Welcome to Shiela's work
About 1980 I found that by weaving diagonally the Klein bottle form can be made perfectly with just one straight line (geodesic) thread. This is a remarkable property. Looked at locally there are two sets of threads ('warp' and 'weft') which are doubly opposed, they lie at right angles each to the other (are orthogonal) and each is upside down to the other, but globally they are all one thread. In this physical model opposites are indeed One, just as the ancient Chinese Taoist wisdom declares. The wire model (pictured) can be used as a conceptual tool for thinking about the Universe. Its breakthrough point is 'read' as the Big Bang.
Introduction..............God In My Handbag
When I was forty-eight I realized that I could weave a figure that could resolve for me the paradoxes and ambiguities of spacetime and relativity. Twenty-six years later I am still astounded that this happened to me; the figure proved to be so fertile in the explanations and parallels that can be drawn from it that I now suspect it to be a valid model for the vastly mysterious reality that lies beyond our familiar spacetime. It models the quantum domain as the arena in which our subsidiary sensory world is embedded and it has resonances with the most recent fundamental theories of cosmology. These are huge claims; they are in no way due to me, they just leap off the figure once you "read" it in a certain way. In the years when I was working with paper models to determine the weavings that produce a perfect figure I would sometimes sit in on Quaker meetings- I was what was known as 'an attender'. I went to one such meeting with a model in my handbag. It is the sober reverential practice to refrain from speaking in Meeting unless 'moved by the spirit', members only speak when they feel they must. I was so overawed by what the figure was revealing that I burst out: "Friends, I've got God in my handbag". The silence did seem to deepen and when the meeting ended the Friends' consternation was evident. Explanations were in order. The figure is my model for All-That -Is; God, for me, has never been limited to a projection of the best that is in us; we may be made in His image but to assume that the reverse is true (old man in the sky concepts) is perilously deluded, egocentric and arrogant. Infinity is essentially unknowable. When I try to think about God I feel like that cartoon ant trying to understand the world that we are not equipped to comprehend. The Model, so precious to me, is just the familiar Klein Bottle shape but it is constructed by weaving, and it is woven in a diagonal direction with just one single geodesic thread.
It has led me to snoop in unfamiliar areas - topology, geometry, group theory, metaphysics, cosmology and most recently into the quantum domain of String- and 'M'-theory. Forced into some serious reading, I became an avid collector of 'hard' books - books on cosmology and physics written by brilliant communicators like Roger Penrose and Mishio Kaku (favourites) who so generously seek to make their disciplines accessible to lay people.
Chapter One............The One-Thread Rhapsody
Consideration of the opposed sets of threads as representing space and time leads to the understanding that time has three dimensions and to the proposal for a new time unit--the Chrono-- to parallel the light year. Stretching the woven mesh shows how space and time are reciprocal, and how space can emerge from time. By interpreting the One-Thread as real and absolute one can regard its intersections as the quanta of spacetime. This then shows our spacetime matrix as a subset of the One-Thread which is outside space and time, is non-local and a-temporal-------i.e. the quantum domain. The universal present moment reads as simply the places where things are on the spacetime matrix. Kinks and energy patterns on the model lead to the idea of particles as twitches in spacetime, to pairs of particles distinguished by spin, to antimatter and to compression waves as possible carriers of telepathic and paranormal information.
Note: All chapters are supplied in MS word format. You can open the document by left-clicking on the link, or use right-click and save the document to your hard drive.
Chapter Two............Two-Faced Surfaces
The Klein bottle form can stream through a sequence of four distinct postures and turn itself radically inside out. The 'Mad Hat' posture resembles a torus, my knitted model is a possible monopole structure. It leads to the conjecture that the fermions may be the missing monopoles. Real Klein bottles and Moebius strips have ugly non-conforming joins which can be avoided by using a double surface. This gives an object with an outward facing face and a hidden, inaccessible inward facing face. This may relate to the hypersphere and the recent theories of two 'branes' in a hyperspace.
(2a)The Postures of the Klein Bottle
(2b)Exploring the Moebius Strip and the Klein Bottle
(2d)A Possible Model for a Monopole
Chapter Three ..........Very Heavy Thinkings--Reconciling the model with the ever-expanding Universe
Reconciling the Cyclic Diagonally Woven Model with the accelerating expansion of our Universe: A standard projection technique wraps our 3d. universe onto a spherical fourth dimension, this shows spacetime changing abruptly to a Lobochevskyan expansion, corresponding to the real change to our ever increasing expansion. Pinching the spherical 4d. reverts to the 'Mad Hat' 'monopole' model, the projection technique gives a holographic image. Multiple meanings of the word 'Universe'. Alternative 'readings' for M Theory and Loop Quantum Gravity. By acting as a template for an infinite progression of cycles the K. B. model economically dispenses with the Anthropic Principle. The K.B. model explores itself in a seemingly purposeful way.
Chapter Four...........The Related Structure of the Tables
The One-Thread weaving can only be achieved by using certain proportions of weaving spaces. Paper models allow thread lines to be traced and tables are built up showing the thread requirements for weaving or winding Klein bottles, Moebius strips and toruses. A complex utterly dense radial pattern of 'signature' lines emerges which lies over a normal grid; the primes show up as a merely coincidental consequence. The torus table is self-generatimg. Apparent abnormalities in the signature lines are resolved when the table is drawn up in four quadrants.
(4a) The Three Tables of Thread Requirements
(4b) Interchanging the Three Tables
(4c)Radial Patterns on the Three Tables
(4d)Radial Patterns on the Klein Table
(4g) The Dense Complex Web of 'Signature' Lines
Chapter Five........... The Geography of the Table
The three tables of information wonderfully mirror the properties of the shapes they report on; the torus has normal and inside-out versions on different areas of its table. These enantiamorphic pairs may model the supersymmetry pairing of particles.
Chapter Six........... The Architecture of the Table
The structure of primary signature lines suggests a layered three dimensional stack of tables with folded valleys. Six of these stacks can be used as the faces of a cube which,in its vastly dense radial structure,imitates spacetime. The cube model is the tangible geometric instantiation of the process of set-generation of the natural numbers. The Klein bottle illuminates the Russel Paradox, when it streams through its postures it progressively contains and releases all parts of itself; it is capable of exploring itself.
Additional Resources
How the Diagonally Woven Klein Bottle Revealed Itself
How to Knit a Perfect Moebius Headband
How to Knit a Shape-Changing Klein Bottle Hat
Making a Perfect Double-Skinned Klein Bottle
Contact Details
Shiela can be contacted via e-mail:shielamorgan1@bigpond.com