ABSTRACT A model is proposed for the functioning of natural language in a mind. The model results from investigating and combining information-processing of two types: that of inexact patterns (e.g., visual images). and that of symbolic code (i.e., natural language). First an underlying model is presented for the input/output data-flows of the sensorium/motorium of the human mind, including its memory. The underlying model is that of a highly orthogonal grid, with input and output flowing vertically, in parallel but opposite directions, while associative interconnections flow back and forth horizontally. In the superstructure model for natural language, an "abstract" memory channel is superimposed to flow in parallel with the input/output channels, in such a way that a spiral of habituation comes to dominate the associative crossflows in a conscious, linguistically generative process of "transabstractivity." 1. INTRODUCTION This article proposes a two-tiered model for the functioning of natural language in a mind. The two tiers derive from the need to have both a concrete level of sensation and an abstract level of mental processing. The concrete and abstract levels correspond to a duality in the types of information to be processed in a mind: inexact patterns, such as visual images, and symbolic code, i.e., natural language. The lower-tier model of pattern-recognition is necessary as an underlying assumption before the upper-tier model of habituated linguistic control can be developed. Since the main endeavor in this article is to present the psycholinguistic model, the author begs the reader's indulgence if the model of pattern-recognition seems far-fetched or is erroneous. 2. OVERVIEW OF THE ASSOCIATIVE GRID OF THE SENSORIUM/MOTORIUM The underlying model organizes the input/output data-flows of the sensorium/motorium of the human mind, including and emphasizing its memory. The rationale is to organize the data-flows as a prelude to controlling them with a "transabstractive" grammar system. The model organizes the data flows into a relatively flat, highly orthogonal grid or array. The inputs and outputs of the sensorium/motorium flow vertically up and down the grid, in respectively parallel but opposite directions. For the remainder of this article, the inputs of the sensorium are to be visualized as flowing vertically downward on the left side of the non-abstract, "concrete" grid, while the outputs of the motorium flow vertically upwards on the right side of the grid. The interface with the outside world is therefore at the top of the grid, consisting of sensors on the left and motor musculature on the right. After pre-processing, the input/output data-paths descend down their respective halves of the grid through experiential memory channels on the left and motor memory channels on the right. There is a strict parallelism of the various memory channels lying vertically in the grid. This article is concerned mainly with interactions among the memory channels, and accordingly the grid is to be visualized as consisting mainly of elongated, vertically parallel memory channels. Interconnecting associative "tags" flow horizontally back and forth among the memory channels in the concrete grid. The grid is highly orthogonal because information can change its path only at right angles. The horizontal associativity is vertically analogous to a time-dimension. The gridwork of memory is gradually filled from the top downward towards the bottom over the psychic lifetime of the organism. The lavishly available memory space is genetically "hardwired," so that the activity of mentation has only to travel gradually downward through the tabula rasa of the memory grid. Any line, drawn horizontally across the grid so as orthogonally to intersect the various memory channels, represents a unique moment in the experiential history of the organism. From this point on, the article follows a method of circumscription by first merely outlining a general system and then addressing those particular elements within that system which are relevant to the development of the "transabstractive" superstructure of natural language. The first circumscription is to drop consideration of the right-hand motor side of the underlying, concrete associative grid. Suffice it to say that motor memory does figure in the genesis or development of a holistic model of the mind, especially as regards volition, but that this article concentrates on the passive, experiential, "left" side of the model as the arena over which natural language operates. In the holistic visualization, the passive left side of the mind-model contains a separate but parallel memory channel for each of the distinct senses which a mind might possess, such as the five commonly acknowledged human senses. An important facet of this general model is the idea that any conceivable sense could be added on in parallel to widen the associative grid, as long as the principle of orthogonality were not violated. An experiential memory channel here is a bidirectional data-path originally and permanently filled in the downward direction from top towards bottom. The temporally successive, horizontal associativity of the quasi-concrete grid absorbs as many sensory memory channels as evolution (or artifice) can provide. A full complement of unimpaired sensory channels provides an organism with full breadth of multi-sensory experience. However, a person can have severe sensory impairments and still function as a highly intelligent mind. This discussion serves to introduce the second circumscription of this article, namely that from this point on the article will develop the superstructure for natural language solely in terms of the senses of vision and audition. The aforementioned duality of pattern and symbolic code is to be discussed using vision to treat pattern and audition to treat code. 3. THE MODEL OF THE AUDITORY CHANNEL Now begin descriptions firstly of the auditory channel, next of the visual channel, and then of the "abstract" memory channel which connects and controls the other two in "transabstractivity." This general model attempts to follow the human mind, however murkily known, but it is directed towards a hardware construction of an automaton. Therefore the discrete memory mechanisms or components are visualized as physical hardware rather than as biological tissue. The basic model is that of perhaps an electronic multivibrator or even of an electromechanical latching relay. The basic requirement of a tabula-rasa memory "cell" here is that it shall retain permanently its status of either "on" or "off" ("full" or "empty') when a brain-wave type control-pulse orders the unerasable "hardening" or fixation of whatever data happen momentarily to be flowing through the cell and its associated cells. The cell shall also be associatively "taggable," typically as part of an aggregate, so that a unitary associative tag, leading orthogonally away from the channel containing the aggregate, can either control and activate the aggregate or be controlled and activated by the aggregate. Thus data are laid down permanently within a channel, but their informational content is free to move either bidirectionally within the channel or orthogonally away from the channel. The auditory memory channel is designed here as the target destination of multitudinous transmission lines carrying the component data of sounds. Although the holistic visualization of this general approach contains a tentative scheme for clusters of short-term memory loops at the entrance to the auditory memory channel, this article requires only the long-term, permanent memory channel for the discussion of "transabstractive" natural language. Within our circumscription we are examining the left side, or passive experiential half, of the flat associative grid. The auditory memory channel is to be visualized as itself a flat cable lying both flat in the plane of the grid and on the right side of this experiential half. We are developing a "transabstractive" area bordered on the left by the visual memory channel and on the right by the auditory memory channel. Our intent with the auditory memory channel is to deposit engrams of sounds and phonemes. The channel consists of thousands of transmission lines flowing vertically downward in strict registry and in parallel with the other memory channels. Each engram-aggregate is a horizontal slice of memory "cells" as nodes upon the transmission lines of the channel. Each slice has (at least) two genetically-provided, tabula-rasa type associative tags exiting the channel. One class of associative tags exits horizontally and orthogonally out towards the visual channel on the left. The other class, which we might as well call the "habituation-class," exits perpendicularly and rises orthogonally out of the associative plane en route to interaction with a grammar habituation system, of which the description comes further on as the main purpose of this article. This auditory memory channel is designed to remember words or parts of words as strings of phonemes. A phoneme is modelled as a distribution of activated nodes within an engram-slice. It may actually require several or many slices in a row to comprise one time-extended phoneme, but for the purpose of clear simplicity we will treat the single phoneme as if it were a unitary engram-slice subject to unitary associative tagging. All sounds and words consciously heard are deposited automatically as engrams within the auditory memory channel, but only those words are "learned" to which access is gained and maintained via the associative tags. In our model, we are discussing the learning of language-words with reference to visual images resting in the visual memory channel, which lies in parallel with and to the far left of the auditory channel. The visual channel, too, has slices and horizontal associative tags, attached to the image-slices. (The feature-extracted image-slices would perhaps be rather unrecognizable if memory-dumped from the system.) A word or morpheme is learned, in reference to vision and all other senses, through a process of associativity based upon simultaneity in the permanent fixation or "hardening" of the horizontal associative tags which interconnect the various sensory memory channels. Let us summarize the function of the auditory memory channel with respect to words and morphemes. As a string of phonemes, a word or morpheme is learned passively when horizontal associative fixation enables another sensory channel to evoke the activation of the phonemic string at its permanently fixed location within the auditory memory channel. An incoming (erstwhile potentially bidirectional) tag which starts the activation of a phonemic string is to be described both as a "recall-tag" while en route and as an "onset-tag" at its point within the auditory memory channel where the tag activates the first phoneme in the phonemic string of a word or morpheme. Here mention must be made of a tentatively proposed "string-effect" within the auditory memory channel. Morphemes accessed by an onset-tag will go into full serial engram-slice string-activation either until the last phoneme in the string shunts the activation-flow orthogonally out along an exiting associative tag, or until the strong activation of the "string-effect" fades abruptly at the end of the string. (For remembered music, the string-effect might go on quite long.) The string-effect is therefore a tendency of related and contiguous memory slices to fire in a serial string. When a morpheme in auditory memory has been accessed by an onset-tag laid down at some time in the past, the phonemic string of the morpheme instantaneously flows serially down through the transmission lines within the auditory memory channel and is deposited anew at the freshest extremity of the gradually downward-travelling "front" of auditory memory of auditory experience. This creeping "front" of auditory experience is in horizontal registry with the other parallel channels that are all moving or filling downward into the tabula-rasa area of the associative memory grid. While an accessed morpheme is flowing through the auditory memory channel, each individually activated transmission line is momentarily energizing or stimulating each of its myriad cell-nodes which have in the past been positively fixated in the status of "on" or "full" as mentioned above. Thus the initial activation of one phoneme, morpheme, or word in the channel can "tickle" or predispose the activation of myriad other such auditory engram-aggregates. We posit now a differentiation-process wherein the relatively largest and strongest summation of individually firing nodes within the engram-slices of a single, aggregate memory trace can cause that memory trace to win out in a sort of competitive race to be the first among other memory traces responding to the activation of the originally accessed memory trace. (Non-activated nodes may act inhibitively to enhance the differentiation.) The competition for primacy of response is quickly happening amid these various parameters, not the least of which is the time-factor, because the extremely free and mobile associativity of mentation will quickly go the path of least resistance without waiting for any delayed response. By now the model has described how an extraneous recall-tag from a sense such as vision can activate an auditory engram with two results: the old auditory memory is laid down anew at the freshest extremity of the auditory memory channel, and a highly similar trace in the auditory channel can be activated in response to the activation of the first trace. When a trace does respond, it outputs a signal along an associative tag which is to be called here an "ultimate-tag," because the tag is attached to the ultimate phoneme in the phonemic string. Of course, that "ultimate-tag" from audition can be a "recall-tag" going over into vision. Thus a visual image can associatively access a morphemic word, which can stimulate the response of an identical or similar word at a different location in the auditory channel, with the result that a totally different visual image can then be accessed back again in the visual memory channel. Associativity can loop in and out of memory channels in an untrammeled fashion. In describing how an associatively accessed, auditory engram-slice would stimulate or elicit the "recall" of an identical or most strongly similar engram-slice, the model has at the same time shown how incoming auditory data from the outside world would be processed. External auditory data, to be laid down in permanent memory, traverse the length of the auditory memory channel and are deposited by fixation at the freshest extremity of the channel. External auditory data are "recognized" if their passage through the channel stimulates and elicits responding trace-activation as described above. However, such responding engram-slices do not travel to the fixation-extremity and therefore can not be redeposited there; they are already permanently fixated in their original locations. It is important to understand that only two sorts of auditory data traverse the auditory memory channel into fixation at its freshest extremity: fresh external auditory data on the one hand, and old, internal, associative-tag-activated data on the other hand. In other words, newly fixated data or newly re-fixated data must come from the active sources of external perception or internal associativity, respectively. (The mind-model remembers both its external and its internal experiences.) At least two rationales militate against the notion that memory-extremity re-fixation might occur of response-slices "flushed out" by incoming perception-data. Firstly, there is no need for redeposit of such old data if they are highly similar to the incoming new data. Secondly, the presently incoming perception-data are already flooding the transmission lines, making it simultaneously impossible for the products of "recall" to move about within the auditory memory channel. Of course, and in accordance with this whole scheme of recognition during perception, massive data-flow can be occurring orthogonally out of and away from the auditory memory channel while incoming auditory data are traversing the channel into fixation at its creeping extremity. When fresh, incoming data are deposited by fixation at the extremity of the auditory memory channel, they also by virtue of simultaneity enter into permanent association with various other memory channels lying in parallel. The associative tags which effect this permanent association and integration of fresh data are the same tags by which access to the data will be maintained in the future. This fixation of association through simultaneity happens not just to fresh data-slices, but also to old data-slices which have been sent coursing down through the memory channel after activation of their associative onset-tags. Thus an old memory-slice can enter into new associations whenever it is redeposited. It should be becoming apparent now that thus an enormous body of belief or knowledge could gradually accrete onto some key reference-memories. The very frequency with which a memory were associatively reactivated, and therefore redeposited, could influence the future likelihood of subsequent reactivation. In this model, a memory can grow stronger by increasing the number of the instances of its reactivation. The foregoing model of the auditory memory channel has contained certain crucial highlights which will come into play when the three channels of visual memory, "abstract" memory, and auditory memory are combined in the development of the linguistic control system for natural language. 4. THE MODEL OF THE VISUAL CHANNEL The whole genesis of this model has hinged upon distinctions in the duality of pattern and symbolic code. It is argued here that code, because of its exact and facile manipulability, is essential for "transabstractivity," while less exact but information-rich pattern is essential for the underlying knowledge that culminates in abstractions. In this article, pattern is to be treated with respect to vision, because the sense of vision is our greatest floodgate of perception. However, vision is not considered essential in this model of artificial intelligence; the autobiography of Helen Keller [1] has strengthened the author's conviction in this regard. Vision was merely the most challenging and the most enabling sense-avenue that the author could choose as a way of getting general information into the mind-model. The author begs the reader to judge the validity of the linguistic model regardless of any invalidity of the visual model. The author was able to advance to the development of the linguistic model only after incorporation of the visual model into the sensorium/motorium grid as an underlying assumption. Having used the visual model as a possibly false lemma, the author would like to see the linguistic model prove valid no matter what happens to the visual model. Articles by Kent [2] enabled this author to develop the visual model. The model as finally adopted resembles one which the author long resisted as being probably too naive, until Kent's exposition of feature-extraction engendered sufficient sophistication in the model as to override the author's feelings of uneasiness. As mentioned above, the visual memory channel flows down through the leftmost side of the flat associative grid. Whereas the auditory memory channel is visualized as flat, the visual memory channel is visualized as more or less round, because it must contain two-dimensional image-slices. However, the class of horizontal associative tags exiting the visual memory channel can be regarded as flat. The visual channel starts as a quasi-retina and passes through two stages of pre-processing before entering the memory grid as an associable memory channel. The first stage of pre-processing is one in which this design allows some time for self-organizing of the visual channel, hypothetically to correspond to extreme infancy in humans. This model regards accurate visual transmission as too great a burden to impose upon genetic design, which is viewed here as part of a duality or polarity with design-by-learning. The self-organizing stage has been allowed for and then left for later development. Basically, the rationale is that the order peculiar to light sources in the external world shall help to create an ordered arrangement of visual transmission lines in the internal world. The second stage of pre-processing is that of feature-extraction. The reference by Kent can be consulted for details, but certain notions are forthcoming here. A typical extraction might be that all retinal points forming lines at a certain slant will converge into single memory fibers, each of which will now unitarily represent a slanting line of multitudinous points. The analog of the retinal optic nerve is modelled here as consisting of about a million fibers. On the one hand, feature-extraction will permit many retinal fibers to be represented by fewer memory fibers. On the other hand, a single retinal fiber can serve as an input to multiple features that are then extracted as multiple memory fibers. So there are tendencies both to reduce and to multiply the number of visual transmission lines. The final inputs at the entrance to the visual memory channel are visual memory lines that represent features rather than retinal points. (These memory lines are called "fibers" above, lest they be confused with lines in retinal geometry.) After more description of the visual channel, a concept of "virtuality" will be explained as the rationale for adopting feature-extraction. The model of visual memory is quite analogous to that of auditory memory. Again, moments of perception are pulsed into slices down through the memory channel. Each slice corresponds to a feature-extracted visual image. The slice cut through the transmission lines has hypothetically a node for each transmission line. Each slice is genetically provided with a tabula-rasa associative tag potentially integrating that slice with the associative grid. The oldest visual images are laid down near the entrance, or top, of the visual memory channel, and the newest images are gradually being laid down at the slowly advancing, lower extremity of the channel. The visual memory channel, in parallel with the other sensory (and perhaps also motor) channels, is associatively connected to them at each instant by virtue of simultaneity in the fixation of horizontal associative tags. It is important to understand the concept of "virtuality" as the author's rationale for adopting feature-extraction. The visual memory channel has two purposes: that of a comparator of patterns, and that of a memory. As a memory, the visual memory channel must associatively retain images by fixating and tagging them. As a comparator, the visual memory channel has the task of announcing to the system by associative tag whenever it finds in memory a highly similar counterpart to either a fresh external image or a reactivated internal image. For purposes of comparison, it would certainly not work to store raw visual images without feature-extraction, because the too detailed images would be too unwieldy to be processed by a non-feature-extracting comparator. Feature-extraction allows the comparator-mechanism to rise a workable distance above point-by-point comparison. Meanwhile, some sharpness and resolution must probably be lost, which loss must be compensated for, but how? And why do we not notice the loss of fine detail? The answer proposed here lies in the concept of "virtuality," which is the self-illusion of consciousness. Throughout this paper, the author insists upon observing the orthogonality of data-flows in the associative grid. Such observance is mainly a help for thinking, because it would not matter if the assembled physical grid were subsequently curved or convoluted. However, the observance of orthogonality leads to a consideration of dimensionality in general. For instance, processes which seem to meander in haphazard directions can initially be difficult to explain. It has helped this author to force emerging facets of "black-box" mechanisms into such orthogonal structures as are described herein. Once orthogonality was compelled here and there within a structure, the whole dimensionality of the structure often became apparent. So it is with vision. The elucidation of "virtuality' is now attempted with regard to "dimensionality." According to this model, when we see an image through an eye, that image briefly floods our whole visual memory channel. Any given feature-extraction line, that happens to be activated throughout visual memory as part of the image, is activating all the myriad historical nodes that were ever fixated as "on" or "full" all up and down the used portion of the transmission line. Within each memory slice of all our previous visual experience, the perchance reactivated nodes are trying in summation to combine forces and "vote" for the selection of their own visual image as the most similar visual memory which ought to be the first, or even only, memory slice to send out over its efferent associative tag a recall-signal. That recall-signal is the announcement that the comparator, i.e., the whole memory channel, is proffering a comparison. Note that that comparison is never exact; it is just the one which has received the most "votes" from nodes. (Does a Rorschach blot operate by exact comparison?) If we stare long at the same image, many associations may come to mind, perhaps aided by a mechanism of neuron-fatigue which would allow initially dominant associations to yield to associations receiving fewer "votes." The main idea here is that this model claims that we perceive visually through a whole visual memory/comparison channel operating all at once in extreme parallel-processing. It was claimed above, in the section on audition, that the informational content of a memory channel could move not only within the channel, but also orthogonally out of the channel. It may seem that that claim loads quite a burden onto the associative tag, because even the largest, fullest memory slice is modelled as having only a unitary associative tag. However, the information escapes its own channel through the "virtuality" of passing over all the associative tags of all the counterpart slices with which it can successively be compared within its own channel. Think of a visual image being rapidly dismantled through its elemental components, each of which is perceived so rapidly through in-channel comparison that the conscious mind is fooled into believing that it is perceiving the image all at once. Viewed in this light, consciousness itself becomes a flickering illusion in which we can never quite see the gaping voids between the flickers. The idea of dimensionality leads to an important, further point involving recursiveness within the mind-model. A proposal is now made to the effect that a valuable test of a perceptual model lies in determining whether or not any information is lost as the information is processed through transformations and reorganizations. For instance, the reader is invited to ask himself or herself (as the author does), whether this visual model suffers the loss of informational content over the orthogonal outputs of its memory channel. If informational content remains rather constant, no matter how circuitously the information flows throughout the system, then it may turn out that the various aggregates of knowledge within the system are defined recursively in terms of all the other aggregates of knowledge. When we discuss the area of "transabstractivity," it may look as though the total system is capable of generating new knowledge from within itself. 5. THE GENESIS OF THE PSYCHOLINGUISTIC MODEL Now that the underlying models of the visual and auditory memory channels have been explained, the rest of the article is devoted to presenting the author's admittedly speculative but perhaps thought-provoking model of a linguistic control system for natural language. Whereas the sensorium/motorium grid has been presented here without much discussion of its lackluster genesis, the author feels that explaining how he arrived at his linguistic model will contribute to the reader's critical understanding of the model and also to the reader's likelihood of seeing where mistakes were made or of devising a much better model. If there is indeed a contribution here, it is time to get help in assessing and developing it. The author developed the various models and perspectives by maintaining and sporadically writing in a "theory journal" from 1972 to 1979. In 1977 the fruitful decision was made to pursue the aforementioned dichotomy of (relatively loose) pattern and (relatively exact) symbolic code. Immediately a torrent of speculation resulted concerning the possible interior organization of psychic structures for processing natural language. The author toyed with elaborate structures for habituating phonemic strings, and then foundered in an abortive attempt to devise a "habituated mechanism for grammar." The problem was that the perceptual system for patterns had not been elaborated, and therefore there was no base of experiential inputs from which to derive control lines for mechanisms generating sentences. As the eventually abortive grammar system became quite complicated, it really became an empty shell as more and more of its control lines became dependent upon the nonexistent perceptual system. A particularly vexing problem was that of how the automaton would keep its languages apart if it knew more than one natural language. The impetus of the duality-approach temporarily ran out in October of 1977, and the project lay dormant for five months. The appearance of Kent's articles in early 1978 led to the present formulation of the visual channel. By November of 1978 the author had at his disposal most of the model of the sensorium/motorium as described in this article. He wanted to integrate the grammar work of the previous year with the new overview of the various memory channels. The first step was to halt at a new impasse involving verb-recall. The author would now like to describe the slow removal of that impasse and the rapid development thereafter of the present linguistic control system. That work culminated in May of 1979 and the author turned to his present attempts at communicating his results. In November of 1978 the first obvious problem was to see how percepts in the visual memory channel would fetch words stored in the auditory memory channel. It seemed simple enough for a visual memory image representing an object to activate a horizontal recall-tag for a noun naming that object. After all, the model regarded both the visual memory slice and the auditory memory string of the word (through its onset-tag) as unitary memory items between which there could exist a one-to-one correspondence, established through simultaneity in the fixation of the horizontal associative tags. For a well-known, thoroughly habituated, concrete noun in the vocabulary of the organism, there would be many randomly placed crossovers of recall between the visual and auditory memory channels. When the organism saw the given object, the percept coursing down through the visual memory channel would stimulate or activate the many various instances where the image of the object had been associated over to the noun. If the signal in just one of many recall-tags reached the auditory memory channel, the noun would be remembered. The author was initially stymied with the problem of how the plurality of nouns would be conveyed from the perceiving visual channel over to the auditory memory channel storing the nouns. He quickly chose instead to be stymied with the similar but more significant problem of how the visual perception of actions would lead to the recall of verbs. For both plurality and verb-recall, it seemed that no single visual percept, with its single associative tag, could be sufficient to recall either a noun-plural, with its added inflectional information, or a verb, with its complex information involving subject and action, plus or minus object. For both phenomena, plurality and verbs, it seemed that a bundle of visual percepts would be necessary just to accumulate the raw information behind each phenomenon. But even if such a bundle were activated within the visual memory channel, the horizontal associative plane was too rigidly simple to transmit the extra information gathered in the bundle. Although the roots of a solution appeared right away in November of 1978, the tentative solution itself was slow in coming via journal entries in January and March of 1979. The rain root to the proposed solution was the idea in November of 1978 (in the theory journal) "that maybe there should be an additional memory alongside the others (sensory and motor). a memory which held perceptual content but not sensory content, a memory which would handle conceptual associations beyond the linear scope of the purely sensory memories: an abstract memory." However, the person authoring these ideas could not make direct use of them, but instead agonized until January of 1979 and then moved backwards from the basic concept of a verb, through the notion of semantic categories as inputs to the verb, and finally back again to the idea of an abstract memory, as a place for the semantic categories to be represented. The plan for verb-recall, as developed in January and March of 1979, is that an abstract memory channel shall permit a process of "intermediation" between raw percepts and stored verbs. It is therefore time to describe the abstract memory channel. 6. THE MODEL OF THE ABSTRACT MEMORY Within our above-described model of the experiential, left half of the sensorium/motorium grid, the visual memory channel flows down along the left side of the grid, and the auditory memory channel flows down along the right side of the (experiential) grid. The abstract memory channel is to be visualized not as a flat channel, but as a three-dimensional channel flowing down through the experiential grid, in between vision on the left and audition on the right. The abstract channel also sideways extends above and covers the auditory memory channel so as to receive the perpendicular outputs of the aforementioned "habituation-class" of associative ultimate-tags rising from the auditory memory channel. The abstract memory is a channel not attached to a sensor, and it would therefore remain empty if it did not receive its inputs from the various "concrete" channels, such as vision and audition. The abstract channel lies in parallel with the concrete channels and it consists of myriad elongated "abstract" fibers or lines analogous to the "transmission lines" of the concrete sensory channels. However, the abstract memory channel is seen as subdivided into "cables" or groups of lines specially organized to suit various purposes of design. The dimensionality of the abstract channel is orthogonal, just as the rest of this model is. One function of the abstract memory channel is to intercept the afferent associative tags coming from the visual memory, those tags which might otherwise proceed directly to the auditory memory and control engrams there. Those afferent associative tags from the visual memory channel flow instead into the "logicoconceptual cable" (L-C cable) of the abstract memory channel. That portion of the abstract channel is called "logicoconceptual" because each of its fibers shall gather up interrelated inputs from vision which in summation constitute a concept or an element of logic. (The logical elements, associated with conjunctions, prepositions, and plurality, may actually require further processing.) The abstract fiber of a concept receives its inputs from vision and then in turn controls the recall-tags which become the onset-tags of words stored in the auditory memory channel. The logicoconceptual cable is visualized as being itself flat and lying flat within the plane of the associative grid. However, the L-C cable has flat layers within it. The afferent visual associative tags empty into the basic, top layer of the L-C cable, which is the layer of the logicoconceptual noun-lines. In other words, the top layer of the L-C cable has fibers representing concepts and their nouns. It has direct control of the recall-lines over to the stored nouns. A visual image must first activate a noun-line in the L-C cable if the image is to activate recall-lines for a stored noun. The descending layers in the L-C cable represent various levels of abstraction. The only secondary level modelled so far is for verbs, but conjunctions, prepositions, and plurality may also have such layers. The top level of the flat L-C cable, that of logicoconceptual noun-lines, is the level of least abstraction. Beneath that level, but moved sideways to the right and out of the way, is a flat level of verb-lines controlling recall-lines heading to the right towards stored verbs. Associative input-lines, or "feelers," move left from the flat level of abstract verb-lines to flow directly underneath the logicoconceptual noun-lines and receive inputs from them. The logicoconceptual noun-lines serve as the above-mentioned "semantic categories" that are inputs in the selection of a verb. Verbs are thus at least doubly abstracted from raw visual perception. Each abstract verb-line sends its "feeler" out leftwards underneath the flat, primary level of the abstract noun-lines. (Other simple percepts may be mingled in with the noun-lines.) Thus the input-feeler of each abstract verb-line has access to all the abstract noun-lines, or "semantic categories." When a verb is to be recalled to describe a visual percept, an extremely parallel differentiation-process operates over all the verb-input-feelers that are sampling the status of each relevant semantic category expressed among the noun-lines. At the junctures of the feelers and the abstract noun-lines, there are nodes fixated by learning. A (complex) verb which has both many nodes on its feeler and most of them activated will win the recall-race over other verbs with many feeler-nodes but few of them activated. The differentiation may be enhanced if available but unactivated feeler-nodes serve to inhibit the input-feeler to a verb-line. A (simple) verb with few feeler-nodes but all of them activated could thus win out over a (complex) verb with many activated and many unactivated feeler-nodes. (The feeler described here is actually one of very many feelers for each verb-line.) The sentient being that is bringing verbs to mind may not realize that the whole vocabulary of verbs is competing. The differentiation-process makes possible both malapropisms and flights of fancy. The mentally proleptic reader may be realizing here that such abstract cables will be used to control the parts of speech in syntax, but first the function of the abstract logicoconceptual cable must be examined in greater detail. It is important to realize that the abstract memory channel always operates upon the basis of old, rather than fresh, memory data. This notion of reliance upon past experience makes sense if the abstract memory channel is a habituated mechanism. This dependency upon past experience becomes clear if we examine how the "abstract fibers" operate. For consistency, only vertical fibers flowing within the abstract memory channel and in parallel with all the other memory channels shall be called "abstract." Any horizontal or perpendicular associative lines or fibers making contact with an abstract fiber shall be called "concrete," to highlight the distinction between the "abstract" fibers of extended experience and the momentary associative fibers that represent a "concrete" influence upon, or function of, the abstract fibers. When an intelligent organism sees the bundle of visual images which constitute the raw information capable of ultimately fetching or recalling a stored verb, the process of abstraction begins immediately. The images within the bundle are deposited in their proper order at the freshest extremity of the visual channel, but these images at the freshest extremity of the channel can not send out signals sideways to activate the necessary abstract fibers within the logicoconceptual cable. As may be clear from previous portions of this article, fresh association can occur through simultaneity, but instances of recall must filter through associative pathways laid down in the past. Since the fetching of a stored verb is recall rather than fresh association, the images in the verb-input bundle must all do their best to activate highly similar counterpart-slices down through the visual memory channel. These counterpart-slices, and not the fresh images, will then associatively access abstract fibers in the logicoconceptual cable. Notice that such spread-out routing of information as inputs for access to verbs permits the process of verb-recall to be a rather catch-as-catch-can, labile, loosely configurational process. Remember, practically all verbs in the active vocabulary end up competing to be the verb which is consciously recalled within the auditory memory channel. The process described here is not meant as faulty or hit-and-miss; rather, the idea is to let such a variety and wealth of inputs serve in selection of verbs that fine differences and subtle nuances can sway the selection-process into vectoring towards the most apt and descriptive verb to name an action or a state of being. An abstract fiber, or cable of such fibers, stands in remarkable isolation. The abstract fiber flows down through the abstract memory channel, hypothetically perhaps for a distance as long as the channel itself. Although some provision is to be made for the control of cables of abstract fibers in syntax, the individual abstract fiber of the logicoconceptual cable unitarily accepts myriad "concrete" associative inputs and governs myriad "concrete" associative outputs. The abstract fiber accomplishes its feat of logicoconceptual abstraction by allowing a great leeway in its inputs while insisting upon a rather restricted target for its outputs: a stored word or morpheme in the auditory memory channel. For instance, an English-speaking organism may permit many sorts of images of a dog to access the stored word, "dog." Of course, a single image stored in the visual memory channel can perhaps be associated over to several or many abstract lines, so that varying degrees of differentiation or specificity can occur. Thus a speaker might refer to a "dog" or to a particular species of dog. The important consideration here is that these processes of selection are forms of extremely broad and parallel competition. Not only do practically all the verbs in an active vocabulary compete, but, from a given abstract line that is going to access the winning verb, there are many competing concrete associative recall-lines going over as the onset-tags of various historical instances of the recording of that verb here and there in the auditory memory channel. It may be that only the more recent instances are likely to win out, so that verbal memory can gradually shift or mature over time, but the abstract fiber is not limited to a single, possibly unreliable, concrete recall-line as an output. Such availability of multiple, but essentially identical, output-lines can perhaps be viewed as an automatic error-reducing mechanism of redundancy. As was mentioned above, a bundle of input-images for verb-selection will be deposited at the freshest extremity of the visual memory channel, after using the internal comparison-mechanism of the visual memory channel to gain access, via horizontal associative lines, to relevant abstract fibers in the logicoconceptual cable. Only after such "supratraversial" associative activation of the abstract fibers can each fresh image-slice, being newly deposited, enter into a fresh associative interconnection with its relevant abstract fiber (or perhaps fibers) at the freshest extremity of both the visual and abstract memory channels. Thus, although language is always used as a habit from the past, there are mechanisms, all along the advancing front between experience and tabula rasa, for the constant reaffirmation, updating, and perhaps gradual change of the way in which a mind perceives and interprets its world. 7. THE BASIC MODEL OF SYNTAX The foregoing sections of this paper have modelled systems of information- flow in basic automatic routing where one flow of information did not govern another. A fresh, unitary flow of information within a sensory channel might associatively scatter eddies and ripples throughout much of the associative memory grid, but such propagation of signals can still be viewed as the single dispersal of a single flow. Syntax, however, involves letting one (habituated, permanent) flow of information control other (freely associated, transitory) flows of information. The above described layers of the abstract logicoconceptual cable will serve to contain some of the transitory flows of information which syntax will control. Whereas the logicoconceptual cable lies in the plane of the flat associative memory grid, we now posit an abstract "syntax cable" lying in a second tier of the abstract memory channel, above and covering both the logicoconceptual cable and the auditory memory channel. The syntax cable will control flows of information within the logicoconceptual cable and the auditory memory channel. The auditory memory channel is unique among memory channels, because, according to this model, it is where conscious verbal thought occurs. The auditory memory channel is a self-perceiving channel. Syntax generates sentences by stringing together morphemes and words residing directly within the auditory memory channel. The basic function of the syntax cable is now described, although the development of the syntax cable is left for the section on the habituation of grammar. A textbook by Liles [3] provided this author with some knowledge of Chomskyan transformational grammar. This paper confines itself to a simple example of syntax and does not treat the selection of transformations. The following discussion of how syntax strings a sentence together is based upon a notion of a very simple English sentence consisting of a noun as subject, a verb, and another noun as direct object of the verb. Almost everything but word-order is disregarded here. The sentence is probably a slightly ungrammatical one, such as a baby might utter, e.g., "Daddy drink water," without the inflectional ending on the verb. Inflection is treated in the next section of this paper. Although transformational grammar expresses such a simple sentence as the tripartite one above as a tree with nodes, this section of the article is concerned with syntactic nodes only in a row representing surface structure. In other words, somehow (explained further on in this paper) the syntax cable will have assembled a sequential series of nodes representing and controlling sentence-elements that are to be activated in the same order as that of the nodes, so as to string together a sentence. The volitional aspect of why the sentence is thought or uttered is not treated deeply here. As for the mere thinking or generation of the sentence, without regard to motor utterance, it does not matter much whether we imagine that syntactic structures are always waiting for the opportunity automatically to assert themselves, or whether an activated mechanism of attention initiates the operation of a syntactic structure (i.e., one of the possible transformations, including what could be regarded as the untransformed, original one). Here we are merely examining how a syntactic structure, once activated, would generate a rather concrete sentence to describe what is being observed through the visual memory channel. Further to eliminate volition from our discussion, let the following be considered. Once the components of a sentence have been assembled, or, to express the idea more carefully, are being assembled within the auditory memory channel, that sentence is free to move down within the auditory memory channel and to deposit itself in a quasi-capsule at the freshest extremity of the channel. As was stated in the section on the auditory memory channel, "old, internal, associative-tag-activated data" will "traverse the auditory memory channel into fixation at its freshest extremity." Thus the elements of the sentence may be gathered from randomly and widely varying locations up and down the auditory memory channel, but the sentence coalesces into an integral whole when it is deposited automatically at the freshest extremity of the channel. Now, motor volition is modelled here as a sort of shifting valence topography of integrating associative potentials dynamically moving, at the elongated associative interface between experiential and motor memory, either towards or away from threshold firing-levels at which positive volitional motor activation occurs automatically, but premeditatively. Physical, motor utterance of a sentence can occur either as the sentence is being generated up and down the auditory memory channel, or after the sentence-capsule has been gathered at the freshest extremity serving as a kind of "pre-elocution register." The reader will please forgive the author for brushing aside the perhaps tantalizing topic of motor volition, but it is not essential to the linguistic model which the author is eager to communicate first. We now examine the generation of an English sentence under the control of three serial syntactic nodes in the syntax cable of the abstract memory channel. Let the sentence be the slightly incorrect one mentioned above, "Daddy drink water." Therefore the three syntactic nodes are one for a noun as subject, one for a verb, and one for a noun as direct object of the verb. Each syntactic node within the syntax cable is actually an elongated abstract memory fiber. Viewed in a cross-slice, it has the unitary quality of being a node, but its elongation through the channel allows it to operate in myriad instances extended over time. The syntactic node-fiber enjoys the isolation attributed to abstract fibers above, in that it is itself unitarily abstract, while access to and from it must occur via the myriad concrete associative lines. Each of the three syntactic node-fibers is associated with the part of speech which it will activate within the auditory memory channel during the generation of a sentence. Although the syntactic node is associated with all members of the class of its part of speech, it must select and activate within the auditory memory channel only one member of the class. In other words, each syntactic node must propose only one candidate-word for a particular spot in the sequence of a sentence being generated. Each syntactic node has concrete associative lines descending to access and govern a whole part-of-speech layer within the logicoconceptual cable. Thus the first syntactic node for our sentence, representing a noun as subject of the verb, accesses and controls the whole noun-layer of the logicoconceptual cable. At the transitory moment of its activation, the syntactic node-fiber "flushes out" from the whole noun-layer whichever noun happens to be "voted for" most strongly on the basis of present inputs from visual perception. The noun-layer, while awaiting a flush-signal from the syntactic node, is to be viewed as being normally inhibited from activating its myriad recall-lines that are the onset-tags of morphemes and words stored in the auditory memory channel. A flush-signal from the syntactic node for subject nouns briefly disinhibits the whole noun-layer to let the perceptually dominant noun escape over to the auditory memory channel. Activation of the onset-tag of that noun causes its phonemic string to be consciously "heard" or "perceived" within the auditory memory channel. The phonemic string travels to the freshest extremity, where it is redeposited by fixation. The activation of the phonemic string is terminated by the ultimate-tag which rises perpendicularly from the string up into the syntax cable. The ultimate-tag from the stored word signals to the syntax cable that the firing of the first syntactic node has produced its results. Control is now passed sequentially to the next syntactic node, that of the verb for our sentence. The syntactic node-fiber for verbs flushes out a perceptually dominant verb from the verb-layer of the logicoconceptual cable. At the speed of thought, the verb is now activated, is now "thought," within the auditory memory channel. A signal rises along the ultimate-tag of the verb up into the syntax cable to pass control from the verb-node on to the noun-node for the direct object of the verb. Neuron-fatigue, plus a slight shift or alteration in perception, will prevent the originally dominant subject-noun ("Daddy") from firing again when the syntactic node-fiber for a noun as direct object is trying to flush out a noun as the final word in the sentence. The noun which actually represents the direct object should be perceptually dominant and should be flushed out for recall-activation in the auditory memory channel. When the ultimate-tag of this final word fires, control can be passed perhaps to a new sentence or to a new focus of attention. The syntactic control-structure causes control to loop quickly in and out of the self-perceiving auditory memory channel at the speed of thought. Although the process is happening over a much wider area than the auditory memory channel alone, the thinking organism is conscious only of the results surfacing within the auditory memory channel. The words seem to flow together naturally and without pause, because the syntactic control structure operates so quickly and automatically. Thoughts are not especially "willed," they just occur to a person's mind and help formulate the person's will. So-called "Freudian slips" of the tongue may occur when a residually dominant concept in the logicoconceptual cable is originally present because of one instance of perhaps strong mentation, and then the concept interferes in a new instance of perhaps weak mentation. If a silent but strongly dominant concept within the logicoconceptual cable does not have time to subside before an unrelated sentence is spoken, a "Freudian slip" can occur involuntarily. In this vein, the author has not yet analyzed how spoonerisms might occur. The problem of how to keep multiple natural languages apart within a fluently multilingual mind may be solved by certain features of this model. Each syntactic structure is probably learned as pertaining to a specific language. Then the syntactic nodes of the structure can probably access only classes of parts of speech containing words that have customarily been included within the vocabulary of the specific language. There probably do not have to be multiple noun-layers and multiple verb-layers within the logicoconceptual cable. Instead, the descending concrete associative fibers from syntactic nodes of a particular language probably access (in blanket fashion) only words of that particular language. Thus a person fluent in several languages can speak continuously in one language without interference from the grammar or vocabulary of any other language. Note that persons who are not truly fluent will still have problems, because they are frequently stopping and thinking, that is, associating every which way, even into divergent languages. 8. AN EXAMPLE OF THE MODEL OF INFLECTION Although English was kept in mind during the development of the basic model of syntax, the model of inflection was developed with a view to such highly inflected languages as Latin and Russian. This paper now presents a rather circumscribed example of how the linguistic control system for inflection would operate in just one instance. The author developed this model in May of 1979, and is eager to communicate it before entering a more leisurely phase of examining many specific or universal aspects of inflection. Suppose that a cybernetic organism is operating in the Russian language and must discriminate between the nominative and accusative forms in the singular number of the Russian noun for "Moscow," which we transliterate here as "Moskva." The nominative form will accordingly be "Moskva" and the accusative form "Moskvu." In the sentence being generated, the mind must use "Moskv-" as a stem and automatically decide whether to add the ending "a" or "u." Within the model of syntax in the foregoing section of this paper, a noun such as "Moskva" is controlled by a syntactic node-fiber which guides the process of recall resulting in the activation of the phonemic string of the noun down through the auditory memory channel. Two aspects of that model must now be changed. Firstly, the syntactic node-fiber will not access the complete phonemic string, "Moskva." Instead, only the stem "Moskv-" will be accessed. Of course, such a stem has an ultimate-tag rising perpendicularly out of the auditory memory channel and into the syntax cable. We will use the ultimate-tag as one of two converging inputs necessary for the selection of the proper case-ending within the paradigmatic engrams of the declension of Russian nouns like "Moskva" in the singular number. (English-speakers are familiar with many such Russian nouns: "vodka," "beluga," "tundra," "Pravda" - to name a few.) Secondly, the syntactic node-fiber governing the noun will now have an additional output beyond that which merely flushes the recall-line of the noun-stem out of the logicoconceptual cable. This new output of the syntactic node-fiber is to be called a "function-vector" and it is based upon the grammatical position and function of the noun within the syntactic string of the sentence. Although we speak of a single function-vector, we really mean numerous concrete associative lines exiting the unitary, abstract syntactic node-fiber. Since these associative vector-lines are all going to the same destination over the short run, we can speak as if there were a single function-vector. Of course, over the long run, a neophyte's use of inflectional endings might change by improving or maturing. In our Russian example, one syntactic node-fiber is perhaps trying to flush out a noun that will be in the nominative case as the subject of a verb. Another syntactic node-fiber is trying to flush out a noun that will be in the accusative case as the direct object of a verb. Let us examine how the system generates the form of the noun in the accusative case- "Moskvu" instead of "Moskva." The flush-line, or "recall-vector," of the syntactic node-fiber flushes out the recall-line for the stem "Moskv-" from the logicoconceptual cable. Meanwhile, the function-vector of the syntactic node-fiber simultaneously sends a signal into a portion of the syntax cable called the "function cable." This function cable is a group of abstract control-fibers or "bars." Each specific control-bar in the function cable receives inputs only from syntactic node-fibers representing certain grammatical functions that require always the same grammatical case. For instance, in our Russian example, possibly several syntactic node-fibers representing direct objects of verbs and accusative objects of prepositions can send their function- vectors to the same accusative-case control-bar within the function cable. Thus the function cable serves as a collecting-point for function-vectors and, as we shall see, as a distribution-point for case-activation lines leading to all declensions. The signal from our Russian example of a syntactic node-fiber generating an accusative direct-object form comes into the function cable and activates a control-bar representing the search for an accusative ending to the noun-stem "Moskv-" presently being activated within the auditory memory channel. The accusative-case control-bar in turn sends out semi- activating signals to all accusative-case endings in all Russian declensions available within the system. The syntactic node-fiber does not "know" in advance the particular declension (among several Russian declensions) to which the flushed-out noun-stem will chance to belong. Only the noun-stem itself is associatively privy to that information. Therefore the function cable must blanket-access and pre-poise all appropriate case-endings in all declensions. We shall name as the "inflection cable" that portion of the syntax cable which contains the various Russian declensions as clusters of abstract inflectional lines controlling concrete associative recall-lines for specific case-endings stored as morphemes in the auditory memory channel. Now the two separate inputs must converge within the inflection cable to select the accusative singular ending "u" for the activated stem "Moskv-." The ending "u" is pre-poised or semi-activated when the accusative-case control-bar blanket-accesses all declensions. Final and full activation of the ending "u" occurs when the ultimate-tag from the end of the fetched stem "Moskv-" carries a signal from the auditory memory channel into the proper declension-cluster within the inflection cable. Thus an intersection of two fan-outs occurs. Syntax distributively accesses all accusative endings, and the fetched noun-stem collectively accesses all the possible endings peculiar to its own declension. Thus the stem "Moskv-" and the ending "u" are combined to yield the accusative singular form "Moskvu" of the Russian noun for "Moscow." Of course, the Russians, a nation of poets, sometimes have their choice between equivalent forms of an inflectional ending, but there are additional factors easily governing the exercise of that choice. Typically, a set, habituated form will come to mind, and then conscious purposes of poesy or archaism can cause the substitution of an equivalent form for the originally occurring form. 9. THE MODEL OF LINGUISTIC HABITUATION Now that examples of basic syntax and rudimentary inflection have been presented, the author offers a general insight into how syntactic structures might come to be habituated in a mind. These thoughts on the habituation or "learning" of language cover how a mind shall learn to generate sentences. The comprehension of sentences, although expected to be more or less a reversal of these processes of generation, is an area of further enquiry from which the author has temporarily withdrawn in his eagerness to communicate what tentative results are already at hand. Of course, the author realizes that comprehension must both precede and accompany that learning by which either a human infant or a newly assembled automaton will habituate syntactic mechanisms for the generation of sentences. The whole abstract memory channel, proposed here as the essential and enabling medium for the linguistic control of data-flows, has been hypothetically divided into several cables in this paper. First it was divided into a "syntax cable," which operated upon an underlying "logicoconceptual cable." Then the syntax cable was described as containing the special mechanisms of a "function cable" and an "inflection cable." In general, the author has found that it is easier and more productive to imagine a superfluous cable that can be eliminated if found unnecessary, than to suffer the frustration of overcaution when a lacking cable would be really valuable if dreamed up for incorporation into the design. An abstract cable can be valuable even if it serves temporarily only to buffer and isolate two mechanisms in the plan of the designer. Accordingly, the author freely designed various cables in May of 1979 in such numbers that the presently described possibility for habituation suddenly appeared. The genesis of this model of habituation followed the idea that first nouns would be learned, and then verbs. First a syntactic node-fiber controlling nouns would be used and practiced so repeatedly as to constitute habituation. Then the organism would become aware that it was also encountering verbs in its environment of language-speaking entities. In our model here, which is now English, verbs are to be associated with the nouns which are their subjects. However, the verb-controlling syntactic node- fiber becomes habitually operative only after the operation of the noun- controlling syntactic node-fiber has been thoroughly and permanently habituated. The key element in the sequenced habituation of the syntactic nodes is the aforementioned "habituation-class" of the ultimate-tags from the auditory memory channel. An ultimate-tag serves as a signal to return control of the sentence- generating process to the syntax cable. Once the control of English nouns is habituated, it is easy for the signals in ultimate-tags from nouns to serve as stimuli to trigger the activation of an erstwhile unhabituated syntactic node-fiber controlling verbs. Over time, any naturally occurring syntactic node-fiber can be added to the syntactic string, because each syntactic node-fiber becomes habituationally active when the morphological phenomenon behind it is being dealt with by the young or curious mind, and because the same syntactic node-fiber becomes habituationally dormant or "transparent" when it has been "embedded" in the syntactic string and the mind is dealing with a new, typically more subtle phenomenon. Thus a syntactic node-fiber for nouns as direct objects can be added to the string after the habituation of verbs. The habituation process forms a gradual spiral over lengthy time in the following manner. Suppose that we start with a positionally superior, syntactic node-fiber for nouns, controlling the positionally inferior noun- layer in the logicoconceptual cable. Thus we have the first downward movement in our spiral, which, by the way, will actually be composed of square-like coils strung together. The logicoconceptual cable sends signals out horizontally to the right to access nouns stored in the auditory memory channel. Then ultimate-tags from accessed nouns rise perpendicularly from the auditory memory channel into the upper tier of the syntax cable. There the ultimate-tags meet and connect with horizontal concrete associative lines that flow leftwards to begin activation, not of the already habituated, dormant noun-node, but of the newly active verb-node, or syntactic node-fiber for the control of verbs. Thus the loop of habituation has gone full circle. The process slowly, over many months in the case of humans, continues to loop around, adding various syntactic nodes in a spiral of habituation. The model of linguistic habituation presented here is new to the author and rather simple, but it may serve as a basis for quite complex elaborations. The author advises that orthogonality should be observed in any elaborations, even those of syntactic "trees." In other words, branches drawn in syntactic trees should contain no angles other than ninety-degree right angles, so that each tree will mesh and conform with the structures around it in the orthogonal model. 10. THE NOTION OF "TRANSABSTRACTIVITY" Within this general model, since the aggregates of conceptual knowledge join pyramidally to culminate punctiformly in highly manipulable words of symbolic code, the conscious, thinking mind can almost endlessly generate thought-sentences by skimming through the uppermost levels of conceptuality, constantly descending only to that depth automatically determined by the free interassociativity of the interacting conceptual aggregates. What we call an "abstraction" or "abstract concept" is modelled here as a pyramidal aggregate of conceptual knowledge, which becomes abstract through the highly manipulable "punctiformity" of its associable tip: the word. Since the mind is modelled here as skimming rapidly across countless such tips, it seems apt and useful to call this uppermost abstract level the level of "transabstractivity." REFERENCES 1. Keller, Helen, "The Story of My Life" (Grosset and Dunlap, New York, 1903). 2. Kent, Ernest W., The brains of men and machines, "BYTE", Vol. 3, Nos. 1- 3 (January, February, March, 1978). 3. Liles, Bruce L., "An Introductory Transformational Grammar" (Prentice- Hall, Englewood Cliffs, 1971).
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Copyright © 2012 Cromwell Enage
Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Table of Contents
Models of this concept represent grid structures by matching their vertices to the corresponding grid points. Only vertices that are next to each other according to the grid structure have out-edges to and from each other.
Notation
Graph
A type that models the Grid Graph concept.
const_graph
An object of type Graph const&
.
v
An object of type boost::graph_traits<Graph>::vertex_descriptor
const&
.
key
An object of type boost::edge_key_trait<Graph>::type
const&
.
dimension
An object of type boost::vertex_dimension_trait<Graph>::type
const&
.
distance
An unsigned integral type.
Two new types are introduced.
|
Name |
Expression |
Description |
Requirements |
|---|---|---|---|
|
Vertex dimension type |
boost::vertex_dimension_trait<Graph>::type
|
The type by which a vertex is indexable. |
Model-specific. |
|
Vertex coordinate type |
boost::vertex_coordinate_trait<Graph>::type
|
The type of each coordinate of a vertex. |
Model-specific. |
In addition to the expressions defined in the Associative Incidence Graph concept, the following expressions must be valid.
|
Name |
Expression |
Return Type |
Semantics |
|
|---|---|---|---|---|
|
Dimension count |
const_graph.dimensions()
|
boost::vertex_dimension_trait<Graph>::type
|
Returns the number of dimensions that the graph straddles. |
Constant |
|
Dimension length |
const_graph.length(dimension)
|
An unsigned integer type. |
Returns the number of vertices lying on a grid line running along the specified dimension. |
Constant |
|
Dimension wraparound query |
const_graph.wrapped(dimension)
|
|
Returns |
Constant |
|
Vertex coordinate |
v[dimension]
|
boost::vertex_coordinate_trait<Graph>::type
|
Returns the coordinate of the vertex at the specified dimension.
Prerequisite: |
Amortized constant with respect to the number of dimensions |
|
Next vertex |
const_graph.next(v, key, distance)
|
boost::graph_traits<Graph>::vertex_descriptor
|
Equivalent to, but more efficient than: boost::graph_traits<Graph>::vertex_descriptor u = v; for ( BOOST_TYPEOF(distance) d = boost::initialized_value; d < distance; ++d ) { u = const_graph.next(u, key); } return u;
|
Linear with respect to the out-degree of |
Last revised: November 05, 2012 at 03:37:53 GMT |


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I was born and raised in Memphis, TN. I grew up on the South side of town and graduated from Whitehaven High School. During those days, I was really into Spelling, Math and Art. I loved art so much that I took advanced placement art in the 12th grade and competed in competitions. I did a variety of things from oil painting to charcoal drawings. I even got into air brushing design for tee shirts and other items that people wanted to add that personal touch to.
My artistic nature also led to me experimenting with different hairstyles and colors. I have tried several ideas on myself, family members and friends. One thing that I have found, however, is that some people are afraid to try a new style or hair color without actually knowing how it will look on them beforehand. To that extent, I plan to build an app that will allow a person to see a style before actually committing to it.
I received college credit for the AP art class and went to the University of Memphis on a scholarship. Once there, however, my interests turned to a more practical course and I pursued Accounting as a major. I did this for two reasons. I loved Math and I was convinced by those around me that I could not make money in the field of Art. I was told that I needed to find another subject that I could actually get a job with. This is what I did. I graduated with a Bachelors and went to work. I stayed in the field of Accounting for over a decade before I finally became burnt out with the political nature of the job I had. I knew it was time to get back to my artistic roots; perhaps even merging my Accounting skills with my artistic nature to build a platform...


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