From the previous descriptions, it is evident that the left and right parietal lobes function differently. The most obvious difference, of course, is that language and arithmetical functions are centered in the left hemisphere. It is hardly surprising, therefore, that verbally mediated spatial and praxic functions are more affected with left-sided than with right-sided lesions. This is ostensible because language function, sited in the left hemisphere, is central to all cognitive functions. Hence cross-modal matching tasks (auditory–visual, visual–auditory, visual–tactile, tactile–visual, auditory–tactile, etc.) are most clearly impaired with lesions of the dominant hemisphere. Such patients can read and understand spoken words but cannot grasp the meaning of a sentence if it contains elements of relationship (e.g., “the mother’s daughter” versus “the daughter’s mother,” “the father’s brother’s son,” “Jane’s complexion is lighter than Marjorie’s but darker than her sister’s”). There are similar difficulties with calculation. The recognition and naming of parts of the body and the distinction of right from left and up from down are learned, verbally mediated spatial concepts that are disturbed by lesions in the dominant parietal lobe.
This syndrome, caused by a left (dominant) inferior parietal lesion, provides the most striking example of what might be viewed as a bilaterally manifest agnosia (the previously mentioned asomatognosia of Denny-Brown and Banker). The characteristic tetrad of features is (1) inability to designate or name the different fingers of the two hands (finger agnosia), (2) confusion of the right and left sides of the body, (3) inability to calculate (acalculia), and (4) inability to write (dysgraphia). One or more of these manifestations may be associated with word blindness (alexia) and homonymous hemianopia or a lower quadrantanopia. The lesion is in the left inferior parietal lobule (below the interparietal sulcus), particularly involving the angular gyrus or subjacent white matter of the left hemisphere.
There has been a dispute as to whether the four main elements of the Gerstmann syndrome have a common basis or only an association. Benton states that they occur together in a parietal lesion no more often than do constructional apraxia, alexia, and loss of visual memory and that every combination of these symptoms and those of the Gerstmann syndrome occurs with equal frequency in parietal lobe disease. Others, including the authors, tend to disagree and have the experience that right–left confusion, digital agnosia, agraphia, and acalculia have special significance, possibly being linked through a unitary defect in spatial orientation of fingers, body sides, and numbers. The relationship between the finger agnosia and the inability to enumerate is especially intriguing and relates to other arithmetic difficulties, discussed below. Attempts to clarify a common or fundamental source for all the elements of the Gerstmann syndrome by functional imaging have been difficult. In healthy subjects, Rusconi and colleagues were unable to find a shared cortical substrate that could give rise to the features of the Gerstmann syndrome.
Dyscalculia has attracted little critical attention, perhaps because it occurs most often as a by-product of aphasia and an inability of the patient to appreciate numerical language. Primary dyscalculia is usually associated with the other elements of the Gerstmann syndrome. Computational difficulty may also be part of the more complex visuospatial abnormality of the nondominant parietal lobe; there is then difficulty in the placing of numbers in specific spatial relationships while calculating. In such cases, there is no difficulty in reading or writing the numbers or in describing the rules governing the calculation, but the computation cannot be accomplished correctly with pencil and paper. Hécaen has made a distinction between this type of anarithmetia and dyscalculia. In the latter, the process of calculation alone has been disturbed; in the former, there is an inability to manipulate numbers and to appreciate their ordinal relationships. Recognition and reproduction of numbers are intact in both. An analysis of how computation goes awry in each individual case is therefore required.