| Annotation Metadata
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^"permissions":^"read":ӶӺ,"update":ӶӺ,"delete":ӶӺ,"admin":ӶӺ°,"user":^"id":6,"name":"Sarah Oberbichler"°,"id":"W69xuyvf2z","ranges":Ӷ^"start":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/pӶ21Ӻ","startOffset":0,"end":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/pӶ25Ӻ","endOffset":1175°Ӻ,"quote":"There are dot patterns and other spatial configurations that are obviously not distinguishable on the basis of qualitative motor characteristics of scan-paths. If two dots are recognized as a characteristic configuration by the sole fact that they are connected by a straight scan-path, then three, four, or more dots in linear arrangement would be considered the same. Yet this is not the case. Starkey and Cooper (1980) have elegantly shown that even infants of less than six months discriminate quite reliably three dots in a line from two, whereas they do not seem to discriminate between four and six. We may safely assume that infants of that age cannot count. On the other hand, the experiment made clear that the discrimination does not depend on the distance between the dots or on the over-all extension of the display. Hence there must be some inherent difference in the process of perceiving two as opposed to three dots.Ӷ11Ӻ That difference, I suggest, arises from the capability of the nervous system to differentiate between the temporal patterns constituted by a succession of two perceptual acts as opposed to one or three. “Perceptual act” in this context means no less and no more than the isolation of any item whatever from the rest of the experiential field which, in the case at hand, can be reduced to the visual field. In other words, I am positing a neural mechanism that distinguishes a dual incidence of a given event from a single or a treble incidence (von Glasersfeld, 1981b). What will be considered a dual event, rather than two single ones in succession, depends of course on temporal parameters which we must assume to be inherent in the system – an assumption that can not be invalidated by the observation that these temporal parameters can, under certain circumstances, be modified by experience, practice, or training. \nThe best-known instances of non-numerical discrimination and recognition of single, dual, treble, etc., events are probably those that occur when we listen to music, where they form the experiential material that goes by the name of “rhythm”. Recent work with children leaves no doubt that the ability to remember, recognize, and replicate simple rhythms (by clapping or tapping) is manifested prior to any abstract or notational representations of such rhythms (Bamberger, 1975, 1980, 1982). That is to say, a sequence of beats which an adult might capture in a conventional notation, is recognized by the child as a figural pattern in a way analogous to that in which visual shapes are first recognized, but with the difference that the rhythm is a configuration in time, whereas the shapes appear as configurations in space (von Glasersfeld, 1979b). From my point of view, it is particularly interesting that the children in that study had little or no difficulty in “drawing” the rhythms by inventing their own visual representations. \nThis readiness to translate a temporal pattern into a linear spatial one strongly supports my assumption that the visual perception of a linear arrangement of items can, indeed, be characterized (and distinguished from other visual experiences of the kind) by its rhythmic properties. In both vision and audition the temporal pattern is constituted by a sequence of perceptual acts which are given their structure by a succession of attentional pulses. This is rather obvious in auditory experience, which is necessarily perceived as an ordered sequence of events in time. In visual experience the sequentially is obscured because, under most circumstances, the individual perceptual acts that constitute a spatial configuration are not subject to an obligatory order.Ӷ12Ӻ That is why linear arrangements are something of a special case: There, a definite order is at least strongly suggested by the ease and economy of the linear scan-path.\nA striking example of the ability to transpose spatial into temporal patterns is the telegraphist’s translation of written Morse code into a sequence of motor acts that make and break an electric contact. Here the conventional order of the left to-right line is turned into a temporal order. The groups of dots and dashes on the source tape are neither counted nor perceived as numerical structures – they are taken as patterns of perceptual acts that can be immediately realized in terms of motor acts because the rhythmic configuration remains experientially the same in both modes.\nIn short, then, I am suggesting that the infants’ ability to distinguish between linear displays of one, two, and three dots (Starkey & Cooper, 1980), young children ‘s facility for depicting auditory patterns graphically (Bamberger, 1975), the telegraphist’s skill of translating visual into motor sequences, and, finally, the general ability to subitize linear arrangements of perceptual items, can all be reduced to an underlying capacity to distinguish, recognize, and represent simple temporal configurations that have a characteristic iterative structure. Such iterative structures have rhythmic patterns that can be empirically abstracted as figural patterns from sensory events, not only in the auditory mode, but also in the kinesthetic, tactual, and visual modes, because, in all these modes of experience, structure is constituted by a patterned succession of attentional moments that was experientially determined by the sequence of sensory signals. Once abstracted, these rhythmic patterns may be semantically associated with number-words. The link to a number word, however, does not turn them into numerical concepts. Conceptually they are still figural patterns. Only “reflective” abstraction – the focusing of attention on their iterative structure rather than on the actual or representational sensory material with which that structure happens to have been implemented – can raise them to the level of “pure” abstraction that is characteristic of the conception of numbers (von Glasersfeld, 1981a).\nOn the other hand, already as figural patterns consisting of sequences of perceptual items, representations of such rhythmic structures make possible the recognition of specific sequential configurations of dots, checkers, fingers, etc., as instances of patterns that are associated with one of the number-words between one and five. Thus, analogous to the way in which a characteristic scan-path serves as the criterial recognition feature for specific classes of spatial patterns (e.g. triangles), a characteristic rhythmic structure serves as the criterial recognition feature for large classes of sensory events which, experientially, can be reduced to temporal patterns. Since these classes comprise not only auditory and motor events (whose nature is sequential in any case), but also visual and tactual events whose sequentiality is created by a relatively fixed linear order of the perceptual process, the recognition of rhythmic structures plays an important role in the phenomenon of subitizing and as a necessary precondition to the reflective abstraction of numerical concepts from linear configurations of items such as dots and tiles, and from Finger patterns.","highlights":Ӷ^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°,^"jQuery321019266462329114922":^°°Ӻ,"text":"","order":"mw-content-text","category":"Argumentation2","data_creacio":1595602933477°
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