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1
“National psychologies” in the late 19th:
Binet vs. Ebbinghaus on memory research
Serge NICOLAS1
Paris Descartes University
Équipe Mémoire et Cognition – Institut de Psychologie – Centre de Psychiatrie
et Neurosciences, INSERM UMR U894, France
1 Université Paris Descartes, Institut de Psychologie, Equipe Mémoire et Cognition, 71 avenue Edouard Vaillant, 92774 Boulogne-Billancourt Cedex, France. Correspondence to: [email protected]
2
Danziger (1990) suggested that the French approach to psychology in the late 19th was
different from the German approach. However, in his recent book (Danziger, 2008) where he
covers memory research he did not pursue the comparison between the two “national
psychologies”. The main aim of this conference is to show that the French scientific tradition
on memory research represented by Binet’s work was very different from the methods of the
German experimental tradition represented by Ebbinghaus’s work.
In a recent paper published in History of psychology Nicolas and Sanitioso (2012)
exposed with some details the experimental psychology of Binet. Among the diversity of
methods he used in his work, one is of particular interest here because it represents an original
French approach to psychology: the study of singular or extraordinary subjects examined
from a variety of perspectives (see Carson, 1999). Indeed in the late 19th, the French style of
psychological examination was characterized by the method of the typical (singular or
uncommon) cases exemplified by the study of the morbid disturbances of some patients and
the anomalies of some prodigies (Carroy & Plas, 1993, 1996). The most known representant
of the first approach was Jean-Martin Charcot (1825-1893; for a biography see Goetz,
Bonduelle, & Gelfand, 1995). For example, Charcot was occupied by the study of a great
neurosis which he has termed hysteria major (Charcot, 1872; Charcot & Marie, 1892; see
Didi-Huberman, 2004; Gauchet & Swain, 1997). Another methodological approach used in
France at the time was the study of non insane extraordinary cases. This line of research was
first initiated by Hippolyte Taine (1828-1893) who considered that more a fact is peculiar, the
more it is instructive for psychological research. For example, in his discussion on mental
images Taine (1870) arguments on their visual basis by observing great mental calculators
who affirmed that they rely on visual strategy to perform mental operations (they have a very
developed representative imagination). In 1892-1893, Charcot and Binet had the opportunity
to study the auditory mental calculator Jacques Inaudi (1867-1950) who is now regarded as
one of the most famous calculating prodigies of the 19th century (Brown & Deffenbacher,
1975, 1988; Smith, 1983). Inaudi was able to solve complex mental calculations, quickly and
accurately, without any external memory aids. The twofold contributions provided by Inaudi’s
case were: (1) it offered a remarkable confirmation of partial memories and (2) it inaugurated
the scientific study of memory expertise.
It is in this context that Binet conducted an original series of original experiments with
Inaudi, while in Germany Hermann Ebbinghaus (1850-1909) and his followers developed
memory research in a classical orientation. The first section of the paper is devoted to the
exposition of the German experimental tradition and of the French experimental tradition in
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memory research. The second section displays more specifically Binet’s work on Inaudi’s
case which offered a remarkable confirmation of the existence of an auditive memory
independent of visual memory.
THE SCIENTIFIC STUDY OF MEMORY IN 1880s
At the time there were very few scientific investigations in memory research. The
American psychologist Burnham (1889) presented an admirable account of the investigation
of memory, historically and experimentally considered (for a more recent review see Murray,
1976). He first exposed recent theories of memory, derived from physiology and pathology
studies, underlining two important views most widely held by contemporary psychologists,
particularly by Ribot (1881): (a) The essence of memory is a functional disposition persisting
in the brain, (b) There is no one memory, but memories ; each sense may be said to have its
memory. Next, Burnham (1889) exposed some recent experimental studies on memory noting
that “the most important attempt to apply the methods of experimental psychology to the
study of memory was made a few years ago by Dr Ebbinghaus of Berlin” (Burnham, 1889, p.
587).
The German scientific approach: The experimental tradition
Hermann Ebbinghaus (1850-1909, for a biography see Nicolas, 1994) is now
considered as the first psychologist who engaged a systematic experimental study on memory
(Gorfein & Hoffman, 1987; Roediger, 1985a, 1985b; Sprung & Sprung, 1986; Traxel, 1987).
Contrary to the experimental psychologists of his time, like for instance the famous Wilhelm
Wundt (1832-1920), Ebbinghaus was convinced that an experimental scientific approach
towards higher mental processes was possible.
Because Ebbinghaus did not want to reduce memory on conscious recall, he decided
to develop an indicator which was based on the measurement of the time or the number of
trials necessary for a second learning episode: This measure or indicator is usually termed
savings for relearning (see Nicolas, 1992). This method had the advantage that it allows to
assess mental representations without the restriction to conscious manifestations.
Furthermore, in order to study memory in an objective way, Ebbinghaus introduced a new
type of learning material (Heller, 1986), namely lists of nonsense syllables, which eliminated
almost completely the influence of connotations and associations on learning (Müller and
Schumann were the first to use not series but just syllables without meaning in 1893-1894)
and, in addition, he used quantitative (statistic) methods to draw his conclusions. Without help
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and without a laboratory he collected for more than one year (1878-1879) in a solitary and
monumental effort (being his own and only experimental subject in all his experiments) a
long series of experimental explorations in this domain. He used to read aloud every list of
syllables in a rather rapid rhythm of 150 units (syllables) per minute. After reaching the end of
a list, he would reread from the beginning and continue doing so till he felt capable to recall
the whole list without error. If he did not succeed in recalling the list, he just continued
rereading it. If he was successful in his attempt to recall the complete list in the correct order
two times successively, he made a break of 15 seconds in which he noted the result (the time
elapsed for learning the list) and prepared for learning a new list. In his experiments on
relearning, the procedure did not differ from the previous study procedure, since Ebbinghaus
repeated the same activity to learn the list until he was able to recall the list according to the
same criterion, namely, recalling it two times successively in the correct order. It should be
noted, that he did not try to recognize or find out, whether a list he was actually studying had
already appeared during a previous study phase. The savings that he achieved in terms of
learning time or number of learning trials denoted an indicator of the amount of information
preserved from the earlier study phase. It was the use of this ingenious dependent variable that
represented the experimental transformation of his theoretic considerations on the issue of
rote learning. In this way he investigated: (1) the number of repetitions necessary to learn a
list; (2) the savings as a function of the number of repetitions during prior learning; (3) the
effects of repeated learning on the savings of relearning; (4) but it is in particular his
experiments on forgetting as a function of time which were in the center of his initial work on
memory. The results of his experiments provided him with the data base for his habilitation
thesis, which he defended on April 29, 1880 in front of the faculty of philosophy at the
Friedrich-Wilhelm University in Berlin [this version of the thesis has been published by
Traxel in 1983] (Bringmann & Bringmann, 1986). Ebbinghaus opened a new research field by
demonstrating that it is possible to investigate higher levels of human behavior like memory
and learning by the means of the experimental method.
Ebbinhaus published in 1885 the results of new investigations in his celebrated
book dedicated to Fechner "Über das Gedächtnis: Untersuchungen zur Experimentellen
Psychologie" (translated into English in the year 1913 as “Memory. A Contribution to
Experimental Psychology”; translated into French by S. Nicolas in the year 2010 as “La
mémoire. Recherches de psychologie expérimentale”). In his book of 1885, Ebbinghaus
completed his work of 1880 on many aspects. First of all the introduction of his monograph
covers a very profound reflection about the concept of memory. This chapter endorses in a
5
downright way the experimental method he has been using to measure memory performance
(savings and relearning). Then, in a series of chapters he uses time and space to justify the
usage of statistical indicators (means and indices of dispersion) for the investigation of
memory, to explain the way to construct his learning materials as well as the complete
procedure of his experiments. Finally, he completed his series of the original experiments of
1880 on learning (effect of the number of repetitions, spacing effects, etc.) and he introduces a
new and original study topic (which he did not cover in his thesis of 1880): The study of the
laws of association, using the method of derived series. As a matter of fact Ebbinghaus tried
to test for the first time the hypothesis advanced by Herbart (Boudewijnse, Murray &
Bandomir, 2001), namely that in the course of memorizing a series of items, the unification
between the first and the second representation is stronger than the unification between the
first and the third representation. Thus, he was able to show, that associations are built not
only between directly neighboring items in a list but beyond intermediate items of a list. The
strength of connections increases furthermore as a function of the number of repetitions. Even
though Ebbinghaus did never adhere strictly to the psychology of Herbart, his experimental
endeavors display a direct inspiration by this philosophy (see Nicolas, 2005b).
This book by Ebbinghaus was very well recognized by the reviewers of the time
(Burnham, 1889; Jacobs, 1885; James, 1885, 1890). Ebbinghaus’ work has certainly had a
very strong impact on the psychological investigation of memory not only in the years
following the publication of his monograph (Schacter, 1982) but as well beyond (Slamecka,
1985a, 1985b) despite the fact that later researchers have preferred to approach the study of
memory with classical methods (recall and recognition) which however covered only
conscious aspects of memory functions (for a discussion: Nicolas, 1992). Among all the
issues that he has investigated, his results on learning and forgetting have contributed in a
conclusive way to encourage new studies in the domain of memory. Indeed, Ebbinghaus’s
work inspired new experimental investigations (see Müller & Schumann, 1893). One of the
most known study inspired by Ebbinghaus’s work was experiments on “prehension”
conducted by Joseph Jacobs (1854-1916) who showed that the amount of memory span
increased with age: e.g., boys of 10 years could repeat 6.8 numerals after one audition; of 18
years, 8.6 numerals. This work inspired several scholars the following years (e. g., Binet &
Henneguy, 1892; Bolton, 1892; Bourdon, 1894) and were extended to other materials like
word lists (e.g., Jastrow, 1891; Bourdon, 1894). We know that Binet used this method in 1892
with children and adults (cf., Binet, 1894c; Binet & Henneguy, 1892).
6
The French scientific approach: The pathological tradition
As noted by Roth (1989), the end of the 19th century in France was a period in which
there was great interest in the mechanisms of memory, especially in their malfunctions.
Diseases of memory attracted the curiosity of many scholars, especially the founder of French
psychology Théodule Ribot (1839-1916, for a biography see Nicolas, 2005a; Nicolas &
Murray, 1999).
In 1880, Ribot, who was not an experimenter but a theorician of memory, published in
a new founded philosophical journal (see Nicolas, 2013) a series of papers on memory and its
pathology (Ribot, 1880a, 1880b, 1880c) which were collected in the following year into a
single volume (Ribot, 1881). Interested primarily by normal memory, Ribot’s method
consisted of throwing light on the nature of normal mechanisms of memory by regularly
referring to case histories reported in the medical literature. Ribot discussed these case
histories, including various forms of amnesia due to brain damage, within an evolutionary
framework borrowed from Herbert Spencer (1820-1903) and Hughlings Jackson (1835-1911).
It is as a consequence of his investigations of progressive amnesia that Ribot was
enabled to formulate his famous Law of Regression, according to which memory loss
following pathological damage was limited only to psychical memory; this amnesia was
restricted only to the most recent events, extending back in time. He wrote: “The progressive
destruction of the memory therefore follows a logical course, a law. It descends progressively
from the unstable to the stable. It begins with recent recollections which, being but faintly
impressed on the nerve elements, seldom repeated, and consequently but feebly associated
with other recollections, represent organization in its lowest stage. It ends with that sensorial,
instinctive memory which, being rooted in the organism and having become a part of it, or
rather become the organism itself represents organization in its most pronounced aspect.”
(Ribot, 1881, p. 94). But Ribot’s contribution in the areas of memory and memory disorders
extended beyond the Law of Regression, commonly known thereafter as Ribot’s Law.
One other advance with which he may be credited: the promulgation within
psychology of the idea that there are multiple systems of memory, a hypothesis anticipated by
Gall (1825) since he assigned to each faculty its own special memory as an independent
function. Indeed, Ribot (1881, p. 107) noted that « memory may be resolved into memories »,
a hypothesis that psychologists at the time either denied or neglected, as it was the case of
Ebbinghaus. However, common experience had long demonstrated the natural inequality of
different types of memory for any given individual. Ribot (1881) refers in his book to
lightning calculators such as Zerah Colburn (1804-1839), who could see figures before their
7
eyes and other calculators who did not see the figures in their problems, but heard them.
However, Ribot did not give any name for the latter kind of lightning calculators (Inaudi?).
“ In the same person, then, an unequal development of the different senses and different
organs induces unequal modifications in the corresponding portions of the nervous system;
hence unequal conditions of recollection, and, finally, varieties of memory. It is even probable
that inequality of memories in the same person is the rule rather than the exception” (Ribot,
1881, p. 110).
Jean-Martin Charcot (1825-1893) was very interested in the reading of Ribot’s book
(Ribot, 1881) on memory as Ribot was one of the first writers to have considered the pheno-
mena of aphasia and amnesia from a psychological standpoint. Interested by the study of
aphasia Charcot followed Ribot's footsteps, and his observations enabled him to design the
remarkable theory of memory classification which attracted so much attention in the scientific
community at the time. During the summer of 1883, Charcot (1884, see Marie, 1883) gave a
series of lectures on the various forms of aphasia which was the alteration of a psychological
function, the language, to be acquired through memory. At the time, these two faculties
(language and memory) were strongly connected to one another in the mind of scholars; the
pathology of language being usually considered as a particular case of the pathology of
memory (cf., Gasser, 1995, p. 143). As memory and language are distinct faculties, they can
thus be altered partially or developed independently from each other. It is in this context that
Charcot (1884) proposed his model of aphasia based on the model of multiple memories.
Thus Charcot described the existence of four types of verbal memories localized in various
areas of the cortex: a special memory for reading; one for understanding spoken words; one
for the utterance of words; and one for writing. It was believed that these verbal memories
were independent from one another and distinguishable by the nature of the images evoked.
Since each individual has his own intellectual style of remembering, of thinking, of
reasoning, etc., individuality results in part from the prevailing of certain sensations and
impressions over others. For example, there are categories of individuals (auditive type) who
hear themselves think. There are other individuals (visual type) who can read their own
thoughts, who see them either in the form of mental pictures of objects, or of mental words.
There is still another class of individuals (motor type) who cannot think without experiencing
the impulse to articulate. Finally, another group of individuals might be called the indifferent
type, as they are able to appeal at will to all three memories. Each individual belonging to a
distinct type resorts at will to one type of memory and neglects all the others. Thus, he may
hold the visual center subordinate to the auditive center, or vice versa. Practically, it is a
8
difficult matter, however, to determine each particular type of memory for each individual
with accuracy.
INAUDI AT THE SORBONNE LABORATORY (1892-1893) WITH ALFRED BINET
The study of Inaudi was a chance for Charcot to study one type of memory: the
auditive type. One experiment (Charcot, 1892; Charcot & Binet, 1893) served to verify this
affirmation. Inaudi learned five numbers of five digits written on a sheet of paper. Then he
was asked to recall from memory either the diagonal of this or that vertical or horizontal
sequence in the pattern. He succeeded, but with difficulty. If Inaudi belonged to the category
of visuals, he would not need to grope for the numbers in this way, since he could read the
answer as it was laid out before him, as on an imaginary blackboard (see Nicolas, Gounden &
Levine, 2011). As a former Charcot’s disciple (specializing, in his time, in the study of
hysteria and of hypnosis, see Binet, 1892a; Binet & Féré, 1887), Binet (1892b) was strongly
interested in the study of aphasia and multiple memory representations (see Binet, 1892b)..
When in February 1892 Charcot invited Binet to study with him Inaudi, he accepted. But
Charcot himself spent only a limited amount of time personally examining Inaudi and left
most of the actual investigation to Binet (see Carson, 1999).
Who was Jacques Inaudi?
Inaudi’s biography was recently presented in some detail in a paper to be published in
the American journal History of Psychology by Burman, Guida and Nicolas (2014). Here, in a
few words is presented some biographical information (see also Binet, 1894a; Inaudi, 1925;
Smith, 1983).
Giacomo (Jacques) Inaudi is born on the 13th of October 1867 in Roccabruna
(Onorato) in the Cuneo Province (Coni), in the northern Italian region of Piedmont. After the
death of his mother, Jacques had to leave his native country to follow his brothers in their
travels to the South of France because their father was unable to meet their need. Living a
nomadic lifestyle for two years they roamed the streets of cities in the southern France. It is in
this period that he discovered his astonishing calculating abilities.
Inaudi’s reputation grew to such an extent that a malevolent barkeeper from Marseilles
engaged young Jacques as a commissionary. Unlike most known calculators, Inaudi did not
seek to give his calculations a material form (neither he nor his brother knew how to read at
the time). He was not a visual calculator, who mentally “see” numbers but an auditory
9
calculator, who mentally “hear” numbers. Thus the whole operation remained mental, and
was performed by using words. At the time, it was assumed that all calculating prodigies were
of the visual type (Scripture, 1891).
Inaudi was about ten, when Bénédict Jules Dombey, an impresario, took him in hand.
Upon their arrival in Paris, the agent began frequenting the editorial staffs of all the
newspapers and introduced Jacques Inaudi's astonishing capacities for mental calculations to
scientific societies. In 1880, as an arithmetician child, Inaudi was welcomed by the Society of
Anthropology of Paris (SAP) directed by Paul Broca (1824-1880) who was interested by the
question of the possibility of mental calculation without the faculty of representing numbers
as though seeing them (see Nicolas, Guida & Levine, 2013). Broca (1880) noted that Inaudi
did not operate on visual images and attributed extraordinary faculty for mental calculation to
his memory. But Broca did not have time to develop his ideas on this subject because he was
elected Senator on February 5th 1880 and died suddenly in Paris in July, 9th 1880 from a
brain anevrism.
The astronomer Nicolas Camille Flammarion (1842-1925) heard about the audition of
Inaudi at the SAP and introduced him in “le tout Paris”. Inaudi gave some sessions to the
Theater Robert Houdin and in the Folies Bergères. Taking advantage of his success with the
public, he began a European tour. Despite his young age, Inaudi continued his shows and his
celebrity increased throughout the 1880s.
Inaudi’s fame was so great in France that he was presented by his new impresario, the
prestidigitator (French magician) de Thorcey (real name Albert Ferdinand Guyot), at a session
of the Academy of Sciences by the mathematician Gaston Darboux (1842-1917) on February
8th 1892. Convinced by Inaudi’s genuine performance, the Academy entrusted a commission
to examine the mathematical techniques used by Inaudi for his calculations with the main goal
of shedding light on the psychological aptitudes which allowed him to solve complex
arithmetical problems without reading or writing. Charcot was specifically charged with the
study of Inaudi's memory status (Charcot, 1892). While Charcot subjected Inaudi to a
primarily anthropometric investigation (see Nicolas, Guida, & Levine, 2013), his former
collaborator Binet conducted at the Salpêtrière Hospital and at the Sorbonne’s laboratory
various memory experiments with Inaudi (Nicolas & Sanitioso, 2012) published in a famous
book “Psychologie des grands calculateurs et joueurs d’échecs” (Binet, 1894a).
Inaudi’s audition at the Académie des sciences in Paris in addition with the publication
of Binet’s book on mental calculators (Binet, 1894a) gave him the necessary publicity to
continue touring around the world. As a naturalized French citizen in 1897, he used his fame
10
to sell calendars and brochures. Up until 1934, he continued appearing in music-hall shows.
He retired in 1937 at Champigny sur Marne near Paris, and he died there on November 25th
1950.
Binet’s new experimental work on Inaudi’s memory (1892-1893)
Alfred Binet would pursue his own work on prodigious calculators from 1892 to 1894
in the laboratory of physiological psychology at the Sorbonne. On June 15th, 1892, Binet
(1892c) published the first draft of a paper in the “Revue des Deux Mondes” in which he
borrowed from Charcot’s report (published on June 7th, 1892) on numerous points. In
addition, he presented some results of a series of new personal experiments. But Binet’s paper
does not report in detail the experiments conducted on Inaudi and we do not see clearly the
“Binet touch” in this synthesis. From these research, other papers were published by Binet
and his collaborators in the Revue Philosophique dated August 1892 (Binet & Henneguy,
1892; Binet & Philippe, 1892) and January 1893 (Binet, 1893) and in the Revue Scientifique
dated June 1893 before all these works were gathered and completed as a book that would be
published one year later (Binet, 1894a, see annex II for an abstract).
Arithmetical prodigies present an inequality of development in memories
As mentioned in the report of the academic commission (Charcot, 1892), the study of
Inaudi lends new evidence to the theory of partial memories. As noted by Binet (1892c, p.
912): “The academic committee sought to take approximate measurements of Inaudi's types of
memory. They convinced themselves that the young calculator had not developed a specific
memory for faces, events, places, or musical airs.” Using special techniques, Binet and
Henneguy (1892) were able to measure his memory for nuances of color: it was extremely
poor. In the case of most prodigies, their memory for things unconnected with calculation is
not remarkable (Smith, 1983, p. 49). His results are surprising only for numbers.
One of the most important characteristics of Inaudi’ memory was the speed of
acquisition. A single hearing sufficed to allow Inaudi to memorize a long series of digits or
the statement of a complicated problem; he did not go back and repeated the numbers several
times, as most people do. Once the number was locked in his memory, it was retained with
astonishing accuracy and confidence. Not only could Inaudi repeat a twenty-five digit number
in the order in which he heard it, but he could also repeat it in reverse order, starting with the
number's final digit; he could repeat half of the number in one direction, and the other half in
the other; all of this without any hesitation, without any fatigue, and without making any
11
error. Binet (1892c, 1893) showed that Inaudi divided constantly figures by groups of three in
his memory: "it is not a uniform succession of figures, the series is given rhythm in a way"
(Binet, 1893, p. 110).
Memory types and operations in arithmetical prodigies
Unlike other arithmetical prodigies in figures Inaudi did not resort to the visual type of
memory. He did not represent any numbers to himself in a visible form, but he heard them
(Binet, 1892c). His phonatory organs were really active as he memorized and calculated in his
head. Using a method for preventing Inaudi from quietly articulating sound, Binet asked him
to sing in one tone during his work. If the sound of the vowel used for this purpose preserved
its purity, it would be quite certain that he was not articulating the figures. This experiment
caused much annoyance. Inaudi still preserved the power of calculating, but it took him four
or five times longer than usual, and then the voice betrayed the fact that he was articulating.
This technique of double task is used today by cognitive psychologists to show the
importance of the hearing register and attention. As noted by Binet (1892c, pp. 919-920):
“For the visual type, numbers have a position in space; but for a pure auditory type, numbers
are ordered only in time; they are laid out in succession.” When we pronounce five series of
five-digit numbers to a person of the visual type, and ask the person to picture the numbers
laid out in groups of five, one below the other, forming a square; this square can be read in
several ways, either from right to left, or from top to bottom, or along a diagonal. The visual
type, having a table of digits in his head, can perform this reading quite easily; he only has to
scan his visual image in the necessary direction, and he will thus understandably read from
this image the requested digits only. For the auditory type, who sees nothing, this task is much
more awkward. If he wishes to read along the diagonal line, he must reason, saying to himself
that the first number provides the first digit in the diagonal, the second number the second
digit, and so on; this is laborious work (Charcot & Binet, 1893; see Nicolas, Gounden &
Levine, 2011).
Memory is not the unique faculty developed by arithmetical prodigies
In his report Charcot (1892) writes: “He seems not to present any exceptional
aptitudes, beyond that for figures and numbers, for which he demonstrates such a remarkable
memory.” Charcot does not quote the information given by Binet in his letter (March 4th,
1892) where he underlines (see Klein, 2011) the power of Inaudi’s faculty of attention
(concentration ability). But Binet and Henneguy (1892) found that Inaudi developed many
12
faculties to a great extent so that it helped him to achieve complex mental calculations.
Perception, attention, and judgment, to the extent and in the shape in which they are needed in
his work, have reached the same perfection as his memory for figures. Thus, in mental
calculation, memory is not the only faculty that is developed by prodigious calculators. Binet
performed many experiments on this topic with Inaudi. In his paper published with his friend
Louis Félix Henneguy (1850-1928), assistant professor at the Collège de France (Binet &
Henneguy, 1892) Binet summarized the results of the experiments carried out with Inaudi in
his laboratory providing all necessary details. By comparing the ability to develop his
memory for figures with that of a pupil from the laboratory (Mr Gaultier), Binet underlines
the exceptional capacities of Inaudi which are based on an exceptional power of attention.
Such a power of voluntary attention (concentration) was tested by the method of reaction
times in the motor, visual and auditive domains (for a non-experienced subject Inaudi was
extremely fast) and by using a metronome (beating simultaneously two metronomes, the
subject is asked to count the beatings; the difficulty of this numeration appears when the
speed of the beatings is increased) where Inaudi was capable of making numerations
(calculation of the number of beatings) in extreme conditions.
Memory expertise and arithmetical prodigies
While Inaudi calculated quickly, he did not surpass any professional calculator (Binet,
1892c) who could do his work on paper. The merit of Inaudi was that he held all of his
operations in his memory. Binet and Philippe (1892) compared Inaudi with four people
employed as cashiers in the Bon Marché stores. They were in the habit of calculating every
day. On average, they had been calculating for fourteen years (they were around thirty-five
years old). They were in the habit of performing many multiplications in their heads. Their
memory for spoken numbers was well-developed in general; they could repeat seven to ten
digits exactly; up to twelve, when the digits were grouped into numbers. Thus, their ability to
calculate had developed to a noteworthy level; but memory for figures had not contributed to
this development. As Binet & Philippe (1892, p. 222) said : “Here we see a dissociation,
which leads us to admit that there exists two memories for figures, quite distinct and quite
independent from one another: the memory for figures as such, and the memory for relations
between figures. The latter alone is the basis for calculation.” All four of the calculators were
able to mentally perform multiplications of two digits; some were able, with a certain effort,
to perform multiplications of three digits (each factor having three digits); none of them was
able to reach four digits. It is memory that imposes these limits; when the operation is
13
complex, the subjects do not recall the partial solutions that they obtain; consequently, they
are obliged to abandon the operation. The results (see Binet, 1894a) indicate that cashiers
gave almost similar results to those of Inaudi for the simplest arithmetical operations which
they could perform mentally. If the duration of the complex operations was longer for them,
their memory is not sufficient. Those calculators had similar calculating abilities to that of
Inaudi, and a much weaker memory for figures.
Natural memory vs. artificial memory
With the collaboration of his pupil Victor Henri (1872-1940), Binet completed his last
series of experiments in the field of memory expertise (Binet & Henri, 1892). These
experiments aimed at establishing that individuals can fake a great memory for figures, but
without possessing it really. We tend to believe that when an individual repeats 27 to 30
figures that have just been read to him, he uses only a single means to remember them: his
memory. A very distinguished prestidigitator, who practiced mnemonics for a long time,
named Gustave Arnould (1850-1920), also an "artificial" calculator (mnemonist), was kind
enough to lend his help for a new study. By means of mnemonics, he memorized a series of
figures in the laboratory of psychology at the Sorbonne. Thus, Binet was able to show the
differences that existed between natural memory and artificial memory (or mnemonics). The
public is easily convinced by a mnemonist who simulates natural memory. Mnemonics are of
several kinds (see Worthen & Hunt, 2011); the only one which is useful for the memory for
figures and numbers is based on the substitution of figures by words. Every figure is formally
connected to one or several consonants; when we want to make the mnemonic translation of a
number, we replace, by thought, each of the figures which composes it with the corresponding
consonant, we thus obtain certain number of consonants, which we transform into words by
the insertion of vowels. Arnould succeeded in learning 36 figures in five minutes: a miracle of
memory which seemed to put him above certain known calculators. To discover signs by
which we recognize a simulation by mnemonics, Binet and Henri (1892) compared
performances from « natural » calculators such as Inaudi (auditive type) and Diamandi (visual
type) with those of the « artificial » calculator Arnould. The difference between these three
calculators was studied from a double perspective using the psychometric method: the
measurement of the time necessary to learn figures, and that of the time necessary to repeat
them. Inaudi was the fastest of the three calculators to learn the 100 figures; Diamandi was a
bit faster than Arnould to learn a small number of figures, but Arnould was faster for bigger
numbers. Thus, the user of mnemonics possessed a considerable advantage over Diamandi to
14
acquire figures. He got less tired and saved time. The difference between artificial memory
and natural memory is evident in the times required for the verbal repetition of figures. To
recite 25 figures which they had just learnt by heart, it took Inaudi 7 seconds, Diamandi 9
seconds, and Arnould 31 seconds, which is a significantly longer time. Arnould’s slow pace
seemed to result from the necessity to translate into figures the words stored in his memory.
He did not worry about figures until he was asked to repeat them; then, he performed a
“translation” that required some extra time even though he had practiced with long exercises.
CONCLUSION
The detailed analysis of Inaudi’s memory by Binet was the first psychological study of
mental calculators. As noted by Carson (1999) this case-study method was derived from the
world of the medical clinic. Indeed, Binet examined Inaudi from a variety of perspectives and
over the long term, he showed that performance of long calculations in the mind relies heavily
on the accuracy of memory. The rise of the new psychology initiated by the works of Ribot
and Charcot made this study possible. Althought the origins of such investigations in France
dates back from the former studies on calculation pursued by phrenologists and
anthropologists, for Binet (1894a), exceptional memory for numbers, such as the one
displayed by Inaudi, is not the result of some anatomical peculiarity, but rather a combination
of mental faculties (attention, will, perseverance) and above all a passionate taste for studies
that are connected with this memory.
The scientific study of Inaudi’s abilities showed 1° the need to consider memory as a
collection of partial memories (for recent conceptions, see Squire, 1987, 2004, 2009; Tulving,
1983, 1995, 2007) and, 2° the importance of studying memory experts who have developed
exceptional ability on one type of memory (Wilding & Valentine, 1994, 1997, 2006). Charcot
initiated the distinction principle among several types of memory (visual, auditive, motor
types) and Inaudi was the first auditory calculator to have been studied scientifically.
According to Smith (1983, 1988), auditory calculators like Inaudi, unlike visual calculators,
have certain typical features: (1) some sort of verbalizing while calculating; (2) self taught
and left-to-right methods of calculation; (3) precocity (they learned how to calculate before
learning written numbers). The popular distinction between visual memory and auditory
memory leads today to the learning-style approach (visual type vs. auditive type).
The originality of Binet’s work was to test a memory model (multiple memory
hypothesis) using subjects who were prodigies from the point of view of some psychological
15
capacities. Binet’s interest in bizarre or prodigious subjects derived from Taine’s work (Taine,
1870) who considered that more a phenomenon is strange more it is instructive. So Binet was
interested in the same period by magicians (see Lachapelle, 2008), chess players (see Nicolas
& Sanitioso, 2012), etc. But it was the study on Inaudi’s calculating abilities which paved the
way for new research. Before World War I, the most extensive and in-depth studies were
conducted on Urania Diamandi (1887-?) (Ioteyko, 1910; Lahy, 1913; Manouvrier, 1908) and
on Gottfried Rückle (1879-1929), a mathematic professor studied by Müller (1911, 1917; see
Murray & Bandomir, 2000). The study of Inaudi is of particular interest in history of
psychology because it represents an original French approach to psychology: the clinical case
study of singular or extraordinary subjects. This French scientific tradition was very different
from the methods of the German experimental tradition. A new path has been opened as
several studies on calculating or memory prodigies have recently been conducted (see Fehr,
Weber, Willmes & Herrmann, 2010; Hu, Ericsson, Yang, & Lu, 2009; Pesenti, Seron,
Samson, & Duroux, 1999; Pesenti, Zago, Crivello, Mellet, Samson, Duroux, Seron, Mazoyer
& Tzourio-Mazoyer, 2001; Seamon, Punjabi & Busch, 2010).
Moreover Binet’s work marks the first attempt to distinguish "natural" memory from
"strategic" memory (see for a more recent attempt Wilding & Valentine, 1994, 1997, 2006).
With his book on calculators and chess players, Binet (1894a) provided the first work on
memory expertise in psychology. As training increases in considerable proportions so does
the memory span (e.g., Ericsson, Chase & Faloon, 1980), more recently Ericsson (1985;
Ericsson & Chase, 1982) have proposed a famous skilled memory theory as a framework for
accounting for individual differences in memory ability (for further developments: see
Ericsson & Kintsch, 1995) and showed that expert memory rely on prior knowledge (see
Guida, Gobet, & Nicolas, 2013; Guida, Tardieu & Nicolas, 2009; Guida, Gobet, Tardieu, &
Nicolas, 2012). The study of expertise in memory and other activities is nowadays a major
challenge in psychological research.
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