Letter Arrays Research Articles

''Masked'' Span of Apprehension in Schizophrenic Subgroups

Background. This study explored the possible impairment in inhibiting irrelevant stimuli (as reflected in the backward masking version of the forced-choice span of apprehension task) in subgroups of individuals with schizophrenia. Method. Subjects included 48 schizophrenics and 54 nonpsychiatric controls. Letter arrays were presented at three stimulus onset asynchronies (SOAs; 60, 100, 250msec) and three levels of complexity (3, 7, 11 distractor letters). Results. As a group, schizophrenics (n = 54) were impaired relative to nonpsychiatric controls (n = 48) for 7-distractor displays at 60msec and 250msec SOA. Cluster analysis of SAPS and SANS ratings produced four symptom subgroups. Opposing masking performances were found for Psychomotor Poverty (impaired for long SOAs) and Reality Distortion (enhanced at short SOAs) subgroups, whereas the Disorganisation subgroup was globally impaired, and the Episodic subgroup performed similarly overall to controls. Conclusion. The results highlight the potential importance of symptomatology in further elucidating the span of apprehension impairment in schizophrenia.

Acetylcholine affects the spatial scale of attention: evidence from Alzheimer's disease.

Location precues were used to manipulate the spatial scale of attention in visual search for a target in an array of letters in patients with dementia of the Alzheimer type (DAT) and in age-matched older controls. Cue size varied in the amount of spatial precision conferred. Scopolamine, a muscarinic antagonist, decreased overall arousal and broadened spatial attention after a precise precue (small and valid) to target location for DAT patients but not for controls, suggesting a selective effect for attentional impairment induced by cholinergic blockade. In contrast, physostigmine, a cholinesterase inhibitor, did not alter the distribution of spatial attention relative to no-drug baseline testing for patients. Results support a differential role for cholinergic mechanisms in the modulation of the spatial scale of visual attention.

The Bible Code

In the Random Samples item “Bible code bunkum” (24 Sept., p. [2057][1]), there is a description of findings by mathematician Eliyahu Rips of Hebrew University and two colleagues that “names of famous rabbis were located closer in the text to their own dates of birth and death than to those of other rabbis.” As one of the authors of a paper ([1][2]) in which a flaw in the study by Rips et al. ([2][3]) is reported, I wish to point out that this is not what they found. The names of most rabbis are actually closer in the text to the dates of birth and death of other rabbis than to their own dates (“closer” is defined in a complicated mathematical fashion that does not correspond to the intuitive sense suggested by their letter arrays). What Rips et al. found is that the “distances” between rabbis' names and their own dates are, on average, less than one would expect by chance. Most misreports of the Bible code findings tend to present the findings as neater than they actually are. However, the Random Samples item got the main point across—whatever “code” is found in the book of Genesis can be replicated in any other text of comparable length. 1. [↵][4]1. B. McKay, 2. D. Bar-Natan, 3. M. Bar-Hillel, 4. G. Kalai , Stat. Sci. 14((no. 2)), 150 (1999). [OpenUrl][5][CrossRef][6] 2. [↵][7]1. D. Witztum, 2. E. Rips, 3. Y. Rosenberg , Stat. Sci. 9((no. 3)), 429 (1994). [OpenUrl][8][CrossRef][9] [1]: /lookup/doi/10.1126/science.286.5447.2057 [2]: #ref-1 [3]: #ref-2 [4]: #xref-ref-1-1 View reference 1 in text [5]: {openurl}?query=rft.jtitle%253DStat.%2BSci.%26rft.volume%253D14%26rft.issue%253D%2528no.%2B2%2529%26rft.spage%253D150%26rft.atitle%253DSTAT%2BSCI%26rft_id%253Dinfo%253Adoi%252F10.1214%252Fss%252F1009212243%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [6]: /lookup/external-ref?access_num=10.1214/ss/1009212243&link_type=DOI [7]: #xref-ref-2-1 View reference 2 in text [8]: {openurl}?query=rft.jtitle%253DStat.%2BSci.%26rft.volume%253D9%26rft.spage%253D429%26rft_id%253Dinfo%253Adoi%252F10.1214%252Fss%252F1177010393%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [9]: /lookup/external-ref?access_num=10.1214/ss/1177010393&link_type=DOI

Response AC/A ratios are elevated in myopic children

In children little is known about the relationship between the AC/A ratio and the development of myopia, although they have been linked in adults. The purpose of this study was to investigate the interaction between accommodation and convergence and its relationship to refractive errors in children. Accommodation was measured for the right eye using the Canon R-1 autorefractor, and concomitant changes in vergence were assessed using a Maddox rod and a Risley prism before the left eye. Thirty-three myopic and 68 emmetropic children were tested wearing best subjective correction while looking at a distant (4.0m) letter array and a near (0.33m) one through additional plus and minus lenses. Lens-induced and distance-induced response AC/A ratios were calculated from the data. Both types of AC/A ratios are elevated in myopic children, who show reduced accommodation and enhanced accommodative convergence. Myopic children with esophoria underaccommodate at near. This suggests that a child who is esophoric must relax accommodation to reduce accommodative convergence and maintain single binocular vision. The reduction in accommodation could produce blur during near work, which could induce myopia as in animal models.

Isolating the interference caused by cue duration in partial report: a quantitative approach.

In bar-probe partial report experiments, subjects are presented with a brief array of letters, followed by a cue that singles out a target letter. Using this procedure, V. M. Townsend (1973) reported a counterintuitive effect: As the duration of a cue was increased, target performance decreased dramatically. The aim of the present study was to isolate the locus of the cue-duration effect. To this end, several characteristics of the bar-probe display were manipulated in a single experiment: the interstimulus interval between the array and the cue, array density, the number of letters, and the number of symbols adjacent to the target. These factors were manipulated on a priori grounds so as to affect the different sources of information used in the bar-probe task--namely, durable storage, abstract identity information, and feature level information. The data were accurately fit by a simple quantitative, multinomial model that assumes that the different sources of information used in the bar-probe task make independent contributions to performance. The critical assumption of the model is that cue duration interferes with only one source of information--namely, feature level information.

Response AC/A ratios are elevated in myopic children.

In children little is known about the relationship between the AC/A ratio and the development of myopia, although they have been linked in adults. The purpose of this study was to investigate the interaction between accommodation and convergence and its relationship to refractive errors in children. Accommodation was measured for the right eye using the Canon R-1 autorefractor, and concomitant changes in vergence were assessed using a Maddox rod and a Risley prism before the left eye. Thirty-three myopic and 68 emmetropic children were tested wearing best subjective correction while looking at a distant (4.0 m) letter array and a near (0.33 m) one through additional plus and minus lenses. Lens-induced and distance-induced response AC/A ratios were calculated from the data. Both types of AC/A ratios are elevated in myopic children, who show reduced accommodation and enhanced accommodative convergence. Myopic children with esophoria underaccommodate at near. This suggests that a child who is esophoric must relax accommodation to reduce accommodative convergence and maintain single binocular vision. The reduction in accommodation could produce blur during near work, which could induce myopia as in animal models.

Lee's Miserables: Life in the Army of Northern Virginia from the Wilderness to Appomattox (review)

BOOK REVIEWS73 hatchet-faced James H. Lane, political mountebank turned cold-blooded killer. The last chapter takes the reader full circle, back to John Brown and his October 16-18, 1859, raid on Harpers Ferry. Events there, told in the words of the participants , depict a stunned citizenry, a small, dedicated band of abolitionists who are determined to free slaves or give their lives trying, and the utter hopelessness of Brown's plan. The epilogue returns to Kansas, introducing a new character, William Quantrill, about whom Goodrich has written inBloody Dawn, a previous book. Well-chosen, appropriately placed pictures and lithographs, mostly from the Kansas State Historical Society collection, liberally adorn the pages. Two nicely prepared maps keyed to the text help readers unfamiliar with the MissouriKansas border place events in a geographical context Though half-a-dozen manuscript sources appear in the bibliography, War to the Knife was written largely from published material. Those who prefer a more complete historical analysis ofthe struggle for Kansas should read James C. Matin's two books on the subject; James Monaghan's Civil War on the Western Border; 1854-1865 (1955); James A. Rawley's Race and Politics: "Bleeding Kansas" and the Coming of the Civil War (1969); or Michael Fellman's Inside War: The Guerrilla Conflict in Missouri During the Civil War (1989). But those looking for a lively, though uncritical account unburdened by analysis or completeness will find in War to the Knife a "you are there" approach in which participants provide in their own words a glance at not only pioneer life on the plains but also the general lawlessness that prevailed in Kansas after 1 854. Marion B. Lucas Western Kentucky University Lee's Miserables: Life in the Army ofNorthern Virginiafrom the Wilderness to Appomattox. By J. Tracy Power. (Chapel Hill: University of North Carolina Press, 1998. Pp. xxii, 463. $34.95.) Recent years have seen the publication of numerous volumes of "new military history" that examine the Civil War's common soldiers. J. Tracy Power's Lee's Miserables, which traces the Army of Northern Virginia through its final year of existence from May 1864 to April 1865, falls into that genre. The period covered by Power's book—including the Overland and 1 864 Valley Campaigns, the siege of Petersburg, and Appomattox—witnessed some of the most sanguine and important fighting of the Civil War, but until the 1980s it attracted little attention, compared to the more famous engagements of 1862 and 1863. Lee's Miserables is chronological in format and features extensive quotations from a large array of wartime letters, diaries, newspaper articles, and official papers such as the invaluable but little-known army inspection reports. The author intends the book to be a "braided narrative," interweaving narrative with 74CIVIL WAR HISTORY analysis. Power's chronicle of campaigns and battles is competent and wellwritten but offers little that is new. The book's last chapter offers more explicit analysis than preceding ones and places Lee's Miserables within the context of other Civil War scholarship. Power does an excellentjob in revealing the reactions of Lee's men to important events, including the 1864 presidential election, the Hampton Roads Conference , and proposals to recruit slaves into the Confederate Army. He likewise provides an insightful look at morale in the Army of Northern Virginia. During the Overland Campaign, Power reveals, the majority of Lee's soldiers maintained good spirits despite the enormous carnage and physical and mental strain of nearly nonstop fighting. Even when the Southerners fell back to the defenses of Richmond and Petersburg, many felt that holding off Grant's army would convince Northerners that the cities were impregnable and the Union could not win the war. The Confederate soldiers' abiding faith in Robert E. Lee and their belief that the Army of Northern Virginia constituted the main hope for Southern independence is clearly evident throughout the book. Attrition from battle losses and desertion had severely weakened Lee's forces by the summer of 1 864, but Power traces the army's final collapse to the winter of 1864-65, when acute hunger in the trenches and terrible conditions on the homefront resulted in a...

Spatial organization of distractors in visual search.

Abstract This paper investigates visual search in displays in which distractors are spatially grouped. Detection of targets at the border of two regions where distractors are coherent is easier than can be predicted by models that do not take spatial organization into account. Thus, models of visual search need to incorporate effects of spatial organization in addition to bottom-up difference calculations. People can quickly locate items of potential interest in a visual scene, despite the fact that these items, and the other items in the scene, are rarely fully known in advance. Because this rapid guidance of visual inspection cannot be completely planned in advance, it is believed that it occurs primarily bottom-up, that is, guided by visual input rather than by expectations. In support, models of visual processing that include local difference calculations have been successful at explaining many aspects of tasks such as texture segregation Julesz, 1981; Nothdurft, 1992, 1993) and search (Bergen & Julesz, 1983; Nothdurft, 1992, 1993; Wolfe, 1994). On the other hand, not all phenomena in visual search can be explained by local accounts, and in this paper we report evidence for non-local influences on search in spatially organized displays. The spatial organization of items in a visual display can affect search efficiency (Banks & Prinzmetal, 1976; Bundesen & Pedersen, 1983; Farmer & Taylor, 1980; Poisson & Wilkinson, 1992; Theeuwes, 1996; Treisman, 1982). For example, Treisman (1982, Experiment 1) arranged 36 distractors of two types into different numbers of coherent groups. Fewer, larger groups yielded faster search times for a conjunction target (a green H among red Hs and green xs, where the target shared one feature with each of the two types of distractor) than more, smaller groups. One important question is the effect on search of target position relative to the boundary between groups. Are targets in the middle of coherent groups (with homogeneous neighbours) detected faster than those near group boundaries (with more heterogeneous neighbours)? Treisman (1982, Experiment 4) investigated the effect of target position relative to coherent groups within the display, using one-dimensional arrays of letters. The arrays consisted of three distractors of one type on the left, three distractors of another type on the right, and a target either within one of the distractor groups (surrounded by only one kind of distractor) or in the middle between the two groups (surrounded by two kinds of distractor). A conjunction target was detected fastest if it was within one of the groups, rather than between the two groups. Treisman investigated only the role of spatial position relative to groups in one-dimensional stimuli, however.' In these stimuli, local neighbourhood is confounded with group membership, because targets within a group of distractors are surrounded by homogeneous distractors and targets between groups are surrounded by heterogeneous distractors. This paper investigates the effects of different local neighbourhoods for targets that were within, rather than between, groups of distractors. We examined the effect on detection of target position within a spatially grouped two-dimensional display containing two distractor types. We compared detection in grouped displays with detection in two kinds of control display, homogeneous (one distractor type) and ungrouped (two distractor types). We were interested in whether detection in grouped displays would be more similar to efficient detection in homogeneous displays than to inefficient detection in ungrouped displays. We found relatively efficient detection in grouped displays. In the General Discussion, we consider extensively whether models failing to take into account the spatial organization of the display can account for our results, and we conclude that they cannot. Chun and Jiang (1998) demonstrated that the spatial configuration of a search display can assist search, using a task in which the observer had to determine which of two targets was present in the display. …

The world within war: America's combat experience in World War II

Historian Gerald Linderman has created a seamless and highly original social history, authoritatively recovering and capturing the full experience of combat in World II. Based on a vast array of letters, diaries, books, and a survey of veterans by the Army College, World Within War cuts through the many layers of protective shielding in soldiers' memoirs to find the shards of direct experiences that lie beneath. The Allied-Axis conflict was far more complex than even the Great War, and much has been made by previous historians of the differences between the European theater and the grimly barbaric Pacific. Yet Linderman demonstrates that there were more similarities than differences, that for American soldiers around the globe the war was disintegrative. Examining how Americans prepared for battle, how they treated each other, how they conceived of the enemy, how they thought of home, and how they reacted to battle itself, Linderman argues that ultimately, in both theaters, combat had its own grim logic, independent of causes and countries, flags and commanders.

Eye Movements, Attention and Trans-saccadic Memory

The eyes make rapid, saccadic movements from point to point in space several times each second. It is generally assumed that some mental representation of the visual environment is maintained across eye movements in a trans-saccadic memory. We examined the role of attention in the encoding of information into trans-saccadic memory using a partial report procedure. A letter array was presented in one fixation, then a bar marker probed report of one array position after a saccade was made to a new location. Accuracy was high for positions that subjects had been told to attend to, but it was also high for positions near the saccade target, even if subjects had been instructed to attend elsewhere. These results indicate that attention determines what information is encoded into trans-saccadic memory and hence remembered across eye movements. Because attention automatically precedes the eyes to the saccade target location, information near the saccade target is likely to be encoded. The results are discussed in terms of VAM, the neurocognitive model of visual attention proposed by Schneider (1995).

The dimensionality of the flanker compatibility effect: a psychophysiological analysis.

The psychophysiological approach was used to evaluate the effects of feature similarity and "intrinsic response mapping" on the flanker compatibility effect. Symbol (e.g., < > < and </<) and letter arrays (e.g., HCH and SCS) were used. Results showed that delays in stimulus evaluation and both peripheral and central response competition contributed to the compatibility effect, with the contribution of these processes depending on feature similarity and the intrinsic response mapping of the stimuli. For letter stimuli, the difference in the size of the compatibility effect for similar and dissimilar arrays could be accounted for in terms of stimulus evaluation. For symbol arrays, differences in size of the compatibility effect could be accounted for by response competition. Thus, symbol and letter arrays do not appear to be processed differently; what is different is the degree to which stimulus and response-related processes are affected by incompatibility.

Kenneth Burke in Greenwich Village: conversing with the moderns, 1915-1931

Capturing the lively modernist milieu of Kenneth Burke s early career in Greenwich Village, where Burke arrived in 1915 fresh from high school in Pittsburgh, this book discovers him as an intellectual apprentice conversing with the moderns. Burke found himself in the midst of an avant-garde peopled by Malcolm Cowley, Marianne Moore, Jean Toomer, Katherine Anne Porter, William Carlos Williams, Allen Tate, Hart Crane, Alfred Stieglitz, and a host of other fascinating figures. Burke himself, who died in 1993 at the age of 96, has been hailed as America s most brilliant and suggestive critic and the most significant theorist of rhetoric since Cicero. Many schools of thought have claimed him as their own, but Burke has defied classification and indeed has often been considered a solitary, eccentric genius immune to intellectual fashions. But Burke s formative work of the 1920s, when he first defined himself and his work in the context of the modernist conversation, has gone relatively unexamined. Here we see Burke living and working with the crowd of poets, painters, and dramatists affiliated with Others magazine, Stieglitz s 291 gallery, and Eugene O Neill s Provincetown Players; the leftists associated with the magazines Masses and Seven Arts; the Dadaists; and the modernist writers working on literary journals like Dial, where Burke in his capacity as an associate editor saw T. S. Eliot s The Wasteland into print for the first time and provided other editorial services for Thomas Mann, e.e. cummings, Ezra Pound, and many other writers of note. Burke also met the iconoclasts of the older generation represented by Theodore Dreiser and H. L. Mencken, the New Humanists, and the literary nationalists who founded Contact and New Republic. Jack Selzer shows how Burke s own early poems, fiction, and essays emerged from and contributed to the modernist conversation in Greenwich Village. He draws on a wonderfully rich array of letters between Burke and his modernist friends and on the memoirs of his associates to create a vibrant portrait of the young Burke s transformation from aesthete to social critic.

Deep Dyslexic Phenomena in a Letter-by-Letter Reader

Numerous accounts of pure alexia have suggested that prelexical impairment precludes rapid access to orthographic information in patients with the disorder. We report a patient with features of both pure and partially recovered deep dyslexia in whom we demonstrate prelexical deficits in maintaining a reliable abstract representation of the right side of letter arrays, as well as in modulating a “spotlight” of visual attention. These deficits, we suggest, encourage the patients's use of a letter-by-letter reading strategy; despite them, however, he demonstrates rapid, accurate reading of some, but not all classes of words. Furthermore, the patient's reading is influenced by both prelexical and lexical–semantic factors such that speed and accuracy are optimal for high imageability nouns of few letters. Finally, the patient accurately names orally spelled words of all classes. Taken together, these data are consistent with the hypothesis that rapid reading may be enabled by lexical–semantic support from a right hemisphere-mediated processing system which recognizes words as wholes, thereby mitigating the effect of the prelexical deficits.

On a failure to replicate: Methodologically close, but not close enough. A response to Hogben et al.

Williams, Brannan and Lartigue (1987) ( Clinical Vision Science, 1, 367–371) reported that poor readers took significantly longer to search letter arrays for a target than did good readers. In addition, they reported that blurring the letter arrays leads to faster search times for poor readers and a loss of the significant differences between the groups seen with unblurred displays. In a recent attempt to replicate these findings, Hogben el al. (1996) ( Vision Research, 36, 1503–1507) found no differences in search rates between good and poor readers using unblurred arrays, and no differences in search rate between the groups when blurred arrays were used. In the present article, we have compared these two research efforts, and a third paper on the same topic, with regard to methodological factors in an attempt to understand how these two different results could occur. It is our belief that the letter spacing employed in the two studies may account for the difference and should be the focus of future studies of the original effect.

Search for letter identity and location by disabled readers.

Reading-disabled boys, reading- and age-matched controls, and adults searched letter arrays for the identity or location of a probe letter. Response time (RT) and accuracy were examined as a function of the temporal relation between probe and array letters (probe first, simultaneous, array first), and array size (1-5 letters). Although disabled readers closely resembled age controls in RT, their accuracy differed significantly when large letter arrays were tested. In the letter identification task, this was only evident when the array letters preceded the probe; in the letter location task, it occurred in all three probe conditions. Correlational analyses showed that all subjects were influenced by the visual, but not the phonological, similarity between letters. Thus, a reading-related impairment is evident in both letter identification and letter location processes, even when the phonological coding of letters has been minimized.

Ethanol‐Induced CNS depression and divided attention

AbstractSubject performed a divided attention task in which they detected occurrences of a target letter in a stimulus figure which was a large letter made up of an array of small letters. Subjects pressed one button if the large letter was the target, another if the small letters were the target.Performance on this task was compared to other attention and psychomotor tasks in a three‐way randomized crossover study comparing two doses of alcohol with placebo in 12 healthy volunteers (six male, six female, aged 19–41). The higher dose of alcohol produced blood concentrations of 43 mg/100 ml, the lower dose 16 mg/100 ml.Subjects reported themselves significantly more drunk on both doses of alcohol than on placebo, showed poorer long‐term recall on the Buschke selective reminding task than on placebo, and made more errors on a letter cancellation task. They performed letter cancellation faster, however. No significant effects were seen on the divided attention or continuous attention tasks, though continuous attention showed a trend towards impairment.These results suggest that the greater sensitivity showed by some multiple task combinations to low doses of drugs such as alcohol is not due to divided attention as such, but results from some aspect of task combination. The coupling of increased errors but increased speed on letter cancellation has obvious implications for the interpretation of the effects of alcohol on complex real‐life tasks such as driving.

On the relation between type of arrays and type of errors in partial-report bar-probe studies

In studies using Averbach and Coriell's (1961) partial-report bar-probe task, the subject is requested to report the name of the indicated letter in a briefly presented visual multi-letter display. In the error analysis for this task, Townsend (1973) distinguished errors that involved report of an item displayed in another than the indicated position ( location errors) and errors that involved report of an item that was not displayed ( item errors). Furthermore, a location error was taken as an indication for inaccurate target localization and an item error for inaccurate target identification. Unfortunately, bar-probe studies that applied this error analysis have yielded contradictory results as to the most frequent type of errors that was observed. Consequently, opposed interpretations were formulated as to the limiting factor (either localization or identification) in human information processing capabilites for briefly presented material. These interpretations have in turn led to opposing views on the locus of selection of incoming information (later or early). In the present study, it is shown that (a) the shape of the exposed letter arrays (linear or circular arrangements) and (b) the letter identities and sampling procedure that are used to compose the arrays (the whole alphabet and random sampling or a limited set of letters and sampling while taking interletter confusabilites into account) can explain the empirical incongruency. These two variables appear to affect (a) the accuracy of localization and identification processes and (b) the degree to which localization difficulties are observable as location errors (and not as item errors) and identification difficulties as item errors (and not as location errors). In contrast with earlier claims, it is concluded that performance in partial-report bar-probe tasks is constrained by two factors: localization and identification.

The effects of spatial filtering and contrast reduction on visual search times in good and poor readers

Recent experiments with reading disabled children have shown that image blurring (produced with frosted acetate overlays) results in an immediate benefit in search performance, eye movement pattern and reading comprehension. This suggests that the contrast and spatial frequency content of visual stimuli are important factors for these children. In the present experiment, spatial frequency filtering and contrast reduction were employed to determine whether either of these factors contributes to the beneficial effects observed. Letter arrays were spatially filtered to produce low pass (<3.5 c/deg) and high pass (>7.0 c/deg) images. In addition, a low contrast control image was generated to match the low contrast of the high pass image. Children classified as good reader controls (CON), specific reading diabled (SRD), attention deficit disordered (ADD) or comorbid SRD/ADD (COM) were asked to perform a visual search task with each type of image. With high contrast, unfiltered arrays, the search times for the CON and ADD groups were much shorter than those of the SRD and COM groups. While both high pass and low pass filter conditions improved the search speed for the COM group, improvement for the SRD group was only obtained with low contrast stimuli. These results support the notion that the beneficial results of image blurring with SRDs derives from the contrast reduction produced by such manipulations.

Focal-attentive and preattentive processes in letter- and figure-search tasks.

Evidence for preattentive and focal-attentive processes was obtained with two reaction-time tasks. In each case, effects of preattentive processes were identified by stimulating different proportions of the visual field. By varying the length of the search path, the effects of focal-attentive processes were identified. The first task, which required scanning arrays of letters, yielded short reaction times whereas the second task, which required the location of figures, led to long reaction times. The difference is explained by low automation and the strong demands of the latter task. The data do not indicate an interaction between preattentive and focal-attentive processes.

Two thousand years of numerical magic squares

A magic square is any square-shaped array of numbers or letters exhibiting certain properties: in numerical squares it is the constant sum of numbers in each row, column, or diagonal. This is the constant of a square, while the number of cells in a row gives its order. Any set of numbers can be used if the condition of a constant summation is met. In natural magic squares only natural numbers from 1 to 2 are used. The same set of natural numbers written sequentially into a square grid leads to a natural square which is not magic. Numerical magic squares attracted attention in the distant past. They have been used in charms, talismans, and in other objects destined to magical use. More rarely, these squares appeared in philosophical or alchemical speculations as expressions of certain ideas, or even as an instruction to experiments. Now studied as problems in number theory, numerical magic squares once had deeper significance, far from purely mathematical questions.