Universal Representation
It turns out there is also a third fundamental class of representations that has heretofore been overlooked. I call this a universal representation. Universal representations combine direct and indirect representation. They can represent themselves and everything else directly and indirectly. Universal representation is based on the representation of abstraction. Anything can be represented by an abstraction indirectly, including the representation of other abstractions, but abstractions themselves are represented and processed directly. This provides complete and consistent direct representation of everything indirectly while avoiding the inconsistency and incompleteness of pure indirect representations and avoiding the limited representational power of direct representations.
The key idea is to represent one and only one thing directly, but that one thing then represents everything else indirectly. The one thing that represents everything indirectly is the ontology of abstraction. We use a direct representation of an instance of the ontology of abstraction to represent each thing we want to represent indirectly. That allows us to represent anything directly as an abstraction, yet the abstraction represents things indirectly. This provides a direct representation of indirect representation. It directly represents everything indirectly. With indirect representations like logic, set theory and mathematics, we represent everything represented by direct representation indirectly. Logic, set theory and mathematics do just the opposite of what the brain does. Instead of directly representing everything indirectly, logic, set theory and mathematics try to indirectly represent everything directly. It is impossible to indirectly represent everything directly because the indirect representation of everything is too complex and it is inconsistent or incomplete or both. Doing things the other way around, the representation only has to represent one thing completely and consistently. If there is only one thing to represent in a domain of discourse, the only way for it to be incomplete or inconsistent is for it to be incomplete or inconsistent relative to itself. If a representation only has to represent one thing, the representation is simple enough that we can make it complete and consistent. This then allows us to avoid the adverse consequences of Gödel’s incompleteness theorems.
Fortunately, it is possible to represent one thing completely and consistently using information, provided the complexity of that one thing is not too great. Therefore, we can use a computer to indirectly represent the direct representation of one thing, and then use that one simulated direct thing to ‘directly’ represent everything else indirectly. We use the same strategy used by nature in the brain, but it is a little less efficient due to the additional level of indirection. Nevertheless, it still provides the means to represent everything indirectly completely and consistently.
The representation of thought is a universal representation. While we have not defined the terms and laid the prerequisite groundwork needed to understand the representation of thought, a brief introduction is possible.
In a universal representation, the intension and extension are direct, but the direct use of the extension within the representation of the intension is indirect. Consequently the intension defines meaning in context from the direct first person perspective, but the extension can be used in multiple contexts and be included as part of the representation of multiple intensions. In this case, the representation of the intension and extension are represented directly by value, but the use of the extension is represented indirectly by reference.
A neuron is a universal representation because its dendritic trees directly represent the intension of a concept and the intension of the set of abstractions that constitute the intensional representation of the concept. Detection of the direct satisfaction of the intensional conditions via the process of dendritic integration triggers the firing of the neuron’s axon which signals the existence of the concept extension and the existence of the particular abstraction extension it represents in all intensional contexts it participates in the definition of. All neural processing is direct, but the representation is simultaneously direct and indirect. The direct processing and direct representation entail self-awareness and first-person understanding of the meaning of concepts and abstractions from the first person direct perspective in context, while the indirect representation of the use of the extension entails third-person reasoning about external things at multiple levels of abstraction in terms of how those things relate to other things in context. If you do not understand this right now, do not worry. We will cover all of this later in much more detail after we present the prerequisite definitions and concepts required to do so.
The diagram below shows how the same system that was represented for direct and indirect representation is represented using a universal representation. From this illustration, you can immediately see how the ontology of a universal representation resembles neural topology. In fact, there is a one-to-one mapping between the ontology of abstraction and the spatial topology of neurons. In the figure below, the solid lines with arrows leading away from each box represent the extension of an abstraction (and the concept it partially represents). They also represent a neurons axon. The dotted lines with arrows pointing toward each box represent the intension of an abstraction (and the intension of all the abstractions that represent the concept represented by the box). They also represent a neurons dendritic trees. Just like the direct and indirect representations, this diagram represents Thing1 as being related to Thing2 by relation R1, and Thing1 being related to Thing3 and Thing4 by Relation R2. When R1's axon fires, it causes synapse R1 to fire at time t. Then Thing2's axon fires at such a time that synapse T2 fires just as the electrotonic potential from synapse R1 reaches the dendritic location of T2. The electrotonic potentials then superimpose and sum and their sum flows down the dendritic tree to the axon hillock of Thing1 and arrives at some time ta. Meanwhile R2's axon fires which causes synapse R2 to fire and send electrotonic potential down the dendritic tree towards Thing1. Synapse R2 fires at just the right time so that its electrotonic potential will reach the axon hillock at time ta. Sometime after synapse R2 fires, Thing3 and Thing4 fire their axons at such a time that the electrotonic potential from their synapses also reaches Thing1s axon hillock at time ta and superimposes with the other electrotonic potentials. Because the electrotonic potentials from synapses R2, T3, and T4 are all spatiotemporally correlated, they superimpose at the position they intersect their common dendritic path and the integrated sum of the superimposed electrotonic potentials travel down to the Thing1s axon hillock together. Of course if the relative firing times are not correct, then Thing1 doesn't reach its activation threshold and doesn't fire its axon. If the relative synaptic firing times are correct, then the electrotonic potential does reach Thing1's activation threshold and it fires its axon. The firing of thing1's axon means the intensional conditions that define how Thing1 is related to Thing2 by R1, and how Thing3 and Thing4 are related to Thing1 by R2 were met. Therefore the firing of Thing1's axon represents the existence of the abstraction that represents Thing1. It signals the satisfaction of Thing1's intensional conditions and thus represents the relation between the intensional meaning of Thing1's definition and its existence. The firing of the axon doesn't encode any information directly. However, when fired, it signals the occurence of an instance of the abstraction represented by Thing1. Therefore it can transmit an arbitrary amount of meaning without the need to encode any information. That means the size of the representation is constant, irrespective of the complexity of the set of abstract relations that it represents. The size of the representation is independent of the complexity of whatever it represents in univeral representations. In addition, this means there is no neural code. There are too many other representational and computational advantages to cover here and we haven't discussed the prerequisites needed to understand them. I will cover them when I discuss the neural knowledge representation in more detail in a future blog.
It turns out there is also a third fundamental class of representations that has heretofore been overlooked. I call this a universal representation. Universal representations combine direct and indirect representation. They can represent themselves and everything else directly and indirectly. Universal representation is based on the representation of abstraction. Anything can be represented by an abstraction indirectly, including the representation of other abstractions, but abstractions themselves are represented and processed directly. This provides complete and consistent direct representation of everything indirectly while avoiding the inconsistency and incompleteness of pure indirect representations and avoiding the limited representational power of direct representations.
The key idea is to represent one and only one thing directly, but that one thing then represents everything else indirectly. The one thing that represents everything indirectly is the ontology of abstraction. We use a direct representation of an instance of the ontology of abstraction to represent each thing we want to represent indirectly. That allows us to represent anything directly as an abstraction, yet the abstraction represents things indirectly. This provides a direct representation of indirect representation. It directly represents everything indirectly. With indirect representations like logic, set theory and mathematics, we represent everything represented by direct representation indirectly. Logic, set theory and mathematics do just the opposite of what the brain does. Instead of directly representing everything indirectly, logic, set theory and mathematics try to indirectly represent everything directly. It is impossible to indirectly represent everything directly because the indirect representation of everything is too complex and it is inconsistent or incomplete or both. Doing things the other way around, the representation only has to represent one thing completely and consistently. If there is only one thing to represent in a domain of discourse, the only way for it to be incomplete or inconsistent is for it to be incomplete or inconsistent relative to itself. If a representation only has to represent one thing, the representation is simple enough that we can make it complete and consistent. This then allows us to avoid the adverse consequences of Gödel’s incompleteness theorems.
Fortunately, it is possible to represent one thing completely and consistently using information, provided the complexity of that one thing is not too great. Therefore, we can use a computer to indirectly represent the direct representation of one thing, and then use that one simulated direct thing to ‘directly’ represent everything else indirectly. We use the same strategy used by nature in the brain, but it is a little less efficient due to the additional level of indirection. Nevertheless, it still provides the means to represent everything indirectly completely and consistently.
The representation of thought is a universal representation. While we have not defined the terms and laid the prerequisite groundwork needed to understand the representation of thought, a brief introduction is possible.
In a universal representation, the intension and extension are direct, but the direct use of the extension within the representation of the intension is indirect. Consequently the intension defines meaning in context from the direct first person perspective, but the extension can be used in multiple contexts and be included as part of the representation of multiple intensions. In this case, the representation of the intension and extension are represented directly by value, but the use of the extension is represented indirectly by reference.
A neuron is a universal representation because its dendritic trees directly represent the intension of a concept and the intension of the set of abstractions that constitute the intensional representation of the concept. Detection of the direct satisfaction of the intensional conditions via the process of dendritic integration triggers the firing of the neuron’s axon which signals the existence of the concept extension and the existence of the particular abstraction extension it represents in all intensional contexts it participates in the definition of. All neural processing is direct, but the representation is simultaneously direct and indirect. The direct processing and direct representation entail self-awareness and first-person understanding of the meaning of concepts and abstractions from the first person direct perspective in context, while the indirect representation of the use of the extension entails third-person reasoning about external things at multiple levels of abstraction in terms of how those things relate to other things in context. If you do not understand this right now, do not worry. We will cover all of this later in much more detail after we present the prerequisite definitions and concepts required to do so.
The diagram below shows how the same system that was represented for direct and indirect representation is represented using a universal representation. From this illustration, you can immediately see how the ontology of a universal representation resembles neural topology. In fact, there is a one-to-one mapping between the ontology of abstraction and the spatial topology of neurons. In the figure below, the solid lines with arrows leading away from each box represent the extension of an abstraction (and the concept it partially represents). They also represent a neurons axon. The dotted lines with arrows pointing toward each box represent the intension of an abstraction (and the intension of all the abstractions that represent the concept represented by the box). They also represent a neurons dendritic trees. Just like the direct and indirect representations, this diagram represents Thing1 as being related to Thing2 by relation R1, and Thing1 being related to Thing3 and Thing4 by Relation R2. When R1's axon fires, it causes synapse R1 to fire at time t. Then Thing2's axon fires at such a time that synapse T2 fires just as the electrotonic potential from synapse R1 reaches the dendritic location of T2. The electrotonic potentials then superimpose and sum and their sum flows down the dendritic tree to the axon hillock of Thing1 and arrives at some time ta. Meanwhile R2's axon fires which causes synapse R2 to fire and send electrotonic potential down the dendritic tree towards Thing1. Synapse R2 fires at just the right time so that its electrotonic potential will reach the axon hillock at time ta. Sometime after synapse R2 fires, Thing3 and Thing4 fire their axons at such a time that the electrotonic potential from their synapses also reaches Thing1s axon hillock at time ta and superimposes with the other electrotonic potentials. Because the electrotonic potentials from synapses R2, T3, and T4 are all spatiotemporally correlated, they superimpose at the position they intersect their common dendritic path and the integrated sum of the superimposed electrotonic potentials travel down to the Thing1s axon hillock together. Of course if the relative firing times are not correct, then Thing1 doesn't reach its activation threshold and doesn't fire its axon. If the relative synaptic firing times are correct, then the electrotonic potential does reach Thing1's activation threshold and it fires its axon. The firing of thing1's axon means the intensional conditions that define how Thing1 is related to Thing2 by R1, and how Thing3 and Thing4 are related to Thing1 by R2 were met. Therefore the firing of Thing1's axon represents the existence of the abstraction that represents Thing1. It signals the satisfaction of Thing1's intensional conditions and thus represents the relation between the intensional meaning of Thing1's definition and its existence. The firing of the axon doesn't encode any information directly. However, when fired, it signals the occurence of an instance of the abstraction represented by Thing1. Therefore it can transmit an arbitrary amount of meaning without the need to encode any information. That means the size of the representation is constant, irrespective of the complexity of the set of abstract relations that it represents. The size of the representation is independent of the complexity of whatever it represents in univeral representations. In addition, this means there is no neural code. There are too many other representational and computational advantages to cover here and we haven't discussed the prerequisites needed to understand them. I will cover them when I discuss the neural knowledge representation in more detail in a future blog.
We have now introduced the direct indirect axis of representation. We learned that there are three fundamental types of representation along the direct indirect axis; direct representations, universal representations, and indirect representations. The representation of existence is a direct representation. The representation of thought is a universal representation, giving thought the power to represent things directly and indirectly simultaneously. The representation of information is an indirect representation. The representation of information provides the basis for natural language, communication, symbolic logic, computer programs, and mathematics among other things.While these descriptions do not cover the direct - indirect axis of representation in exhaustive detail, they do provide enough of an introduction to make it worthwhile to move on to describe the second principal axis of representation – the intensional – extensional axis.
It will take me some time absorb, but I am intrigued by your article and wonder if you plan on releasing any code or data structures you used.
ReplyDeleteBarry:
ReplyDeleteAre you going to release a 2010 update on your Blog? We are curious as to any progress and/or verification your theory has had since your last post.
Have you been able to build a working prototype of your universal representation thinking machine? Has your theory of the relationship of existence and non-existence been updated or changed?
Please favor us with an update at your convenience.
Thank you.