Impressionist Theory of Everything


The holy grail of physics is the future discovery of a theory that would unite all the forces of Nature into one mathematical principle - a Theory of Everything for the Universe. The Impressionist Theory of Everything presents the argument there can be no such thing. Paradox is identified as the fundamental mechanism that prohibits this. What should be discoverable as singular fundamental truth, the meaning of everything, categorically breaks down, and gives rise to dualism as fundamental. Beyond the subjects of physics and mathematics, the same applies for all contexts to the nature of "universal meaning". Paradox is the mechanism behind the natural dualism we find in all things.

Since the dawn of critical rationalism, when considering what is infinite, we have made one universal assumption that falls short.

We have assumed that there are no limits to human information and knowledge.

Now, with the great advances in our science and critical thinking we are lead to draw exactly the opposite conclusion.

The paradoxes that arise, naturally, in all infinite systems are not anomalies.

Rather, paradox is the critical formative element that makes possible the very existence of observable Universe and all that is contained within it.

The Universe is a sea of complexity that opens to observation not in the form of singular truths, but rather as a dualism of perspectives in each view - across which paradox is the mechanism.

                                              Main Menu (to return to the main menu click <M>)


          What Is the Question?

          Paradox as a mechanism

          The Russell paradox


         The Term "Impressionist"

         Why Impressionist?

Topic Summaries and Document Links for IToE:

          1. The Philosophical Concept: Its Mathematics and Geometry

                  Chapters 1.1 to 1.9

          2. Application of IToE to EPR-Type Phenomena

                  Chapters 2.1 to 2.2

          3. Classical Phenomena

                  Chapter 3.1

           Author and Background



What is the Question? Infinity and the observer

A "Theory of Everything" is a very special case of formal argument. It is meant to represent, universally or infinitely, all factors that apply in the defining the given structure which is, itself, an infinitude for causality. Intrinsically, whether or not such a theory is possible depends on representation of an infinitude in a formal logical structure. Is there an absolute limitation to such representation that falls short for conclusion in theoretic terms? To consider this point, the general subject of infinity (as defined under the framework of IToE) is examined. Well-documented empirical and theoretic examples exist for what we should expect in regard to observing an infinitude and, for that matter, how we should define infinity in the most general terms. These examples lead to the conclusion that it is not possible to construct a "Theory of Everything". In some regard, any such structure will display inconsistency or remain incomplete. <M>

The "Impressionist Theory of Everything" seeks to establish the general property of infinity and how this property places an absolute barrier on the observer to draw conclusion. The best way to analyze this is through the examination of dualism as it applies within given examples of infinities. <M>

There are many subjects areas the "Impressionist Theory of Everything" can be applied to. This study touches on only a few in physics and mathematics. Others include: in philosophy, the relationship between art and science; 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. All of these examples point to how dualisms, within a common structure, are joined paradoxically. The diversity of examples having this form shows that paradox is a fundamental mechanism in the universe for our view of reality. <M>

Paradox as a mechanism in formally representing the physical Universe

When we explore the interior of any infinitely defined structure, the existence of an absolute dualism is irrevokable. In the most general sense, whenever we seek the singular meaning of anything, we have invoked some aspect of infinite and circular self-reference. In all examples of infinitudes, the mechanism that creates absolute self-referential dualism (and equally the prohibition to declaring absolute truth) is the mechanism of paradox. Paradox is the only mechanism that allows a self-referential structure to be closed absolutely. In the same instance, the consequence is that we are denied the information necessary to draw complete formal conclusion. Paradox is not an anomaly to understanding reality, but rather is a systemic mechanism in the creation of all reality. <M>

An important area of study for defining the framework of IToE is physics. To date, our attempts to define the Universe according to a single, complete, formal, mathematical system have failed. Although two of the competing theories (relativistic and quantum-mechanical) have been completely validated to the very high limits of our measurement tools, they each remain incomplete. In simple terms, neither addresses the issues raises by the other about the nature of the Universe. The same situation shows up in the laboratory in the structure of Einstein, Podolsky, Rosen (EPR) type experiments. Both classical (reality-based) and quantum-mechanical (nonreality-based) models apply and neither addresses the issues raised by the other. We are being informed of something very important at the most complex level our quest to create a Theory of Everything. A fundamental dualism always arises in the interpretation of meaning. An absolute and nonresolvable dualism is invoked. <M>

For the dilemma found in EPR experiments, the prevailing bias held in academic discussions is that the classical format is only an approximation. However under IToE, classical and quantum-mechanical structures in EPR experiments are place on an equal and complementary footing by understanding the natural 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 has a uniquely separate format between the classical and quantum-mechanical views for the observer that are as follows: <M>

1. Self-reference is internal to the system and observer is found outside. This is the associated quantum-mechanical form. In this case, paradox is openly displayed between the relationship of the parts. The relationship of these parts is necessarily inconsistent. Consequently, the overall structure is closed to observation, and it is stationary. For example, in EPR experiments, that display a dualism for path, these paths are classically entangled. In other words, they are classically inconsistent. For more complex quantum-mechanical states this entanglement is spread finely among all the states, but the same general principle applies. <M>

2. Self-reference applies externally and the observer is found inside of the system. In this case the observer can be thought of as inside the system, and the system extends beyond the absolute limit to reference for the observer. From the perspective of dualism, the listing that is complete and the rules that apply (as infinite) to the view of the observer remain incomplete in a larger frame of reference. This results in an overall inconsistency between two frames of reference (one of which applies to the observer and one which is outside of the frame of reference of the observer). <M>

Paradox is the mechanism ideally suited to prevent the singular resolution of what is described infinitely as a dualism. This perspective on singularism (the whole) and dualism (its parts) 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>


In common language, we use the term "infinite" to describe the extent of anything that is absolutely beyond enumeration of its extent -- for example, the Universe. <M>

Infinity is the identity of any system in which complete, well-ordered reference to property is categorically prohibited. The mechanism of this prohibition is non-reducible paradox. <M>

The ultimate form for such an infinitude is the Universe itself. Both formats for the display of infinite self-reference, as described above, are separately found. For each form, when we attempt to formally or informally draw conclusion or understanding we are prevented. Endless change is found within, and an irrational linkage is found 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. We are denied the information that allows conclusion to be drawn and consequently remain in an uncertain state. <M>

The Term "Impressionist"

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>

Why Impressionist?

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>

The Impressionist Theory of Everything 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 complement to understanding what it means to experience reality and have knowledge of it through formal and informal description. <M>

I invite discussion and welcome all critical comments on IToE. Please correspond to me at

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>


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)


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 (December 22, 11)


Chapters in Section 3

3.1 Emergence and Entropy (March 4, 03) (Under Rewrite as of May 2013)




            The author wishes to thank Jacqueline Dinsmore for her indispensable assistance in editing. The Impressionist Theory of Everything 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 papers has added immeasurably to their presentation. <M>


Doug Gill       updated: May 14, 2013

                                                                        A Zen koan for contemplation: Meaning is not possible, unless meaning is not possible.