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. Any system, for 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. It can be shown that the elements of such dualisms are inherently incongruous; yet, this incongruity is also the basis on which these juxtapositions are able to form closure that is fundamental, complete and entirely self-contained. This form 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 of its extent -- for example, the Universe. Nevertheless, the critical property for any representation of infinity is that it contains completeness for self-reference in the absolute sense.

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An infinity can be defined as any theoretic or empirical structure that displays some property that is complete for its enumeration and self-reference. <M>

Curiously, it is always found that, for the display of any internal relationship of parts (minimally as a dualism), such parts are always juxtaposed incongruously. The mechanism of this type of relationship is paradox.

When we try to draw conclusion, for 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, as enumeration proceeds, and the second is that an irrational linkage exists between the parts. In this case, the parts are complete for their description of the infinity, but they are necessarily inconsistent as a rational grouping. <M>

The ultimate form for such an infinitude is the Universe itself. In this example, we find both forms of self-reference separately displayed when any attempt is made to formally or informally draw conclusion or understanding. Specifically, 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. In whatever form is appropriate to our line of enquiry, we are denied the information that allows conclusion to be drawn, and we remain in an uncertain state. <M>

Infinity, the observer, and the meaning of truth

The Impressionist Theory of Everything (IToE) explores the meaning of "infinity" and the inferences that exist for such complete self-containment in regard to our ability to have information. The observer necessarily has one of two relationships to any example of an infinity. In each case, the completeness of information is always limited, and the observer is denied the ability to draw absolute conclusion. The Impressionist Theory of Everything 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 and, for religion, the meaning of God -- in the Arts, the relationship between humor and literalism, and 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, the nature of the dualism we find in political systems. <M>

In any information available on an infinity, absolute dualism is irrevokable. In the most general sense, whenever we seek the singular meaning of anything, we have entered the topic of the meaning of absolute and singular truth. We have also invoked some aspect of infinite self-reference. The study of this issue in limited academic terms teaches us the valuable lesson that there are no absolute answers. IN any example of infinity, the mechanism for the separation into dualism and the prohibition to declaring absolute truth is paradox. Paradox allows a self-referential structure to be closed absolutely and deny us the information necessary to draw conclusion. <M>

Paradox as a mechanism in formally representing the physical Universe

An important area of study for defining the framework of IToE is physics. Our attempts to define the Universe according to a formal mathematical system and provide complete information on the nature of the Universe always fail. Dualism arises for the interpretation of meaning. This is the situation between classical and quantum-mechanical descriptions of the Universe. It also shows also shows up in the laboratory in the structure of Einstein, Podolsky and Rosen (EPR) type experiments. An absolute and nonresolvable dualism is invoked. <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 nature role of paradox in the limitation on what we can know about any infinite system. <M>

For any dualism formed within the context of a infinite system, the mechanism of paradox is a necessary component in order to close the system and create absolute self-reference. This mechanism or device takes a unique form in each example but always shows up in one of two general ways to the observer:

1. Self-reference is internal to any outside observer of the system. In this case paradox (again for the instance of dualism) 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 and it is stationary. An example of this is any quantum-mechanical structure.

2. Self-reference applies externally relative to the observer. In this case the observer can be thought of as inside the system, and the system extends beyond any reference point for the observer. Again from the perspective of dualism, any listing that is complete (as infinite) can also be shown to be incomplete in a second frame of reference (that is self-referential to the first). This results in an overall inconsistency between two frames of reference. Alternatively, if we attempt to list all the members of the system (not just as a grouping of dualistic elements), then it is found that the enumeration of all the members of the system is not possible. In both cases, the observer either finds that change is not stoppable, or there is the presence of an undefinable and nonobservable part. <M>

For both of the above formats for the appearance of an infinity relative to an observer, the mechanism responsible for inconsistency or incompleteness is paradox. Under IToE, paradox is considered a fundamental and legitimate mechanism in the universe. 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 a 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. The defining characteristic of such a structure is that it is paradoxically composed. 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 and relative to its own boundary for property, we find, for R a dualism of rational true placements both within and not within. 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>

Why Impressionist?

The Impressionist Theory of Everything (IToE) presents a very simple model for how all infinite structures must be composed. This includes the universe itself. The frame of reference for IToE is interdisciplinary and understanding the model does not require any advanced working knowledge in academic subjects. Nevertheless, the inferences and conclusions of IToE are seen to apply at the boundary of our current understanding of the universe. <M>

Any study of paradox as a mechanism in infinite systems 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 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 correspond to me at douggill@pathcom.com.

The material on this web site is the first in a more extensive series of topics. New and updated articles will be published on this site. <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 (March 4, 03) (Under Rewrite as of January 2010)

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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: January 6, 2010

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