A direct representation is the thing itself; i.e., everything that exists in the universe is a direct representation of itself. For example, the direct representation of a particular proton is that particular proton. In fact, there is, and can only be, one direct representation of each particular thing that exists in the universe. Hence, the referent (i.e., extension) of a direct representation IS directly composed of the representations intension, where the extensional representation is the only instance of the thing represented. Composition in the sense used here is equivalent to containment; i.e., in a direct representation, the extension is composed of its intension because it contains its intension. The existence of the intension is equivalent to the existence of the extension. Everything that exists represents itself. In short, existence represents itself. This can be represented symbolically by the equation: Existence = Representation. Mathematically, a direct representation is endomorphic. Each particular or “thing” that exists in the universe is the only direct representation of its own existence. Direct representations are “first-person” representations. They represent things from the first person “inside-out” perspective of the things themselves instead of from the third person indirect “outside-in” perspective of an external “observer”. In a direct representation, any calculations, computations, or processes occur directly on, and in terms of the actual thing itself, and hence directly on its own representation. The importance of direct representation has been seriously underestimated. Development and application of direct representations is the key to solving many of the deepest unsolved problems in Philosophy, Physics, Cognitive Science, Artificial Intelligence (AI), and the theory of representation. One of the most difficult unsolved problems in logic, AI, and cognitive science is how to create a knowledge representation that can perform computation from a “first-person” perspective. How do we make a computer self-aware? How do we give a computer the ability to represent and understand meaning from a first person perspective? How do we give it an intrinsic sense of self; e.g., cogito ergo sum? I think, therefore I exist. How do we create a conscious machine? Direct representation is the key to the solution to ALL of these problems.
Direct representation is also the key to the creation, representation and ongoing construction and operation of existence itself. Everything that exists must have some representation. Without representation, there can be no existence. The direct representation of existence IS existence. Furthermore, things must be able to exist independent of the existence of an observer. Existence cannot represent itself from the perspective of an observer. Existence is logically prior to observation. Thus, the representation of each thing that exists must exist independent of the existence of an observer. Just because nobody is around to observe a thing does not mean that thing does not exist. Space-time, matter and energy were all present in the universe long before there were any observers to experience them. This means the representation of existence cannot depend on an observer in any way whatsoever. The representation of existence must be entirely observer independent. The only way to eliminate the observer in representation is to define a type of representation in which everything that is represented is its own observer. We must use an endomorphic representation in which the referent of the representation of a thing refers to the things own representation. Everything in existence is then represented from its own “first person” perspective. In existence, things are not represented relative to an observer. The representation of everything in existence is represented relative to itself. Existence represents itself. Understanding this is critical. If you do not understand this, you will never fully understand existence. Do not despair if you don’t fully understand this immediately. Direct representation is actually very simple, yet it can be a difficult concept to grasp because we are so used to representing things indirectly to express them as information.
Direct representations are also context dependent. Direct representations always represent things in context. Their representation is defined in terms of and relative to the context in which the representation exists. Everything that exists exists in, and is represented relative to some context. By contrast, indirect representations are context free. In an indirect representation, the representation does not vary as a function of the context the object is contained in or used in. For example, the representation of the letter ‘e’ does not vary as a function of the word it is contained in or as a function of the sentences it is contained in. The same word can represent different meanings in different contexts, but it is spelled the same way in every context. In an indirect representation, the meaning is not encoded as part of the representation so the fact that the meaning of a word may be interpreted differently in different contexts is independent of the representation of the word.
Direct representations are encapsulated because they are defined and encoded relative to, and in terms of, the context they are represented in, and because each thing represents itself. Consequently, each particular requires its own representation. The representation of each particular can only be used once in the context it is part of. There is always a one to one relationship between the representation and its only instance. By contrast, indirect representations are unencapsulated. In an indirect representation, the representation of a particular is indirect. The extension is a substitute for the thing represented by its intension, not its intension itself. In addition, in an indirect representation, the encoding of the relations that define the intension are independent of the encoding of the intension, not defined relative to, and in terms of it. Hence, in an indirect representation, the ontology does not constrain the completeness of the intensional representation, so it can be incomplete unless constrained by domain specific ontological consistency rules outside the ontology itself. In an indirect representation there can be a one to many relationship between its representation and its instances. Many instances of the same thing can occur in many different contexts. In a direct representation the extension is an identity for its intension.
Direct representation can seem very odd because it is counter to the way we normally represent information. We must use information to communicate. The meaning of information is always defined and understood relative to an observer. A book does not understand the words it contains. The letters and words in a book have no meaning, in and of themselves. The meaning is only in the mind of the book’s reader. Each observer interprets and understands the meaning of information relative to their individual state of knowledge when they read the book. The point is, the meaning of ALL information is inherently relative to an observer. Yet we know logically that the representation of existence cannot depend on ANY observer. Therefore, the representation of existence must not be based on information. If the representation of existence is not based on the representation of information, but we only use information to communicate and reason about existence, we constrain our ability to reason to that which can be represented and communicated using information. If existence itself is not represented using information, then how can we hope to fully understand it? If we base our understanding solely on information, our understanding will always be constrained by the limits of the representation of the information, logic and mathematics we use to reason and communicate it.
To understand existence fully, we must create and use a system of representation that has the same, or fewer limits and constraints than the representation of existence itself. We must create a logic and mathematics based on the first person direct representation of existence instead of the third person indirect representation of information. After we do this, things that are extremely complex and difficult to understand, represent and compute using information will be simple and optimally efficient. Once we use the proper representation, we will be able to represent how anything relates to anything else in any combination of any number of dimensions in any context and perform logical and mathematical operations irrespective of the dimensionality of the representation. Put in less abstract terms, we will be able to perform arithmetic directly on systems of any combination of dimensions. We will be able to represent everything in its most efficient number of dimensions and perform all calculations the same way regardless of the dimensionality of the representation or the complexity of the computation. For a less abstract example, imagine being able to directly add vectors of any combination of different dimensions together, or imagine being able to directly take the dot product of vectors of any combination of different dimensions. Imagine a single operation that is the universal of computation in the same sense that an entity is the universal of information. In terms of the representation of thought, imagine being able to calculate directly in terms of concepts and abstractions at the speed current computers calculate in bits. That is the magnitude and import of what I am talking about here. The potential gains in human understanding through application of this knowledge boggle the mind.
Our ability to understand the representation and operation of existence is not as hopeless as it may seem from the discussion above. We are all born with an internal knowledge representation that can transcend and surpass the constraints and limitations of logic and information. The human brain’s knowledge representation is actually less constrained, and more capable than the representation of existence. It is not our innate ability to reason that is fundamentally limited. It is our inability to fully communicate the results of our reasoning via the translation to and from information that limits our understanding.
We think directly at the level of concepts and abstractions. We just cannot communicate and transfer that knowledge directly to others. Instead, we have to convert it to information first. It is not that we cannot represent anything we want to with information. Subject to language limitations, we can. It is just impractically complex, lengthy, and time consuming to do so.
Information does not encode the meaning of knowledge. It can only encode information about knowledge. Normally, pragmatic time, space, and complexity constraints only permit us to encode a minuscule fraction of a small portion of selected aspects of our knowledge for communication. Even then, the information transmitted is subject to misinterpretation and may be misunderstood by its recipients if their preexisting knowledge of the topic of communication is not sufficiently similar to that of the sender. Even worse, if we only think in terms of symbolic information, we hobble our intellect. We limit our thinking to that which can be represented by information, and we slow our thought by making things combinatorially more complex than they really are if we allowed ourselves to think and reason directly in our brain’s direct internal representation.
Have you ever wondered why you can think much faster than you can reason using symbolic logic, or perform mathematical calculations? Have you ever wondered why a picture is worth a thousand words? Have you ever wondered why we can grasp complex relationships almost instantly with the help of a good illustration or recognize an image in a picture almost immediately, yet trying to understand the same content if it is described in words or mathematical equations is slow and error prone if it can be expressed in words or equations at all? The same is true of listening to music, tasting a good wine, or smelling a flower. Representing these things using symbolic information is complex, slow, and often difficult or impossible. Sometimes we can teach ourselves specialized languages or specialized notations and train ourselves to do it but it really slows things down.
What if there was a way to think about, analyze and understand highly abstract concepts as easily as you can understand a picture? By understanding and internalizing the representation of thought, and the representation of existence, you will be able to do so. It will not happen overnight. At first, the change will be very slow, almost imperceptible. It will not seem like anything is different. Then you will catch yourself understanding how you thought about something right after you thought about it. Gradually, you will notice an increased ability to understand abstract topics like mathematics and quantum physics. The rate at which you can understand abstract topics will continue to accelerate. Learning the representation of existence and the representation of thought is the gift that keeps on giving. The only thing that will slow you down is the necessity to convert your understanding into words to communicate it and teach it to others. Alas, that cannot be avoided. Communication is only possible using the representation of information.
A block diagram that shows how things are represented using direct representation is shown below. In this diagram Thing1 is related to Thing2 by relation R1. It is also related to Thing3 and Thing4 by relation R2. The intension of the representation of each thing is composed of the representations of the things that compose it. Therefore the representation is fully encapsulated. All items are represented "by value", and each item is a singleton. In other words, each item has a unique identity and there is only one instance of each item. The consistency and completeness relations are part of the ontology of direct representation. No intelligent observer is required to define them, and no extra representation is required to represent them. In the representation of existence, representation = existence. We can use a variant of a direct representation in a computer to represent things directly, as long as we maintain a one-to-one relationship between each thing in existence and its representation in the computer. In other words, a direct representation is characterized by a one-to-one relation between the existence of each thing and its representation.
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