self-inducing ephemeral acalculia


<para>Taking a pulse with an analog watch is an everyday clinical task. But, taking a pulse with a digital watch is next to impossible! Why? An instantaneous, fleeting Gerstmann-like syndrome (confusion in calculating) is invariably induced in the mind of the clinician – nurse or doctor.</para> <para>The difference between the use of digital and analog watches is important and easy to demonstrate. Try it on yourself. OK don’t, but please read on. Why is it so – that digital watches do not work in taking a pulse? Is it significant? If so, what are its implications?</para> <para>In answer, I’ll describe the main neural pathways, tactile and visual, involved in taking a pulse. Integrating these and other medical facts with a bit of computational knowledge nicely explains this unique, seemingly spurious clinical observation on simple pulse-taking. But, along with some references to the extant literature on acalculia and dyscalculia, a wider ‘developmental’ implication surprisingly springs forth. And that is, as noted, during the taking of a pulse with any digital timepiece, an instant but fleeting acalculia (a state of confusion blocking calculating) is almost invariably induced in the mind of the examining clinician. May this observation have heuristic value? This piece of news about pulse-taking may be alien to many modern physicians who may never take a pulse directly by hand, but only indirectly with a fancy electronic instrument. Be that as it may, with the foregoing enticing words under our belts, we can go back a bit in time and take a preliminary look at,</para> <para><br></para> <para>A most serendipitous observation</para> <para><br></para> <para>In 1974, giving in to popular sales promotions, I discarded my trusty old watch with its sweep second-hand and bought an expensively glowing digital watch – only to find that I could not take an ordinary wrist-pulse with it. It confused my counting of the pulse-beat. Totally. The ‘phenomenon’ was much the same as trying to read a phone number from a phone book at the same time as someone else is spilling it out by mouth. Anyway, I threw my nice new digital watch into a drawer and went back to wearing my old analog one, incidentally, with new-found appreciation, pleasure and trust in it. But, from time to time I thought about this little oddity and conjured up a,</para> <para><br></para> <para>Hypothesis and a thought-experiment of sorts</para> <para><br></para> <para>Analog watches are a very good medical tool; digital ones are not so okay. Why should it be so? As only a doctor could, I thought about my digitally scrambled thoughts in anatomically neurological terms. As one feels a pulse-beat with right index finger on patient’s right radial wrist-pulse, the signal travels up ones arm (via what nerve?) passes through the brachial plexus, enters the posterior horn of the spinal cord (at what cervical level?). Anyway, it somehow crosses the mid-line and gets to the left side of the brain. Where? Not in the frontal lobe, but in an anterior part of the parietal lobe (in what gyrus?) Into Broca’s little speech area? No, but close.). You can look it all up again as I did, if you wish. It is a small area just behind Broca’s – an area devoted to counting and such.</para> <para>Now all of that above is just for feeling and roughly counting the pulse. What about looking at and seeing and registering a watch-face? That is, accurately counting and documenting the end-results with a measuring piece, a watch, a thing we hardly ever think of anymore, at least in scientific terms? Well, visual signals from any watch-face travel to the brain by an entirely different route and arrive and are processed by an entirely different part. Or is that entirely true? To cut to the quick of the matter and make it simple, we all know that any visual picture, after traversing the eyes sweeps around both sides of the brain, then goes to the occipital lobes. Then where? That is the crux of things. The sweeping second-hand of an analog watch is a tidy spatial picture that is analyzed where it should be – right in the right parietal lobe. And that’s where it stays. But the intermittent digital count of a digital watch ultimately must go to the left side of the brain to be counted. Where? Exactly where the finger’s pulse count is going on.</para> <para>Presto! The answer is now obvious. Digital watches confuse the brain’s counting area by demanding an accounting at the same spot and at the same time as the finger’s input is undergoing its own ongoing accounting. Both are digital. Both are intermittent. Together they confuse each other – and the clinician. On the other hand, watching an analog watch requires a recording of only two points in time, the start and the end. And nothing in between. Put another way, the watching of a smoothly continuous analog watch is done subconsciously on the right side of the brain where it does not interfere with the discrete left-sided finger count. (Of course, all of this may be reversed in a left-handed individual. But the basic principal is the same.)</para> <para><br></para> <para>An aborted experiment in the field</para> <para><br></para> <para>The real life experiment turned out to be a nuisance to family and friends alike. As I couldn’t get them all to learn how to properly take a pulse, in order to garner independent observations, I subtly compared their reactions to my input in various other venues.</para> <para>As my young daughter kept ‘metronomic’ time while practising at the piano, I hummed an ad lib and tuneless medley of exasperatingly reverse numbers. This single, brilliant experiment was stopped cold with, “Dad, please stop that! I cant keep track.” So I thenceforth confined myself to exasperating others with 7-10 digit numbers while they dialled the phone. It was not long before more displeasure came my way, so the sans digital watch trial drew to a premature close. I can only suggest that the interested clinical reader try to take patients’ pulses alternately with analog and digital watches and prove the point to her own satisfaction.</para> <para>Anyway, the above neurological hypothesis still stands – at least to my own satisfaction. It explains why analog watches work and digital watches fail in taking any pulse. But digital watches don’t merely fail – they can plunge us into a short-lived state of almost utter confusion where it counts upstairs. So, what sort of phenomena could this be? Well, medicine, this time pathology, again came to the rescue. The phenomenon is much akin to clinical acalculia or dyscalculia. And it may now behove us to take a closer look at what is known of these particular things.</para> <para><br></para> <para>Some roots &amp; definitions</para> <para><br></para> <para>Dyscalculia means counting badly. It comes from both Greek and Latin roots. The prefix ‘dys’ means ‘badly’ in Greek. ‘Calculia’ comes from the Latin ‘calculare,’ ‘to count.’ The word ‘calculare’ comes from ‘calculus,’ which means ‘pebble’ or one of the counters on an abacus. The word acalculia strictly means not being able to count at all – as its first letter ‘a’ means ‘not’ in Greek. Obviously, the modern medical terms acalculia and dyscalculia should not be confused with each other and used interchangeably. But not for strictly lexical reasons.</para> <para>Medically defined, acalculia is an impairment acquired late in life in which patients have real difficulty performing simple mathematical tasks, such as adding, subtracting, multiplying and even simply stating which of two numbers is larger. It is due to neurological injury such as stroke. Dyscalculia, on the other hand, as described by child psychiatrists, is a specific developmental disorder first observed during the acquisition of mathematical knowledge.</para> <para>Now let’s dig a little deeper. Here are the usual variations: Acalculia is associated with lesions of the parietal lobe (especially the angular gyrus) and the frontal lobe and can be an early sign of dementia. Acalculia is sometimes observed as a ‘pure’ deficit, but is commonly observed as one of a constellation of symptoms, including agraphia, finger agnosia and left-right confusion, after damage incurred to the left angular gyrus. Acalculia of this sort is known as Gerstmann’s syndrome (Gerstmann, 1940; Mayer et al, 1999).</para> <para>Yet deeper: Studies of patients with lesions to the parietal lobe have demonstrated that lesions to the angular gyrus tend to lead to greater impairments in memorized mathematical facts, such as multiplication tables, with relatively unimpaired subtraction abilities. Conversely, patients with lesions in the region of the intraparietal sulcus tend to have greater deficits in subtraction, with preserved multiplication abilities (Dehaene and Cohen, 1997). These double dissociations lend support to the idea that different regions of the parietal cortex are involved in different aspects of numerical processing.</para> <para><br></para> <para>Some key medical studies</para> <para><br></para> <para>In support of the notion that the right side of the brain processes spatial phenomena such as an analog watch-face, here, as cited in the Archives of Neurology, is what Weintraub and Mesulam had to say as far back as 1987: Tasks based on visuomotor scanning and tactile exploration were used to quantitate neglect behaviour in patients with unilateral brain damage and in normal control subjects. The results confirm previous observations that contralateral neglect is markedly more severe following right-hemisphere injury and that it is independent of the modality of sensory input or motor output. In addition, patients with right-hemisphere injury also showed multimodal neglect for targets in the hemisphere ipsilateral to the brain lesion. The emergence of both contralateral and ipsilateral neglect in these patients strongly supports a model of right-hemispheric dominance for the distribution of attention within the extra-personal space. (Weintraub, S. and M. M. Mesulam. Right Cerebral dominance in spatial attention. Further evidence based on ipsilateral neglect. Archives of Neurology, Vol. 44 No. 6, June 1987.)</para> <para>Now, I quote from Takayama et al as regards the left side of the brain and acalculia as cited in the Archives of Neurology (1984): Objectives: To clarify the characteristics and the localization of isolated calculation disturbances due to left parietal lesions. Design: Case series. Setting: Tertiary care hospital. Patients and other participants: Three referred patients with isolated calculation disturbances due to stroke in the left parietal region. Sixteen volunteers for age and education constituted the control group. Outcome measures: Neuropsychological tests, including a battery of tests for acalculia and the Wechsler Adult Intelligence Scale, and magnetic resonance imaging were performed. Results: Three patients made calculation errors in the process where a number of steps were carried out simultaneously. The patients showed no aphasic components in number operations. They understood the basic processes of calculation. They showed little difficulty in the retrieval of table values. The patients had no impairment in aligning arithmetic problems or in assigning and maintaining place-holding values. They did not show any deficit of immediate memory for calculation problems. Overlapping lesions were located along the left intraparietal sulcus. Conclusion: The area lying along the left intraparietal sulcus is critical for isolated parietal acalculia. The profile of isolated acalculia suggests that it results from the disruption of the working memory for calculation. (Takayama Y., M. Sugishita, I. Akiguchi and J. Kimura Department of Rehabilitation, Tokyo Metropolitan Institute for Neuroscience, Japan. Isolated acalculia due to left parietal lesion. Archives of Neurology. Vol. 51 No. 3, March 1994.)</para> <para>Back in 1987, PeBenito addressed the Gerstmann syndrome tetrad as follows: The tetrad of finger agnosia, dyscalculia, dysgraphia, and right-left confusion constitutes the Gerstmann syndrome (GS). A case of developmental Gerstmann syndrome (DGS) that occurred in a normal, highly intelligent child with exceptional reading skills is reported, together with a review of the literature. DGS occurs in both brain-damaged and seemingly normal children. Multiple neurological and behavioural manifestations coexisting with the Gerstmann elements suggest brain injury, whereas the occurrence of the Gerstmann tetrad (plus constructional apraxia) in an otherwise normal and intelligent child implies what is herein referred to as “constitutional.” The scarcity of reported cases indicates the rarity of the syndrome in children. Routine testing for the Gerstmann elements in learning-disabled children may uncover unrecognized cases. (PeBenito R. Developmental Gerstmann syndrome: case report and review of the literature. J Dev Behav Pediatr. 1987 Aug;8(4):229-32. PMID: 3611364 [PubMed – indexed for MEDLINE])</para> <para>Ardila et al also looked at the Gerstmann Syndrome in 2002: Even though it is generally recognized that calculation ability represents a most important type of cognition, there is a significant paucity in the study of acalculia. In this paper the historical evolution of calculation abilities in humankind and the appearance of numerical concepts in child development are reviewed. Developmental calculation disturbances (developmental dyscalculia) are analyzed. It is proposed that calculation ability represents a multifactor skill, including verbal, spatial, memory, body knowledge, and executive function abilities. A general distinction between primary and secondary acalculias is presented, and different types of acquired calculation disturbances are analyzed. The association between acalculia and aphasia, apraxia and dementia is further considered, and special mention to the so-called Gerstmann syndrome is made. A model for the neuropsychological assessment of numerical abilities is proposed, and some general guidelines for the rehabilitation of calculation disturbances are presented. (Ardila A and Rosselli M: Acalculia and dyscalculia. Neuropsychol Rev. 2002 Dec;12(4):179-231.Department of Communication Sciences and Disorders, Florida International University, Miami, Florida, USA.alfredoardila@cs.comPMID: 12539968 [PubMed – indexed for MEDLINE])</para> <para>And here, not to be outdone, is a reference to my own contribution to eye preference and handedness made in the far distant past. (Hogg, William F. Reversal of eye preference at reading distance, associated with specific reading disability (dyslexia). Can Psychiat Assoc J. 1968 Feb;13(1):85-6. PMID: 5640476 [PubMed – indexed for MED LINE] The author includes this ancient reference to show that many years ago, long before digital watches, he was interested in handedness and eye preference problems. The paper shows that in vision the concept of eye preference is preferable to the term dominance. As the visual fields have bilateral point to point connections to the occipital lobe, there is no dominant eye. But in reading one or the other eye is preferred. In dyslexia eye preference switches at reading distance! A simple clinical method for the determination of eye preference, that also demonstrates this switchover, was developed and presented.)</para> <para><br></para> <para>The counting vicissitudes of cognitive science</para> <para><br></para> <para>Numerical cognition is a sub-discipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavours, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics. This discipline, although it may interact with questions in the philosophy of mathematics is primarily concerned with empirical questions. The diverse topics included in the domain of numerical cognition include: How do non-human animals process numerosity? How do infants acquire an understanding of numbers (and how much is inborn)? How do humans associate linguistic symbols with numerical quantities? How do these capacities underlie our ability to perform complex calculations? What are the neural bases of these abilities, both in humans and in non-humans? What metaphorical capacities and processes allow us to extend our numerical understanding into complex domains such as the concept of infinity, the infinitesimal or the concept of the limit in calculus?</para> <para><br></para> <para>The basics of digital and analog communication</para> <para><br></para> <para>Information-communication theory, so central to computational science, has a peripheral relevance to our topic, that, for completeness sake, cannot be left out. Feeling a pulse and reading its rate correctly is information input, a purely nonverbal form of communication from patient to doctor that has two key modes – digital (the finger) and analog (the eyes). This is unusual for most nonverbal communication is purely kinesic and continuous – emotional. Pure speech, outside of poetry, is digitally discrete, wholly intermittent and emotionally bland. The neopallium is its playground. The archipallium, tinkered with by evolution, is an emotional playground. And never the twain shall meet. And that is the paradox. The semantics of one don’t mesh with the syntactics of the other. And that is enough. The reader must now see that words can be as confusing as misread pulses.</para> <para><br></para> <para>A very short discussion with a conclusive result</para> <para><br></para> <para>Now that I may have impressed the reader with a late-found capacity to do irrelevant homework and cite loads of references, let’s get back to the topic in hand. First, don’t try to use a digital watch to take a pulse. You cant. I know medical interns who try to do so and actually report getting a true count. They lie. Second, doing so, using a digital watch, will confuse you. You will be instantly precipitated into an induced, fleeting Gerstmann-like acalculia. More seriously, I think that my ‘discovery,’ recognition and interpretation of a fleetingly induced and easily reproduced acalculia has heuristic research value.</para> <para><br></para> <para>Post-amble</para> <para><br></para> <para>This little article, aside from its serious acalculia content, is a light (pulsating, pulse-taking) piece of dark medical humour. It is riddled with dense sarcasm directed at the sometimes pseudo-seriousness of doctors – especially some super-specialists such as myself. The fact that I don’t later name the nerves in the arm indicates how well all doctors forget what they once knew and some don’t bother keeping up and sharp and simple. I figured that no kind of self-respecting medical journal would ever publish such a paper. Nevertheless, the essential facts and conclusions presented are correct and this tidbit of medical minutiae may have heuristic relevance in future research on acalculia. And, reader, don’t feel shot down, as hardly any MD could all that early catch on to the sarcasm either. /wfh</para>

Appendix 1

<sec><heading></heading><para> </para></sec>