BRIEF
An Investigation BY
A. LEWIS
of Calendar
HILL,
Calculating
by an Idiot
COMMUNICATIONS
Savant
PH.D.
Three mechanisms (eidetic imagery, high-speed calculation. and substitute compensation for normal learning) were investigated and rejected as possible explanationsfor the calendar-calculating ability of a particular idiot savant. Reaction timesfor calendar calculations indicated that he used neither an idiosyncratic nor a calendar-basedsystem. Rote memory and a special ability to concentratefor extended periods oftime were postulated to explain this individual’s performance.
telligence. He entered a state school for the mentally retarded in 1928 at the age of 6’/2 with an IQ of 54 (Stanford-Binet). At that time he was described as a poorly developed boy suffering from congenital syphilis. At the time of testing, he possessed several abilities that placed him within the classification of idiot savant. He was able to play 1 1 musical instruments by ear, rcmember important dates such as birthdays, and draw elaborate pictures of houses. However, his most outstanding ability was calendar calculating. There are no indications in his records as to when or how his abilities developed, although it is clean that he possessed them at the time of his transfer to a second state school for the
AN IDIOT SAVANT 15 an individual of low general intelligence who possesses one on more highly developed skills. Probably the most well-known of these skills is calendar calculating, the determination of the day of the week on which a particular date has fallen on will fall. Although there is a mathematical formula for this determination, it is very doubtful that idiots savants use this method. Honwitz and associates ( 1 ) suggested three mechanisms as possible explanations for this ability. The first of these, cidetic imagery, is especially attnactive because it offers an explanation that does not require any mathematical ability. The second hypothesis is that these individuals may be able to calculate at great speeds. Ofcounse, this is not an explanation at all, and most idiot savants are very poor at even simple addition and subtraction. The third possible mechanism is that “the skill represents a mechanism utilizing memory and serving as a substitute compensation for normal learning” (p. 1075). It is not clean whether “substitute compensation” implies a normal learning ability which is focused to the extent that the savant learns particular items at the expense of learning other material or that the process by which the
mentally
material
is learned
is different
from
“normal
learning”
(e.g., cidetic imagery). The specific purpose of this study was to examine these possible mechanisms in a particular patient.
BACKGROUND
This man, whom we will call B, was born on August 20, 1921. He was the first of two children born to reportedly normal
parents.
His sister is also reportedly
of normal
in-
INITIAL
New York State Institute for 1050 Forest Hill Rd., Staten
Ba-
Is-
in 1949.
TESTING
During his first visit to the laboratory, B appeared a little nervous but highly motivated to do well. He was tested on visually presented and auditory digit span, cidetic imagery, a paired-associate task, and his calendan-calculating ability. The auditory digit span was taken from the Wechslcn Adult Intelligence Scale. He was able to recite up to 5 digits forward and 3 digits backward when the presentation rate was 1 digit pen second. Random series of numbens, ranging from 3 to 7 digits, were also presented to him typed on three-by-five index cards. Although an attempt was made to have him view each card for the same number of seconds as there were digits on the card, he would look at each card, read it rapidly to himself, and immediately look at the experimenter and recite as many numbers as he could. For the visually presented digit span, he was able to recall up to 5 digits forward and 5 digits backward. This increase in backward digit span might have been due to his reading the digits backward on the cards, as he had prior knowledge of the order in which he was to report them. The tests for eidctic imagery followed the methodology of Haber and Haber (2) and also included the checkenboand figures of Gummerman and associates (3). No indications of eidetic imagery were found. His recall of the items and colon. He was he was
Dr. Hill is Senior Research Scientist, sic Research in Mental Retardation, land, N.Y. 10314.
retarded
within then
presented
pictures given
was
very
poor
in both
the paired-associate
with pictures
of the heads
task
content in which
of 10 females
at a rate of 5 seconds per picture. During each presentation he was told a fictitious month and date of birth and
A mJ
Psychiatry
/32:5,
May
/975
557
BRIEF
COMMUNICATIONS
asked to remember these. The pictures were presented for a total of three runs. For each picture he guessed the month and day of birth and was then told the “correct” answer. None of his guesses was correct, and the expeniment was terminated. After these tests, it seemed evident that his ability to calendar calculate was not based on cither cidetic imagery, a normal learning ability, or a large short-term memory capacity. B was given a preliminary test ofhis ability to calendar calculate and was questioned on several ofhis answers negandless of whether or not he was correct. When questioned, he often referred to the previous year, to another month within the same year, on to a specific event that had happened to him a day on two from the date questioned. When questioned directly as to how he figured out the day, he denied using any mathematical formula on eidetic imagery. His responses to the direct questioning suggested the possibility that he was using some type of system, perhaps involving key dates and counting. If this were the case, his reaction times for dates closer to these anchor points should be faster than those distant from it. To test this possibility, an experiment was designed to further
test his calendar-calculating
EXPERIMENTAL
ability.
INVESTIGATION
First Session A series of I 68 dates was constructed so that 1 date per month was given for each of the 14 odd-numbered years from 1943 to 1969. However, no date was given twice within a calendar year, and no month, date, day, on year followed itself in order of presentation within the list. The experimenter read the dates at a rate of approximately 1 second pen item (month, date, year) and waited for B’s rcsponse. When he responded, the experimenter nodded his head “yes” and went on to the next date. Thus B was neinforced for all responses regardless of correctness. For those dates for which no answer was given within 2 mmutes, the experimenter simply went on to the next date. The testing lasted for approximately 2 hours, including a 10-minute break near the middle ofthe list. Both reaction times and self-corrections were measured by three mdcpendent judges from a tape recording of the experimental session. Only those reaction times to the first response, when that response was correct, were used. Overall, B’s first answer was connect for 134 dates (80 percent). The median reaction time was 7.9 seconds. On 6 of the dates, no answer was given. He caught himself on 10 errors and successfully corrected himself on 7 of these. He answered 18 dates incorrectly and did not attempt to correct himself. The 14 years used in this experiment comprise 7 pairs of identical years. The 4 years in which B’s responses were 100 percent correct were 1943, 1945, 1951, and 1965; these arc years in which January 1 falls on a Monday or Friday. The two years with which he experienced the most difficulty were 1947 and 1969-both began on Wednesdays.
558
In posttest
A mJ
Psychiatry
questioning,
132:5.
May
he reported
1975
that he
had been punished.
“framed” in No explanation
1947
and had was given
been for
unjustifiably his relatively
performance for 1969. Table I presents a summary of the correct responses arranged according to months, days of the week, and 7day periods. While the differences in median reaction times suggested that certain months may have been more difficult than others, this was based on only 10 to 12 data points for each month. No striking trend was found in days of the week (i.e., while Mondays might seem to be the most difficult in terms of reaction times, Mondays were highest on the percentage connect). When responses were broken down into periods of7 days, the most prominent feature was the consistency of both reaction times and correct responses. The results of this experiment seemed to indicate that B was not using a specific system of key dates and counting. However, there were certain variables within the repoor
action
time
data
that
appeared
to call
for
further
exam-
ination. Second
Session
The best and worst months, days of the week, and weeks were tested for 4 years that began on a Friday or a Wednesday and had not been previously tested. Thus, a new series of 128 dates was compiled to specifically test the dates of the month between the I 5th and 28th that fell on a Saturday, Sunday, Monday, on Tuesday within the months of April, May, June, and December of 2 years (1937 and 1954) that began on a Friday and oftwo years (1941 and 1958) that began on a Wednesday. These dates were arranged and presented to B in the same manner as previously described. A series ofaddition and subtraction problems of numbcrs between 1 and 17 was also devised to test B’s ability in simple arithmetic skills. To test his use of a nonsystematic idiosyncratic code, dates of importance according to his state school records and general conversations were obtained. The testing consisted of giving him the list of 128 dates with a break approximately in the middle of this list. The test of arithmetic skills was given during this break. When the original list was completed, he was tested for an idiosyncratic code. For this testing, he was asked to give the day of the week as well as what happened to him on that day. As in the previous session, this session was tape recorded for later analysis. B’s accuracy and reaction time were considerably improved, even though this session included the dates that should have been the most difficult for him based on his previous performance. Overall, his first answer was conrect for 1 16 dates (91 percent). The median reaction time for these answers was 3.7 seconds. He corrected himself on 6 dates and gave no answer on the remaining 6. When these remaining 6 were given to him again at the end of the session, all of his responses were correct. Separate analyses of variance were computed on the reaction times by dates (15th to 28th), weeks (15th to 21st versus 22nd to 28th), and days (Saturday, Sunday, Monday, Tuesday). Since none of these was significant, the reaction times were combined for an analysis of variance of
BRIEF
TABLE
I
Correct
First
FIGURE Median
Responses
1 Reaction
Times
for
Dates
Presented
Friday (1937 and 1954) and on a Wednesday Percent of Connect Responses
Category
Month January February March April May June July August September October November December Day of the week Sunday Monday Tuesday Wednesday Thursday
Median
Reaction (in seconds)
9.3 6.4 7.0 5.0 14.5 12.1 6.9 6.5 8.2 11.5 7.5 6.2
79 91 74 79 79 68 79
6.3 10.5 10.6 7.5 8.2 8.6 7.1
88 74
7.3 8.0
15to21
82
6.6
22 to 28 29+
73 82
9.0 7.4
the years action
and times
Years
Beginning
on
a
Time 20
16 0 C 0 LI
a)
uJ
12
z
10
0 0
Friday
of the
in
(1941 and 1958)
18 86 71 86 86 79 71 79 79 79 86 71 86
Saturday 7-day period lto7 8to14
COMMUNICATIONS
w z
4
month
months. were
2
This significantly
analysis
indicated different
that between
May
April YEAR
the neyears
beginning on a Wednesday and those beginning on a Friday (F=25.42, p
An Investigation BY
A. LEWIS
of Calendar
HILL,
Calculating
by an Idiot
COMMUNICATIONS
Savant
PH.D.
Three mechanisms (eidetic imagery, high-speed calculation. and substitute compensation for normal learning) were investigated and rejected as possible explanationsfor the calendar-calculating ability of a particular idiot savant. Reaction timesfor calendar calculations indicated that he used neither an idiosyncratic nor a calendar-basedsystem. Rote memory and a special ability to concentratefor extended periods oftime were postulated to explain this individual’s performance.
telligence. He entered a state school for the mentally retarded in 1928 at the age of 6’/2 with an IQ of 54 (Stanford-Binet). At that time he was described as a poorly developed boy suffering from congenital syphilis. At the time of testing, he possessed several abilities that placed him within the classification of idiot savant. He was able to play 1 1 musical instruments by ear, rcmember important dates such as birthdays, and draw elaborate pictures of houses. However, his most outstanding ability was calendar calculating. There are no indications in his records as to when or how his abilities developed, although it is clean that he possessed them at the time of his transfer to a second state school for the
AN IDIOT SAVANT 15 an individual of low general intelligence who possesses one on more highly developed skills. Probably the most well-known of these skills is calendar calculating, the determination of the day of the week on which a particular date has fallen on will fall. Although there is a mathematical formula for this determination, it is very doubtful that idiots savants use this method. Honwitz and associates ( 1 ) suggested three mechanisms as possible explanations for this ability. The first of these, cidetic imagery, is especially attnactive because it offers an explanation that does not require any mathematical ability. The second hypothesis is that these individuals may be able to calculate at great speeds. Ofcounse, this is not an explanation at all, and most idiot savants are very poor at even simple addition and subtraction. The third possible mechanism is that “the skill represents a mechanism utilizing memory and serving as a substitute compensation for normal learning” (p. 1075). It is not clean whether “substitute compensation” implies a normal learning ability which is focused to the extent that the savant learns particular items at the expense of learning other material or that the process by which the
mentally
material
is learned
is different
from
“normal
learning”
(e.g., cidetic imagery). The specific purpose of this study was to examine these possible mechanisms in a particular patient.
BACKGROUND
This man, whom we will call B, was born on August 20, 1921. He was the first of two children born to reportedly normal
parents.
His sister is also reportedly
of normal
in-
INITIAL
New York State Institute for 1050 Forest Hill Rd., Staten
Ba-
Is-
in 1949.
TESTING
During his first visit to the laboratory, B appeared a little nervous but highly motivated to do well. He was tested on visually presented and auditory digit span, cidetic imagery, a paired-associate task, and his calendan-calculating ability. The auditory digit span was taken from the Wechslcn Adult Intelligence Scale. He was able to recite up to 5 digits forward and 3 digits backward when the presentation rate was 1 digit pen second. Random series of numbens, ranging from 3 to 7 digits, were also presented to him typed on three-by-five index cards. Although an attempt was made to have him view each card for the same number of seconds as there were digits on the card, he would look at each card, read it rapidly to himself, and immediately look at the experimenter and recite as many numbers as he could. For the visually presented digit span, he was able to recall up to 5 digits forward and 5 digits backward. This increase in backward digit span might have been due to his reading the digits backward on the cards, as he had prior knowledge of the order in which he was to report them. The tests for eidctic imagery followed the methodology of Haber and Haber (2) and also included the checkenboand figures of Gummerman and associates (3). No indications of eidetic imagery were found. His recall of the items and colon. He was he was
Dr. Hill is Senior Research Scientist, sic Research in Mental Retardation, land, N.Y. 10314.
retarded
within then
presented
pictures given
was
very
poor
in both
the paired-associate
with pictures
of the heads
task
content in which
of 10 females
at a rate of 5 seconds per picture. During each presentation he was told a fictitious month and date of birth and
A mJ
Psychiatry
/32:5,
May
/975
557
BRIEF
COMMUNICATIONS
asked to remember these. The pictures were presented for a total of three runs. For each picture he guessed the month and day of birth and was then told the “correct” answer. None of his guesses was correct, and the expeniment was terminated. After these tests, it seemed evident that his ability to calendar calculate was not based on cither cidetic imagery, a normal learning ability, or a large short-term memory capacity. B was given a preliminary test ofhis ability to calendar calculate and was questioned on several ofhis answers negandless of whether or not he was correct. When questioned, he often referred to the previous year, to another month within the same year, on to a specific event that had happened to him a day on two from the date questioned. When questioned directly as to how he figured out the day, he denied using any mathematical formula on eidetic imagery. His responses to the direct questioning suggested the possibility that he was using some type of system, perhaps involving key dates and counting. If this were the case, his reaction times for dates closer to these anchor points should be faster than those distant from it. To test this possibility, an experiment was designed to further
test his calendar-calculating
EXPERIMENTAL
ability.
INVESTIGATION
First Session A series of I 68 dates was constructed so that 1 date per month was given for each of the 14 odd-numbered years from 1943 to 1969. However, no date was given twice within a calendar year, and no month, date, day, on year followed itself in order of presentation within the list. The experimenter read the dates at a rate of approximately 1 second pen item (month, date, year) and waited for B’s rcsponse. When he responded, the experimenter nodded his head “yes” and went on to the next date. Thus B was neinforced for all responses regardless of correctness. For those dates for which no answer was given within 2 mmutes, the experimenter simply went on to the next date. The testing lasted for approximately 2 hours, including a 10-minute break near the middle ofthe list. Both reaction times and self-corrections were measured by three mdcpendent judges from a tape recording of the experimental session. Only those reaction times to the first response, when that response was correct, were used. Overall, B’s first answer was connect for 134 dates (80 percent). The median reaction time was 7.9 seconds. On 6 of the dates, no answer was given. He caught himself on 10 errors and successfully corrected himself on 7 of these. He answered 18 dates incorrectly and did not attempt to correct himself. The 14 years used in this experiment comprise 7 pairs of identical years. The 4 years in which B’s responses were 100 percent correct were 1943, 1945, 1951, and 1965; these arc years in which January 1 falls on a Monday or Friday. The two years with which he experienced the most difficulty were 1947 and 1969-both began on Wednesdays.
558
In posttest
A mJ
Psychiatry
questioning,
132:5.
May
he reported
1975
that he
had been punished.
“framed” in No explanation
1947
and had was given
been for
unjustifiably his relatively
performance for 1969. Table I presents a summary of the correct responses arranged according to months, days of the week, and 7day periods. While the differences in median reaction times suggested that certain months may have been more difficult than others, this was based on only 10 to 12 data points for each month. No striking trend was found in days of the week (i.e., while Mondays might seem to be the most difficult in terms of reaction times, Mondays were highest on the percentage connect). When responses were broken down into periods of7 days, the most prominent feature was the consistency of both reaction times and correct responses. The results of this experiment seemed to indicate that B was not using a specific system of key dates and counting. However, there were certain variables within the repoor
action
time
data
that
appeared
to call
for
further
exam-
ination. Second
Session
The best and worst months, days of the week, and weeks were tested for 4 years that began on a Friday or a Wednesday and had not been previously tested. Thus, a new series of 128 dates was compiled to specifically test the dates of the month between the I 5th and 28th that fell on a Saturday, Sunday, Monday, on Tuesday within the months of April, May, June, and December of 2 years (1937 and 1954) that began on a Friday and oftwo years (1941 and 1958) that began on a Wednesday. These dates were arranged and presented to B in the same manner as previously described. A series ofaddition and subtraction problems of numbcrs between 1 and 17 was also devised to test B’s ability in simple arithmetic skills. To test his use of a nonsystematic idiosyncratic code, dates of importance according to his state school records and general conversations were obtained. The testing consisted of giving him the list of 128 dates with a break approximately in the middle of this list. The test of arithmetic skills was given during this break. When the original list was completed, he was tested for an idiosyncratic code. For this testing, he was asked to give the day of the week as well as what happened to him on that day. As in the previous session, this session was tape recorded for later analysis. B’s accuracy and reaction time were considerably improved, even though this session included the dates that should have been the most difficult for him based on his previous performance. Overall, his first answer was conrect for 1 16 dates (91 percent). The median reaction time for these answers was 3.7 seconds. He corrected himself on 6 dates and gave no answer on the remaining 6. When these remaining 6 were given to him again at the end of the session, all of his responses were correct. Separate analyses of variance were computed on the reaction times by dates (15th to 28th), weeks (15th to 21st versus 22nd to 28th), and days (Saturday, Sunday, Monday, Tuesday). Since none of these was significant, the reaction times were combined for an analysis of variance of
BRIEF
TABLE
I
Correct
First
FIGURE Median
Responses
1 Reaction
Times
for
Dates
Presented
Friday (1937 and 1954) and on a Wednesday Percent of Connect Responses
Category
Month January February March April May June July August September October November December Day of the week Sunday Monday Tuesday Wednesday Thursday
Median
Reaction (in seconds)
9.3 6.4 7.0 5.0 14.5 12.1 6.9 6.5 8.2 11.5 7.5 6.2
79 91 74 79 79 68 79
6.3 10.5 10.6 7.5 8.2 8.6 7.1
88 74
7.3 8.0
15to21
82
6.6
22 to 28 29+
73 82
9.0 7.4
the years action
and times
Years
Beginning
on
a
Time 20
16 0 C 0 LI
a)
uJ
12
z
10
0 0
Friday
of the
in
(1941 and 1958)
18 86 71 86 86 79 71 79 79 79 86 71 86
Saturday 7-day period lto7 8to14
COMMUNICATIONS
w z
4
month
months. were
2
This significantly
analysis
indicated different
that between
May
April YEAR
the neyears
beginning on a Wednesday and those beginning on a Friday (F=25.42, p
