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Mirror man: A case of skilled deliberatemirror writingRobert D. McIntosha, Natascia De Luciab & Sergio Della Salaa

a Human Cognitive Neuroscience, Psychology, University of Edinburgh,Edinburgh, UKb Neuropsychology Laboratory, Psychology, Second University of Naples,Caserta, ItalyPublished online: 05 Mar 2014.

To cite this article: Robert D. McIntosh, Natascia De Lucia & Sergio Della Sala (2014): Mirror man: A case ofskilled deliberate mirror writing, Cognitive Neuropsychology, DOI: 10.1080/02643294.2014.887006

To link to this article: http://dx.doi.org/10.1080/02643294.2014.887006

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Mirror man: A case of skilled deliberate mirror writing

Robert D. McIntosh1, Natascia De Lucia2, and Sergio Della Sala1

1Human Cognitive Neuroscience, Psychology, University of Edinburgh, Edinburgh, UK2Neuropsychology Laboratory, Psychology, Second University of Naples, Caserta, Italy

Mirror writing is a striking behaviour that is common in children and can reemerge in adults followingbrain damage. Skilled deliberatemirror writing has also been reported, but only anecdotally. We providethe first quantitative study of skilled deliberate mirror writing. K.B. can write forward or backward,vertically upright or inverted, with the hands acting alone or simultaneously. K.B. is predominantlyleft handed, but writes habitually with his right hand. Of his writing formats, his left hand mirrorwriting is by far the most similar in style to his normal handwriting. When writing bimanually, he per-forms better when his two hands make mirror-symmetrical movements to write opposite scripts than ifthey move in the same direction to write similar scripts. He has no special facility for reading mirroredtext. These features are consistent with prior anecdotal cases and support a motor basis for K.B.’s ability,according to which his skilled mirror writing results from the left hand execution of a low-level motorprogram for a right hand abductive writing action. Our methods offer a novel framework for investi-gating the sharing of motor representations across effectors.

Keywords: Mirror writing; Motor; Perceptual.

Mirror writing, put simply, is writing back to front(McIntosh & Della Sala, 2012). Partial mirrorwriting can occur when individual letters areformed back to front, but complete mirror writingentails spatial reversal of the whole script. Thewriter begins with the first letter of the word andproceeds through to the last, but production flowsin the opposite direction to normal with each ofthe letters individually back to front. For adextrad language like English, mirror writing isright to left; it can be read normally when held toa mirror. Mirror writing has three cardinal forms:“spontaneous”, “involuntary”, and “deliberate”(Lebrun, Devreux, & Leleux, 1989). Spontaneousmirror writing is common amongst pre- and

early-school-age children undergoing literacydevelopment (Cornell, 1985; Gordon, 1920).Involuntary mirror writing refers to the productionof mirrored script by adults following brain damage(Balfour, Borthwick, Cubelli, & Della Sala, 2007;Critchley, 1927, 1928; Della Sala & Cubelli,2007). Mirror writing can also be deliberate andskilful. This form has been described anecdotally,but never studied experimentally. In this paper,we provide the first quantitative case study ofskilled deliberate mirror writing.The most-celebrated deliberate mirror-writers,

name-checked routinely in any overview, areLeonardo da Vinci and Lewis Carroll (e.g.,Schott, 1999, 2007). Mirror writing with the

Correspondence should be addressed to Robert McIntosh, Psychology, University of Edinburgh, 7 George Square, Edinburgh,

EH8 9JZ, UK (E-mail: r.d.mcintosh@ed.ac.uk).

© 2014 Taylor & Francis 1

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dominant left hand was Leonardo’s habitual scriptwhen writing for himself, though he wrote forothers in a forward direction. Schott (1999) hascommented on the striking stylistic resemblancebetween Leonardo’s mirrored and forward hand-writing. Contrariwise, Lewis Carroll usually wrotewith his right hand, and his mirror writing was rec-reational rather than habitual, albeit highly skilled.It has been speculated that Carroll was a natural lefthander, schooled to write with his right hand (seeSchott, 1999), though there is no direct evidencefor this. Indeed, with a logical circularity thatCarroll himself might have enjoyed, his mirrorwriting is one of the most common arguments infavour of his left handedness (M. Richards,Chairman of Lewis Carrol Society, personal com-munication, August 29, 2012).

A less illustrious but better documented case ofdeliberate mirror writing is that of Frank JamesAllen, a professor of physiology who described hisexperience in Brain in 1896. He reported himselfto be ambidextrous, and he had discovered “acci-dentally”, at 13 years old, that he could write back-ward fluently with his left hand. His reversedproductions, when viewed in a mirror, are verysimilar to his normal handwriting (Allen, 1896,Figure 1). Allen offered several interesting obser-vations: that it was easy to write the same word sim-ultaneously with both hands (presumably inopposite directions); that a sign language alphabetlearned with his right hand could be executedeasily with his left; that reversed writing movementscould be made with the left foot; that visual feed-back did not aid performance; and that he had nofacility for reading mirrored script, even self-penned. He speculated that everyone has theability to mirror write, to some degree, but that itis usually undiscovered, surfacing mainly in con-ditions where injury or disease obliges the unaccus-tomed hand to pick up a pen.

Allen’s (1896) interpretation was that mirrorwriting demonstrates the superordinate nature ofthe relevant graphic representations. He proposedthat a high-level command can direct writing withany effector, with lower level processes translatinginto an appropriate sequence ofmuscle contractions.His idea foreshadowed the concept of a generalized

motor program, developed more fully during thelatter half of the twentieth century (e.g., Bernstein,1967; Lashley, 1951; Rosenbaum, 1980; Salzman,1979; Schmidt, 1975).Generalizedmotor programscode for action in relatively abstract, effector-inde-pendent terms. For instance, the spatial path of anunspecified end effector may be coded initially inenvironmental coordinates. Such generalized pro-grams occupy the top of a motor control hierarchy,with lower levels becoming effector-specific andmore detailed, translating the movement plan intojoint movements, and ultimately into the precisemuscle activations required for that effector.Several approaches to human and robotic motorcontrol adopt this general hierarchical structure(e.g., Bernstein, 1967; Hollerbach, 1982; Salzman,1979).

Handwriting (in a forward direction) hasbecome a textbook example to illustrate theconcept of effector independence in action (e.g.,Tresilian, 2012). At least some aspects of aperson’s handwriting style are recognizably pre-served when using unpractised effector systems,such as the shoulder and elbow when writing verylarge (Merton, 1972), the nondominant hand, oreven a pen taped to the foot or held in the teeth(Raibert, 1977). The two influential sources justcited compared individual writing samples pro-duced by different effectors, interpreting simi-larities of shape to imply the involvement of acommon, generalized motor program. However,these analyses were limited to a qualitative evalu-ation of the static shape of the writing and didnot consider dynamic aspects of its production.These limitations were highlighted by Wright(1990), using the analogy of signature forgery:The forger may fool us quite easily if she needonly produce something that looks like the targetsignature, but her job is much harder if we alsocompare her sequence of pen strokes against thosethat produced the original. For evidence thatgraphic representations are shared at an interest-ingly deep level of the motor control hierarchy,written words should not only look similar, but beproduced in similar ways.

Wright (1990) compared normal writing withthe dominant hand against writing very large with

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the dominant arm and writing with the nondomi-nant hand, analysing static and dynamic featuresacross multiple writing samples in each condition.Whilst confirming broad qualitative similaritiesbetween conditions, he also identified systematicchanges in the letter shapes and in the dynamicsequence of pen strokes. The nondominanthand’s writing diverged more from normalwriting than did the dominant arm’s, leadingWright to suggest that the two hands share onlyrather high-level abstract spatial representationsfor writing, whilst writing with the dominanthand and arm share representations at a deeperlevel in the motor hierarchy. Wright’s workimplies that we can differentiate degrees of related-ness between different formats of writing. Thecloser the relatedness, the deeper down thecontrol hierarchy are the shared motorrepresentations.

Wright’s (1990) insights can be extended to thestudy of mirror writing. For instance, F. J. Allen’s(1896) deliberate nondominant hand mirrorwriting, when viewed in a mirror, may look stylisti-cally similar to his dominant hand forward writing,but we could assess the true relatedness more deeplyby considering the dynamic and not just the staticcharacter of the writing, across multiple samples.This would more formally test Allen’s intuitionthat mirror writing with the nondominant handreflects the sharing of motor programs betweeneffectors. The predictions for this test will bedrawn out in due course, but for now we shouldnote that Allen’s hypothesis of deliberate mirrorwriting converges with a classical motor accountproposed to explain cases of involuntary mirrorwriting following brain damage. The core idea of(at least some) classical motor accounts is that askilled action developed by one hand will mostnaturally be executed by the opposite hand inmirror reversal, since homologous muscles wouldbe activated in the same sequence (Critchley,1928; Erlenmeyer 1879, cited in Critchley, 1928;Vogt, 1880). In a right handed, dextrad languageculture, mirror writing may be the natural“unthinking” script of the left hand.

To transpose these classical ideas onto a moremodern motor control hierarchy, we might

suggest that motor plans for writing are associatedwith the hand that has learned them, so becomerepresented strongly at an effector-relative levelof the motor hierarchy. At this lower level of rep-resentation, there is no explicit specification ofhow the pen should move, but rather of how thejoints should move, for instance specifying hori-zontal arm movements as abductive (away fromthe body midline) or adductive (toward the bodymidline) rather than as rightward or leftwardthrough the environment (e.g., Salzman, 1979).Thus, for right handers in dextrad languageculture, handwriting is ingrained as a low-levelabductive motor plan for the right hand. If thisabductive plan is then sent to the left handinstead of the right, the movement will flowfrom right to left, producing mirror writing. Thismight arise through some sort of disinhibition inpatients with brain damage, or as an innate and/or cultivated ability in deliberate mirror-writers.In either case, fluent mirror writing should bestrongly associated with the nondominant hand;and provided that this hand is reasonably dexter-ous, the mirror writing (when viewed in amirror) should be similar to normal writing inboth static and dynamic features, because itderives from a shared representation at a lowlevel of the motor hierarchy. Indeed, the similarityshould be stronger than that between forwardwriting for the two hands, which share only ahigher level, environment-relative representation(Wright, 1990).

Motor accounts of mirror writing have been for-mulated in various ways (see Discussion). As a classof explanation, they can be contrasted with percep-tual accounts, according to which mirror writing isguided by reversed perceptual representations ofwords and letters (e.g., Heilman, Howell,Valenstein, & Rothi, 1980; Orton, 1928). Thesereversed perceptual representations would give riseto high-level effector-independent plans forwriting reversed words and letters, inducingmirror writing with either hand. As with motorhypotheses, the perceptual accounts can takevarious specific formulations, but all predict thatmirror writing should be associated with a facilityfor perceptual recognition of mirrored letters and

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words. Two clinical observations strongly favour amotor over a perceptual account of mirrorwriting. First, involuntary mirror writing is typicallyconfined to the nondominant hand; and, second, itis not normally accompanied by mirror reading(Critchley, 1927, 1928; Della Sala & Cubelli,2007; for possible exceptions, see Durwen &Linke, 1988; Heilman et al., 1980). Similarly,deliberate mirror writing is, at least anecdotally,associated with the left hand, especially amongstambidextrous or left handed people schooled towrite with the right hand. In a letter to Nature,Smetacek (1992) mentioned four such “corrected”sinistrals who mirror wrote fluently with the lefthand. One woman apparently drafted her master’sthesis by mirror writing onto transparent paperwith her left hand, editing it later on the flip sidewith her right.

However, whilst skilled deliberate mirror writinghas long attracted interest, the literature lacks anyobjectively described case. We provide the firstsuch data, concerning a German academic, whopractises as an amateur artist under the pseudonymKasimir Bordihn (K.B.). K.B. has a more than 50-year history of mirror writing and has developedthis ability to a flamboyant degree.Hewrites, appar-ently quite fluently, with either hand, forward orbackward, upright or inverted, and unimanually orbimanually (see Figure 1). Although it is impossibleto separate out, retrospectively, innate ability fromthe effects of practice, we aim to provide an objectivecharacterization of K.B.’s mirror-writing skills andto assess how these bear upon perceptual andmotor hypotheses of mirror writing. The specificpredictions will be detailed alongside our methods,following a brief description of this unusual man.

Figure 1. A letter from K.B., reproduced with K.B.’s permission, providing samples of his eight forms of handwriting. The original is on the left,

and a horizontally reflected version is shown on the right.

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CASE REPORT

K.B. describes himself as ambidextrous; but onexamination with the Edinburgh HandednessInventory (Oldfield, 1971), he reports a left handpreference for all manual activities except forwriting, for which he has a strong right hand pre-ference. His laterality quotient (−64%) thereforereflects incomplete left hand dominance, and heis left-eye dominant, as assessed by the Porta test(Della Porta, 1593). This pattern suggests that K.B. is a natural left hander, schooled to write withhis right hand, a practice common in Germany(and elsewhere) at that time (Smetacek, 1992).However, he does not recall having been requiredto write right handed, so this inference cannot becertain. In addition to his first language, German,K.B. is fluent in English, which he studied fromthe age of 12. He also studied French at school,and later some Spanish.

K.B. “discovered” mirror writing at the age ofnine, finding that he could reduce his timewriting lines for a teacher by writing forward withhis right hand and simultaneously backward withhis left. He went on to practise writing backwardsand forwards with either hand, unimanually andbimanually. He revived these amusements in hisearly twenties. For instance, when paying aparking fine, he wrote a cheque and letter inmirror reversal as a humorously subversive act. Healso posted himself mirror-addressed envelopes,to see whether they would be delivered. They were.

As a university lecturer in veterinary medicine,from the age of 35, K.B. found a more practicaloutlet for these abilities. He used mirror writing ofwords and letters to illustrate the concept of knotchirality, teaching that a compound surgical knotwill be strongest if its component knots are of alter-nating chirality. This novel demonstration provedpopular with students, and he was invited toperform at university events. For these, he developedmore elaborate tricks, adding vertical inversions tohis forward and backward writing (Figure 1). Asan amateur artist, he incorporated these reflectionsand inversions into a distinctive “mirror-art”,which deals with concepts of symmetry and asym-metry (Figure 2).

Figure 2. An example of K.B.’s “mirror-art”, reproduced with K.B.’s

permission. [To view this figure in colour, please see the online

version of this Journal.]

Figure 3. (a) The terminology used to refer to K.B.’s eight

handwriting formats and the symbol shapes that denote them on

our data figures; (b) the word “butter” as written by K.B. in each

of the eight formats.

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At the time of testing, shortly before his 65thbirthday, K.B. was able to write in eight ways:forward and reversed combined with upright andinverted, executed with either hand (Figures 1and 3). He reports that left hand mirror writinghas always felt natural to him, but that other non-standard writing patterns have required morepractice.

METHOD AND PREDICTIONS

Reading tasks

A cardinal prediction of the perceptual hypothesis isthat, since the ability to mirror write implies accessto reversed perceptual representations of wordsand letters, it should be associated with a facilityfor mirror reading. However, like F. J. Allen(1896), K.B. reports that he does not find it easyto read mirrored text and is unable to read his ownmirror writing without the aid of a mirror.

We attempted to test this more formally by pre-senting K.B. with short abstracts from CurrentBiology news articles, such as he might read in hisacademic life, to be read aloud under timed con-ditions. He was first presented with a 109-wordabstract, printed normally, which he read withouterror in 38 s. Next, given a mirror-printed abstract,he struggled severely, reading four words correctlyand two incorrectly before refusing to continueafter 25 s. This was considered sufficient to estab-lish that K.B. does not have any special facilityfor mirror reading, and we did not press himfurther with this task that he did not enjoy.

Writing tasks

K.B.’s writing, in its various formats, was assessed bysingle-word writing. All words were written with apen-like stylus on the touch screen (260 × 163mm, 1280 × 800 pixels, 60-Hz refresh) of aToshiba Portégé tablet laptop, with the screen inthe flat landscape orientation. The tasks werecontrolled by customized LabVIEW software,which sampled the stylus coordinates every 13 ms(+3 ms).

Unimanual writing taskK.B. has eight unimanual writing formats. Figure 3shows examples of these eight formats and illus-trates the terminology used to refer to them andthe symbol shapes that denote them on our datafigures.

K.B. performed four blocks of unimanual trials,with hand and vertical orientation blocked in theorder: right hand upright, left hand upright, righthand inverted, left hand inverted. In each block,he wrote each of nine words in each of four ways:forward with visible trace, forward with no trace,reversed with visible trace, reversed with no trace.On visible trace trials, the stylus left a black line,two pixels thick, on the screen, mimickingwriting with a normal pen. Each word was a legalsix-letter word in English and German (butter,design, editor, farmer, finger, garage, hammer,helium, isomer). Trial order was randomizedwithin blocks.

Each trial was preceded by a grey rectangularbox (300 × 150 pixels), stating the trial number,at the bottom centre of a white screen. K.B.touched the box with the stylus to initiate thetrial. The box disappeared, and 500 ms later thetarget word appeared in normally oriented, black,lower-case, 138-point Times New Roman font atthe top centre of the screen. The word was under-lined or not, indicating visible trace and no tracetrials, respectively. After 3000 ms, the word disap-peared, and a grey triangle (325 × 465 pixels)appeared at the left or right of the screen, pointingto a grey circle (475 pixels diameter) on the otherside. The two shapes were centred vertically andseparated by 1060 pixels of blank space, withinwhich K.B. was required to write the word in thedirection indicated by the triangle, touching thecircle with the stylus to end the trial. His instruc-tion was to write each word at a comfortablepace. Consistency of handwriting style, not speedor neatness, was emphasized as important.

Scoring procedures and dependent measures. To indexhow similar each of K.B.’s nonstandard writingformats is to his standard right hand uprightforward handwriting, we used three scoring pro-cedures. Static similarity of the final written forms

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was derived from the subjective ratings of multiplenaive observers, who did not know the purpose ofthe study or the provenance of the stimuli.Dynamic similarity was derived from a rule-basedcomparison of the sequence of pen strokes by anobserver who did not know which writing con-dition he was scoring. Fluency cost was calculatedas the amount of extra time required to write eachnonstandard format, relative to the standard.

Static similarity to the standard was rated by 20naive observers (13 women, 7 men; mean age 27.7years, SD = 3.61), each of whom completed abooklet of 18 A4 rating sheets, bound with acover sheet of instructions. There was one sheetfor each of the nine words in the visible trace andno trace conditions separately. Figure 4a shows anexample rating sheet. On every sheet, a standardword was shown within a central box, with eighttarget formats of the same word arranged aroundit. The eight target words were from K.B.’s eightunimanual formats, and the central standard wasfrom K.B.’s right hand upright forward format forthe same trace condition (visible trace or notrace). Observers were required to rate each targetword for similarity to the standard by using anumerical scale underneath the target (where 1 istotally dissimilar, and 5 is identical). To facilitatethis, every word had been digitally reflected and/or inverted as required to normalize to the canoni-cal orientation. The spatial assignment of writingconditions to the eight target word positions wasvaried across sheets, to offset any rating biasesrelated to word position. Note that the right handforward format appears twice on each sheet, onceas the standard and once as a target. This providesa check on the validity of the observer ratings, asthis target should be rated as identical to thestandard.

Dynamic similarity was scored by an exper-imenter (R.D.M.) replaying the sequence of penstrokes, moment by moment, comparing eachtarget word side by side with the same word pro-duced in the standard right hand forward conditionof the corresponding trace condition (visible traceor no trace). To facilitate comparison, every wordwas normalized digitally to the canonicalorientation. To reduce subjectivity, a set of rules

was followed. Each letter within each word wasrated as different from the standard only if any ofthe following differences were identified: (a) amajor feature (e.g., decorative loop) was missingor added; (b) a cursive link to the next letter wasmissing or added; (c) the direction of a major penstroke differed categorically (e.g., an anticlockwisevs. clockwise loop, a leftward vs. rightward orupward vs. downward stroke); (d) the orientationof a major pen stroke differed by more than 45°;(e) there was a difference of stroke order (typically,crossing a “t” or dotting an “i” at a different point

Figure 4. (a) Example sheet from a unimanual rating exercise. The

standard word (“butter”) is in the central box. The target words were

produced with visible trace in the following conditions (clockwise

from top left): left hand upright forward; left hand inverted

forward; left hand upright reversed; right hand upright forward;

right hand inverted forward; left hand inverted reversed; right

hand upright reversed; right hand inverted reversed. (b) Example

sheet from bimanual rating exercise. The standard word (“jaguar”)

is in the central box. The target words were produced by the right

hand in the following conditions (clockwise from top left): forward

unimanual; reversed unimanual; reversed bimanual motorically

congruent; forward bimanual perceptually congruent; reversed

bimanual perceptually congruent; forward bimanual motorically

congruent.

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during the word formation). For each word, thenumber of letters recorded as different was sub-tracted from six to produce a similarity score fromzero to six. Dynamic similarity has some overlapwith static similarity, as it is affected by major(though not minor) differences of shape, but it pro-vides a complementary measure that is sensitive todifferences in the sequence of pen strokes.

Fluency cost was the time taken to write thetarget word minus the time taken to write the stan-dard, with writing time calculated from the onset ofthe first pen stroke to the offset of the last.

Predictions and analysis strategy. Our predictions forthe unimanual task are predicated on Wright’s(1990) analysis, which states that writing acts willbe more similar to one another if they share amotor representation at a lower level of thecontrol hierarchy. A highly simplified motor hierar-chy for writing is shown in Figure 5, to illustrate thecritical predictions of the perceptual and motorhypotheses. These predictions are specifically forupright writing.

According to the perceptual hypothesis, forwardwriting with either hand would depend on acommon high-level plan, and reversed writingwith either hand would depend on a differentcommon high-level plan. The perceptual hypoth-esis therefore predicts that left hand forwardwriting would be more similar to normal writingthan would left hand reversed writing. A morespeculative, and thus less critical, prediction of theperceptual hypothesis is that, if mirror writing isguided by a reversed perceptual representation ofhow the word should look, then its accurate pro-duction might require visual monitoring of thewritten form, so the visible trace condition shouldaid reversed writing disproportionately.

According to the motor hypothesis, left handreversed writing would derive from the left handexecuting the low-level effector-relative plan forright hand forward (abductive) writing. Themotor hypothesis thus predicts that left handreversed writing should be more similar to normalwriting than is left hand forward writing. Figure5 also implies that right hand reversed writingcould be produced by right hand execution of a

left hand adductive plan for forward writing.However, this is highly speculative and is not acritical prediction of the motor hypothesis (whichproperly concerns only left hand mirror writing).Left hand adductive writing is not any moreprimary or canonical than right hand adductivewriting, so it is not obvious that the latter shouldbe derived by co-opting the former. An alternativemight be that right hand reversed writing descendsfrom a separate high-level motor plan for reversedwriting. The only firm prediction of the motor

Figure 5. A highly simplified motor hierarchy, showing routes by

which the four upright writing formats could be produced under

(a) the perceptual and (b) the motor hypotheses. The high-level

plan specifies the spatial path of the movement in environment-

relative coordinates; the low-level plan specifies the movement in

effector-relative (e.g., joint) coordinates. In the perceptual account,

the high-level motor plan would be derived from a perceptual

representation of how the word should look, so reversed writing

would descend ultimately from a reversed perceptual

representation. In the motor account, left hand reversed writing

would be produced by co-opting the effector-level plan for right

hand abductive writing. The right side of the figure indicates that

right hand reversed writing could similarly be produced by co-

opting a left hand adductive motor plan, but this is not a critical

prediction of the motor hypothesis (see text). The degree of

similarity to normal handwriting depends on the lowest level of

the hierarchy at which a representation is shared with normal

handwriting. In the perceptual hypothesis, the closest relative of

normal handwriting would be left hand forward writing, which

shares a high-level plan. In the motor hypothesis, the closest

relative of normal handwriting would be left hand reversed

writing, which shares a low-level plan.

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hypothesis for right hand reversed writing is that itshould be more distantly related to normal writingthan is left hand reversed writing. Finally, themotor hypothesis provides no reason to think thatthe provision of a visible trace should aid mirrorwriting disproportionately.

To target these predictions, for each dependentmeasure, we ran a repeated measures analysis of var-iance (ANOVA) by condition (left hand reversed,left hand forward, right hand reversed) and tracevisibility (visible trace, no trace), with Huynh–Feldt corrections to the degrees of freedom tocompensate for violations of sphericity. Plannedcontrasts were used to compare left hand reversedwriting against the other two formats. The percep-tual hypothesis predicts that left hand forwardwriting will have the greatest similarity to normalwriting, and that trace visibility may aid the reversedwriting conditions disproportionately. The motorhypothesis predicts that left hand reversed writingwill have the greatest similarity to normal writing,with no specific influence of trace visibility. Inorder to save degrees of freedom for these criticalquestions, we do not include inverted writing inany inferential statistical analyses. Indeed, at thisstage, we make no specific predictions for invertedwriting, except that it could not be produced byco-opting normal writing programs at any level ofthe motor hierarchy, so presumably requires a dis-tinct high-level plan, in which case it should bearlittle, if any, resemblance to K.B.’s upright writing(Figures 3 and 4 suggest that this is the case).

Bimanual writing taskBimanual writing was assessed on the day after theunimanual task. The bimanual task used twomatching tablet laptops, with trial sequences syn-chronized. All words were written upright, with avisible trace. K.B. performed two blocks of 40trials. In each block, each of five words waswritten unimanually or bimanually in each of theeight possible combinations of script: left handtask (inactive, forward, or reversed) crossed withright hand task (inactive, forward, or reversed),excluding the double inactive combination. Thetrial procedure was similar to that of the unimanualtask, except that K.B. worked on the two directly

adjacent laptops, with a stylus in each hand. Heinitiated each trial by touching the starting box oneach screen simultaneously. Trials in which onehand was inactive were indicated by a single greycircle (475 pixels diameter) at the centre of thatscreen. The words were always the same for thetwo hands in bimanual trials, and each was a legalsix-letter word in English and German (Block 1:jaguar, karate, kitsch, magnet, minute, plural.Block 2: puzzle, quasar, radius, satire, bitter).Trial order was randomized within blocks.Consistency of handwriting and simultaneity ofbimanual writing were emphasized as important.

Table 1 lists the eight writing conditions. Notethat we class each bimanual condition as either per-ceptually congruent or motorically congruent. Whenthe two hands write the same word in the sameenvironmental direction (both writing forward, orboth writing reversed), the condition is perceptuallycongruent, because a matching perceptual rep-resentation of the word could guide both hands.When the two hands write the same word in envir-onmentally opposite directions (one writingforward and the other reversed), the condition ismotorically congruent, because the same effector-relative representation (abductive or adductive)could guide both hands.

Table 1. The eight writing conditions of the bimanual writing task

Trial type

Writing condition Left hand Right hand Congruence

Unimanual Forward

Reversed

Forward

Reversed

Bimanual Forward Forward Perceptual

Forward Reversed Motoric

Reversed Forward Motoric

Reversed Reversed Perceptual

Note: The first four conditions involve unimanual writing only.

Bimanual trials are subclassified according to whether the

trial type is perceptually congruent (visually matching word

forms) or motorically congruent (anatomically matching

writing actions). Across two blocks of trials, K.B. wrote

each of 10 words in each of these eight ways, producing 120

written words across the two hands.

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Scoring procedures and dependent measures. Thescoring procedures were similar to those for theunimanual task, with minor differences.

Static similarity to K.B.’s normal writing wasrated by 20 naive observers (13 women, 7 men;mean age 26.7 years, SD= 2.86), each of whomcompleted a scoring booklet of 20 A4 sheets.Figure 4b shows an example rating sheet. Thecentral standard word was always from the uniman-ual right hand forward condition, with six targetformats of the same word arranged around it. Thesix target formats were from the same hand (rightor left) and came from the six writing formats forthat hand (unimanual forward, unimanual reversed,bimanual forward perceptually congruent, biman-ual forward motorically congruent, bimanualreversed perceptually congruent, bimanual reversedmotorically congruent).

Dynamic similarity was rated according to thesame rules as those for the unimanual task, withthe experimenter (R.D.M.) unaware of whichwriting format he was rating. For each word, eachwriting format was compared against the standard(unimanual right hand forward).

Fluency cost was the time taken to write thetarget word minus the time taken to write the stan-dard, with writing time calculated from the onset ofthe first pen stroke to the offset of the last.

Predictions and analysis strategy. The bimanual taskincludes unimanual writing conditions, whichreplicate the critical upright conditions from theunimanual task. To test for replication of results,we conducted a repeated measures ANOVA, sep-arately for each dependent variable, by unimanualwriting condition (left reversed, left forward, rightreversed), with Huynh–Feldt corrections to thedegrees of freedom to compensate for violationsof sphericity. Planned contrasts were used tocompare left hand reversed writing against theother two formats.

The eight writing formats from the bimanualconditions provide a further exploration of K.B.’swriting abilities and allow an additional assessmentof the relative importance of perceptual and motorrepresentations. If a perceptual representation iscritical to performance, then the bimanual task

should be easier when the writing direction is thesame for the two hands, since a single perceptualrepresentation could guide performance. If effec-tor-relative motor plans are more important, thenperformance should be aided when the hands actin opposite directions. For each dependentmeasure, we conducted a repeated measuresANOVA by hand (left, right), direction (forward,reversed), and congruence (perceptual, motoric).The perceptual hypothesis predicts an effect ofdirection, such that forward writing is closest tothe standard, and an effect of congruence, suchthat perceptually congruent conditions are per-formed better (more fluently and/or more similarto the standard). The motor hypothesis predictsan interaction of hand by direction, such thatabductive writing (right hand forward, left handreversed) is closest to the standard, and a maineffect of congruence, such that motorically congru-ent conditions are performed better.

RESULTS

Unimanual writing task

Main analysis of upright formatsFigure 6 shows the mean scores for static simi-larity, dynamic similarity, and fluency cost ineach of the nonstandard writing conditions.Inferential analyses are restricted initially to theupright writing conditions (left panels); theinverted conditions (right panels) are includedfor descriptive purposes.

A repeated measures ANOVA by upright con-dition (left hand reversed, left hand forward, righthand forward) and trace visibility (visible trace, notrace) found a significant main effect of condition,for static similarity [F(2, 16)= 75.23, p< .0005;η2p= .90], dynamic similarity [F(1.88, 15.07)=14.20, p< .0005; η2p= .64], and fluency cost [F(2, 16)= 12.96, p< .0005; η2p= .62]. Plannedcontrasts confirmed that, for all three measures,left hand reversed writing was significantly closerto the standard than was left hand forward orright hand reversed writing (p< .005 in all cases).Trace visibility had no significant effect, nor

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significant interaction with condition (p≥ .15).These results are closely concordant with the pre-dictions of the motor hypothesis.

Supplementary analysis of right hand reversedwritingFigure 5b suggested that right hand reversedwriting could be produced by co-opting a low-level motor plan for left hand adductive writing.This is not a critical prediction of the motorhypothesis, which properly concerns mirrorwriting with the nondominant hand. Nonetheless,we explored whether K.B.’s right hand reversedwriting conforms to the scheme depicted inFigure 5b. To do this, we performed an analysisof dynamic similarity for upright writing, usingleft hand forward writing as the standard.1

The motor hypothesis predicts that right handreversed writing will be more similar to this stan-dard than will right hand forward or left handreversed writing. An ANOVA was performed byupright condition (right hand reversed, right handforward, left hand forward) and trace visibility(visible trace, no trace). Trace visibility had no sig-nificant influence either as a main effect or in inter-action (p > .68). The analysis of the effect ofcondition was compromised by a severe violationof sphericity, with consequent reduction in thedegrees of freedom, and the effect of conditionwas not significant [F(1.16, 9.25)= 3.05, p= .11;η2p= .28]. However, the pattern of means didqualitatively follow the predictions of the motorhypothesis, with right hand reversed writinghaving a higher mean dynamic similarity to theleft hand forward standard that did right handforward or left hand reversed writing (4.06 vs.3.28 and 2.89, respectively). This intermediateresult does not confirm, but neither does it ruleout, the motor account of K.B.’s right handreversed writing depicted in Figure 5b.

Supplementary analysis of inverted formatsFigure 6 indicates that inverted writing was alwaysmore dissimilar to the standard than was uprightwriting. The difference is most clear when consid-ering dynamic similarity, which takes account ofnot only the final shapes of the letters, but the

Figure 6. Unimanual task, average static similarity, dynamic

similarity, and fluency cost, relative to the right hand upright

forward standard, for each nonstandard writing format. The letter

(L or R) indicates the hand used, its orientation indicates the

writing format (forward/reversed and upright/inverted), and its

colour indicates visibility of trace (black for visible trace, grey for

no trace). The vertical side bar in each panel represents the

average standard deviation across the plotted conditions.

1 Although not reported last, this was the final analysis conducted. We did not include static similarity, because this would have

required recruitment of a further group of observers, and because prior analyses suggested that static similarity provides relatively

little unique information, over and above dynamic similarity.

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strokes by which they were produced. K.B.’sinverted writing thus bears scant resemblance tohis normal writing (see samples in Figure 3) andis produced by different pen strokes. However,this general dissimilarity is compatible with atleast two interpretations. First, K.B.’s invertedwriting might be produced in a manner similar tohis upright handwriting, but from a distinct high-level motor plan for inverted script. If so, althoughK.B.’s inverted writing is dissimilar to his uprightwriting, the pattern of similarities between hisformats of inverted writing should be like thoseobserved for the upright formats. An alternative,null hypothesis is that K.B.’s inverted writing issimply less consistently structured than hisupright writing, in which case there should be nospecific pattern of similarity between invertedformats.

A supplementary analysis of K.B.’s invertedwriting was performed to address this issue. Themethods of analysis followed those for the mainexperiment, with all words normalized digitally tothe canonical orientation prior to analysis. Staticsimilarity was derived from the subjective ratingsof 24 naïve observers (15 women, 9 men; meanage 28.8 years, SD = 4.05) each of whom com-pleted one rating sheet for each of the ninewords. On each sheet, the right hand invertedforward production was the standard, with alleight writing formats (two hands by two directionsby two visible trace conditions) as targets. Dynamicsimilarity was assessed by the rule-based compari-son of pen strokes between each nonstandardformat and the right hand forward standard.Fluency cost was the amount of extra time requiredto write each nonstandard format, relative to thestandard.

Figure 7 shows the mean scores for static simi-larity, dynamic similarity, and fluency cost in thenonstandard inverted writing conditions. We rana repeated measures ANOVA by inverted con-dition (left hand reversed, left hand forward, righthand reversed) and trace visibility (visible trace,no trace), with Huynh–Feldt corrections to thedegrees of freedom to compensate for violationsof sphericity, and planned contrasts to compareinverted left hand reversed writing against the

other two formats. The effects of writing conditionwere compatible with those observed for uprightwriting in the main experiment, with a significantmain effect for static similarity [F(1.92, 15.33)=

Figure 7. Unimanual task, average static similarity, dynamic

similarity, and fluency cost, relative to the right hand inverted

forward standard, for each nonstandard inverted writing format.

The letter (L or R) indicates the hand used, its orientation

indicates the writing format (forward/reversed and upright/

inverted), and its colour indicates visibility of trace (black for

visible trace, grey for no trace). The vertical side bar in each panel

represents the average standard deviation across the plotted

conditions.

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32.91, p< .0005; η2p= .80], dynamic similarity[F(1.76, 14.05)= 60.25, p< .0005; η2p= .88],and fluency cost [F(1.71, 13.66)= 10.29,p< .0005; η2p= .56]. Planned contrasts confirmedthat left hand reversed writing was significantlycloser to the standard than was left hand forwardor right hand reversed writing (p< .005), exceptin the case of fluency cost, for which left handreversed writing was not significantly faster thanright hand reversed writing (p= .14). In contrastto the main experiment, in which trace visibilityhad no significant effect, trace visibility did have asignificant influence on static similarity for invertedwriting [F(1, 8)= 6.29, p< .05; η2p= .44], withoverall greater similarity to the standard when thetrace was visible.

As for the upright formats, then, the effect ofinverted writing condition is consistent with amotor hypothesis, whereby inverted writing des-cends from a high-level motor plan for invertedscript, with left hand reversed writing producedby the sharing of an effector-level motor programfor right hand forward writing. It is worth empha-sizing that K.B. developed inverted writing only inmature adulthood and has given much less practiceto it than to his upright formats. The fact that themotor hypothesis is supported for inverted as wellas upright formats strengthens this hypothesis ingeneral and helps rule out the more prosaic possi-bility that the advantage seen for left hand reversedupright writing is simply due to this being K.B.’smost highly practised nonstandard script.However, the relative lack of practice with invertedscript may account for the improvement in staticsimilarity when visual feedback is available. K.B.’sability to produce consistent inverted scriptdepends partly on the ability to monitor perform-ance visually, suggesting a less automatic executionthan for upright formats.

Bimanual writing task

Figure 8 shows the mean scores for static similarity,dynamic similarity, and fluency cost in each of thenonstandard writing conditions of the bimanualtask. Unimanual conditions (left panels) were ana-lysed separately from bimanual (right panels).

The unimanual conditions were submitted toseparate repeated measures ANOVAs for eachdependent variable, finding a significant effect ofwriting condition for static similarity [F(2, 18)=20.47, p< .0005; η2p= .70], dynamic similarity [F(1.64, 14.79)= 3.89, p= .05; η2p= .30], andfluency cost [F(1.71, 15.38)= 8.12, p< .01;η2p= .47]. Planned contrasts confirmed that, forall three measures, left hand reversed writing wassignificantly closer to the standard than was lefthand forward writing or right hand reversedwriting (p< .05 in all cases), except that the com-parison with right hand reversed writing failed toreach significance for fluency cost (p= .06).Overall, the pattern of unimanual performancereplicates that obtained in the upright conditionsof the unimanual writing task (compare leftpanels between Figures 6 and 8) and further sup-ports the motor hypothesis.

The bimanual conditions were submitted, separ-ately for each dependent variable, to repeatedmeasures ANOVAs by hand (left, right), direction(forward, reversed), and congruence (perceptual,motoric). There was a slight superiority overall forthe right hand in terms of static similarity [F(1,8)= 6.79, p< .05; η2p= .46] and fluency cost [F(1, 8)= 9.48, p< .05; η2p= .54], modified by apowerful crossover interaction of hand and direc-tion that was significant for static similarity [F(1,8)= 91.11, p< .0005; η2p= .919], dynamic simi-larity [F(1, 8)= 27.27, p< .005; η2p= .77], andfluency cost [F(1, 8)= 56.30, p< .0005;η2p= .88]. For the right hand, forward writingwas more similar to the standard than was back-ward writing, but this was reversed for the lefthand.

The main effect of congruence was also signifi-cant for static similarity [F(1, 8)= 9.02, p< .05;η2p= .53], dynamic similarity [F(1, 8)= 19.98,p< .005; η2p= .71], and fluency cost [F(1, 8)=20.87, p< .005; η2p= .72], confirming better per-formance when the hands moved in environmen-tally opposite directions, despite the fact thatthese trials required the production of perceptuallyincongruent words. Figure 8 suggests that theadvantage for motorically congruent conditions(black symbols) was greatest, at least for dynamic

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similarity and fluency cost, when the right handwrote forward and the left hand reversed. Thiswas confirmed by a significant three-way inter-action of hand by direction by congruence for

dynamic similarity [F(1, 8)= 37.21, p< .0005;η2p= .82] and fluency cost [F(1, 8)= 23.53,p< .005; η2p= .75]. This pattern suggests aspecial facilitation of K.B.’s mirror-writing abilitywhen the left hand could simultaneously mirrorthe right hand’s normal writing movements.

As an aside, visual comparison of correspondingwriting formats between the unimanual and biman-ual panels of Figure 8 suggests an interestingpattern. For static similarity, K.B.’s writing in eachcondition was rated as closer to the standard whenhe wrote unimanually than when he wrote bimanu-ally. This general unimanual advantage might arisebecause K.B. can produce a neater product whenhe can concentrate on writing in just one place at atime. By contrast, no general unimanual advantageis seen in terms of the sequence of pen strokes(dynamic similarity) or the fluency of their pro-duction (fluency cost). For these measures, theremay instead be a specific facilitation of left handmirror writing under bimanual motorically congru-ent conditions. Thus, even for K.B., a highly prac-tised mirror-writer, writing backward with the lefthand may be most natural when writing simul-taneously forward with the right. He reports thisas his subjective experience, as do many peoplewho try mirror writing in unimanual and bimanualconfigurations (e.g., Allen, 1896).

DISCUSSION

K.B. is a mirror-writer of exceptional skill who,across more than 50 years, has developed thisability more completely than any person previouslydocumented. He writes forward or backwardsscript, upright or inverted, with either hand, andhe can do this unimanually and in diverse bimanualcombinations. We have assessed K.B.’s single wordwriting, across his eight unimanual scripts, withand without vision of the pen trace, and forupright script across bimanual combinations. Ourfocus has been on the similarity of each format toK.B.’s normal forward handwriting, in terms ofthe appearance of the writing, the sequence ofpen strokes, and the speed of execution. Here, werelate our findings to earlier anecdotal descriptions

Figure 8. Bimanual task, average static similarity, dynamic

similarity, and fluency cost, relative to the unimanual right hand

upright forward standard, for each nonstandard writing format.

The letter (L or R) indicates the hand used, its orientation indicates

the writing format (forward/reversed and upright/inverted). For

the bimanual conditions, symbol colour indicates congruence (black

for motorically congruent, and grey for perceptually congruent). The

vertical side bar in each panel represents the average standard

deviation across the plotted conditions.

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of deliberate mirror writing and to theories of thephenomenon.

It seems likely that K.B. is a natural left handerwho was schooled to write with the right hand,giving incomplete left hand dominance. If so, thisis a history he shares with the four cases mentionedby Smetacek (1992), and possibly also with LewisCarroll (Schott, 1999). As noted in theIntroduction, a degree of ambidexterity may be aprerequisite for skilled mirror writing, since eitherhand needs sufficient dexterity for legible writing.Also in common with prior descriptions of deliber-ate mirror writing (e.g., Allen, 1896; Smetacek,1992), and despite his extensive experience of mir-rored text, K.B. has no special facility for mirrorreading. If he had enhanced access to perceptualrepresentations of mirrored letters and words,then such text should be easily decipherable forhim; on the contrary, his attempts to read mirror-reversed text ended in frustration. This makes aperceptually based interpretation of his mirrorwriting unlikely. K.B.’s performance in our hand-writing tasks reinforces this conclusion, asdescribed below.

The central finding is that K.B.’s left handupright mirror writing has a privileged status,being significantly more similar to his normalwriting than is any other nonstandard format,including forward writing with the left hand. Thisresult thus undermines the claim, long cited as aprime example of motor equivalence, that aperson’s forward handwriting style is invariantacross effectors (Merton, 1972; Raibert, 1977; cf.Wright, 1990). Deeper equivalence may requirethat handwriting actions can share a lower level,effector-relative motor representation (Figure 5).The privileged status of left hand reversed writingis consistent with the idea that “true” mirrorwriting derives from nondominant hand executionof motor programs for abductive handwritingdeveloped by the dominant hand.

One possible counterargument might be thatleft hand reversed writing is advantaged justbecause it is K.B.’s earliest and most familiarformat of nonstandard script. However, a sup-plementary analysis of K.B.’s inverted script like-wise found that the left hand reversed format

most closely resembles the right hand forwardformat, even though none of K.B.’s invertedwriting is particularly similar to his normal hand-writing. His inverted writing is presumablyguided by a distinct high-level representation forinverted script, but the left hand mirrored formatmay nonetheless be produced by co-opting a low-level right hand abductive motor plan. The factthat this pattern obtains even for a format ofmirror writing that K.B. did not develop until hislate 30s suggests that mere practice and familiaritycannot explain it. In any case, the argument frompractice seems to confuse cause and effect: Lefthand upright reversed writing is surely the earliestformat precisely because of its privileged status, asattested by the strong association of mirrorwriting, deliberate and involuntary, with the non-dominant hand (Critchley, 1927, 1928; Della Sala& Cubelli, 2007; Schott, 2007).

K.B.’s performance also accords with Allen’s(1896) observation that left hand mirror writing isnot much helped by vision. In our tasks, we didnot manipulate vision of the hand itself, butvaried the visibility of the word written. Thevisible trace condition might be expected to aidmirror writing disproportionately if mirror writingis guided by a reversed perceptual representationof how the word should look. In fact, trace visibilityconferred no differential advantage for mirrorwriting, offering no support for this idea.Nonetheless, trace visibility did significantlyenhance static similarity of inverted writing ingeneral, suggesting that visual feedback allowedK.B. to achieve greater consistency of shape inthis relatively unpractised task.

In the bimanual task, we pitted perceptualfactors directly against motor, requiring the twohands to write the same word in the same or inopposite directions (Table 1). If the perceptual rep-resentation is critical, then this task should be easierwhen the writing direction is the same, since asingle representation can guide both actions. Ifmotor factors are critical, then the task should beeasier when the hands act in opposite directions,since the actions are motorically congruent.Motoric congruence strongly dominated thequality of bimanual performance, consistent with

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a motor basis for mirror writing. Figure 8 suggeststhat K.B.’s left hand mirror writing in the motori-cally congruent condition may even be slightlybetter than his unimanual mirror writing, at leastin terms of dynamic similarity and fluency cost.This accords with the common experience ofnon-mirror-writers who try the task; people oftenfind it easier to mirror write (for instance) theirname backward with the left hand, if they simul-taneously write it forward with the right. It maybe that we can take advantage of an automatic ten-dency toward mirror-symmetrical movements ofopposite limbs to piggy-back left hand perform-ance upon established forward writing habits.Indeed, K.B. himself first discovered left handmirror writing in childhood via this bimanualtechnique.

The clear primacy of K.B.’s left hand mirrorwriting, the relative unimportance of visual feed-back, and the beneficial effect of motoric congru-ence in bimanual conditions are all consistentwith a motor rather than a perceptual basis formirror writing. Here, we have framed the motorhypothesis in terms of a motor control hierarchy,interpreting increased similarity between formatsto reflect a shared representation at a relativelylow level of the hierarchy (Wright, 1990). Thisupdating of the classical motor hypothesis(Critchley, 1928; Erlenmeyer, 1879, cited inCritchley, 1928; Vogt, 1880) provides a con-venient framework for deriving clear predictionsin the present study. However, as flagged in theintroduction, motor accounts of mirror writingtake various forms, so there may be more thanone motor account that could be consistent withour data.

For instance, Corballis and Beale (1970, 1976)have suggested that the right hemisphere containsmirror-reversed motor engrams for writing, laiddown automatically by interhemispheric transferof forward writing plans. These reversed planswould be available most directly to the left handwhich could account for the primacy of left handmirror writing. In this scheme, a possible linkbetween mirror-writing ability and non-right-handedness might be explained by enhancedcallosal function amongst non-right handers

(Haberling, Badzakova-Trajkov, & Corballis,2011), aiding the establishment of reversedmotor patterns between hemispheres. An alterna-tive idea is that motor plans for writing arestored separately from information about thecorrect direction of execution, and that there isan innate preference for abductive movements ofthe limbs (Della Sala & Cubelli, 2007). Thisabductive preference might selectively advantagethe right hand forward and left hand backwardformats, consistent with K.B.’s generally fasterabductive writing in the present study. Our datastrongly favour a motor hypothesis over a percep-tually based account, but further work will benecessary to distinguish between alternativemotor hypotheses.

This investigation is one step toward an objec-tive account of deliberate mirror writing. It con-cerns one notable individual whom we hope isrepresentative of the phenomenon. Overall, K.B.’s skilled mirror writing seems like an elaboratedversion of that described subjectively by F. J. Allenin 1896. Both men have sufficient ambidexterityfor skilled writing with either hand, and neitherobtains special benefit from visual monitoring ofthe mirror-writing act, nor finds it easy to mirrorread. Allen’s abilities were confined largely to mir-roring with the left hand, whereas K.B.’s havebeen practised to include bidirectionaland inverted writing with either hand.Notwithstanding these embellishments, K.B.’sleft hand mirror writing retains privileged status;all of his other formats pale by comparison. Ourinterpretation has been that “true” mirror writingis indeed confined to the nondominant hand andthat it reflects the sharing of low-level motor pat-terns associated with the dominant hand.However, other motor accounts of deliberatemirror writing are possible, and further exper-iments will be required to disentangle these andto assess whether they can also be applied to invo-luntary mirror writing after brain damage. Finally,it remains to be seen whether or not there isanything neurologically unusual about skilleddeliberate mirror-writers, beyond a degree ofambidexterity and a curiosity about their ownabilities.

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Manuscript received 11 September 2012

Revised manuscript received 20 January 2014

Revised manuscript accepted 20 January 2014

First published online 5 March 2014

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