IToE (Impressionist Theory of Everything)

The term "Impressionist" is adopted from the well-know style of art called "Impressionism" (see The Impressionists - Biography on A&E). In their period, the Impressionist artists, began new exploration of the relationship and balance between form and content. They shifted this balance away from the direct representation of content, in order to study the richness of colour and shape for its own sake. While recognizing the role of content, at the deepest of levels, without the pure rules of placement and colour, there can be no beauty. The creation of beauty, depends on this dualism of complementary factors. <M>

The Impressionist Theory of Everything focuses on the natural place of such dualisms in the Universe. These dualisms are inherently incongruous; yet, this incongruity is also the basis on which a juxtaposition is formed that allows closure of the pair as a complete and self-contained singularism. This basis of construction is found systemically throughout Nature, in any regard that completeness is represented -- the format is the same but its representation is always unique. The purpose of IToE is to present the theory behind this fact of Nature through diverse examples. <M>

Infinity

In common language, we use the term "infinite" to describe the extent of anything that is beyond enumeration -- the Universe is one example, but in limited contexts there are many others. The critical property for any such structure is that it contains only self-reference, and consequently, the subject has the property of absolute self-containment.

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In the broadest sense, an infinity can be defined as any theoretic or empirical structure that displays self-reference in an identified property. In this composition, correlated parts are juxtaposed as incongruous by the mechanism of paradox. <M>

When we try to draw conclusion, for the relationship of the parts, in any such dualism, an inconsistency always arises. Regardless of the example chosen, a boundary is always found that categorically separates the parts and disallows a consistent or complete framework for conclusion. There are two possible forms for the expression of such dualism. The first is endless change, and the second is an irrational linkage between the parts. <M>

The ultimate form for such an infinite boundary is the Universe itself. In this example, we find both forms of self-reference separately displayed. Endless change is found within, and an irrational linkage exists to the outside. On the grand scale, the concept of IToE points to the fact that, in any format of observation and conclusion, the universe cannot be completely and consistently viewed for its totality. This larger totality is best referred to as a "meta-state". A boundary exists for the observer, beyond which the meta-universe is necessarily inconsistent. <M>

Infinity, the observer, and the meaning of truth

The Impressionist Theory of Everything (IToE) explores the meaning of "infinity" and its inherently associated property of self-containment. In particular, IToE studies the relationship of the observer to such structures. There are many subjects for this exploration, and I have only touch on a few of the more academic ones. Others include: The relationship between religion and science -- for religion, the meaning of God -- in the Arts, the relationship between humor and literalism -- within humor, the structure of humor -- for literature, the relationship of plot and story -- for philosophy, the relationship between art and science -- and finally to complete this partial list, for our coexistence together, the nature of the dualism we find in political systems. <M>

In all of these topics, we can point to a critical element of self-containment that is created through paradox for the given absolute dualism. It is of great important to understand that such dualism is irrevokable. In the most general sense, whenever we seek the singular meaning of anything, we have broached the topic of absolute and singular truth, and we have also invoked some aspect of infinite self-reference. The study of this issue teaches us that there are no absolute answers. The mechanism of separation for dualism and the prohibition to absolute truth is found in the natural and legitimate element of paradox. Paradox allows a self-referential structure to be closed absolutely. <M>

Paradox as a mechanism in formally representing the physical Universe

An important area of study for defining the framework of IToE is physics. Infinity and the mechanism of paradox show up in our attempts to define the Universe according to a formal mathematical system. For example, this arises in the relationship between correlated classical and quantum-mechanical structures, found in EPR experiments (after a thought experiment discussed by Einstein, Podolsky and Rosen). An absolute and nonresolvable dualism exists. <M>

The prevailing bias held in academic discussions is that classical format is only an approximation, and this is seen to resolve the issue. However, under IToE classical and quantum-mechanical structures in EPR experiments are place on an equal and complementary footing by understanding the role of paradox. <M>

The structures examined, in this application of IToE, include theoretic arguments and empirical experiments. The central premise of IToE is that such structures cannot be properly closed as infinite unless we find the presence of a strong element of self-reference created through paradox. This mechanism or device takes a unique form in each example but always shows up in one of two general ways:

1. Self-reference is internal, in which case paradox is openly displayed between the relationship of the parts. The relationship of these parts is necessarily inconsistent, and consequently, the overall structure is closed to observation of its parts. An example of this is any quantum-mechanical structure, or

2. Self-reference applies externally relative to the observer, in which case a listing that is complete (as infinite) is shown to be incomplete in a second frame of reference that is self-referential to the first. This results in an overall inconsistency between the two parts. This takes the form of change, to the observer or as the presence of an undefinable, nonobjectifiable and nonobservable part. This part is excluded from the whole, to the observer. <M>

In both cases, the mechanism responsible for this inconsistency or incompleteness is paradox (albeit in a different format). Rather than representing an anomaly to be resolved, under IToE, paradox is viewed as a fundamental and legitimate mechanism in and for the universe. Again, the general consequence of this is that, in any view of infinity, our ability to draw conclusion always suffers from either inconsistency or incompleteness. <M>

Paradox is the mechanism ideally suited to prevent the singular resolution of what is described infinitely as an absolute dualism. This perspective on singularism and dualism is not resolvable. <M>

The Russell paradox

The Russell paradox is the linguistic statement of the inferences that apply when a property is described infinitely (by self-reference) within a boundary. Paradox is a necessary feature. The Russell set R is, the set of all sets that are not members of themselves. <M>

For R, the issue of nonresolution arises in the context of whether R is a member of itself or not. As a minimum, we find a dualism of rational true placements both within and not within, for R, relative to its own boundary for property. Paradox arises because these placements are mutually false. Consequently, a fundamental and absolute dualism exists for the description of the singular domain of R. <M>

This study is interdisciplinary and based on a model that does not require advanced working knowledge in academics. Nevertheless, the inferences and conclusions of IToE are seen to apply at the boundary of our current understanding of the universe. <M>

Why Impressionist?

Any study of paradox as a mechanism is inherently impressionistic, since it is the comparison of nontransformable opposites, that are, nevertheless strongly linked in a larger common structure. The Impressionist Theory of Everything has application for deeply understanding the relationships that exists within and across perspectives of philosophy, science, social science, and art. The principles set forth in the concept of IToE do not replace or contradict the description of Nature found in our formal models. Rather, IToE is a true complement to the process of formal description. <M>

I invite discussion and welcome all critical comments on IToE. Please write to me at douggill@pathcom.com.

The material on this web site is the first in a more extensive series of articles in the topics I have outlined. I would also like to invite anyone to contribution to this series or to provide me with linkages that I may include to similar web sites. <M>

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Topic Summaries and Document Links

Section 1. The Philosophical Concept: Its Mathematics and Geometry

This section introduces the fundamental elements that form the Impressionist Theory of Everything (IToE):

1. Paradox is a systemic and fundamental mechanism in the universe. This is justified by reference to a diverse collection of theoretic arguments.

2. A mathematical and geometric model is derived from analysis of the consequences naturally inferred by the presence of paradox.

3. A principle of conservation is identified for the collapse of the wavefunction across the quantum mechanical and classical structure of a common domain. <M>

Chapters in Section 1

1.1 The Frame of Reference for the Impressionist Theory of Everything (Nov 30, 02)

1.2 The Paradoxical Reversal of Property in Three Theoretic Structures (Oct 25, 02)

1.3 Two Mathematical Spaces, One Roof: The Local and Nonlocal Structures of the Unit Circle (Feb 8, 04)

1.4 Two Geometric Spaces, One Roof: The Local and Nonlocal Structures of the Unit Circle (Feb 8, 04)

1.5 The Cross-Dimensional Development of Angularity (Nov 30, 02)

1.6 Primordial Cycle (Nov 30, 02)

1.7 The Hexorthogonal Geometry of Subclassical Space (May 23, 04)

1.8 The Photon, Graviton, Electron, and Quark (Feb 8, 04)

1.9 Time: the Binding Mechanism of the Universe (Dec 2, 02)

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Section 2. Application of IToE to EPR-Type Phenomena

All EPR-type experiments, whether they are thought or empirical experiments, present examples of the inherently paradoxical structures that arise naturally in the relationship between quantum mechanical and classical descriptions of a common space. In these experiments, the classical limit of the speed of light is violated. This sets quantum and classical mechanics against each other as rationally paradoxical formats for the nature of causality. <M>

Each experiment examined displays, from a unique perspective, the same fundamental features described by IToE. It is the wealth of commonality across divergent phenomena that is the best supportive evidence that IToE is valid. These features are:

1. The presence of two paradoxical spaces in the same structure.

2. The mechanism of paradox in the physical and theoretic representations of each experiment reverses the relationship of properties in a single domain. <M>

Chapters in Section 2

2.1 The Half-Silvered Mirror Experiment (May 4, 04)

2.2 Polarization (May 18, 04)

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Chapters in Section 3

3.1 Emergence and Entropy (removed for rewrite March 18, 06)

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Acknowledgment

The author wishes to thank Jacqueline Dinsmore for her indispensable assistance in producing this web site, especially editing all the documents. The Impressionist Theory of Everything (IToE) is the description of that which is not describable. Jacqueline's understanding of the theory and her drive to improve the style and phrasing of the documents has added immeasurably to the presentation of this concept. <M>

updated: March 1, 2006

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