Projective Synthetic Geometry
in Lady Frieda Harris'
Tarot Paintings and in A. Crowley's Book of the Law
Claas Hoffmann
It was in 1904 when the English magician Aleister Crowley
wrote the the Book of the Law. It was dictated by a praeter-human
intelligence calling itself Aiwass. The book consists of
three chapters written down in Cairo on 8th, 9th and 10th
April at noon.
33 years later, Crowley met the artist painter Lady Frieda
Harris. He had decided to create a new Tarot deck and asked
Harris to paint the cards according his ideas, that is
according to his instructions. Harris agreed, became a
member of the O.T.O. and they began their work. A lot of
the cards had to be painted several times. The drafts still
are in private possession while the final originals can
be found at the Warburg Institute London, a part of the
University Library.
The Library Warburg was founded in 1903 by the jewish
son of a banker, Aby Warburg in Hamburg. At the beginning
of the Nazi regime in 1933, the complete collection (80,000
books) was sent to London where the Warburg Institute now
was founded. There, I was able to study the original Tarot
paintings. I also saw the unpublished drafts of earlier
versions, in private ownership. Lady Frieda Harris painted
far more versions than the published ones. All in all,
she worked five years on them.
At the end of his life, Crowley wrote a book about this
new Tarot, called The Book Thoth. About the card 'The Aeon'
[equiv. to the World card] Crowley wrote: 'This new Tarot
may therefore be regarded as a series of illustrations
to the Book of the Law; the doctrine of that Book is everywhere
implicit.' (Book of Thoth, page 115)
If you cut out these cards and remove their frames, especially
the trumps can be put together in a very harmonic fashion.
Why so?
Crowley noted in the Book of Thoth that the harmony of
the cards was proof of the correct application of symbols
and colours of the holy cabballa, upon which this tarot
was created. By making collages of these cards, I learned
that the link between the peculiar cards was not only made
through their colours or symbols but through their geometry.
Which kind of geometry was used by Harris, which made these
links possible? [the image is one from several examples
on the site]
The Geometry she used was an evolution of the strict Euclidian
geometry. Its roots had been developed by the mathematician
Descartes in the 17th Century. It's called "Projective
Synthetic Geometry" and was developed by many mathematicians
and scientists throughout Europe. Many of Descartes' ideas
were based on both mathematical and mystic assumptions,
e.g. his axiom of parallels meeting at infinity. The ends
of parallel lines lie in two opposite directions, but the
idea of the point in infinity is that the point, infinitely
distant in a direction, is the same as those infinitely
distant in the opposite direction.
This step in the development of Projective Geometry, based
on the idea of elements in infinity, brought movement and
perspective to the Euclidian concept of rigid, fixed forms.
In the following centuries the next step based on the idea
of polarity (center and periphery) was taken; in other
words, the concept of a polarity between a central point
and an infinitely distant surface.
These thoughts then had the consequence that each point
in each conceivable space is the same distance from a surface
in infinity.
The next step, taken in the 20th century, comes from the
concept of space, polar or opposite to our three-dimensional
space. Can one move one's concept of a surface in infinity
into an infinite center? ...
How did Frieda Harris come into contact with the concepts
of Projective Geometry and their practical, graphical conversion?
Three people, whose spiritual paths were different from
Crowley's, were responsible for this: Rudolf Steiner, George
Adams and Olive Whicher.
Rudolf Steiner was the founder of Anthroposophy, from
which, among other things, come Waldorf (Rudolf Steiner)
schools, Eurythmy and biodynamic agriculture.
George Adams was one of the people who helped to bring
Anthroposophy to England. He met Rudolf Steiner personally
during a trip to Dornach and at the same time belonged
to a group of scientists who worked on the advancement
of Projective Geometry. They worked on the concept of a
space whose center is infinity.
Rudolf Steiner recognized that people required in their
concepts the idea of infinity in the center as well as
infinity in the periphery. Mankind needed the concept of
infinity in the center in order to find their mental and
emotional equilibrium, and in order to further develop
spiritually. Steiner assumed infinity in a center in the
sun. That is, infinity can be found in the sun, or perhaps
better said, infinite nothing.
Olive Whicher tried patiently to explain the principles
of Projective Geometry to me. She wrote and published together
with George Adams books about Projective Geometry and worked
after Adams death until today as an author, Anthroposophical
researcher and teacher. Her last large publication was
the book Sonnenraum (Sun Space), in which she explains
in particular the mathematical research through the spiritual-scientific
realizations of Rudolf Steiner. It is taught at Emerson
College, a Rudolf Steiner school in Forest Row, South England.
In March, 1935, she met the Anthroposophical Society in
London and therefore also George Adams a short time later.
Adams taught Projective Geometry in the Rudolf Steiner
house. Whicher attended Adams' lectures and soon began
to work together with him. Adams and Whicher gave courses
in Projective Geometry when Frieda Harris visited the Rudolf
Steiner house.
This occurred as Harris began work on the Crowley Tarot
cards, probably in the year 1937, because from this time
on there are entries in Crowley's diaries about his work
with Harris.
Harris took courses in Projective Geometry and made friends
with Whicher and Adams. George Adams called her Diana,
because he found that this name fit her substantially better
than Frieda. A representation of Diana can be found on
the tarot trump Art. Frieda sometimes told George and Olive
about her work with Crowley, and that she used what she
learned in the courses for her work on the tarot pictures.
Whenever Olive told me about Harris, she spoke of what
a special and friendly person she was.
The meetings with Harris also gave Adams and Whicher quite
practical impulses in their own graph-ical work. Harris
suggested that they use very hard colored pencils as well
as very soft pastel colors for work with plant pictures.
Some of these plant pictures that Adams and Whicher worked
on still hang in the Rudolf Steiner House in London. On
these plant pictures they worked in order to show the ideas
of Projective Geometry in the world that is visible and
well known to us.
They also wanted to include Goethe's scientific ideas
in their work. For me, the essential contents of Goethean
research is a revolt against the mistake that one can analyze
and understand something alive in the same manner as something
dead. One can not attain an understanding of a tree by
taking it apart and analyzing it like an automobile.
Goethe's idea of changing forms in the plant world is
referred to by Adams and Whicher in their understanding
of the constant process between space and anti-space, whereby
anti-space is better described by the word Sun-space, because
it is the source of the power that makes life on earth
possible. That this power in the plants is visible to everybody,
was recognized by Adams on a spring day in 1947 with Olive
in Regents Park (it lies about a minute from the Rudolf
Steiner House), as they walked by a budding hedge Adams
suddenly stopped and exclaimed to Olive (I quote from Whicher's
book George Adams): 'Naturally! That IS an ethereal space!'
And then he described in geometric terms how the germinating
impulse - the united group of small flat leaves or an individual
leaf, how it emerges as a cone from a point of growth and
as it grows it loses ever more of its vitality - actually
the living substance is a physical manifestation of an
etheric space. This growth process is found, instead of
in an ethereal space, in the space and with the powers
of the 'point of growth', which contains an infinity in
the inside. So a seed or a germinating embryo is physically
small, but ethereally large! It was an exact analog to
the concept from higher mathematics.
Also in the Book of the Law the infinitely small point,
which contains the vitality of the infinity, is clearly
emphasized. The book calls this point Hadit. Hadit describes
itself in the Book of the Law as follows:
'I am not extended' and: 'I am the flame that burns in
every heart of man, and in the core of every star. I am
Life, and the giver of Life, yet therefore is the knowledge
of me the knowledge of death'.
The three chapters of the Book of the Law refer to the
three Egyptian gods Nuit, Hadit and Horus.
Had or Hadit stands for the internal center of each human.
It is the spark of light which transcends death and rebirth.
Hadit is not extended. Its space is of the quality of the
sun space.
Nu or Nuit is the goddess of the sky. She is the starlit
sky and encloses everything that surrounds us.
Hoor or Horus is the child of Nuit and Hadit. He is the
result of the interaction between the infinity in a center
and the infinity in the periphery.
The second chapter of the Book of the Law begins with
the following verses:
'1. Nu! the hiding of Hadit.
2. Come! all ye, and learn the secret that hath not
yet been revealed. I, Hadit, am the complement of Nu, my
bride. I am not extended, and Khabs is the name of my House.
3. In the sphere I am everywhere the centre, as she,
the circumference, is nowhere found.
4. Yet she shall be known & I never.'
In these verses we find a reference to the thoughts contained
in Projective Geometry and to the concept of the sun space.A
quotation from Adams' essay Die Weltenkrþfte des Umkreises
und die Pflanze (The World Power of the Circumference and
the Plant) will clarify this:
'We should as clearly as possible build the concept of
real picture forces, which float over the universe as two-dimensional
pages, instead of like terrestrially constituted forces
of punctual centers shooting outward like arrows. Thus
we obtain in a scientifically accurate manner the concept
of forces with no focal point, but having a perimeter ...'
We can also find an analogy to sun space in our sensory
organs: If we look into the distance, things appear smaller
the further they are away from us. It is not possible for
me to clearly describe how my eyes are connected with my
soul in the sun space, but I know that the laws of optics
corresponds with the laws of the sun space: The nearer
visible things come to me, the larger they become, the
nearer things are to the center of my perception, also
coming to my soul in the sun space, the more space is available
for them.
With reference to the concept of sun space I would also
like to discuss the following verses from the first chapter
of the Book of the Law:
'6. Be thou Hadit, my secret centre, my heart & my
tongue!
7. Behold! it is revealed by Aiwass the minister of
Hoor-paar-kraat.
8. The Khabs is in the Khu, not the Khu in the Khabs.
9. Worship then the Khabs, and behold my light shed
over you!'
Aiwass is the envoy of the passive, introverted part of
Horus. His nature corresponds to the sun. Hadit is located
completely in the sun or anti-space; likewise the Khabs,
the house in which Hadit lives. The connection between
our soul and our body exists in the Khu. The Khu is our
light- or astral body. Steiner wrote in Die Geheimwissenschaft
im Umriss (An Outline of Occult Science) that all of our
passions and feelings are located in the astral body. In
Occult Science Steiner writes further that this astral
body penetrates a further body in us, which animates our
physical body.
The astral body, the Khu, also penetrates the life-body,
which further penetrates our physical body. This life-body
exists in an interrelationship between space and anti-space.
It alternates between material and non-material existence.
Since the Khu penetrates the life-body and this consists
of an interplay between material and non-material, the
Khu is always in direct contact with our flesh body and
through our flesh body it can be influenced. The Khu has
the proportion and nature of the Material, such that it
is transitory. This is not so of the house of the soul
and the soul itself. The house Khabs and its inhabitant
Hadit are immortal. With the request 'worship the Khabs',
Aiwass requires us to worship the eternal and therefore
our internal, and to the things around us he counts not
only our rough-, but also our fine-material body.
The space- and time-structures described here aim at our
internal and holiest and finally pursue a single target:
They are to help each human to carry out his free will.
This free will rises from the spiritual world: Our higher
self, our soul.
Postscript 10. October 1999
Since September 18, 1999, I am again attending Emerson
College and have the possibility of continuing discussion
with Mrs. Whicher.
In March, 2000, Olive turns 90 years old, health permitting.
She has strong memory problems and did not recognize me
at first.
With obvious effort and after several discussions she
remembered our meetings from 1990/91.
Whicher read the above article about Projective Geometry
in the Harris-Tarot in its corrected prototype form and
con-firmed the relevant facts. Today Olive describes the
history of Projective Geometry in the Harris-Tarot somewhat
differently:
Around the year 1938 she became aquainted with Frieda
Harris. Frieda's studio was very close to Regent Park and
also very close to the Rudolf Steiner House. Olive remembers
visiting Harris several times in her studio, which must
have been on an upper floor, since she remembers stairs.
Deviating from the 1990/91 version, Olive today tells
me that she privately taught Harris in her studio during
the time she worked on Crowley's Tarot. The difference
from the first version is that in the earlier version Harris
learned Projective Geometry from Adams' and Whicher's courses
in the Rudolf Steiner House. I personally assume that both
are the case.
Whicher also remembers that Adams became friends with
Harris and they were very impressed by her personality.
Whicher acknowledged again that Adams called Harris "Diana",
which refers to the goddess represented on the card "Art" in
the Crowley Tarot. Olive told me that Harris had colored
her hair red, which at that time must have been very special
and unusual. Harris was a woman of liberal politics and
had a very free-living, spirited and strong personality.
Olive told me that she regretted when Harris left England
for the rest of her life to spend her old age on a houseboat
in Kashmir.
Quite particularly, Whicher expressed her regret that
Harris did not turn to Anthroposophy.
In 1991 I requested permission from Whicher for me to
publish an article about the connection between Projective
Geometry taught in the Rudolf Steiner House and the Harris
Tarot, with the help of some pictures from Whicher's Sonnenraum
(Sun Space). After much hesitation Whicher gave me permission,
with the reason being the freedom of information, as in
Steiner's philosophy of the three-way arrangement of society
(freedom in culture and religion, fraternity in economics
and equality before the law).
Of Thelema and Aleister Crowley, Whicher holds nothing
good.
It is completely incomprehensible to her why Harris did
not find her way to Anthroposophy. At our last meeting,
Whicher told me that it seemed to her as if Harris had
been "under Crowley's spell", because she held to him so
strongly. It caused Harris much grief that Crowley suffered
so much due to asthma. Adams and Whicher both had an absolutely
good opinion of Harris. Harris held absolutely to Crowley.
Whicher considered each work with the person or the teachings
of Aleister Crowley to be false and dangerous. She regards
a connection between Anthroposophical and Thelemic philosophy
to be a mistake. To clarify this, finally a quotation from
our last discussion: Forget everything that you know and
read all of the books that Rudolf Steiner wrote!
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