Calendrical Savants

Get out your stop watches. Press start, and then answer this question:

What day of the week was August 17, 1932?

How long did it take you? Oh, the answer is Wednesday, by the way. I cheated, and used a calculator, because I'm not very good at calendrical calculations, but some people, usually of relatively low overall intelligence, can calculate the day of the week for any date from the 20th or 21st century in fewer than three seconds (dates from other centuries take longer, with times increasing with distance from the present, especially for dates in the future)1. Over the last few years, researchers have been trying to figure out how they do this.

For most of us, there are some fairly simple rules that we can use to calculate dates. These rules are detailed by Thioux et al.2:

There are 52 weeks and 1 day in a non-leap year (365 days). Consequently, if a non-leap year begins on Sunday, the next year will begin on Monday. Because a year may begin with any day of the week, there are only 14 possible calendars: 7 for non-leap years and 7 for leap years. The 14 calendars appear recurrently following certain rules. Two years 28 years apart and from the same century always have the same calendar. Within 28 years, all 7 leap year calendars appear once and all 7 non-leap year calendars appear three times (7 + 3 x 7 = 28). Hence, if 2001 began on Thursday, there are two other non-leap years before 2029 starting on the same day. Two rules determine the position of these two years in the 28-year interval: Two non-leap years 6 years apart have the same calendar if there is only one intervening leap year, and two non-leap years 11 years apart have the same calendar if there are exactly three intervening leap years (e.g., 2001, 2007, 2018, and 2029 have the same calendar). The 28-year rule does not apply for years belonging to different centuries because in accordance with a rule introduced by Pope Gregory in the year 1582 century years (e.g. 1800, 1900) are not leap years except when divisible by 400 (e.g., 2000, 1600, 2400). Across centuries, the exact same succession of calendars is repeated every 400 years. (p. 1155)

Whether calendrical savants use these rules is one of the questions researchers have been asking. It's clear that they are using calculation3, often mental calculation (especially after practice)4, but some of them seem to be unaware of Pope Gregory's leap year rule. Thus, outside of a two-century period (between March 1, 1900, and February 28, 2100), their answers show systematic deviations5.

Thioux et al.'s paper, in the October issue of the Journal of Experimental Psychology: Human Perception and Performance, describes the abilities of a calendrical savant named "Donny." Donny doesn't use Pope Gregory's rule, his response times get longer for future dates further from the present but not (within the range tested) for the past (see the graph below, from Thioux et al's Figure 1, p. 1157), he doesn't seem to be able to answer questions about dates after the year 10,000, and he can answer "reverse questions" (e.g., questions in which he's given the day of the week, month, and year, and asked to give the date).

Using Donny's data, Thioux et al. developed a model of calendrical calculation in savants. Here's how they describe it:

Given a date in the year 2079, Donny uses calculation based on the rules of calendars (e.g., the same calendar is repeated every 28 years) to find a year closer to the present with the exact same calendar structure. Here, 2079 has the same calendar as 1995, because 1995 = 2079 - 84, and 84 is a multiple of 28. When a year close to the present has been reached and its calendar is available in memory, the day and month information can be used to retrieve the correct weekday from within the calendar. There are only 14 calendars in memory because a year can start on each day of the week and one must count 7 additional calendars for leap years. These calendars are stored as 14 distinct networks of direct verbal associations between a month-day pair and a weekday (e.g., "two fifteen [is] Monday"), such that retrieval of days of the week is automatic inside a given calendar. (p. 1159)

In other words, what Donny's doing is using calculations and the rules of calendars to get to a date that's stored in his memory, and once he's done that, he can use his memory to retrieve the date. To test this model, they first confirmed that Donny could perform the sorts of calculations necessary to get from a distant date to one close to the present. So they gave him addition problems using multiples of 28 (the number used in calendrical calculations) and 26, and compared his performance to six male Yale University undergraduates. Donny outperformed them all, by a pretty wide margin. Next, they gave him subtraction problems involving figures with four or five digits. He did very well with four-digit numbers (though not as well as he did with the addition problems), but only got 23% of the problems involving five-digit numbers right, which would explain why he has trouble with dates after the year 10,000. They then trained Donny on how to compute subtraction problems involving five-digit numbers, and after the training, his accuracy on dates after the year 10,000 increased dramatically. Each of these results indicate that he is able to do the calculations necessary for the model, and the fact that his performance for dates after 10,000 increased after training indicates that he was in fact using calculations of this sort to compute the days of the week.

In order to test the memory component of the model, Thioux et al. had Donny match the calendars for different years (see the rules above to see what this involves). He was able to match distant years to years near the present very accurately, except for years after the year 10,000 (this was prior to the subtraction training), and when supplied with a year, he was able to produce other years with the same calendar (most of those he produced were years close to the present). In a memory test, his response times for dates from recent years were shorter for more recently used calendars (calendars from the last few years), indicating that they were easier to retrieve from memory. Finally, Donny's performance on questions about days of the week was worse with verbal interference than with visual interference, indicating that his calendar memory is stored verbally, rather than visually. Each of these findings supports the memory component of the model.

It's important to note that there is some level of variation among calendrical savants' abilities, and Donny is a particularly impressive one (look at those response times for past dates in the graph above; many of them are under 1 sec). Unlike Donny, some calendrical savants do use Pope Gregory's rule in their calculations, some show increasing response times for past dates as they move away from the present, and the range of years that savants can calculate varies6. Thioux et al.'s model could explain these differences, but other savants with differences in their abilities will have to be tested to make sure that the model is generalizable. But let's face it, the model is an afterthought: Donny is able to calculate days of the week from the 5th century AD in under a second, and that's just cool!

¹Thioux, M., Stark, D.E., Klaiman, C, & Schultz, R.T. (2006). The day of the week when you were born in 700 ms: Calendar computation in an autistic savant. Journal of Experimental Psychology: Human Perception of Performance, 32(5), 1155-1168.
²Ibid.
³Cowan, R., O'Connor, N. (2003). The skills and methods of calendrical savants. Intelligence, 31(1), 51-65.
⁴Cowan, R., & Carney, D.P. (2006). Calendrical savants: Exceptionality and practice. Cognition, 100(2), B1-9.
⁵Cowan & O'Connor (2003).
⁶Ibid.