The skills and methods of calendrical savants

Calendrical savants are people with considerable intellectual difficulties that have the unusual ability to name the weekdays for dates in the past and sometimes the future. Three criteria are proposed to distinguish savants whose skill depends on memorization from those who calculate: range of years, consistent deviation from the Gregorian calendar, and variation in latency with remoteness from the present. A study of 10 calendrical savants showed 5 met one or both of the criteria concerning range and deviation and 9 met the third criterion. The second study assessed their arithmetical abilities using tests of mental and written arithmetic. This broadly validated the attribution of calculation as the basis for some savants? skills. The results are discussed in relation to views that calendrical savants imply the existence of a modular mathematical intelligence or unconscious integer arithmetic

Calendrical savants: Exceptionality and practice

The exceptionality of the skills of calendrical savants and the role of practice were investigated. Experiment 1 compared four autistic calendrical savants to Professor Conway, a distinguished mathematician with calendrical skills. Professor Conway answered questions over a greater range of years but some savants knew more calendrical regularities. Experiment 2 studied the development of a calendrical savant's ability to answer date questions for very remote future years. He started by making written calculations and progressed to mental calculation. His variation in response time for remote dates was similar to that for near dates. The findings are consistent with the view that calendrical savants develop their skills through practice

The development of calendrical skills

Calendrical calculation is the unusual ability to name days of the week for dates in the past and sometimes the future. Previous investigations of this skill have concerned savants, people with pervasive developmental disorders or general intellectual impairment. This research has yielded a hypothesis about how calendrical skills develop but no direct evidence. This study attempts to learn about the development of savant skills by investigating the development of calendrical skills in two boys (aged 5 and 6) along with more general cognitive and social assessments. Consistent with the hypothesis, they initially demonstrated knowledge of regularities but limited range and accuracy in answering date questions and they were slower than many adult savants. At follow up, neither had improved their calendrical skills and they were less willing to answer date questions. Possibly this is because, unlike savants, they had developed interests more commonly shared by their peers and they now received praise for more conventional achievements

Do calendrical savants use calculation to answer date questions? : a functional magnetic resonance imaging study

Calendrical savants can name the weekdays for dates from different years with remarkable speed and accuracy. Whether calculation rather than just memory is involved is disputed. Grounds for doubting whether they can calculate are reviewed and criteria for attributing date calculation skills to them are discussed. At least some calendrical savants possess date calculation skills. A behavioural characteristic observed in many calendrical savants is increased response time for questions about more remote years. This may be because more remote years require more calculation or because closer years are more practised. An experiment is reported that used functional magnetic resonance imaging to attempt to discriminate between these explanations. Only two savants could be scanned and excessive head movement corrupted one savant's mental arithmetic data. Nevertheless, there was increased parietal activation during both mental arithmetic and date questions and this region showed increased activity with more remote dates. These results suggest that the calendrical skills observed in savants result from intensive practice with calculations used in solving mental arithmetic problems. The mystery is not how they solve these problems, but why

Orbital Elements of Comet C/1490 Y1 and the Quadrantid shower

The Quadrantid shower, one of the most intense showers, has been observed at the beginning of January each year. However, the origin of the meteors is still unknown. It was Hasegawa (1979) who first suggested comet C/1490 Y1 to be the likely origin of the shower based on the historical records of East Asia. We analyse the records of Jo-Seon-Wang-Jo-Sil-Lok (the Annals of the Joseon Dynasty in ancient Korea) and calculate the preliminary orbital elements of comet C/1490 Y1 using a modified Gauss method. We find that comet C/1490 Y1 was a periodic one and its orbital path was very similar to that of the Quadrantid meteor stream. The determined orbital elements are perifocal passage time Tp=2265652.2983 days (7.8 Jan. 1491 in UT), perifocal distance q=0.769 AU, eccentricity e=0.747, semimajor axis a=3.04 AU, argument of the perifocus omega=164.03 degrees, longitude of ascending node Omega=283.00 degrees, and inclination i=70.22 degrees for the epoch of J2000.0. We, therefore, conclude that our result verifies the suggestion that the comet C/1490 Y1 is the origin of the Quandrantid meteor shower, but was a periodic comet. We dicuss a possible link between this comet and the asteroid 2003 EH1 as well.Comment: 7 pages, 2 figures, accepted for publication in MNRA

The Assimilation of Astrology in the Tibetan Bon Religion

International audienceThe sciences subsumed within the Tibetan category tsi (rtsis), "calculation," include calendrical reckoning and astrology (kartsi; dkar rtsis) and, secondly, elemental divination (naktsi; nag rtsis). The former is essentially based on the Kālacakra, a late tantra that was introduced from India in the twelfth century, and the latter on Chinese precedents. Although scholarly literature concerning the Tibetans' assimilation of these sciences is steadily growing, there has so far been almost no discussion of the way in which they have been adopted into the Bon religion. Using the example of the educational curriculum of a Bonpo monastery in India, this article explores the pedagogical context within which astrology and (to a lesser extent) elemental divination are taught to young monks. A number of didactic works are then examined with a view to discerning their distinctively Bonpo features

Khipu UR19: Inca Measurements of the Moon’s Diameter and its Distance from the Earth

This study explores the functions of tukapu as possibly important elements that are directly involved in the khipu construction process, i.e., when used by khipukamayuqs as a useful rudimentary outline for organising ideas, points, and details when constructing their forthcoming khipu. My re-study of the khipu sample UR19, which was previously investigated by Urton (2003) for other purposes, involved using the additional pieces of information that were identified in the graphical representations of the organisation of three different knot types that were tied into pendant and subsidiary strings. Proceeding one step further, we can sketch out a structure for the various meanings that are contained in these devices, which takes us much closer to developing an approach that could help us attempt to decipher the khipu. The irrational number π (first used by Archimedes and Liu Hui in the third century B.C.), the diameter of the Moon, and its distance from Earth (first measured by Aristarchus in the third century B.C.) could account for the observed results