Morphology_of_Forms_-_Stei#1.htm 

Morphology

''Towards a Morphology Section of a School of Spiritual Science''

by John Blackwood, Sydney, Australia

This page is under continual construction ... initiated 6/10/1998, modified 11/01/2003, modified 03-01-2004

What is it all about?

Fibonacci Spirals 3 anticlockwise and 5 clockwise from center 

This page is concerned with the study of morphology or the shapes and forms of nature, their genesis, transformations, interelationships, design and understanding. This not only includes physical mineral forms but also all organic forms. Beyond this are the further specialisations within which the animalic expresses itself and, as a yet further independent kingdom, humanity.

The use of Synthetic or Projective Geometry as a guide in this work and the insights, indications and suggestions expressed by Rudolf Steiner, George Adams Kaufmann, Lawrence Edwards and Nick Thomas have proved enormously helpful to me in this work in how to make a beginning with approaching ''the Gate of Form'', as Rudolf Steiner describes it.

As I amend this page now (5th Jan 2004) I have just been told (by email from Denis Wight in Scotland) that Lawrence Edwards has just passed on. He died peacefully at home with Barbara and their five sons on the evening of Saturday 3rd January 2004 in Strontian, Scotland.

Spiritual Science

The degree to which notions of modern Chaos Theory enter into this study is yet to be seen. The interdependency and connection between what will be called here structuring form fields and any genetic determinism has also yet to be explored. Is there a justification for seeing this work within the framework of what might be called a spiritual science?

I believe there is in that the perception of what we interpret as form might depend initially on our physical senses, the sense of and for form itself depends at a bare minimum on some kind of mental activity, or spiritual activity - initially of the capacity to think relationships and structures in our imagination.

And that at the very least has some kind of spiritual dimension if there is anything at all to which we can apply the word ''spiritual''. The question is ''can we develop new eyes for nature?'' and if so, how? Is there a language of form that we can learn to read? What does the ''Book of Nature'' have to say to us if we are attentive enough to it?

Avenue of Bunya pines outside Brisbane, Australia

The content is derived from work done locally in Australia and found throughout the world. Some of the individuals whose work is known to me and whose directions appear to interface with this theme are: D'Arcy Thompson, Johann Wolfgang von Goethe, Rudolf Steiner, Lawrence Edwards, Rupert Sheldrake, Nick Thomas, Graeme Calderwood, Theodore Andreas Cook, Samuel Colman, Lancelot Law Whyte, George Adams Kauffmann, Olive Whicher, Peter Stevens, James Lovelock, Brian Goodwin, Ian Stewart, Chris Illert, Keith Critchlow, ................. to name but a very few.

Path curve system in the semi-imaginary tetrahedron

One of the aims of this work is to draw together insights and observations that will enable us to see more deeply into nature, not only academically, but on a day to day experiential basis. To this end one direction of work has to do with recognising the forms around us as the consequence of a deeper structuring world, an inherent wisdom which gives architecture to the physically visible. This can enhance our wonder and, I believe, add to an ecological and environmental consciousness.

A working group.

A small working group in Sydney, Australia would welcome any interest from others in this work and would hope to share in developing this area of research. In the group were David, Roger and John. Christal often joined us. Write to me in Sydney at jblckwd@ozemail.com.au if you are interested in this work. A friend in Newcastle, Marcel Maeder, is also interested in this direction.

Roger has now left us physically (he died in 2001) but one thing he did leave with us, among much else, was an elegant pair of special dividers. It was a device for finding the Golden Ratio, Golden Section or Golden Cut very simply, given a particular distance.

Rogers golden section dividers

David and I still meet fairly regularly and I would welcome any communication or ideas in relation to the following topics.

Some notes or sketches on ''reading form''..........

Notes are in alphabetical order beginning with the the commenement date of the note.

A Background Architecture

Note that a meaning of ''architect" is ''one who designs and frames any complex structure; esp the Creator; 1659'', (Oxford English Dictionary). I do not know much about creators but negentropy seems just as busy as entropy in our world, i.e. building up seems to happen just as much as does breaking down, so morphology and matter are essential polarities in our natural existence. A crude structural morphology is proposed based on all three geometric elements not just the atomic - or point-wise.

Anastomosis in leaves

From a single branch to many branches, and many more and more - then interacting with the neighbours.

Banana #1 - unfurling leaf

Watching the leaf of a banana plant unfurling day by day seems to lead to a distinct vortex stage some time before being fully opened out more or less flat into the distinctive banana leaf form ….

Tuesday 17-12-2002

Bi-lateral Symmetry

How many phenomena display bi-lateral symmetry? Quite a few since we see this kind of symmetry in all four kingdoms, in the human, the animal, the vegetative and the mineral. Is there a bit more to this than mere reflection?

Body, Soul and Spirit

A three fold description of the human creature.

Spirit

Through the body we learn that there are things, through the soul - how we engage with them, and through the spirit - we get a glimpse of what they actually are. ''.. the third we hold as a good to strive for unceasingly''. (p23, Steiner, 1904)

Friday 13-12-2002

Bunches, mounds and treelets

Even in the overall form of the tree we often see somewhat self-similar forms. I will call these treelets. Also in a paddock or field or moor the tussocky nature of the plant bunches is noticable.

Bunya Pine Cone

What can we tell about this form?

Calculus history

Two directions are suggested by some writers. The one works from a global perspective and the other that of minutiae.

Canopies of trees

The canopy profile represents the limit of the growth of the tree. This is like a living surface and beneath it the living activity often dies away as evidenced by much dead material.

Chladni

When things vibrate ………….

Tuesday 17-09-2002

Colour Shadows

We did some simple colour shadow experiments to help answer a few queries that Paul had. He wondered about the objectivity of the effect and how we might understand it. (By Paul Beasly and John Blackwood)

Friday 03-01-2004

Cycad cone growth

In the Botanic Gardens a slowly growing cone

Cycad (?) cone in the Botanical Gardens, Sydney, Australia

Thursday 20-03-2003

D'Arcy Thompson and invariance …..

Thompson was looking, in about 1916, for something that was constant in the forms of the organic.

Sunday 08-12-2002

Death and life

Order and disorder, negentropy and entropy, design and designoid, life and death ......

Saturday 19-04-2003

Death as a subset of life, a geometric analogy.

A comparison of the living and the dead with the metric of Euclidean space and the flexibility of synthetic or projective geometry. Considerations are limited to what happens in the line.

"e", so why does it appear all over the place and what is it?

The appearance of "e" again and again in mathematics and in the description of many natural phenomena must cause some amazement - but perhaps it shouldn't if we accept an intimate connection between these two worlds, the mental/spiritual and the phenomenal/physical.

Sunday 21-07-2002

Earth, as a tetrahedron

Is the basic structure of the Earth a tetrahedron projected onto a sphere?

Edwards Forms and Thomas Spaces

Lawrence Edwards worked extensively with path curve forms, including egg, bud, heart and vortex forms and Nick Thomas has worked deeply with counter-space ideas in particular in their relation to physical phenomena as well as organic structures. I would like to see this recognized much more widely so why not name names!

Eggs-hibition 2001

An appreciation of the work of Lawrence Edwards in July and August 2001 at Rudolf Steiner House.

Tuesday 29-10-2002

Ellipse construction - projective

Constructing an ellipse or a conic using a projective technique starting from two lines and three points etc.

Epsilon (e) variation in a palm tree stem

There sometimes appears to be an angular change in ''epsilon'' in plants stems, with high epsilon near the base and lower epsilon as we move upwards. The part icular case of a Queensland palm is shown.

''Ethers'' - working with Marti's ideas

Elements and ethers, their polarities, interactions and geometry, - working with Marti's notions of the four ethers.

What are these so-called ethers?

In his little book Ernst Marti describes his picture of four ''ethers'' (Marti, 1984). These ethers are not complete without considering the ''elements'' as well. The elements as we know, and conceive of them, today are not the same - it appears - as the elements pre-Renaissance. Elements such as Sodium, Helium, Oxygen, Rhodium etc are todays way of seeing them. The old elements were Earth, Air, Fire and Water. I will interpret these as referring to conditions of material and not Earth as in compost or Air as in Nitrogen and Oxygen mixed, with a few other modern elements thrown in and compounds as well.

Fibonacci in plant sections

Consecutive Fibonacci numbers appear very often as the number of spirals in cross sections of plants as well as the layout of the leaves and seeds.

Wednesday 013-03-2003

Fibonacci spirals

How do Fibonacci spirals work …

Form experiment - a "sea urchin"

Natural forms mirrored in geometrical form fields? Worth an experiment.

Form Spectrum

A range of form fields that belong to a specific kind of Tetrahedron. This is the semi-imaginary tetrahedron where the imaginary points are in a horizontal line at infinity and the two real (fixed) points are in the local vertical line.

Frayed at the ends …

Frayed at the ends ….. or are they? Leaves that appear to be progressing along definite lines or veins suddenly stop or finish raggedly. Even an orderly raggedness! What is going on here?

Graphic Projective Geometry in the High School

A summary of and background to the workshop given at the MANSW conference at Manly by John Blackwood.

Monday 09-12-2002

Growth measures

The simplest natural transformation along a line appears to be very similar to a number of measures revealed in nature.

Hierarchies

The ten hierarchies - a little thought on each - from studies in Spiritual Science.

Sunday 01-12-2002

Hinge of the Mollusc

The amazing fact that Bi-valve Shells have a plan that is akin to a very special case of path curves which have a single straight line and has itself a built in straight line and that is the hinge. The Pteria shell is a glaring example.

Tuesday 01-12-2002

Holes and Crinkles

The idea that the worlds in counter-space can attempt to be either in excess or insufficiency when there is cross-over into Euclidean space.

Hollow tubes everywhere

A view that sees the structure of many organic forms as having a fundamental architecture around a line segment that isn't there! Plant stems, hollow bones and centromeres are examples.

Sunday 08-12-2002

Houses and homes

Shells, eggs, capsules, skins are all very special houses for very many different kinds of creatures. Is there some commonality of architecture for these very small to larger houses?

Saturday 24-08-2002

Hunter BD Group Workshop

Workshop task

Using the prepared field structure draw in the selected path curve field profiles …. as follows:

Path curves in the plane, one point at infinity, two local 

Wednesday 05-02-2003

Hypothesis

It is as if what we physically see is a minute expression of a mighty field structure. Can such fields be articulated in some consistent fashion mathematically/geometrically regardless of our understanding of their essential nature (as gravity is still today)?

Inversions galore!

The idea if inversion, or a 'turning inside out' appears in many places. This can be temporal (through time) or spatial (space related forms).

Johannes Kepler (1571-1630)

Kepler's Law - a relation between planetary distances and orbital times - notes for a main lesson with Class 8 on RHYTHM.

Friday 10-01-2003

Lambda, as a form factor

One projective method for finding lambda, ? of egg and bud like forms.

Lambda, by averages of three pairs of points

Average three pairs of points

Thursday 09-01-2003

Lambda , projective calculation

One projective method for finding lambda, of egg and bud like forms.

Sunday 08-12-2002

Language of Form

Is there a language by which we can read 'form', what are the letters, the words, and the syntax of such a language by which we might be able to read in the ''book of nature'' and discover her ''open secret''.

Leaf - from point via line to plane

Goethe said something like 'the plant is all leaf'. One aspect of the leaf is what often appears as a transformation through the linear from point like (seed or node) towards the flatter or plane like (the leaf form itself).

Leaf - what is its secret?

The morphology of the leaf must have a mysterious secret all its own. What special architecture lies hidden in this form with so much beauty, living, nourishing and chemical potential?

Lemniscates and tetrahedrons

The tetrahedron is to space what the lemniscate is to time, …. a speculation.

Life was first - wasn't it?

The appearance of life on the Earth is deemed to have been well after the material Earth appeared. May not this material be in fact a precipitation from an original living condition which preceded that mineral stuff? Instead of looking for how life might have arisen out of physical/mineral concatenations it may be an idea to reverse this - and suggest that the mineral is a dead subset of the originally living. Try that idea for size!

Looking at landscape

With what eyes do we look at landscape?

Sunday 26-12-2002

Looking for the line …

The line, may be more than, as well as, a straight line. It is also the trace of an activity. First we need to see the line then to see what activity it is the trace of.

Mathematics Main Lessons

An outline of mathematics main lessons given by John Blackwood in the high school at Glenaeon Rudolf Steiner School.

Mid-winter talk (outline)

Seasons, ritual and the future group forms, and two mutually interlocking research paths.

Tuesday 04-03-2003

Mytho-sophia, Philo-sophia and Anthro-posophia

The expression of the Sophia must change depending upon the inspiration she has to bring in any particular age for the education of humanity.

Mytho-sophia

Myth, story and legend. Once upon a time there was revelation ....

Philo-sophia

Education in thinking. ''You tell us there are Gods'' - Plato is challenged.

Anthropo-sophia

Individualized understanding and wisdom. ".. if such a thing is possible"

Oak bud - geometrical analysis

The following notes outline very briefly an analysis of the form of oak buds on an Oak tree on the nature strip at the western end of Chaleyer Street, North Willoughby, Sydney, Australia. This is the fifth year this work has been undertaken and photographs have been taken during the ''budding'' season, which, in this country is from about mid January to late August. The hypothesis entertained is basically that the form of the buds varies in a particular way with the astronomical position of the Moon and a specific planet combined. Among other things this research is aimed at an understanding of plant morphology and its possible relationship to the planetary system.

12-08-1995

Oloid

From two unit circles giving square root of 3 straight line length

Pattern continuity

How are patterns pursued and continued beyond what is initially visible or available.

Pattern continuity #2

How are spiral patterns pursued and continued beyond what is initially visible or available.

Pentagon and pentagram

What is the internal angle of a regular pentagon? How do we transform a pentagon and pentagram? How are the pentagram and the pentagon related to the Golden section?

Pole and polar formations

Pole and polar formations with respect to a reciprocating circle.

Pole and polar - planar basics

Pole and polar formations (in a plane) with respect to a reciprocating circle, a basic construction.

Sunday 01-06-2003

Pole and polar - planar basics

Pole and polar formations (in a plane) with respect to a reciprocating circle, a basic construction.

Polyhedra, plants, pockets and presence

The primal form characteristics of the four primal earthly kingdoms.

Tuesday 17-12-2002

Pooh-sticks and Form Fields

How good is this an analogy I wonder?

Projective Geometry Main Lesson

Outline for a year 11 Mathematics main lesson in Graphic Projective Geometry (from 16 to 17 years)

Thursday 12-12-2002

Protea

A protea like bud examined for profile and for spiral path curves.

Pumpkins a-growing

Pumpkin leaf deveIopment …

Queen of the night

This was some happening! To watch the entire development over about 12 hours …

Ratio ruminations

How do we relate one thing to another? Or compare sizes. Or …

A very special ratio (a little project for the holiday)

What is the ratio where the ratio of a small distance to a large distance is the same as the ratio of the larger distance to the sum of larger and small? A clue: it's in your face!

Another clue: Fibonaccis get to it somehow. Yet another clue: It's the measure of the pentagram. TRY TO FIND IT. Attach your exploration notes to this sheet and hand up first up next term. Please.

Saturday 18-01-2003

Reductionism and holism

The fight between fragments and fullness is enduring. But surely both are needed to help us understand our world.

Reflective pelican

Reflection gives back. This is the case with water, - is it the case with thought too? If this is so then what is the mirror and what happens when the water is roughened or stormy? If our soul life is 'roughened' by gossip, prejudice, fear or fantasies what chance has it of reflecting reality?

Repetition

Seemingly simple .... but

Root and fruit …

Opposite gestures that seems to live in fruit and plant root structures.

Saturn-Sun-Moon-Earth evolutions

Is there a geometric counterpart to these incarnations of the Earth. Stephen Eberhardt thought there was.

Scottish stone balls

Mostly in the North East of Scotland some strange little rock lumps - often finely carved - have been found. No one knows what they are or what they were for or even who made them. This makes them interesting. Very interesting.

Seeing the unseen in the seen.

We usually do not see what we see when we see it. It sometimes needs a hint as to what can be seen - but with the awakened eye of the mind not just the physical eye. Then we can even ask - can you make the mathematics do that? … and the answer is ………….

Sequences in plant growth

Is there a systematic and sequential change in the forms that central plant organs exhibit as they grow over the season? Can this slow metamorphosis be related to a variation in Lawrence Edwards form factor, lambda?

Sequences of Terms

1 and 3 and 5 and etc is part of a sequence. 1 + 2 + 3 + 7 + etc is a series if taken to infinity. This latter is the result of a pattern, not in space (or geometry) but in number.

Shepherds, Magi, & the cognitive life

Two directions in our soul life suggest that we grow by both inner and outer practice. This means enhancing our concept life imaginatively and deepening our perceptual life by warmth of interest in what we sense.

Saturday 11-01-2003

Spaghetti - and structure

The bits aren't the form and the form is not the bits - but the form might inform the bits to bring about a form of bits.

Species, more and more and more species

Few species in the mineral, more in the plant and still more in the …

Tuesday 10-12-2002

Spinal directions

An outline of .....

Tuesday 17-12-2002

Spirals in tree trunks

The trunk of the tree is not always straight - meaning that the wood and the bark often spiral around the trunk center. Is there any overall structure of which this spiraling may be a part?

Steam turbine project

The making a simple steam driven fan or turbine as an example to demonstrate use of heat in the science of the industrial revolution.

Symmetries

Three symmetries from Desargues Theorem, reflection, translation and rotation.

Sunday 22-12-2002

Tetrahedrons galore

Is this the ''philosophers'' after all?

Three Dimensions Views

Some examples of double pictures that can be viewed as three dimensional.

Trees - as ''eggs''?

Is your basic tree a basic egg form and if so, to what extent?

Trees - from seed to staff to shell

I have often noticed, when observing trees how the whole rising branch structure appears to be rising into surface shell.

Friday 6-12-2002

Urchins

Is the profile of an urchin like unto an egg?

Vertebra

A drawing that a colleague spontaneously said ''that looks like a vertebra''. So that is what I call it. Even if the vertebra of the human is a trifle more complicated! Obviously.

Tuesday 29-10-2002

Vortex drawing

Plan and elevation blackboard drawing.

Vortex forms

Research into Living Forms Seminar at Strontian, Scotland. Outline of part of a talk given by John Blackwood

Warp and Weft

In this idea is the notion that many a phenomena show a bi-directional story. We often notice that nature appears to weave her forms. There is an ongoing warp across which is the line of the weft.

This means to say that there often seems to be an ongoing flow of striation in time while across this is a rhythmic expression of striations or nodes but appearing periodically.

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Neolithic, Egyptian and Platonic solids

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