—persist from
season to season, year to year, even though every cell
of our bodies is changing: perishing, to be recreated.
Every seven years we are filled out anew. The familiar
countenance is familiar not for its substance but for its
lineaments, its shape or gesture. In it we recognize a form
that passes through all change. As Heraclitus put it two
thousand years ago, “It is in changing that things find
repose.” The world, in constant flux, rests.
Such considerations as these have stirred philosophic
and scientific reflections since at least the time of ancient
Greater Plantain (Plantago major)
Greece. Plato raised form to the realm of incorruptible,
eternal eidos. His pupil Aristotle paired form with matter
and named them the twin principles that underlie all being Since ancient times, arithmetic and geometry divided
and becoming. Throughout the history of science, the the universe of mathematics between them. The queen,
mystery of form’s origins has been the central question. however, was geometry, who reigned unchallenged
Why are things formed as they are? Why does the pyrite from the time of Euclid until the eighteenth century.
crystal show itself as cube and dodecahedron only? Why Only during the Enlightenment, at the hands of men
do leaves spiral around the stem? Why is the heart shaped such as Lagrange and Laplace, was geometry dethroned
and structured as it is? Again and again one encounters and purely algebraic, abstract analysis put in her place.
among biologists the judgment expressed by Joseph Lagrange informs us with evident satisfaction in his
Needham that “the central problem of biology is the form Mécanique analytique that “no diagrams will be found
problem.” in this work. The methods which I expound in it demand
It is this aspect of nature, the aspect of form, that neither constructions nor geometrical or mechanical
we shall explore here, in a brief introduction to a man reasonings.”
whose discoveries open new avenues of inquiry, not only By contrast, we shall be drawn into that realm of
into the forms of nature, but into the very nature of form mathematics that speaks directly and visually of form,
itself. His particular study, and ours for the purposes of namely geometry, for our ultimate goal will be to
this article, is that of mathematics, which is concerned describe a visible and highly ordered domain of natural
with pure form, form winnowed completely from the phenomena.
corporeality that always accompanies it in the sense To date, the geometry of the living world has
world. essentially defied our attempts to imitate it. Perhaps our

17
 The forms of plants and animals have been more
resistant to precise mathematical description. True,
individuals such as the Scottish biologist D’Arcy
Thompson have in their treatment of organic forms drawn
upon geometry to establish connections between a great
variety of plants and animals. The apparatus of geometry,
however, is introduced only toward the end of D’Arcy
Thompson’s classic On Growth and Form, and only in
an elementary way. In the famous last chapter, “On the
Theory of Transformation or the Comparison of Related
Forms,” he lays systems of coordinate nets over various
animals or skeletal members. By imagining these nets as
subject to particular systematic distortions, the form of
one species can be geometrically transformed into that of
another with remarkable fidelity. The adjoining drawing
shows what I mean (figure 1). As an example, he takes the
fish Polyprion and places over it a rectangular coordinate
system and then transforms it to an alternate coordinate
system to yield the species Pseudopriacanthus altus. The
original form, that of the Polyprion, is given rather than
constructed, and thereafter is transformed point by point
via his “method of transformed coordinates.”
D’Arcy Thompson’s work is only a hint at a more
Figure 1.
general and powerful use of geometry in the study of
form in nature. As I hope to show, if we consciously
approach has been too limited in scope or too inflexible. develop geometry with the principles of transformation
The concepts we bring to bear are often bound by our foremost, we gradually move from the most elementary
very conception of space and the movements we think to more and more complex transformations. In so doing
possible within that space. To comprehend the geometry we are following the program put forward in 1872 by the
of forms in the living world, new concepts may be brilliant mathematician and pedagogue Felix Klein. His
needed, ones intimately wedded to organic phenomena. work, and especially that of his Norwegian collaborator,
The task of finding such concepts is not a simple one, Sophus Lie, provides the basis for a geometry that can
but there are paths that beckon and individuals who be used to study certain of nature’s forms. This study has
have begun to explore them. The path we are going to been pursued by several geometers, of whom Lawrence
pursue here is that of projective geometry. It embraces a Edwards is the most recent and most successful. Much
vision of space far more dynamic, far more general, than of this article concerns the discoveries he has made and
the one implicit in Euclidean geometry. By giving up the continues to make. But before we enter into Edwards’s
rigid, restricted movements of Euclidean geometry, we study of organic forms, I would like to try to give the
gradually rise to a wonderful, fluid form of geometry, reader some sense for the mobility and beauty of the
one with which we may hope to capture at least a small mathematical thought with which he works.
portion of those forms the living world displays before When asked by King Archelaos for an easier way
us. This is, after all, a world characterized by becoming, into geometry, Euclid is said to have replied, “There is no
by development, by growth and decay. It seems royal road to geometry.” The nineteenth-century German
somehow appropriate to approach the living world with mathematician Hankel was certainly thinking of Euclid
a geometry of becoming. when he called projective geometry the royal road to all
The study of geometry and pattern in the inorganic mathematics. Once one travels a way along that road,
world is an old and honorable pursuit. From the Morris Kline’s more recent sentiment quickly becomes
hexagonal forms of the snowflake to the intricate dance one’s own: “In the house of mathematics there are many
of the planets, both the static and dynamic patterns mansions, and the most elegant is projective geometry.”
of the physical universe have been systematically Yet for all that it is a mostly forgotten mansion today, and
described. so we must spend a moment or two retracing its elements.

18
 Pyrite crystals–cubic and dodecahedral.
From the editor’s collection, found in Austria

It is to the Renaissance artists of the fifteenth and is touched by each visual ray and the object is thereby
sixteenth centuries that we must turn for projective perceived. Now between the eye and the lute place a
geometry’s beginnings. The discovery of perspective screen. The rays from the eye to the lute are intercepted
brought about the extraordinary transition in painting from by the screen, forming a “perspective” view of the lute
two to three dimensions. We need only compare the spatial on the screen, as Dürer shows us. Here we have the key
arrangement and composition of medieval paintings by construction of projective geometry: projection from a
such artists as Giotto, Duccio, and Simone Martini to center (the eye) and section by a plane (the screen). In the
those of works by Dürer and Leonardo to realize that process we have “transformed’’ the object, that is, created
before 1500 space, size, and composition obeyed spiritual an image by identifying each point on the screen with
or symbolic laws, not the physical laws of perspective. each point on the lute. This is the mathematical definition
With the discovery of perspective is born the basis of a “point transformation.” By tipping the screen or
for projective geometry. Dürer’s 1525 woodcut, “The moving the center of projection, an enormous range of
Designer of the Lute,” shows clearly the fundamental transformations becomes possible. We can also take the
operation of projection and section so central to projective screen as a new object and transform it in the same way by
geometry (figure 2). To assist us in understanding this a second transformation, placing a second screen between
construction, let us imagine that “visual rays” are emitted the first one and the center of projection. The business
from the eye. The object before us, in this case the lute, of projective geometry is to investigate the laws of the
patterns that arise in space through a series of such
transformations.
When confronted by the whirl of movement
that projective transformations entail, it may
seem difficult to imagine any stable ground or
lawfulness. However, by making the transition
slowly from the simple transformations associated
with ordinary Euclidean geometry to the far more
general ones of projective geometry, we can be
led to experience an element of order that persists
throughout.
As the following discussion will show, a
triangle projected onto a surface can assume many
different triangular forms, depending on the angle
of its projection. Yet certain properties will remain
unchanged. The straight lines that compass the
Figure 2. Woodcut by Albrecht Dürer illustrates the principle of projection triangle, for instance, will always reappear as
and section. In the woodcut the artist marks the points at which the rays straight lines. Thus is “straightness” one of the
from the eye to the lute intersect the screen. invariants, or unchanging elements, of projective
19
geometry. What other elements exist such that “in triangle, not only lengths, but angles too were invariant.
changing they find repose”? By pursuing this question We then allowed the lengths of the sides to vary, yet
we come not only to the stable ground of geometry, the only in such a way that all the angles remain the same.
laws of space that govern projective transformations, In other words, the sides all grew simultaneously. Now
but also to a special set of forms, some of which will be we will change angles as well as size, thus entering
startlingly familiar. the realm of “affine geometry.” We can do this by
To learn how these special forms arise, we must replacing our original triangle with one of rubber. Such
first bring geometry into motion, for only against the deformations occur constantly in nature. Consider a
backdrop of incessant change does the concept of repose, stream of water. If you could enclose a portion of a brook
or “invariance,” gain meaning. Imagine you have before in an imaginary flexible cube, then the cube, through
you a triangular piece of paper. It can be slid easily about which the brook flows, would tip and stretch because the
the tabletop to assume any number of positions. The water nearer the brook bed moves more slowly. D’Arcy
accompanying figure shows three such positions (figure Thompson often uses such transformations as these in his
3). To move from one to the other I can push the triangle On Growth and Form.
up and to the right, and then rotate it. If I take my ruler, And so we may continue our pursuit of ever
I find the corresponding sides of the triangles are still of more flexible transformations. Though not obvious,
the same lengths. My protractor likewise shows that the certain invariants remain, even in this last class of
corresponding angles are of unchanged magnitudes. The transformations. It is rather remarkable, for instance,
triangles are, as Euclid would say, congruent. Neither that under these transformations a set of parallel lines
length nor angle has changed in the process I have just is transformed into another set of parallel lines—all the
described. Formally, one would say that lengths and more astonishing when we remember that the angles
angles are “invariant” under translations and rotations. between intersecting lines may change in general.
Here we discover one kind of motion, by noticing that One may state the invariance in another way. In plane
lengths and angles remain unchanged. geometry, two lines intersect at one point, unless the
lines are parallel. We may overcome the exceptional
character of parallel lines by defining a new “ideal”
point, namely the point at infinity. Since under affine
transformations, a set of parallel lines remains parallel,
then the point at infinity remains a point at infinity. In
projective geometry, even this invariant disappears.
Infinitely distant elements can be brought into the finite
by a projective transformation. We can easily see how
this occurs in the next set of figures.

Figure 3. A triangle can be moved from one position to another

by translation (left arrow) and by rotation (right arrow). Such A
simple transformations fall within the bounds of elementary
Euclidean geometry.
Yet clearly there are other kinds of motions or
A1
changes possible. The cubic form of a pyrite crystal is
forever the same, yet it may grow in size. That is, the
lengths of its sides will change, but without an associated
change in the angles. Here we encounter a new kind of
transformation, one that involves a change in size but not
in shape. Thus to translation and rotation we add dilation
Figure 4. A triangle, illumined by a small bulb (the center
as a possible transformation.
of projection), casts a shadow onto a plane. The shadow
We may proceed stepwise to ever freer types of represents a “projection of the triangle; point A1 in the shadow
transformations, ones that will take us beyond Euclidean corresponds to A in the original triangle. As the center of
geometry. With each step, what was before an invariant projection is gradually lowered, the apex of the shadow (A1)
enters the realm of change. In the case of our original recedes and passes to infinity, and even returns from infinity in
the opposite direction (not shown).

20
 Imagine our ever-ready triangle as standing upright Path curves can be seen as arising in the following
on a plane surface (figure 4). A small light bulb illumines way. Recall our discussion of Dürer’s drawing of the lute.
the triangle, casting a shadow onto the plane. The shadow I commented there that we could take the screen as a new
we call a “projection” of the triangle onto the plane. The object and project it onto another plane or screen by means
apex A of the triangle is projected to A1. But notice what of a second projective transformation. Clearly there is no
happens if the light is lowered. The apex of the shadow end to the number of times such an operation could be
triangle recedes farther and farther, until it vanishes into repeated, the new screen now becoming the object.
the infinite horizon. The finite has become infinite. In Now imagine three lines forming a triangle drawn onto
projective geometry, we replace the light bulb with its a thin glass plate; several points around the perimeter of
mathematical analog, a center of projection. By lowering the triangle are carefully marked with blue dots (figure 5).
the center of projection, the apex can be made not only Some distance above the glass plate is a small lamp, our
to recede to infinity, but even to return again from the center of projection. We imagine the shadow to fall on a
other side! It is as if passing to infinity in one direction second, cleverly fabricated glass plate, which turns black
brought one back from the opposite. Such is the nature exactly where the shadow falls and produces blue dots at
of a projective transformation. With it we attain a very the proper corresponding points. We have just performed
high order of freedom, yet even here there are properties the fundamental transformation of projective geometry,
and forms that remain unchanged. “Straightness” is one projection and section. (Whereas in the Dürer drawing, the
of them. Another is the property of “incidence.” That is, plane is between the object and the center of projection, in
if two lines intersect in a point before transformation, this instance the object is between the plane and the center
they will intersect in a corresponding point after of projection.) Placing the two plates together and looking
transformation. There are still other invariants, but for through them, we see two triangles, one slightly different
our purposes we can limit our treatment and turn now to from the other, the degree of difference depending on the
Sophus Lie, in whose work the idea of invariance meets particulars of the projection and section. If the second
with that of form in space, the heart of our considerations. plate was very close to the first, then the difference
can be small indeed. Thus one has two triangles in one
plane. Mathematicians formalize the process by saying
that the first plane and the second are united after the
transformation.
The process can be repeated with the object plate,
image plate, and projecting lamp all situated exactly as
before. The image plate is now projected. After the planes
are united, three triangles appear, each with its set of
blue dots. By repeating the process over and over, many
triangles appear, all with blue dots. The mathematician
would say that we have transformed the plane onto
itself many times via a series of identical projective
transformations. Now forget the triangles and attend only
to the blue dots. They will form a set of curves. Following
the trajectory of one of the dots, a point in a plane, we
have been led to a path curve. Although we have chosen
to watch only a few blue dots, clearly all the points of
the plane are brought into movement by the series of
projective transformations. Transforming the plane onto
Figure 5. itself has produced path curves. They are forms of the
Nearly one hundred years ago Lie presented a plane, structures that remain unchanged throughout the
systematic discussion of a special set of curves in two movement. By changing the angle of projection, we could
dimensions, which he termed Bahncurven or “path arrive at a different series of projective transformations
curves.” These curves, and the analogous surfaces in three and a different set of path curves.
dimensions, possess the remarkable property of remaining If we considered the entire plane, we would find that
unchanged when acted upon by repeated application of a three and only three points never move at all. They are
projective transformation.

21
completely invariant.2 All other points move along path
curves that cross only at the three invariant points of the Let us begin with the bud of the wood sorrel
plane. We can watch the points of a path curve march (Oxaliacetosella), which gives forth its small white
dutifully along behind one another, never deviating from flower during midsummer. By carefully collecting
their designated path, as if moving through the veins of several samples, mounting them for photography,
some organism. The whole plane is in movement. Yet and enlarging the prints, we can make very exact
within the flux, there abides form: The pattern of path measurements of the bud shape in profile. In constructing
curves does not evolve, although every aspect and point the corresponding path curve, we find that by placing two
of the plane (save three) are in motion! One cannot help of the invariant points at the upper and lower poles of
noticing the kinship between such form within movement the bud and following an exact mathematical procedure,
in geometry and the similar biological phenomenon. we can determine the path curve that best fits the wood
Every human cell is replaced within a seven-year span, yet sorrel bud. This can be done for many wood sorrel buds
our countenance remains, in all essentials, unchanged. The at the same stage of development, regardless of size.
beauty apparent in the contemplation of these concepts The agreement between the pure mathematical form and
and forms quickly wins the heart of anyone with the least the living one is striking. Perhaps the most immediately
affection for the elegance of pure mathematics. convincing evidence is found in the simple visual
While far more difficult to imagine, an entirely comparison of an ideal path curve with the actual form
analogous procedure can be followed in three dimensions. of the bud. Often the difference is little more than the
In this case, surfaces as well as curves fill out space with width of a pencil line—well within the precision with
forms. These are the invariant forms of space, invariant, which one can make reliable measurements on these frail
that is, under repeated applications of an identical little buds. Not all species follow path curve forms so
projective transformation. It is just these dynamic yet perfectly, but in over eighty percent of the cases studied,
invariant path curve forms that we shall discover around the plant buds are found to reflect path curve geometry
us in the plant and animal kingdoms. with remarkable fidelity.
Path curves present a rich variety of spatial forms. Correspondences can be found elsewhere in the
These include egg shapes, cones, and vortices (figure 6). living world. The spiral tendency of leaves on a stem has
Using a particular mathematical procedure, one can assign long engaged botanical and mathematical researchers.
a number, called lambda, the Greek letter l, to each shape Similar spiral configurations are to be seen in pine
that appears. For instance, positive values between zero cones and in bud formations, in the way petals arrange
and infinity are associated with various egg-shaped path themselves around the bud center. It turns out that the
curves. Negative values give all the vortex forms. The path curve surfaces of the bud are themselves covered
forms so created on the geometer’s drawing table bear a with a spiral pattern, each spiral being a path curve. Very
striking resemblance to certain forms in nature. Lawrence often one can capture the gesture of these spiral patterns
Edwards starts with the question: Is this resemblance by suitable path curve analysis. Such agreement seems
merely superficial, or does a genuine correspondence unlikely to occur by chance, for it can be found in many
exist?
During twenty years of research, Edwards has
explored the kinship between path curves and natural
forms as diverse as pine cones, plant buds, eggs, the
human heart, and developing embryos. The results of his
research and his reflection on their meaning are summed
up in his recent book, The Field of Form. In it he tells
of the blind alleys into which he wandered but also of
the moments of excitement when he saw clearly how
transformations of projective geometry touch the earth and
gather up substance to clothe their forms. We will inquire
into only two of his findings, those concerning plant buds Figure 6. Path curve forms in three dimensions resemble
and the human heart. With them the beauty of his work egglike/vorlexlike figures, depending on the manner of their
construction. The examples shown here represent path curve
will become apparent. forms differing only in the important mathematical parameter,
____________________________
2. The basis of this statement can be shown mathematically but lambda (l). If l = 1.2, the form is round and egglike. As l
is too complex to present within the confines of this article. increases, the form becomes sharper and blunter at its ends.
Negative values of l produce vortex forms.
22
Figure 7. The solid lines represent tracings of the actual living form of the ventricle as detected by an X-ray procedure. The broken
lines illustrate the path curve forms calculated to fit the actual forms. During one full heart cycle (of about 0.8 seconds’ duration), the
path curve forms change dramatically and reveal a rhythmic sevenfold process.

The left ventricle of the human heart at the moment of full diastole or relaxation (left).

The same ventricle 0.14 seconds before systole or contraction (middle).

The ventricle 0.04 seconds before full systole (right).

other biological forms, including that of the heart. One of Edwards’s most dramatic accomplishments
The heart in animal or man can be thought of as the must surely be his study of the living human heart, made
perfect or archetypal muscle. Other muscles may be possible through a kind of X-ray moving picture. Every
seen as variations of this central organ, whose whole fiftieth of a second an X-ray image was taken of the
existence is ceaseless rhythmic activity. Beginning beating heart. The technique provided a picture of the
with the detailed studies of the heart made by Scottish inside surface of the heart, the innermost of Pettigrew’s
anatomist J. Bell Pettigrew in his book Design in Nature, seven layers (figure 7). Edwards followed the changing
Lawrence Edwards worked to uncover the path curve form of the heart throughout the duration of a pulse and
form of the heart. In this instance, not only was the outer found that the movement from full expansion to full
form of the heart significant, but so were the particular contraction is in itself a rhythmic sevenfold process, one
circling patterns made by the several layers of muscle beautifully revealed through his path curve analysis.
that together comprise the heart. Pettigrew distinguished So far we have seen a remarkable congruence
seven layers. Moving from the outermost inward, the between those forms inwardly created by the human
muscle patterns change from a left-handed to a right- mind, that is, path curves, and the tangible forms of
handed spiral at the fourth layer. In addition, the left plant bud and heart. Lawrence Edwards has made
ventricle, which Pettigrew terms the “heart of the heart,” preliminary studies in several other directions, but we
changes its form as one moves from layer to layer. must leave these aside for want of space. Of much
Would it prove possible to follow these changing forms greater importance is his discovery of what he terms
as one moved inward? Indeed, by changing the positions the “pivot transformation,” which relates forms in
of the invariant points, the slightly asymmetric form of space to those of a complementary realm, one that is
the heart can be geometrically sometimes called counterspace.
reproduced. The form of the I shall conclude by spending
left ventricle also proved a few moments considering
possible of capture in a path the general character and
curve. Even the spiral gesture significance of these ideas for
of the muscle layers, like the the understanding of plant
spiral of the wood sorrel bud, forms.
finds its expression in path When visualizing a
curves, as a second set of circle, we tend to see it as a
curves that cover the surface. Figure 8. Pointwise Circle Figure 9. Linewise Circle continuous curve formed of

23
points all equally distant from the circle’s center. The one point to another, or a line to a line, Edwards uses those
circle is formed from the center out, point by point (figure projective transformations that transform a point to a line,
8). It is initially surprising to learn that there is a second or a point to a plane.
means of forming a circle. We must free ourselves from Such transformations immediately call to mind what
the habit of thinking of points as somehow more primary the quantum physicist David Bohm termed “the implicate
than the line. For in this other view, it is just the line, order,” wherein the entirety of a line can be“enfolded”
and not the point, that is used to generate a circle. The into a point. In such instances the relationship between the
construction can easily be understood by visualizing one whole and the part is clearly unusual, for the whole is in
line after the next as touching a circle. The set of lines has the part, the line is in the point!
thereby created a tangent envelope that also completely We cannot delve here into the complexities of
defines the circle (figure 9). If we generalize still further counterspatial geometry. Suffice it to say that once we
to three dimensions, the infinitely extensive, unitary, and have explored its properties mathematically, we are free
undivided plane becomes the generative entity of space. to move between space and counterspace, between point
Thus is the sphere formed no longer of points equidistant and line, by means of Edwards’s pivot transformation. Can
from a given point. Rather, planes shape the sphere, just this possibility be exploited in the study of organic forms?
as the sculptor shapes his clay with the flat of his hand. So Lawrence Edwards saw the means for doing so. Working
may the infinitely many planes of space fashion geometric with the hip of the wild rose, he was able to discover the
forms from the periphery inward. It becomes possible to beautiful “plane-wise” vortex that stands in counterspace
imagine a new kind of space, a “counterspace,” wherein behind it. Moreover, the character of the pivot
point becomes plane. transformation is such that the bud of the wild rose (itself
a path curve) mediates the transformation from vortex to
hip (figure 10). Thus are all three elements—bud, hip, and
vortex—brought into a harmonious interrelationship. Other
plant species show similar fidelity to the geometric forms
generated from his counterspatial vortex.
The discovery of the counterspatial vortex as he
describes it in his book, is a grand moment to rehearse
with Mr. Edwards. Through it he seems to approach the
nature of life itself. And now the full strength of projective
geometry becomes clear. In addition to providing
transformations that are highly mobile, it establishes,
through the development of counterspace, a new
relationship between the whole and the part.

Wild rose bud with immature seed capsule.

Working from indications for projective geometry

given by the Austrian philosopher and scientist Rudolf
Steiner, George Adams and Louis Locher Ernst sought
to develop a geometry of counterspace and to connect
it with the botanical kingdom. (Adams’s work is to be
found in his books The Plant between Sun and Earth and Figure 10. Through use of the pivot transformation, it can be
Physical and Ethereal Spaces, both coauthored with Olive shown that a path-curve vortex form mediates between the form
of the bud and the form of the seed capsule, in this instance, a
Whicher.) Lawrence Edwards, who worked with Adams, rose hip. The seed-bearing organ of the plant is usually not a
has continued these efforts. In particular, he has explored path curve, but its form can be delineated with great accuracy
a novel class of projective transformations that involves a by the pivot transformation.
change in space element. That is, instead of transforming

24
 In his work, Edwards is not only concerned with Suggested reading:
describing mathematically the natural forms he studies,
but also tries to find the origins of these forms. He has On Growth and Form, W. D’Arcy Thompson, abridged
not, as do most contemporary researchers, sought to edition, John T. Bonner, editor, Cambridge: Cambridge
find them through molecular biology, but instead by University Press, 1961.
developing a science of form. When reading about what
he terms “fields of form,” one is reminded of the great The Field of Form, Lawrence Edwards, Edinburgh:
English physicist Michael Faraday, developer of the field Floris Books, 1982.
concept. The fields in Edwards’s work, however, are
conceived not as physical forces but as insensible, ideal The Geometry of Life, Lawrence Edwards, New York:
forms that are nevertheless imaged in the tangible shapes Proceedings, The Myrin Institute, in press.
of the living world. He is convinced, as was Goethe,
that nature creates her infinite forms according to a plan, The Plant between Sun and Earth, George Adams and
according to an Idea. Goethe wrote: “The Idea is eternal Olive Whicher, Boulder, Colorado: Shambhala,1982.
and unitary .... All that of which we become aware and of
which we can speak are only manifestations of the Idea.” “Projective Geometry,” Morris Kline, Scientific
The Idea is not to be identified with a purely material American, Volume 192 (1), pages 80–86, 1955.
or molecular basis—the building blocks of life. Rather,
we should attend to the forms themselves. In writing Elementary Mathematics from an “Advanced Standpoint:
of biology, Aristotle made use of an analogy, that of a Geometry,” Felix Klein, New York: Dover Publications,
house: 1948.

The object of architecture is not bricks, mortar, The Waldorf Science Newsletter was given permission to
or timber, but the house; and so the principal print by the author. The article was first printed in Orion
object of natural philosophy is not the material Magazine, from whom permission was also obtained.
elements, but their composition, and the www.orionmagazine.org.
totality of form, independently of which they
have no existence. Arthur Zajonc is associate professor of physics at
Amherst College, where he teaches physics and the
Lawrence Edwards has attended to the composition history of science. His research interests include laser
and form of organic nature as few before him and has spectroscopy and atomic physics.
shown that through careful observation of nature and the
free activity of human thinking, the Ideas that seem to
touch nature may also unfold in the human mind. When
Kepler brought forth the great laws of planetary motion,
he said he had stolen the golden vessels of Egypt. Kepler
heard through these geometric laws the harmony of
the spheres, and his decades of labor were requited.
Lawrence Edwards shares Kepler’s vision of the world
as created and formed according to an image, fashioned
not simply by a field of forces, but rather in accord with a
“field of form.”

25
 Phenomenology:
Husserl’s Philosophy and Goethe’s Approach to Science

by
Michael Holdrege

Introduction
extensa).
It may seem surprising that Goethe’s scientific meth-
Husserl saw clearly that once a distinction between
od and the philosophy of Edmund Husserl, which was
mind and nature is posited, the question must inevitably
developed half a century after Goethe’s death, would be
arise as to how the two are related. He considered the
grouped under the same heading: phenomenology. To
shift in focus that this question brought with it had led
show the justification for this and to outline the nature
modern philosophy—beginning with Descartes—down
of the profound project that Goethe and Husserl shared
an unproductive path of inquiry. In his quest to establish
will be the task of this article.
a firm, irrefutable foundation for knowledge, Descartes
(1968) had employed the “method of doubt,” which
Husserl’s Phenomenology and the Cartesian Split involved rejecting all previous opinions that allowed for
Husserl saw his phenomenology as addressing a even the slightest incertitude. Through this process of
crisis that faced the western sciences. In his last great methodologically doubting, Descartes was led to ques-
work, The Crisis of European Sciences and Transcen- tion even the apparent reality of the physical world and
dental Phenomenology, Husserl spoke of how positivis- his own body. The only certainty that remained for him
tic science—blinded by the prosperity it produced—had was that he, the doubter, existed: Cogito, ergo sum (I
reduced the idea of science to a focus on purely factual think, therefore I am). From this point of certainty, Des-
data. This form of scientific endeavor, he maintained, cartes then deduced the necessary existence of a perfect
turns away in indifference from the questions that are God, who—because perfect—would not deceive him.
decisive for a genuine humanity. All valuative ques- Therefore, the reality of the eternal world as it appeared
tions, questions of the meaning or meaninglessness to him must be guaranteed.1 Nonetheless, two distinct
of human existence, were banned from the realm of worlds still presented themselves to Descartes. First,
scientific endeavor. According to Husserl, this form of there is the res cogitans: the thinking dimension that one
science “strives for and achieves nothing but ‘theoria’. perceives within and which can be known with inner
In other words, man becomes a nonparticipating specta- certainty. Entirely separate and fundamentally different
tor, surveyor of the world” (Husserl 1970, p 285). from this is the res extensa—the extended substance: the
Husserl’s efforts to return science to “the things outer “objective” world of the physical universe (Des-
themselves” were held by many to be so significant that cartes 1968; Husserl 1970, 1982; Tarnas 1991; Brady
the historian of philosophy Hans Stoerig—speaking in 1998).
the late 1970s—called Husserl one of the two most in- Using Galileo’s distinction between primary and sec-
fluential philosophers of the 20th century (Stoerig 1978). ondary qualities, Descartes concluded that the scientist
After all, Husserl’s work had a fundamental impact should not rely on the qualitative secondary qualities
on such prominent philosophers as Heidegger, Sartre, (color, sound, taste, etc.) that are merely manifestations
Recoeur, Scheler, Gadamer and Merleau-Ponty. Central
1. It should be noted that with the deduction of a perfect God
to Husserl’s project was the overcoming of the split who would not deceive him, Descartes fell back into the same
erected by Descartes between our inner life of mind (res medieval practice of deductive reasoning that he was attempt-
cogitans) and the outer world of extended things (res ing to overcome.

26
of the “subjective” organization of our senses (as part of Although it was Thomas Kuhn’s now famous book on
the res cogitans), but should address only those primary The Structure of Scientific Revolutions that brought the
qualities (duration, shape, number, extension) that can decisive paradigm shift in the philosophy of science to
be analyzed quantitatively and “objectively” because general awareness,3 the approach of Yale philosophy pro-
they belong to the outer world of the res extensa. This fessor N. R. Hanson4 relates more directly to the context
assertion of the essential dichotomy between thinking of this article. Hanson’s often quoted words that “there is
substance and extended substance (between secondary more to seeing than meets the eye” encapsulate a central
and primary qualities, respectively) led to the ordain- theme in his analysis of the nature of perception. In Pat-
ing of mechanics—a form of inquiry permeated with terns of Discovery (1958), for example, Hanson discusses
mathematics and based on the “eternal” testing through the familiar Perspe cube (Figure 1).
experiment of the “internally developed” hypothesis—as
the primary form of scientific endeavor by which the
physical universe could be understood (Descartes 1968;
Husserl 1970, 1982; Tarnas 1991; Brady 1998).
Husserl (1970) considered this dualistic basis for
modern science to be naïve, particularly if one took into
account Kant’s analysis of sense perception as developed
in his Kritik der reinen Vernunft (1781). In this work,
Kant argued that our experience of the sense world is not
actually based on direct sense perception alone. The ob-
jects of experience point to a hidden mental accomplish-
ment of which we are normally not aware. According
to Kant’s analysis, we do not passively receive sensory
input, but actively integrate and structure it. Once this is
realized, Galileo’s so-called primary qualities no longer
appear to be so “objective”; they cannot be abstracted
from the formulaic activity of the mind and thus do not
“stand alone” (Kant 1781, 1783; Kemp 1968; Husserl Hanson asks if all individuals who see this figure—
1970; Tarnas 1991; Brady 1998). and who, if they are requested to, are able to produce
This insight did not escape modern philosophers of essentially identical drawings of this figure—actually
science (Brown 1977), even if they addressed the ques- see the same thing. Although the tiny inverted images
tion of the theory-laden nature of perception quite dif- on each viewer’s retina will be virtually the same, some
ferently from Kant. Before considering Husserl’s funda- will see it viewed from above, others from below, and
mental concept of intentionality—which provides a way still others as a kind of polygon-like gem. A fourth group
of avoiding the Cartesian/Galilean conundrum—a brief might see only lines criss-crossing in a plane, and so on.
look at one of the key contributors to the “new view” of Using many examples of this sort (such as Koehler’s
science will be helpful. famous “Goblet and Faces” drawing, Toulouse-Lautrec’s
old and young woman picture, etc.), Hanson makes clear
N. R. Hanson and the New View of Science that—although nothing essential changes at the level of
optics or physiology—people see different things! What
Science in the first half of the 20th century was
changes is not the sensory data as such, but the organiza-
dominated by logical empiricists, who saw the system
tion of what one sees. Organization is not an element in
of postulates that made up a theory as hovering freely
the visual field, however; it itself is not seen as are lines
above the plane of empirical facts, whereas these facts—
or colors. In a related sense, Hanson points out, the plot
since they could be known independently of any theory
—guaranteed the objectivity of science (Brown 1977). 3. Amrine (1998) remarks that the influence of Kuhn’s book
Beginning in the 1950s, this view came under sustained was so profound that one is tempted to divide the history of the
philosophy of science in B.K. and A.K.—“before Kuhn” and
attack by a diverse group of philosophical thinkers.2
“after Kuhn.”
2. N. R. Hanson, Michael Polanyi, Stephen Toulmin, Paul Fey- 4. Hanson—in the words of Amrine (1998)—“fired the open-
erabend and Thomas Kuhn wrote pivotal works that founded ing shot” in this revolution with his classic work Patterns of
this new approach (Brown 1977). Discovery, 1958.

27
is not another detail in a story, nor is the melody merely conscious of something, it can no more doubt of what it
one more note in a song. Yet in the absence of plots and is conscious than it can doubt that it is conscious. The
melodies, the elements of a story and the notes of a song indivisible unity between the conscious mind and that of
would not hang together. In a similar manner, the organiz- which it is conscious overcame for Husserl the Cartesian
ing activity that lets the cube become a cube cannot to bifurcation. The dualist dilemma that had faced western
be seen. The following words of Charles Babbage (1830, philosophy ever since Descartes was thus not to be over-
cited in Hanson 1958, p 184) illustrate vividly how this come by eliminating one of the two categories—subject
influences the process of scientific research: or object, mind or body—but by recognizing that that
distinction itself6—even if it informs every individual’s
An object is frequently not seen from not knowing daily experience—is problematical. Husserl recognized
how to see it, rather than from any defect in the that every cogito intends a cogitatum.7 Consciousness
organ of vision…[Herschel said] I will prepare itself is unified, although within this unity two poles
the apparatus, and put you in such a position that can be identified, the cogito and its content (Stewart and
[Fraunhofer’s dark lines] shall be visible, and yet Mickunas 1974; Brady 1998; Husserl 1999).
you shall look for them and not find them: after Even though experiences can be of very different
which, while you remain in the same position, I kinds, Husserl demanded that each experience be taken
will instruct you how to see them, and you shall in its own right as it presents itself to consciousness (as
see them, and not merely wonder you did not see it shows itself). Husserl’s phenomenological method
them before, but you shall find it impossible to expanded the meaning of “experience” beyond sense ex-
look at the spectrum without seeing them. perience alone to include anything of which one is con-
scious. We can be aware of many different things, such
Different ways of seeing lead to different scientific re- as mathematical entities, natural objects, moods, feel-
sults. In Hanson’s understanding, then, we must recognize ings, values, desires and much else. Husserl called such
that all observation undertaken in the name of science experiences phenomena and saw phenomenology as the
is “theory-laden.” This was the fundamental insight that systematic investigation of the content of consciousness.
led to a revolution in the philosophy of science (Hanson This project required an awareness, however, that differ-
1958; Brown 1977; Brady 1998; Amrine 1998). This ent kinds of content—such as mathematics and values,
insight that eternal reality can no longer be understood as for example—have different kinds of reality, none of
divorced from the mind also provided Husserl (decades which are reducible to the others. Husserl considered
before) with a starting point free from the Cartesian split.5 anything of which one is conscious to represent a legiti-
mate field of inquiry, and that each phenomenon must be
taken as it is, without imposing upon it a methodology
Husserl and Intentionality taken from elsewhere that is inappropriate to that par-
Although Husserl emphasized the role that conscious- ticular subject matter. It would be nonsense, for example,
ness plays in “constituting” the world, he did not con- to investigate mathematical questions by the same means
clude with Kant that beyond the—from consciousness that one investigates creatures such as birds and bees,
co-shaped—phenomenal world, there exists a deeper or feelings such as affection. The acts of consciousness
level of reality—the thing-in-itself (the Ding-an-sich)— and their objects are very different in all these cases8
which is unknown and unknowable to us. Husserl was
able to avoid such dualism, as well as the Cartesian ver- 6. In everyday life, we do not notice the organizing activity of
our intentionality. We bring to consciousness only the results
sion, with the help of one central concept: intentionality. of that activity—“I see the Perspe cube from below”—rather
Consciousness, as Husserl had learned from his teacher, than the act of composition itself. Although my internal act
Franz Brentano, is always directed toward an object—it does not create the perception of the cube—I cannot see it as
is consciousness of…. For Husserl, this consciousness a sphere, for example—it shapes it from a particular point of
was inseparable from its object and hence not solely view.
“a thinking thing” (res cogita) as it was for Descartes. 7. “[T]he word intentionality signifies nothing else than
this universal fundamental property of consciousness: to be
Since consciousness always has an object, is always conscious of something; as a cogito, to bear within itself its
cogitatum” (Husserl 1999, p 33).
5. It is also fundamental for an understanding of Goethe and 8. It would go beyond the scope of this paper to explore the
the way in which he attempted to “organize” his perceptual method of “phenomenological reduction,” or “bracketing,”
activity so that it harmonized with (corresponded to) the kind of that Husserl applied to the pre-philosophical “natural
phenomena he was studying.
28
(Husserl 1962; Stewart and Mickunas 1974). A rigorous his views on morphology,9 as well as one way that his
science in Husserl’s sense would, then, pay close atten- scientific approach can be applied to the study of plant
tion to the kind of thinking (organizing activity) that it life.
applies to various realms of phenomena. Its goal would Goethe recognized the value of a detailed analysis
be to find a close fit (correspondence) between the phe- of the anatomy and chemical make-up of living organ-
nomena under examination and the intentional activity isms, but was convinced that a one-sided emphasis in
that beholds and investigates them. this direction (an exclusive application of this form of in-
tentionality) made one blind to that which distinguishes
Goethe’s Phenomenological Approach the living from the nonliving—in particular the fact that
within an organism the totality is active in every organ.
Husserl’s double perspective that a) takes the phe-
This is evident at death, when this all-parts-permeating
nomena seriously as they appear to us—as they show
principle disappears and “dis-integration” sets in. Goethe
themselves—and that b) finds for each field of inquiry
characterized the one-sided redutionistic approach in
a methodology—a way of thinking—appropriate to it,
Faust (1971, verses 1936–1939):
brings us back to Goethe, for whom these two tenets
were fundamental. Goethe’s approach to the natural
world was characterized by Rudolf Steiner, the first edi- Who wants the living to know and describe,
tor of Goethe’s natural scientific writings, in the follow- Seeks first the spirit from it to drive.
ing way: Now has he—indeed—the parts in hand,
Lacks merely—alas—the spiritual band.
Goethe’s view of the world is the most many-
sided imaginable. It proceeds from a central In Goethe’s view, the overall coherence-creating
point, which rests in the unified nature of the principle within the organism cannot be comprehended
poet, and it always brings to the fore that side by detail-analysis alone. Morphology in his sense in-
which corresponds to the nature of the object. volved shifting one’s intentionality from a predominant-
The unity of the activity of intellectual forces ly analytical (reductionistic) mode to a more synthetic or
lies in the nature of Goethe; the temporary holistic one10 that attempts to grasp the overriding unity
form of that activity is determined by the object of an object as it develops both spatially and temporally.
concerned. Goethe borrowed his manner of For Goethe, the analytic-synthetic contrast was also re-
observation from the eternal world instead of flected in the German expressions Gestalt, which intends
obtruding his own upon the world. Now, the the more fixed and finished final forms of an organism,
thinking of many men is effectual only in one and Bildung, which refers more to the dynamic, forma-
definite way; it serves only for a certain type of tive processes that lead to the fixed Gestalt (Steiner
object; it is not unified, as was Goethe’s, but only 1968; Naydler 2000).
uniform… All sorts of errors arise from the fact Goethe’s efforts were strongly directed toward de-
that such a way of thinking, entirely appropriate veloping the capacity to apprehend the plant not only in
to one type of object, is declared to be universal. the spatial jutaposition of its organs, but in the way those
(Steiner 1968, p 7) forms constantly transform—“changing ever, the same
forever.” He, himself, put it best:
Rather than summarizing how Goethe’s many-sided
approach expressed itself in a wide range of phenome- In observing objects of Nature, especially those
na—for Goethe’s pioneering work includes studies in the that are alive, we often think the best way of gain-
realms of geology, meteorology, anatomy, zoology, and
optics, among others—this paper will briefly consider 9. Goethe coined the term morphology and is recognized as
the founder of modern comparative morphology (Naydler
2000).
attitude” that accepts the natural world in an unquestioned 10. This distinction can also be found in the German philoso-
way. The reduction involves calling into question all of one’s phy of Goethe’s day, which followed Kant in distinguishing
presuppositions about the world. It is reminiscent of Descartes’ the intellect (Verstand), or normal analytical forms of thought,
method of doubt—and is undertaken in a similar spirit—but from the capacity of reason (Vernunft), which referred to
it leads, in contrast to Descartes’ approach, to a non-dualistic higher intuitive or synthesizing insight (Steiner 1968; Naydler
phenomena-based relationship to the world (Stewart and 2000).
Mickunas 1974; Husserl 1982).
29
 ing insight into the relationship between their inner How does such an emphasis on Bildung and dynamic
nature and the effects they produce is to divide play itself out when faced with the concrete Gestalt of
them into their constituent parts. Such an approach the plant? Instead of demonstrating this using Goethe’s
may, in fact, bring us a long way toward our goal. own writings, this paper will employ an example of leaf
In a word, those familiar with science can recall metamorphosis typical of the approach developed by Ger-
what chemistry and anatomy have contributed hard Grohmann and Jochen Bockemuehl,11 two pioneer
toward an understanding and overview of Nature. practitioners of Goethe’s phenomenological method in the
But these attempts at division also produce many latter half of the 20th century.12
adverse effects when carried to an extreme. To be
sure, what is alive can be dissected into its compo-
nent parts, but from these parts it will be impos-
sible to restore it and bring it back to life….

The Germans have a word for the complex of

existence presented by a physical organism: Ge-
stalt (structured form). With this expression they
exclude what is changeable and assume that an
interrelated whole is identified, defined, and fixed
in character. But if we look at all these Gestalten,
especially the organic ones, we will discover that
nothing in them is permanent, nothing is at rest
or defined—everything is in a flux of continual
motion. This is why German frequently and fit-
tingly makes use of the word Bildung (formation)
to describe the end product and what is in pro-
cess of production as well. Thus in setting forth a
morphology we should not speak of Gestalt, or if
we use the term we should at least do so only in Figure 2. Leaves taken from the common buttercup
reference to the idea, the concept, or to an empiri- (Ranunculus acris).
cal element held fast for a mere moment of time. Ordered from bottom of stem (lowest left) to top (bottom right).
When something has acquired a form, it metamor- Downloaded from
phoses immediately to a new one. If we wish to www.hyattcarter.com/goethe’s_way_of_seeing.htm
arrive at some living perception of Nature we our-
selves must remain as quick and flexible as Nature
When one observes a series of foliage leaves such as
and follow the example she gives (Miller 1988, pp
those in Figure 2, it is striking that—despite considerable
63–64).­
differences between individual leaves—the transforma-
tion from one to the next is gradual enough to give the
Since the plant world presents itself to us as a realm impression of overall unity. What Nature presents to us
of ongoing transformation and change, Goethe attempted are individual leaf forms (Gestalt). If we focus our at-
to meet it with an understanding that is “as quick and tention (intentionality) on those individual forms them-
flexible as Nature.” Cassirer (1950, pp 138–139) charac- selves, we have difficulty identifying a single form—or
terized Goethe’s unique approach to the organic world as
follows: 11. Grohmann’s two-volume work, The Plant (1974), and
Bockemuehl’s numerous publications—see, for example, Bock-
emuehl 1998—have stimulated a great deal of research over the
[Goethe] did not think geometrically or statically, past 40 years into the nature of plant metamorphosis.
but dynamically throughout. He did not reject 12. In this section I follow Ron Brady’s (1987) illuminating
permanence, but he recognized no other kind than analysis of leaf metamorphosis in light of the concepts Bildung
and Gestalt. His paper was first read at a symposium sponsored
that which displays itself in the midst of change….
jointly by the departments of Germanic Languages and the
Form itself belongs not only to space but to time as History of Science at Harvard University and the Boston Col-
well, and it must assert itself in the temporal. loquium for the Philosophy of Science.

30
schema—that reveals much about the entire series. Even cutting off an individual leaf from the plant as a whole
the simplest schema—such as one based on the three- results in its withering and death, so does considering
part leaf at the lower right—tells us little about the more the leaf merely as Gestalt—statically, in isolation—cut
complex forms. If we intend, on the other hand, a con- it off from its true context: the unfolding sequence out of
tinuous movement from one to the next, then an impres- which it arises. Attending to the parts of the plant as Bil-
sion of gradual modification arises. By intending a dy- dung, by contrast, allows the form to be grasped dynami-
namic context for the individual forms, a lawful relation cally, as a moment in the process of becoming (Steiner
between them becomes apparent. Although the empirical 1968; Brady 1998).
forms appear separately, we can dissolve that condition
in our minds by shifting our intentional focus from static
Conclusion
particulars to movement, which allows us to detect a re-
lationship that unites the individual forms. Brady (1987, Why does this view of organic nature appear so
p 278) puts an even finer point on this insight by inviting inaccessible to mainstream scientific thinking? One
the observer to compare two leaves from different zones reason is certainly that the prevailing mode of scientific
of the series—for example the second and the second to observation arose historically in the realm of physics,
last leaves—in isolation. Seen side-by-side they appear which calls for a different form of intentionality than that
quite dissimilar. On the other hand, if one moves through suited to the organic world. Since the advent of modern
the series “backward and forward” until it becomes a science, the focus of most researchers has been on that
continuous movement—as Goethe (1949, p 35) would which has already become (Gestalt), a level of existence
have done—then a relationship becomes apparent well suited for investigation with analytic thought forms.
despite significant differences between the individual The form of intentionality that this entails is firmly
leaves. The separate leaves now appear to us as different anchored in the mindset of the modern age—it signifies a
phases of one dynamic series (Brady 1987).13 deep-seated habit in our way of engaging Nature. A way
of thinking that is better suited to grasping transforma-
Further reflection reveals that although the individual
tion and change in a holistic manner is still—almost 160
forms provide the basis for intending the movement
years after Goethe’s passing—quite new and unusual to
between them, they themselves cannot produce the
us. Moreover, it requires significantly more intentional
movement—for no individual Gestalt as such is able
effort. The willingness to make this effort will first arise,
to generate the transformation to the next form. On the
I believe, when the role that our own consciousness
other hand, the intended movement is able to reveal a
plays in the coming into being of perceptual experience
unity within the individual forms that is not apparent
is more widely seen and appreciated.13 For that reason,
when they are viewed statically. One grasps the individ-
Husserl and Goethe belong together. What Goethe devel-
ual Gestalt as something like a frozen moment (in space)
oped through the concrete study of Nature—in the field,
of a process of becoming (Bildung) that unfolds over
so to speak—received a significant foundation through
time. When forms are intended in this dynamic way, they
Husserl’s efforts to overcome Cartesian/Galilean dual-
are no longer independent and complete in themselves.
ism.14 Husserl’s insights into the nature of intentionality
Every form calls for a preceding form and for one that
provide the foundation for a differentiated phenomeno-
follows—a before from which it arises and an after into
logical understanding of the world as it “shows itself”
which it develops. Each individual leaf (Gestalt) finds its
to human consciousness. It provides the groundwork for
full expression only through the continuous transforma-
understanding the significance of Goethe’s “Bildung-
tion of the series. Each image is thus representative of all
oriented” approach to the plant world,15 an approach
the others and yet incomplete without them.
Viewing the plant in this dynamic manner is ap- 13. Even though Hanson (1958) and others shed a bright light
on this relationship over a half century ago, it still appears to
propriate because individual leaves are, in fact, parts of
be largely ignored in the day to day practice of the biological
a living whole that—in contrast to the nonliving—pos- sciences.
sesses an internal potency for growth and change. What 14. Albeit those investigations were undertaken without any
exists in the seed as mere potential unfolds in space and direct consideration of Goethe’s approach to natural science.
time when suitable conditions present themselves (light, 15. To reiterate what was said earlier, Goethe’s scientific
water, etc.). Furthermore, the parts of this living whole method is very differentiated in the sense that it attempts
to approach different realms of phenomena with a form of
unfold in a specific sequence. The plant as such is not a
intentionality fitting to each. This essay has limited its focus,
finished entity, but a transition of states, one into another. however, to the plant alone.
Its “way of being” is one of constant becoming. Just as

31
that attempts to activate our thinking in a way that is “as
quick and flexible” as the plant that it beholds.

Literature Cited
Amrine F. 1998. The metamorphosis of the scientist. In Grohmann G. 1974. The Plant. NY: Biodynamic Farming
Seamon D, Zajonc A, editors. Goethe’s Way of Sci- & Gardening Assoc, p 209.
ence. Albany: State Univ. of New York, pp 33–54. Hanson N. 1958. Patterns of Discovery. Cambridge:
Babbage C. 1830.  Reflections on the Decline of Science Cambridge Univ. Press, p 241.
in England and on Some of Its Causes, London: B. Husserl E. 1962. Ideas, General Introduction to a Pure
Fellowes and J. Booth. Cited in Hanson 1958. Phenomenology. Transl. Gibson B. New York: Col-
Bortoft H. 1996. The Wholeness of Nature. Hudson, NY: lier Books, p 446.
Lindesfarne Press, p 407. ____________. 1970. The Crisis of European Sciences
Bockemuehl J. 1998. Transformation in the foliage and Transcendental Phenomenology. Transl. Carr D.
leaves of higher plants. In Seamon D, Zajonc A, edi- Evanston: Northwestern Univ. Press, p 405.
tors. Goethe’s Way of Science. Albany: State Univ. ____________. 1999 (12th impression). Cartesian Medi-
of New York, pp 115–128. tations. An Introduction to Phenomenology. Trans.
Brady R. 1977. Goethe’s natural science. Some non- Cairns D. Dordrecht: Kluwer Academic Publication,
cartesian meditations. In Schaefer K, Hensel H, p 157.
Brady R, editors. Toward a Man-Centered Science. Kant I. 1781. Kritik der reinen vernunft. Stuttgart: Rec-
Mount Kisco, NY: Futura Press, pp 137–165. lam, p 1011.
____________. 1987. Form and cause in Goethe’s ____________. 1783. Prolegomena zu einer jeden
morphology. In Amrine F, Zucker F, andWheeler H.
künftigen metaphysik. Hamburg: Felix Meiner Ver-
Goethe and the Sciences: A Reappraisal. Dordrecht:
lag, p 200.
Kluwer Academic Publishers Group, pp 257–300.
Kemp J. 1968. The Philosophy of Kant. NY: Oxford Uni-
____________. 1998. The idea in nature: rereading
versity Press, p 130.
Goethe’s organics. In Seamon D, Zajonc A, editors.
Goethe’s Way of Science. Albany: State Univ. of Miller D. 1988. Goethe’s Scientific Studies. NY: Surkamp,
New York, pp 83–111. p 344.
Brown H. 1977. Perception, Theory and Commitment, Naydler J. 2000. Goethe on Science. Edinburgh: Floris
the New Philosophy of Science. Chicago: Univ. of Books, p 141.
Chicago Press, p 203. Steiner R. 1968. A Theory of Knowledge Based on
Bubner R. 1981. Modern German Philosophy. Cam- Goethe’s World Conception. Trans. Wannamaker O.
bridge: Cambridge Univ. Press. p 223. NY: Anthropsophic Press. p 131.
Cassirer E. 1950. The Problem of Knowledge. New Ha- ____________. 1988. Goethean Science. New York: Mer-
ven: Yale Univ. Press, p 334. cury Press, p 278.
Descartes R. 1968. Discourse on Method and the Medi- Stoerig H. 1978. Kleine weltgeschichte der philosophy.
tations. Trans. Suttcliffe F. London: Penguin, p 188. Frankfurt: Fischer Verlag, p 713.
Goethe J. 1949. Geschichte meines botanischen studi- Stewart D. and Mickunas A. 1974. Exploring Phenom-
um. In Goethes naturwissen-schaftliche schriften. enology. Chicago: ALA. p 165.
Steiner R, editor. Bern: Troler Verlag, pp 61–84. Tarnas R. 1991. The Passion of the Western Mind, NY:
____________. 1971. Faust. Stuttgart: Phillip Reklam. Random House, p 544.

32
 FIRST APPROACH TO MINERALOGY

by

Frederick Hiebel

Rhodochrysite specimen
from the editor’s collection.
Found in Colorado.

In one of his lectures, at the opening of the Waldorf School, Rudolf Steiner
told his teachers that the age of twelve is an important turning point in a child’s
development. We have all noticed that just before and at about the age of puberty
children gradually lose their grace of movement. They can become clumsy and
spasmodic in the use of their limbs, their manners and, even their facial expressions.
Their long arms hang awkwardly in sleeves which are always too short. In fact, at
this phase of life, we can say a child is actually under the domination of his bony
structure, his skeleton. Parallel with this physical phenomenon, there awakens within
the child a more independent attitude toward his environment. His judgment of
parents and teachers becomes more critical.
This is the age at which a child should learn the fundamentals of physics and
approach, for the first time, abstract arithmetic in algebra. It is also at this time,
while under the influence of his own bony structure, that a child can best learn about
the “bony” structure of the earth.
Nature Study in a Waldorf/Steiner school begins in the fourth grade with “Man
and Animal,” and continues in the fifth with botany. During these two years the
natural science classes, which always keep the human being in the center of his
natural surroundings, work their way closer and closer to the earth until, in the sixth
grade, we reach the study of geology and mineralogy.
Steiner advised the widest sort of approach toward the study and understanding
of nature as a whole and of minerals in particular. Following his valuable indications
we start with geography, and in close connection with geographical teaching the
children learn to discriminate between a primitive mountain range (granite) and a

33
limestone range. For a class in New York City it seems natural to start with a study
of the geological formation of Manhattan’s own granite foundation. The countless
subterranean ‘tunnels’ of the subways and the iron foundations of the highest
buildings on earth are possible only because of the foundation provided by this solid
ground. Even the inner vigor of this city’s inhabitants appears to depend upon these
layers of granite.
It is important that children should learn and actually grasp the fact that granite
originated from the oldest era of our earth’s development and is for that reason
the firmest and strongest of stone formations. Countless ages ago granite was a
vast mass of fiery-fluid substance which cooled slowly while other rocks formed a
covering over it. During later ages these overlying rocks were destroyed by water
and glaciers until granite appeared as the axis of the highest mountains.
In telling of these slow, majestic changes the teacher should try to arouse
a feeling of “devotion towards the oldest altar of the world’s creation.” Let the
children dwell upon these words from Goethe.
The children draw and paint the stages of the earth’s development with pleasure
and a sense of discovery. Through poetry, too, a feeling for the earth’s wonders and
hidden beauties can be brought forward.

From placid mountain brow, so solemn, old,

the mysteries of days long fled unfold.
There in time’s far-distant dawning morn
the word of worlds in trinity was born.
Its first faint echo, rising from this hour,
bespeaks primeval harmony of power
and strives in white of quartz and dark-hued gneiss
and golden mica like rosin bound in ice
to spread forth pure the altar-table here,
presented long ago to that first year.

The granite mountains are the products of fiery eruption. The opposite of the
granite mountains are the limestone ranges which were created by sediment, uplift,
and erosion. Fire and water as the primeval forces in the development of our earth’s
surface are understood by children without giving them theories. They seem able to
grasp how creative and divine forces were at work much as in olden times Vulcan
and Neptune were understood when spoken of in connection with the earth’s
development.
Here is the place for a sketch or diagram of a volcano and the children draw the
different layers of the earth’s surface descending from sandstone, limestone, coal,
devon, gneiss, to granite and the magma—the fiery original foundation of earth.
We soon find out that our whole subject can be divided into four parts: rocks,
minerals, metals, and gems. Rocks contain many minerals and they in turn are
composed of numerous chemical substances which often contain metals. Minerals
and metals can appear on a higher level of development under the special condition
of crystallization. Crystals and gems are the rarest and noblest forms of the solid
element. And so we lead the children from the description of the rocks and minerals
to that of metals and crystals, stressing the point that within these minerals the
architectural plan of the earth has become far more spiritual and refined than it is in
the crude forms of rocks and minerals.
As we always try to proceed from the whole to the details, from the original
to the descendants, quartz appears as the primeval phenomenon of all mineral
substances.
34
 As honey held within the white-brown wax
Was gathered gladly in the day-long task,
So one day with a hundred thousand suns
Saw quartz, now hid in mountain-deeps, outspun.
Beside sun-radiance of quartz appear
The many other stones but dark and drear.
For this outshines in age and naturewise
What in the other stones imprisoned lies.
It is the oldest child of light, first-born.
Reminding us how blinded we are grown.

Metals are purified ores. The obvious place to begin this study is with gold, for
gold is the archetype of all metals. In teaching about gold we should never neglect to
speak of the important part gold has played in all legends, fairy stories, and myths,
delved from an age of mankind which we call the Golden Age. Then we speak of the
unique qualities of gold in regard to its malleability, ductility, flexibility, its quality of
being insoluble. We can beat gold as thin as 1/250,000 of an inch. A piece of gold less
than the size of a pinhead can be drawn out into a wire 500 feet long. That is its high
ductility. Finally, it never loses its color and splendor: It does not tarnish.
We must always find the threads which lead from the human being to the natural
world. When we describe these five qualities of gold which make it the “king” of all
metals, we can draw parallel lines with the five most important qualities inherent in
everyone who wants to become a spiritual “king”—that is, a person who knows first
of all how to lead himself. Can we not apply these five qualities to our inner and moral
self-education in relation to guidance of thoughts, strengthening of will, calmness of
emotions, positiveness in judgment and impartiality towards life? (See the fundamental
writings of Rudolf Steiner.) In the Middle Ages there lived people who ‘searched’ for
gold in this way—the true students of Spiritual Science. They did not want to “make
gold” in the superficial sense of the word, but to develop these five “golden” abilities
for attaining their “spiritual kingdom.” This is the underlying significance of gold in all
fairy stories and legends. To the children, of course, the teacher never mentions these
facts or comparisons in literal form, but this connection must live as an inner impulse
of conviction and enthusiasm within his own mind.
Such a presentation of the subject, including as it does a moral and uplifting
undercurrent, prevents a one-sided, materialistic idea about gold and, by indirection,
becomes a living force in the child’s mind. It reaches the child through the wisdom of a
trusted teacher, leaving an impression more lasting than would the mere restatement of
fact out of a textbook.
It is clear that after this the study of silver, copper, and iron is easier. We point out
that historically gold was the first discovered metal. Silver and copper were used later,
and iron does not come into use until the first millennium bc. Iron is the true Roman
metal. Lead was discovered still later than iron (about 500 bc). We may conclude the
study of metals by speaking of one of the very latest, such as radium in connection with
the tremendously mysterious X-rays.
In the final chapter of our mineralogy, we touch upon crystals and gems. Here
we look at the greatest works of art which the kingdom of the minerals can produce.
Crystals and gems consist of the same products as the rocks and minerals, but in them
the art of building up the earthly element has reached its highest perfection. Crystals
have the most amazing geometrical forms, frozen into stone after an eternal law of the
world. The ancient Greeks said that “God is a geometrician,” and surely crystals and
gems are products of this divine geometry. Does it not seem, in precious stones, as
though the splendor of the stars had been brought down into the earth itself?
35
 Familiar to most of us is the snowflake—the simplest crystal in the making. The
shape of the ice crystal is the hexagonal prism. The Greeks called ice kristallos, and
from this our word crystal is derived. Starting with the crystals of the quartz family
(rock crystal, amethyst, rose quartz), we go on to the garnets and to the corundum
family (pointing to sapphires and rubies, emeralds, and topaz) and finally come to
the diamond—truest archetype of all crystals and gems.
Diamond is the strongest of all minerals. It cannot be cut by another mineral
for it is 140 times harder than corundum which stands next in hardness. All other
gems consist of two or more chemical substances. The diamond alone contains but
one. When pure carbon, or graphite, crystallizes in the form of an octahedron, the
greatest miracle of transformation takes place­—from
the blackest opaque substance to the whitest most
transparent one—the diamond. The diamond, then,
can symbolize the discrimination between good
and evil. We conclude our study of mineralogy by
developing moral and idealistic thoughts on this
phenomenon. We can see in diamonds the pure
splendor of sunlight­—as though, in them, the whole
earth had begun to turn toward a future in which its
darkness will be overcome by the power of light.
Mineralogy brings to a close the study of Natural
Science as given in a Waldorf/ Steiner school. It is
African diamond in matrix important that we should not terminate such a period
of teaching unless we have given to the children a feeling of true veneration for the
greatness of nature.

Herkimer diamond from Fonda, NY, in matrix—from the editor’s collection

36
 “In the Crystals We Recognize the Presence of the Gods.”

As we look at the salt crystal, we realize that a spiritual principle is

active in the universe. The salt crystal is the manifestation of that spirituality
which permeates the whole universe; it is a world unto itself. Then, from an
examination of a dodecahedron, we discover that there exists in the universe
something that permeates the world of space; the crystal is the impress, the
manifestation of a whole world. We are gazing on countless beings, each of
which is a world unto itself. As human beings here on Earth, we conclude that
the Earth-sphere is the focal point of the activities of many worlds. In all that
we think and do here on Earth are reflected the thoughts and deeds of a wide
diversity of beings. The infinite variety of crystal forms reveals the multitude of
beings whose activities find consummation in the mathematical-spatial forms
of the crystals. In the crystals we recognize the presence of the gods. “As an
expression of reverence, of adoration even towards the universe, it is far more
important to allow the sublime secrets of this universe to possess our souls than
to gather theoretical knowledge on a purely intellectual basis. Anthroposophy
should lead to this feeling of at-one-ment with the universe . . . able to perceive
in every crystal the weaving and working of a divine being. Then cosmic
knowledge and understanding begins to flood man’s whole soul. The task of
anthroposophy is ... to enlighten the whole man and show his total involvement
in the universe and to inspire him with reverence and devotion towards it.
Every object and every event in the world shall be invested with a spirit of
selfless service proceeding from the heart and the soul of man. And this selfless
service will be rewarded by knowledge and understanding.” (pp. 61–62)

– From True and False Paths of Spiritual Investigation,

Lecture 3, August 12, 1924, Devon, England

37
 Salt Crystals

Evaporated salt around the Dead Sea, the lowest point on the earth’s landmass

38
 Growing Salt Crystals

Table salt or sodium chloride crystals are simple salt solution into a clean container (so no undissolved salt
crystals to form if you’ve never grown crystals before.1 gets in), allow the solution to cool, then hang the seed
The ingredients needed are salt and water, the crystals are crystal in the solution on a pure cotton thread attached to
non-toxic, and no special equipment is required. a pencil, popsicle stick, or twig balanced across the top of
the container. You could cover the container with a coffee
Procedure: filter if you like.
Obtain a clean, sterile container like a glass Mason
jar. Heat water to just before it boils and add the water Set the container in a location where it can remain
carefully to the container until it is 1 to 2 inches from undisturbed. You are more likely to get a perfect crystal
the top. Next pour salt into the hot water and stir until no instead of a mass of crystals if you allow the crystal to
more salt will dissolve. (A white scale will appear at the grow slowly (cooler temperature, shaded location) in a
bottom of the container. These are minute crystals upon place free of vibrations.
close observation.)
Tips: Experiment with different types of table salt.
If you want crystals quickly, you can dip a piece of Try iodized salt, uniodized salt, sea salt, or even Epsom
cardboard into this supersaturated salt solution and allow salt. Try using different types of water, such as tap water
it to soak. Once it is soggy, place it on a plate or pan and compared to distilled water. See if there is any difference
set it in a warm and sunny location to evaporate. Numer- in the appearance of the crystals.
ous small salt crystals will form.
If you are trying for the ‘perfect crystal,’ use
If you wish to form a larger, perfect cubic crystal, uniodized salt and distilled water. Impurities in either the
you will want to make a seed crystal. To grow a big crys- salt, the container or the water can cause dislocation, a
tal from a seed crystal, carefully pour the supersaturated condition in which new crystals will not stack perfectly
on top of previous crystals.
1. For many more examples see The Wonders of Waldorf DSM
Chemistry, AWSNA Publications by David Mitchell.

Cubic salt crystal

Salt crystal generator

with supersaturated
solution

39
 The Beauty of Slime Molds

Slime molds is a term describing fungus-like When they exist scattered about in single cell
organisms that use spores to reproduce. The term conjures organisms and a chemical signal is secreted into their
up in most of us a gelatinous, viscous fluid that is to be environment, they are able to respond to the chemical
avoided. It is, in fact, only one stage of the slime mold’s stimulant, find one another, and assemble together into a
life cycle and is seen mostly with the myxomycetes which cluster that then acts as one organism.
exist as a macroscopic mold. There exist many myths about slime molds. For
Slime molds have been found all over the world and example, traditional Finnish lore describes how malicious
feed on microorganisms that live in any type of dead plant witches used yellow Fuligo (in Finland called “paranvoi,”
material. For this reason, these organisms are usually or butter of the familiar) to spoil milk. Also, the giant
found in soil, lawns, and on the forest floor, commonly on amoeba-like alien that terrorizes the small community
deciduous logs. However, in tropical areas they are also of Downingtown, Pennsylvania, in the 1958 American
common on inflorescences, fruits and in aerial situations horror/science-fiction film The Blob might be based on
(e.g., in the canopy of trees). In urban areas, they are slime molds.
found on mulch or even in the leaf mold in gutters. Slime molds have almost no fossil record. Not only do
Most slime molds are smaller than a few centimeters, slime molds produce few resistant structures (except for
but some species may reach sizes of up to several square spores, which are often overlooked or unidentifiable), but
meters and masses of up to 30 grams. Many have striking they live in moist terrestrial habitats, such as on decaying
colors such as yellow, brown and white. wood and fresh cow dung, where their potential for
I first encountered the form while reading Ernst preservation is low. A few fossil slime molds have been
Haeckel’s Kunstformen der Natur (Art Forms in Nature), found in amber (Poinar and Waggoner, 1992).
written in 1904. This fantastic There are more than 500 species of slime molds.
study is profusely illustrated with They creep on decaying wood and in moist soil, ingesting
forms he observed, and I was bacteria and decaying vegetation. They help give the
overwhelmed by the geometric forest soil the strong, unique, “earthy,” smell with which
symmetry and profound beauty in we are all familiar.
these simple organisms. The photographs on the next two pages illustrate how
For example, a plasmoidal beautiful and colorful slime molds are—those organisms,
slime mold involves numerous which are responsible for breaking down forest substances
individual cells attached to into brown rich mass that feeds new growth and renewal.
each other, forming one large
membrane. This “supercell” (a DSM
syncytium) is essentially a bag of
cytoplasm containing thousands of individual nuclei.

40
41
42
 Mutualism between Elk and Magpies

by Jeff Mitton

Elk love magpies, which gently remove their

ticks. Elk dislike and distrust ravens, which rip
out their fur for nesting materials.

A large herd of elk had settled into Moraine Park and deliberately.The elk looked more silly than
at Rocky Mountain National Park to bask in the sun majestic with a magpie on its head, but the elk was
of an early-spring afternoon. They sat motionless probably more concerned with its ticks than with
except for their ears, which they flicked constantly. my opinion of its appearance.Two more magpies
Something was bothering their ears. Probably ticks. arrived and began foraging on elk. One magpie
A magpie glided over the herd and landed among the started at the head, walked down the elk’s neck and
elk. In a determined manner, it approached a sitting along the back to stand on the rump, when the elk
elk, hopped onto its flank and continued up onto its obligingly lifted its tail. The magpie probed the
back, where it paused to survey its surroundings. The edge of the tail and beneath the tail. No doubt about
elk did not move. The magpie climbed onto the head, it, elk and magpies were cooperating to transfer
and the elk remained unperturbed and motionless. ticks from the skin of elk to the bellies of magpies.
The magpie probed an ear with its bill and then A cleaning mutualism is a mutually beneficial
stuck its head inside the ear to probe deeper. The elk relationship between two species in which one
did not move. Then the magpie withdrew, turned removes ectoparasites, most commonly ticks, from
its attention to the other ear and groomed it slowly the other. One individual is relieved of bothersome,

43
usually blood-sucking hitchhikers and the other yanked again. The elk quickly stood up and walked
gains an easy meal in a safe interaction. Several away. The other raven also approached a young elk
cleaning mutualisms involve birds and large and yanked out a tuft of hair. One raven took five
mammals. The textbook example is red-billed and yankfuls from several elk before it could hold no
yellow-billed African oxpeckers cleaning rhinos, more in its bill. Both ravens flew off to line their
cape buffalo, zebras and giraffes. Several lesser- nests with elk fur.
known mutualisms have been described in North Elk responded differently to magpies and
America. Scrub jays remove ticks and insects from ravens. When a magpie approached them, they
Columbian blacktail deer, and both scrub jays and sat or stood still, even when the bird probed deep
crows groom wild boars. Magpies forage on feral into their ears. Ravens approached only young elk.
horses in Nevada. Jays, crows, ravens and magpies Perhaps the ravens knew that the older elk had
are all members of the family Corvidae, meaning already learned to avoid ravens collecting nesting
they are closely related. Many corvids engage in material. Each young and presumably naïve elk
cleaning mutualisms, but not all; Steller’s jays and responded to being plucked with alarm if not
ravens are not known to groom large mammals. indignation and moved away from the aggressive
Two ravens dropped into the herd and I raven.
wondered whether they would also groom elk, but
they had a surprise for me and for the young elk.
One of them walked up to a young elk, grabbed Jeff Mitton (mitton@colorado.edu) is chair of the
a bill full of fur and yanked. The elk glared at the Department of Ecology and Evolutionary Biology
raven, but the bold raven grabbed more fur and at the University of Colorado.

Nurse shark with remora removing parasites

The Red-billed Opecker feed on ticks off the

impala’s coat. Mutualism is any relationship
between two species of organisms that
benefits both species. This is the relationship
most people think of when they use the word
“symbiosis.”

Giraffe licking salt and minerals from a

ground squirrel. Parasites and lice are also
removed in the process.

44
 Symbiotic Relationships

Many organisms live together in beneficial • Parasitism—one organism is dependent on another

relationships toward each other within an ecosystem. for its energy supply and usually harms its host or
Symbiosis is the term used for this type of relationship. exists at its expense to some extent.
These liaisons play an important part of the community
structure in ecosystems. Similar interactions within a The complex interplay of these relationships
species are known as co-operation. demonstrates the intricate nature of the interdependence
Generally, only lifelong interactions involving of organisms within any environment. For example,
close physical and biochemical contact can properly mutualistic interactions are vital for terrestrial
be considered symbiotic. There are three distinctly ecosystem function, as more than 70% of land plants
different types of symbiotic relationships, depending rely on mycorrhizal relationships with fungi to provide
on the nature of the benefits and yields to those them with inorganic compounds and trace elements.
organisms involved. In addition, mutualism is thought to have driven
the evolution of much of the biological diversity we
• Mutualism—describes any relationship between see, such as flower forms (important for pollination
individuals of different species in which both mutualisms) and co-evolution between groups of
individuals derive a benefit. species.
• Commensalism—concerns an interaction that A few plants, animals, insects, and fish that have
benefits one organism but does not harm the other. symbiotic relationships are listed below. There are
many more.

Biological Pairs Type of Symbiosis

Human ↔ All plants ➛ Mutualism (gas exchange)

Human ↔ Intestinal bacteria ➛ Mutualism

Human ↔ Tapeworm ➛ Parasitism

Rhinoceros ↔ Oxpecker Bird ➛ Mutualism

Deer ↔ Tick ➛ Parasitism

Barnacle ↔ Whale ➛ Commensalism

Algae ↔ Aquatic Turtle ➛ Commensalism

Flowering plants ↔ Pollinators such as bees ➛ Mutualism

Remora ↔ Shark ➛ Mutualism

Eel ↔ Coral ➛ Mutualism

Nomeous Fish
↔ Man o’ War
➛ Mutualism

45
 Hermit Crab ↔ Sea Anemone ➛ Mutualism

Bass ↔ Wrasse Fish ➛ Mutualism

Clownfish ↔ Sea Anemone ➛ Mutualism

Blood Fluke ↔ Snail ➛ Parasitism

Flea ↔ Mouse ➛ Parasitism

Honeybee ↔ Flowers ➛ Mutualism

Monarch Butterfly ↔ Milkweed ➛ Mutualism

Lice ↔ Horses ➛ Parasitism

Nematodes ↔ Sheep ➛ Parasitism

Honey Guide Bird ↔ Badger ➛ Mutualism

Cowbird
↔ Bison ➛ Commensalism

Crocodile Bird ↔ Crocodile ➛ Commensalism

Wren ↔ Osprey ➛ Commensalism

Red-billed Oxpeker
↔ Impala ➛ Mutualism

Magpie ↔ Elk ➛ Mutualism

Plants ↔ Aphids ➛ Mutualism

Mycorrhizal Fungus ↔ Corn ➛ Mutualism

Lichen Algae ↔ Lichen Fungus ➛ Mutualism

Shelf Fungus ↔ Hickory Tree ➛ Parasitism

Moss ↔ Maple Tree ➛ Commensalism

Woodpecker ↔ Pine Tree ➛ Parasitism

White Rot Fungus ↔ Oak Tree ➛ Parasitism

Spanish Moss ↔ Oak Tree ➛ Commensalism

Spruce ↔ Mistletoe ➛ Parasitism

Saguaro Cactus ↔ Gila Woodpeckers ➛ Commensalism

Rhizobium Bacteria ↔ Legumes ➛ Mutualism

Algae ↔ Sloth ➛ Mutualism

46
 An Interview with Daniel Pink

Why Waldorf?

by

Tracy Stevens

Daniel Pink is a horizontal the arts will be the way to prosper and succeed in the new
thinker. He has had his hand in economy. The arts are also a way to help people reach
business, government, law, and their potential and find their element.
writing among other things.
He worked with U.S. Labor How can teachers use the arts as a tool to teach?
Secretary Robert Reich and was The arts in education enable teachers to explore subjects
formerly chief speechwriter in ways that can be better understood and inter-related.
for Vice President Al Gore. History, math, science and any other subject can be taught
He is a contributing editor through the arts in ways that brings them to life. The arts
of Wired magazine and an provide a way to connect subjects, as they are in the real
independent business consultant world.
as well as a best-selling author
who chronicles the changing of the work world. Pink How do Waldorf schools fit with the dawning of the
postulates that in the future right-brained thinking will Conceptual Age?
dominate and drive the new economy. It will no longer Waldorf schools get the idea that the arts are fundamental,
be enough to rely on left-brained thinking alone. He not ornamental. They focus on the unit of the child, not
describes the Conceptual Age as the newest phase of the the school as an institution. They customize education
modern economy in which we will need to develop and for each child. Waldorf promotes autonomy and self-
incorporate the six senses of design, story, symphony, direction. whereas most schools actively squelch those
empathy, play, and meaning for success. qualities in favor of compliance, which seems to be the
Pink, the author of A Whole New Mind: Why Right most important value. The irony is that compliance is
Brainers Will Rule the Future sees Waldorf education much harder to achieve and it is less important in the
as not only addressing the 21st century’s need for right work world. I think Waldorf schools are very much in
brain skill development, but doing it in a manner that synch with the notion of the Conceptual Age and the ideas
creates lifelong motivation by de-emphasizing the of A Whole New Mind. They foster internal motivation in
reward-and-punishment, high-stakes test environment students, as well as mastery and persistence. They teach
characteristic of the No Child Left Behind legislation.
the habits of the heart that children need to do well in life
Following are excerpts from Tracy Stevens’s interview.
after school.

How can schools improve performance through the

Can you identify any education system specifically that
arts?
integrates daily art into its curriculum?
It starts with realizing that arts education is fundamental,
Waldorf does it. Montessori does it. There are some arts
not ornamental. We urgently need people to think like
and design charter schools that do it well. There is an
artists. This is especially important in the work place,
art-centered elementary school in Maryland near where I
where everything is abundant, automated, or made in
live that does a good job of it. The teachers and principals
Asia more cheaply than it is here. Creativity, design and
in these schools understand the necessity of the arts in

47
education. We are not talking about replacing math music, theater, etc., and parents are great coaches
with art! We are talking about bringing out math more and facilitators in this self-discovery. Through any
strongly through art. The arts train people to become of these activities, kids learn valuable skills of
horizontal thinkers who can make connections. We need collaboration, teamwork, persistence, and mastery.
to rethink this whole notion of frog-marching kids from We should not be forcing them to learn a musical
one isolated subject to another. The world does not work instrument or play a team sport if they are not
that way, and we are doing kids a disservice to train interested.
them that subjects are separate and unrelated before they
get out into the work world. The world has very porous If a school devotes only thirty minutes a day to
borders and is a tangle of interconnections. Schools creativity, what would be the most beneficial
should be preparing them for that. activities they could engage in with their
students?
What kinds of programs or features should parents The students should sit down and write letters to
be looking for when exploring school options for their their principal asking why they have only thirty
children, be it pre-school or secondary grades? minutes a day for creativity! That is not useful!
It really depends on the kid. There isn’t a formula for We shouldn’t be having separate, isolated time
this, but it is not the one-size-fits-all approach that for creativity and then tell them, “Stop thinking
we have. Figure out what is engaging for your child, creatively because now it is time for the real
what he likes and is good at and pursue that. I think learning. Time for math.” The idea is to master
the schools have a tremendous burden on them. They skills and content, become curious and engaged.
can’t do everything that is expected of them from Compartmentalizing is not going to help them
parents and the government. They can’t be all things achieve this. It is contrary to it.
to all people. Schools are expected to teach academics, ___________________
provide healthcare, nutrition, and sex education. They For more on Daniel Pink, go to www.danielpink.
are supposed to build character and morals and even com.To learn more about Waldorf education, go to
participate in community service. The burdens on our www.whywaldorfworks.org.
schools are outrageous. Parents have to share some of the
load or it will collapse. To read more by and about Tracy Stevens, please
visit her website: www.abettereducation.blogspot.
How can parents help to improve a child’s com.
opportunities for success in the Conceptual Age?
Pay attention to what your child likes to do and is
good at and give him plenty of opportunities to follow
his interests toward mastery. We want them to be
intrinsically motivated and to be persistent. There is a
process of discovery in trying out new things: sports.

48
49
50
 Teaching Sensible Science Course to Begin in

October, 2010

The next Teaching Sensible Science Course will begin at the Chicago Waldorf
School in October 2010. This is an excellent training course for class teachers who
want to prepare themselves for teaching the science curriculum in Grades 6 through
8. The course is comprised of three, one-week sessions, each focusing on the Physics
and Chemistry curriculum of a specific grade. Led by Michael D’Aleo, participants
will enrich their understanding of the philosophical underpinnings of the phenom-
enological approach to teaching science and benefit from lots of practical advice and
experience in presenting the demonstrations and experiments. This course is highly
recommended. The tentative dates for the three sessions are:

• Session One: Wednesday 6 October to Monday 11 October, 2010

• Session Two: Friday 18 February to Thursday 24 February, 2011
• Session Three: Mid-June, 2011 (specific dates tbd).

For more information or to register, contact the director of the program, Michael
D’Aleo, at: spalight@verizon.net.

Sponsored by AWSNA and the Research Institute for Waldorf Education

51
 Index of Past Issues
Waldorf Science Newsletter
edited by David Mitchell
© AWSNA Publications

This newsletter is published once a year and is dedicated to developing science teaching in the Waldorf schools.
Teachers are in­vited to pose questions, seek resource material, discuss experiments, write about their classes (suc-
cessful and not very successful), and investigate phe­nomena. The editor also translates relevant science articles from
Waldorf periodicals from around the world. The following past editions are available from:


AWSNA Publications
E-mail: publications@awsna.org
458 Harold Meyers Road
Earlton, NY 12058
fax: 518/ 634-2597
phone: 518/ 634-2222

available on-line at: http://www.whywaldorfworks.org/books_sciencenews.htm

Volume 1, #1
Partial contents—Acoustics in Grade 6; Teaching about Alcohol in Grade 8 Chemistry; The Chemistry Curriculum:
The Debate over Teacher Demonstration vs. Student Experimentation; Spiritual Aspects of 20th Century Science;
Overview of the Waldorf Science Curriculum; Water; Characteristics of the Major Sugars; Goethe’s Meditation on
Granite; Book Reviews; Humor; Poetry; Conferences; and Sample Experiments

Volume 1, #2
Partial contents—The Characteristics of Drugs; Eratosthenes Revived; The Golden Number; Educational Guidelines
for a Chemical Formula Language; The Properties of Acids and Bases; Walter Lebendörfer on Chemistry; Biology
in the 11th Grade; What Is Home?; The Waldorf Environmental Curriculum; Environmental Education; Women in
Science; Book Reviews; Humor; Poetry; Conferences; and Sample Experiments

Volume 2, #3
Partial contents—Grade 12 Physics—Von Mackensen; Biology Teaching in the 11th Grade; Euclid’s Algorithm; The
Logos and Goethean Observation; Nature Education; Aristotle’s Taste Spectrum; Book Reviews; Humor; Poetry;
Conferences; and Sample Experiments

Volume 2, #4
Partial contents—Current Research; Strange Theories; Science Education and Wonder; The Human Earth; Steiner’s
Counterspace Examined; The Cow; Language and the Book of Nature; Book Reviews; Humor; Poetry; Confer-
ences; and Sample Experiment

Volume 3, #5
Partial contents—Book Reviews; First Lessons in Astronomy; Steps in the Development of Thinking (Power of
Judgment); Computer Science and Computers in the Waldorf School; Technology; Computers in Education; Some
Characteristics of the Computer; Computers and Consciousness; Experiments

Volume 3, #6
Partial contents—Space and Counter Space; New Eyes for Plants; Experiments of Academia dell Cement; Physics
and Chemistry in the Grades; Goethean Science Credits; Chemistry Workshop; Table of Important Salts; Goethe’s
Scientific Imagination; To Infinity and Back in Class 11; ∏ and Trigonometry; Science in the Waldorf Kindergarten;
A Note on Pascal’s Triangle; Experiments

Volume 4, #7
Partial contents—The Message of the Sphinx; Honey; Cell Cosmology; Einstein’s Question; What Is Goethean
Science?; Prototype Computer Program; River Watch as a Classroom Activity; Thoughts on Curriculum Standards;
Comments on Building a Waldorf School; Experiments

52
Volume 4, #8
Partial contents—Towards Holistic Biology; How DNA Computers Work; Solar System Facts; What Is Goethean
Science?; Human Movement and the Nervous System; What Is Science?; What Is Meant by “Teaching the Chil-
dren to Breathe?”; Experiments

Volume 5, #9
Partial contents—The Globe Inside Our Planet; Music, Blood and Hemoglobin; Standards in Science; Cognitive
Channels—the Learning Cycles and Middle School Students; 8th Grade Physics, From Dividing to Extracting
Roots; What Is Lambda?; Waldorf Science Kits

Volume 5, #10
Partial contents—Reading the Rocks; Why the Arts Are Important to Science; The Three Groups of Rocks; In-
troduction to Geology; The Rock Cycle; Mineralogy for Grade 6; Metals and Minerals, Precious Stones—Their
Meaning for Earth, the Human Being, and the Cosmos; Experiments

Volume 6, #11
Partial contents—A Chemistry of Process; Sponges and Sinks and Rags; How to Read Science; Experiences and
Suggestions for Chemistry Teaching; Experimentation as an Art; Biographies—Dmitri Mendeleev, Joseph Priest-
ley, Marie Curie; Destructive Distillation; Experiments

Volume 6, #12
Partial contents—Light and Darkness in 6th Grade Physics; The Relation of “Optical Elevation” to Binocular Vi-
sion; Description of Curves in Connection with Elevation Phenomena; Water Treatment at the Toronto Waldorf
School; A Lime Kiln that Can Be Assembled and Disassembled; Experiments

Volume 7, #13
Partial contents—Thoughts on Returning to an “Education Towards Freedom”; Pedagogical Motives for the
Third Seven-Year Period; Social Education through Mathematics Lessons; A Vision for Waldorf Education; Our
Approach to Math Doesn’t Add Up; International Mathematics Curriculum

Volume 7, #14
Partial contents—Conferences; Physiology, Update on Taste; Pictorial Earthquake; Boiling with Snow; Towards
a Waldorf High School Science Curriculum for the 21st Century; The Thermal Decomposition of Calcium Car-
bonate; Crystals Reveal Unexpected Beginnings; Cosmic Ray Studies on Skis; Experiments

Volume 8, #15
Partial contents—Book Reviews; Arabic Science; Arabic Mathematics: Forgotten Brilliance; Making Natural
Dyes; Exploring the Qualities of Iron; Von Mackensen Chemistry Conference; Oalic and Formic Acid; Hydraulic
Rams; What the Water Spider Taught Me

Volume 8, #16
Partial contents—Waldorf High School Research Papers; Inside the Gulf of Maine; How Do Atomistic Models
Act on the Understanding of Nature in the Young Person?; The House of Arithmetic; Origami Mathematics;
Sixth Grade Acoustics; Sixth Grade Kaleidoscopes; Tricks with Mirrors; The Flour Mill and the Industrial Revo-
lution; Web Gems; Understanding Parabolic Reflectors; The Capacitor; Oscillation and Waves; Crystal Radio;
Qualifications for High School Mathematics Teaching

Volume 9, #17
Partial contents—Book Reviews; Acknowledgement from a Waldorf Parent; Raising Money for Science; The
Twelve-Year-Old Child and Orpheus; Towards a Sensible Kind of Chemistry, Part One; The Lightning Bug; The
Ladybug; Exploratory Experimentation: Goethe, Land, and Faraday; Faraday’s Synthetic Investigation of Sole-
noids; Faraday’s Analytic Investigation of Induction; Geometric Addition Table: A Curious Configuration

Volume 9, #18
Partial contents—Book Reviews; Towards a Sensible Kind of Chemistry, Part Two; The Evolution of the Fast
Brain; Professors Vie with Web for Class Attention; The Teenage Edge; Oscillator Coil Demonstration Using an
Ultra-Low Frequency LC-“Tank” Circuit; Thermodynamic Experiments for the Middle School

53
Volume 10, #19
Partial contents—Book Reviews; The Beaver; Nature in the Human Being; Astronomy Verses for the Middle
School; Child Development and the Teaching of Science; Bibliography for Middle School Teachers; What Is
Phenomenology?; The Design of Human and Animal Bodies; The Brain and Finger Dexterity; Observations of a
Neurophysiologist

Volume 10, #20

Partial contents—Book Reviews; A Number Story for the Sixth Grade; Novel Entries for a Trig Table; An In-
troduction to the Sine and Tangent; Toss Out the Toss-Up: Bias in Heads or Tails; Phlogistron Theory; Song of
the Rain; Refrigeration in Physics; The Poetry of Astronomy; Build Your Own Sextant; Highlights from Recent
Science-teaching Periodicals; Websites of Interest

Volume 11, #21

Partial contents—Books of Interest; A Sampling of Poems for Botany; How Does Sense-Nerve System Activity
Relate to Conscious Experience?; Acoustics in Sixth Grade; Fun Facts of Physiology; About Formative Forces
in Vertebrates and Human Beings; Global Perspective; Points to Consider in Science Teaching; Deconstructing
Black Box, Aspects of a Computerized Physics Lab

Volume 12, #22

Partial contents—Books of Interest; Preserving a Snowflake; Environment, Morphology, and Physical Principles
for Waldorf High School Teachers and Students, Part 1; Homemade Audio Speaker for Grade Eight; Mathemat-
ics and Natural Science: A Reflection from the Viewpoint of Pedagogy and the History of Ideas; Animal Sight;
Kepler’s Model of the Universe; Teaching Sensible Science; Mug on a Glass: An Optics Demonstration for
Grade Seven; Chemistry Challenge for Grade Eight; On Being an Insect; Surveying and Mapping: An Attempt to
Integrate New and Emerging Technologies into the Class 10 Curriculum

Volume 13, #23

Partial contents—Books of Interest; Advice on Teaching 8th Grade Meteorology; An Explanation of the Phe-
nomenological Approach for Parents of Middle School Children; Astronomy (Hubble Space Telescope Photo-
graphs); Environment, Morphology, and Physical Principles for Waldorf High School Teachers and Students,
Part 2; Sensible Science Workshop; How Parachute Spiders Invade a New Territory; Pluto Is No Longer a
Planet; Computer Curricula in U.S. Waldorf Schools; Experiments

Volume 14, #24

Partial contents—Books of Interest; Robotics; A Seventh Grade Fresco Project; A Pinhole Camera Project for the
Seventh Grade; Other Projects for Elementary Physics Classes; The Aurora Borealis; Phenomenological Science
Equipment; The Karma of Calculus—Involving Isaac Newton and Gottfried Leibniz; Award-Winning Photos of
Nature and Animals; Humor

Volume 15, #25

Partial contents—Books of Interest; Doing Phenomenology in Science; The Western Screech Owl; Sea Turtles
Use Earth’s Magnetic Field to Navigate; The World’s Biggest Bug; Tree Talk; The Phenomenology of Colored
Shadows; Analemma; Photos from Hubble; Mechanics in 7th Grade Physics

Volume 16, #26

Partial contents—Books of Interest; Going through, Taking in, Considering: A Three-Phase Process of Learning
as a Method of “Teaching in Main Lesson Blocks,” The Geometry of Life: Toward a Science of Form; Phenom-
enology: Husserl’s Philosophy and Goethe’s Approach to Science; First Approach to Mineralogy; Growing Salt
Crystals; The Beauty of Slime Molds; An Interview with Daniel Pink; Mutualism between Elk and Magpies;
Symbiotic Relationships

54