Borovik A. Shadows of the Truth: Metamathematics of Elementary Mathematics

Подождите немного. Документ загружается.

References 235

229. F. Viéte, The Analytic Art. Translated b y T. Richard Witmer. Kent,

Ohio: The Kent State University Press, 1983.

230. J. Vincent and C. Vincent, Japanese temple geometry, Austr. Senior

Math. J. 18 no. 1 (2004), 8–20.

Psychology, Psychophysiology, Cognitive Sci-

ence, Linguistic, and Artiﬁcial Intelligence

231. E. Abravanel , The development of intersensory pattering with re-

gard to selected spatial dimensions. Monographs of the Society for

Research in Child Development 33, 2 whol e no. 11 8 (1968).

232. A. Achim and M. Corballis, Mirror-image equivalence and the ante-

rior commissure. Neuropsychologia 15 (1977), 475–788.

233. J. W. Adams, and G. J. Hitch, Working memory and children’s mental

addition. J. Exp. Child Psychology 67 (199 7), 21–38.

234. G. L. Allen, Children’s control of reference systems in spatial tasks:

Foundations of spatial cognitive skill? Spat. Cogn. Comput. 1 (1999),

413–429.

235. F. J. Allen, Mirror writing. Brain 19 (1896), 385–387. DOI: 10.1093/

brain/19.2-3.385.

236. M. H. Ashcraft and B. A. Fierman, Mental addition in third, fourth

and s ixth graders. J. Experimental Chi ld Psychology, 33 (1982), 216–

234.

237. M. H. Ashcraft and J. A. Krause, Working memory, math perfor-

mance, and math anxiety, Psychonomic Bulletin & Review 14, no.

2 (2007), 243–248.

238. L. Atkins, A radical treatment for obsessive-compulsi ve dis-

order patients, The Guardian, 1 2 December 2009. http:

//www.guardian.co.uk/lifeandstyle/2009/dec/15/

obsessive-complusive-disorder-gamma-knife, accessed

15 December 2009. Author’s proﬁle: http://www.guardian.co.

uk/profile/lucy-atkins.

239. J. Atkinson, F. W. Campbell, and M. R. Francis, The magic number

4 ± 0: A new look at vi sual numerosity judgements, Perception 5, no.

3 (1976), 327—334.

240. P. L. Ayres, Systematic mathematical errors and cognitive load. Con-

temporary Educational Psychology 26 (200 1), 227–248.

241. J. D. Balakrish nan and F. G. Ashby, Is subitizing a unique numerical

ability, Perception and Psychophysics 50 (199 1), 555–564.

242. S. Balfour, S. Borthwick, R. Cub el li, and S. Della Sala, Mirror writing

and reversing single letters in stroke patients and normal elderly. J.

Neurol. 254 (2007), 436 –441. DOI: 10.1007/s00 415-006-0384-8.

243. S. Baron-Cohen, P. Bolton, S. Wheelwright, V. Scahill, L. Short, G.

Mead, and A. Smith, Autism occurs more often in families of physi-

cists, engineers, and math emati cians, Autism 2 (1998), 296–301.

244. S. Baron-Cohen, The Essential Difference. The Truth about the

Male and Female Brain. Bas ic Book, New York, 2003.

245. J. Barth and J. Call, Tracking the displa cement of objects: A s eries of

studies with great apes and young children. J. Exp. Psychol. Anim.

Behav. Process. 32 (2006), 239–252.

246. G. Basso, P. Nicheli, F. Frasinetti , and G. di Pellegrino, Time percep-

tion in a neglected space. Neuroreport, 7 (1996), 2111

U–2114.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

236 References

247. D. B. Berch, E. J. Foley, R. J. Hill, and P. M. Ryan, Extracting par-

ity and magnitude from Arabi c numerals: Developmental changes

in number processing and mental representation. J. E xperimental

Child Psychology, 74 (1999), 286–308.

248. L. Boroditsky, Metaphoric structuring: understanding time through

spatial metaph ors. Cognition 75 (2000), 1–28.

249. L. Boroditsky, Does language shap e thought? English and Mandarin

speakers’ conceptions of time. Cognitive Psychology 43 no. 1 (2001),

1–22.

250. L. Boroditsky an d M. Ramscar, T he roles of body and mind in abstract

thought. Psychological Science 13 (2002) 185–188.

251. E. M. Brannon, The d evelopment of ordinal numerical knowledge in

infancy, Cognition 83 (20 02), 223–240.

252. G. Bremner, Space from infantŠs point of view. Bull. Br. Psychol. Soc.

31 (1978), 164.

253. G. Briggs and R. Nebes, Patterns of hand preference in a student

population. Cortex 11 (1975) 230–238.

254. P. Bryant, C. Christie, and A. Rendu, Chil dren’s understanding of the

relation between addition and s ubtraction: Inversion, identity and

decomposition. J. Experimental Child Psychology 74 (1999), 194–212.

255. P. Bryant and S. Squire, T he inﬂuence of sharing on children’s initial

concept of di vision, J. Exper. Child Psych. 81, no. 1 (Jan. 2002), 1–43.

256. V. V. Burdakov and E. B. Lyubchinskii, A rare case of “mirror writ-

ing”, Neuroscience and Behavioral Physiology 31 no. 2 (200 1), 169–

170.

257. L. J. Buxbaum, H. B. Coslett, R. R. Schall, B. McNally, and G. Gold-

berg, Hemispatial factors in mirror writing. Neuropsychologia 31

(1993), 1417–1421

258. J. F. Cantlon, S. Cordes, M. E. Libertus, and E. M. Brannon, Com-

ment on “Log or linear? Distinct intuitions of the number scale in

Western and A maz onian indigene cultures.” Science, 323 (2009), 38.

259. L. Carmichael and H. Cash man, A study of mirror writing in relation

to handedness and perceptual and motor habits. J. Gen. Psychol. 6

(1932), 296–329.

260. M. Carr, J. Alexander, and T. Folds-Bennett, Metacognition and

mathematics strategy use. Applied Cognitive Psychology 8 (1994),

583–595.

261. D. Casasanto, Similarity an d proximity: When does close in sp ace

mean close in mind? Memory an d Cognition, 36 no. 6 (2008), 1047–

1056.

262. D. Casasanto and L . Boroditsky, . Time in the mind: Using space to

think about time. Cognition 106 (2008), 579 –593.

263. D. Casasanto, O. Fotakopoulou, and L. Boroditsky, Space and time

in the childŠs mind: Evidence for a cross-dimensional asymme-

try. Cogni tive Science 34 ( 2010), 387–405. DOI: 10.1111/j.1551-

6709.2010.01094.x.

264. J.-L. Cha n and E. Ross, Left-h anded mirror writing following right

anterior cerebral artery infarcti on: evidence for non-mirror transfor-

mation of motor programs by ri ght s upplementary motor area. Neu-

rology 38 (1988), 59–63.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

References 237

265. K. Cheng and N. S. Newcombe, Is there a geometric module for spa-

tial orientation? Squaring theory and evidence. Psychonomic Bulletin

and Review 12, no. 1 (200 5), 1–23.

266. K. F. Condry and E. S. Spelke, The development of language and a b-

stract concepts: The case of natural number. J. Exp. Psych.: General

137 (2008) , 22–38.

267. M. Corball is and I. Beale, The Psycho lo gy of Left and Right. Lon-

don: Lawrence Erlbaum, 1976.

268. J. M. Cornell, Spontaneous mirror-writing in children. Can. J. Psy-

chol. 3 (1985), 174–179. DOI: 10.1037/h0080122.

269. N. Cowan, The magical number 4 in short-term memory: a reconsid-

eration of mental storage cap acity. Behavioral and Brain Sci. 24, no.

1 (2001), 87–154.

270. R. Cubelli and S. Della Sala, Mirror writing in pre-school children: a

pilot study, Cogn. Process 10 (2009), 101–104. DOI: 10.1007/s10339-

008-0233-z.

271. M. Curd, Showing and telling: Can the difference between right and

left be explained in words? Ratio 26 (1984), 63–66.

272. J. Davidoff and E. K. Warrington, A particular difﬁculty in discrim-

inating between mirror i ma ges. Neuropsychologia 39 (2001), 1022–

1036. DOI:10.1016/S00 28-3932(01)00039-2.

273. M. D. de Hevia, L. Girelli, E. Bricolo, and G. Vallar, The representa-

tional space of numerical magnitude: Illu sions of length. Quarterly J.

Experimental Psychology, 61 (2008), 149 6–1514.

274. M. D. de Hevia and E. S. Spelke, Spontaneous mapping of number

and space in adults and young children. Cognition, 110 (200 9), 198–

207.

275. M. D. de Hevia and E. S. Spelke, Number-space mapping in hu-

man infants, Ps ychological Science, published onli ne 19 March

2010. DOI: 10.1 177/0956797610366091. http://pss.sagepub.

com/content/early/2010/03/19/0956797610366091.

276. M. D. de Hevia, G. Vallar, and L. Girelli , Visualizing numbers in the

mind’s eye: The role of visuo-spatial processing in numerical abilities.

Neuroscience and Biobehavioral Reviews, 32 ( 2008), 1361–1372.

277. S. Dehaene, Varieties of numerical abilities. Cognition 44 (1992), 1–

42.

278. S. Dehaene, The Number S ense. Penguin Books, 20 01.

279. S. Dehaene, The neural basis of the Weber-Fechner law: A logarith-

mic mental number line, Trends in Cognitive Sci . 7 (2003), 145–147.

280. S. Dehaene, S. Bossini, and P. Giraux, The mental representation

of parity and number magnitude. J. Exp. Psychology: General 12

2(1993), 371–396.

281. S. Dehaene and J .P. Changeux, Development of elementary numer-

ical abi lities: A neuronal model, J. Cognitive Neuroscience 5 (1993),

390–407.

282. S. Dehaene, V. Izard, P. Pi ca, and E. S. Spelke, Log or linear? Distinct

intuitions of the number scale in Western and Amaz onian indigene

cultures. Science, 320 (2008), 1217–1220 .

283. S. Dehaene, V. Izard, P. Pica, and E. S. Spelke, Response to comment

on, “Log or linear? Distinct intuiti ons of the number scale in Western

and Amazonian indigene cultu res.” Science, 323 (2009), 38.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

238 References

284. S. Dehaene, M . Piazza, P. Pinel and L. Cohen, Three parietal cir-

cuits for number processing, Cognitive Neuropsychology 20 (3–6)

(2003)487–506.

285. S. Dehaene, E. Spelke, P. Pinel, R. Stanescu, and S. Tsivkin, Sources

of mathematical thinking: Behavioral and brain-imaging evidence.

Science 284 (1999), 970–974.

286. S. Della Sala and R. Cubelli, “Directional ap raxia”: a unitary ac-

count of mirror writing foll owing brain injury or as found in nor-

mal young children. J. Neuropsychol. 1 (2007),3–26. DOI: 10.1348 /

174866407X180783.

287. D. Delis, L. Robertson, and R. Efron, Hemispheric specia lization of

memory for visual hierarchical stimuli. Neuropsychologia 24 ( 1986),

205–214.

288. Y. Dong, H. Fu kuyama, M. Honda, T. Okada, T. Hanakawa, K. Naka-

mura et al. Essential role of the right superior parietal cortex in

Japanese kana mirror reading: an FMRI study. Brain 123 (2000),

790–799.

289. N. J. Enﬁeld, The body as a cognitive artifact in kinship representa-

tions. Current Anth ropology 46 no. 1 (2005), 51 –81.

290. G. Ettlinger and A. Elithorn, Transfer between the h ands of a mirror-

image tactile shape discrimination. Nature 1 94 (1962), 1101–1102.

291. R. Falk, Inﬁnity: a cognitive challenge, Theory and Psychology 4 no.

1 (1994), 35–60. DOI: 10.1177/0959354394041002.

292. M. W. Faust, M. H. Ashcraft, and D. E . Fleck, Mathematics anxiety

effects in simple and complex addition, Mathematical Cognition 2

(1996), 25–62.

293. L. Feigenson, S. Carey, and M. Hauser, The representations under-

lying i nfants’ choice of more: Object-ﬁles versus analog magnitudes.

Psychological Science 13 (20 02), 150–156.

294. L. Feigenson, S. Dehaene, and S. Spelke, Core systems of number.

Trends in Cognitive Sciences 8 (2004), 307– 314.

295. T. Feinberg and G. Jones, Object reversals after parietal lobe

infarction—a case report. Cortex 21 (1985), 261 –271.

296. F. Fischer, I. Liberman, and D. Sh ankweiler, Reading reversals and

developmental dyslexia: a further study. Cortex 14 (1978), 496–510.

297. J. Flavell, Cognitive Development: Children’s Knowledge About the

Mind. Annu. Rev. Psychol. 50 (1999), 21–45.

298. J. Freyd and B. Tversky, The force of symmetry in form perception.

Amer. J. Psychology 97 (1984), 109–126.

299. A. J. Fürst and G. J. Hitch, Separate roles for executive and phonolog-

ical components of working memory in mental arithmetic. Memory

and Cognition 28 (2000), 774–782.

300. M. Gaf fron, Right and left in pictures, Art Quarterly 13 (1950), 312.

301. C. R. Gallistel, Language and spatial frames of reference in mind a nd

brain. Trends in Cognitive Sciences 6, no. 8 (2002) , 321–22.

302. C. R. Gallistel and R. Gelman, Preverbal and verbal counting and

computation, Cognition 44 (1992), 43–74.

303. C. R. Gallistel and R. Gelman, Non-verbal nu merical cognition: From

reals to integers. Trends in Cognitive Science 4 (2000), 5 9–65.

304. W. R. Garn er, Interaction of stimulus dimensions in concept and

choice processes. Cognitive Psychology 8 (1976), 98–123.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

References 239

305. D. C. Geary, C. C. Bow-Thomas, L. Fan, and R. S. Siegler, Even before

formal instruction, Chinese children outperform American children

in mental additi on. Cognitive Development 8 (1993), 517–529.

306. D. C. Geary and S. C. Brown, Cognitive addition: Strategy choice and

speed-of-processing differences in gifted, normal and mathematically

disabled children. Developmental Psychology 27 (1991), 39 8–406.

307. R. Gelman and C. R. Gallistel, The Child’s Understanding of

Number. Harvard University Press, 1978.

308. R. Gelman an d C. R. Gallistel, Lan guage and the origin of numerical

concepts. Science 306 (2004), 441–443.

309. S. P. Gennari, S. A. Sloman, B. C. Malt, and W. T. Fitch, Motion events

in language and cognition. Cognition 83, no. 1 (2002), 49–79.

310. D. Gentner, M. Imai, an d L. Boroditsky. As time goes by: Evidence

for two systems i n processing space!time metaphors. Language and

Cognitive Processes 17 no. 5 (2002), 537–56 5. DOI: 10.1080/01690960

14300031 7.

311. R. W. Gi bbs, Why many concepts are metaphorical. Cognition 61

(1996), 309–319.

312. R. Goebel, D. Lin d en, H. L anfermann, F. Zanella, and W. Singer,

Functional imaging of mirror and inverse reading reveals s eparate

coactivated networks for occulomotion and spatial transformations.

Neuroreport 9 (1998), 71 3–719.

313. S. Goldin-Meadow, Hearing Gesture: How Our Hands Help Us

Think. Harvard University Press, C ambridge, MA, 2003.

314. S. Goldin-Meadow, M. W. Alibali, and R. B. Church, Transitions in

concept acquisi tion: Using the hand to read the mi nd. Psychological

Review 100 (1993), 279–297.

315. S. Goldin-Meadow, S. Kim, and M. Sin ger, What the teacher’s hands

tell the student’s mind about math. J. Ed. Psychology, 91 (1999), 720–

730.

316. S. Goldin-Meadow, H. N usbaum, S. D. Kelly, and S. Wagner, Ex-

plaining math: Gesturing lightens the load . Psychological Science 12

(2001), 516–522.

317. S. Goldin-Meadow and M. A. Singer, From children’s hands to adul ts’

ears: Gesture’s role in teaching and learning. Developmental Psychol-

ogy 39 (200 3), 509–520.

318. A. Gopnik, The Philosophical Baby: What Children’s Minds Tell

Us About Truth, Love, and the Meaning of Life. Farrar, Straus

and Giroux, 2009, 28 8 pp.

319. J. A. Gottfried, F. Sancar, and A. Chatterjee, Acquired mirror writ-

ing and readi ng: evidence for reﬂected graphemic representations.

Neuropsychologia 41 (2003), 96–107. DOI:10.1016/S0028-3 932(02)

00130-6.

320. E. L. Grigorenko, Developmental dyslexia: An update on genes,

brains, a nd environments, J. Chi ld Psych. and Psychiatry 42, no. 1

(2001), 91–125. DOI: 10.1017/S0 02196 3001006564.

321. C. G. Gross and M. H. Bornstein, Left and right in science and Art,

Leonardo 11 (19 78), 29–38.

322. M. A. K. Halliday, Aspects of sociolinguistic research, UN-

ESCO, Paris, 1974. A survey paper prepare d for Sympo sium

on the Interactions Between Linguistics and Mathematical

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

240 References

Education, Nairobi, Sept. 1–11, 1974. UNESCO document ED-

74/CONF.808/COL.7. Paris: U N E SCO, 1975.

323. M. S. Hamann and M. H. Ashcraft, Textbook presentations of the

basic addition facts. Cognition a nd Instruction, 3 (1986), 173–192.

324. D. B. M. Hau n, J. Ca ll, G. Janzen, and S. C. Levinson, Evolutionary

psychology of spatial representations in the hominid ae. Current Bi-

ology 16 (2006), 1 736–1 740. DOI: 10.1016/j.cub.2006.07.049.

325. D. B. M. Haun, C. J. Rapold, J. Call, G. Janzen, and S. C. Levinson,

Cognitive cladistics and cultural override in hominid spatial cogni-

tion. Proceedings of the Nati onal Academy of Sciences USA 103 no.

46 (2006), 17568–17573.

326. S. A. Hecht, Counting on working memory in simple arithmetic

when counti ng is used for problem solving. Memory and Cognition

30 (2002), 447–455.

327. K. M. Heilman, G. Howell, E. Valenstein, and L. Rothi, Mirror-

reading and writing in association with right-left spatial disorien-

tation. J. Neurol. Neurosurg. Psychiatry 43 (1980), 774–780.

328. J. Henrich, S. J. Heine, and A. Norenzayan. The weirdest people in

the world? Behavioral and Brain Sciences 33 (2010), 61–135. DOI:

10.1017/S0140525X0999152X.

329. A. Herskovits, Langua ge and Spatial Cognition. Cambridge

University Press, 1986. ISBN-10: 05211091 83. ISBN-13: 978-

0521109185.

330. I. D. Holloway and D. Ansari, Mapping numerical magnitudes onto

symbols: The numerical distance effect and individual di f ferences in

children’s math achievement, J. Experimental Child Psychology 103

(2009), 17–29.

331. H. C. Hughes, Sensory Exotica: a World Beyond Human E xpe-

rience. C ambridge, MA: MIT Press, 1999.

332. B. Inheld er and J. Piaget, Mental imagery in the child. New York:

Basic Books, 1971.

333. V. Izard, C. Sann, E. S. Spelke, and A. Streri, Newborn infants per-

ceive abstract numbers. Proc. Nat. Acad. Sci. 106 (2009), 10382–

10385.

334. K. E. Jordan and E. M. Brannon, T he multisensory representation of

number in infancy. Proc. Nat. Acad. Sci. 103 (2 006), 3486–3489.

335. K. Lander, A. Bevan, and B. Butterworth, Developmental dyscalcu-

lia and basic numerical capacities: A study of 8–9 year old students,

Cognition 93 (2004), 99–125.

336. M. Lambon-Ralph, C. Jarvis, and A. Ellis, Li f e in a mirrored world:

report of a case showing mirror reversal in reading and writing and

for non-verbal materials. Neurocase 3 ( 1997), 249 –258.

337. J. Lave, Cognition in Practice: Mind, Mathematics and Culture

in Everyday Life. Cambridge Universi ty Press, N ew York, 1988.

338. M. LeCorre a nd S. Carey, One, two, three, four, nothing more: An

investigation of the conceptual sources of the verbal counting princi-

ples. Cognition 105 (20 07), 395–438.

339. What counts in the development of young children’s number knowl-

edge? S. C. Levine, L. W. Suriyakham, M. L. Rowe, J. Huttenlocher,

and E. A. Gunderson, Developmental Ps ychology 46 no. 5 (Sep 201 0),

1309–1319. DOI: 10.1037/a0019671.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

References 241

340. P. Li and L. Gleitman, Turning the tables: language and spatial rea-

soning, Cognition 83, no. 3 (2002), 26 5–294 .

341. J. S. Lipton and E. S. Sp el ke, Origins of number sense: Large number

discrimination in human infants. Psychological Science, 14 (2003),

396–401.

342. A. Majid, M. Bowerman, S. Kita, Daniel B.M. Haun, an d S. C. Levin-

son, Can language restructure cognition? The cas e for space. Trends

in Cognitive Sci. 8, no. 3 (2004), 108–114.

343. B. Malt, S. Sloman, and S. Gennari, Universality and language speci-

ﬁcity in object naming. J. Memory and Language 49, no. 1 (2003),

20–42.

344. I. Mathewson, Mirror writing ability is genetic and probably trans-

mitted as a sex-linked dominant trait: it is hypothesised that mirror

writers have bilateral language centres with a callosal in terconnec-

tion. Med. Hypotheses 62 no. 5 (2004), 733–739.

345. T. Matlock, M. Ramscar, and L. Boroditsky, On the experiential link

between spatial and temporal language, Cognitive Science 29 (2005)

655–664.

346. M. G. McGee, Human spatia l abilities: Psychometric studi es and en-

vironmental, genetic, hormonal, and neurological inﬂuences. Psycho-

logical Bulletin, 86 (1979), 889–918.

347. M. S. McGlone and J. L. Harding, Back (or forward?) to the future:

The role of perspective in temporal language comprehension. J. Ex-

perimental Psychology: Learning, Memory, and Cognition 24 (1998),

1211–1223.

348. B. M cNaughton, L . Chen, and E. Markus, ‘Dead reckoning’, land-

mark learning and the sense of direction: a neurophysiological and

computational hypothesis. J. Cognitive Neuroscience 3 no. 2 (1990),

191–202.

349. B. P. Meier and M. D. Robins on, Why the sunny side is up. Associ-

ations between affect a nd vertical position. Psychological Science 15

(2004), 243–247.

350. N. K. Mello, Mirror image reversal in pigeons. Science 149 (1965),

1519–1520.

351. E. R. Michener, Understanding understanding mathemati cs. Cogni-

tive Science, 2 (1978), 361–383.

352. K. S. Mix, Preschoolers’ recognition of numerical equivalence: Se-

quential sets. J. Experimental Child Psychology, 74 (199 9), 309–332.

353. K. S. M ix, The construction of number concepts. Cognitive Develop-

ment 17 (2002), 1 345–1 363.

354. K. S. Mix, J. Huttenlocher, and S. C. Levine, Do preschool children

recognize auditory-visual numerical correspondences? Child Devel-

opment 67 (1996), 1592–1608.

355. A. Muir, The psychology of mathematical creativity, Math. Intelli-

gencer 10, no. 1 (1988), 33–37.

356. E. Munnich, B. Land au, and B. Dosher, Spatial language a nd s pa-

tial representation: A cross- linguistic comparison. Cognition 81 no. 3

(2001), 171–207.

357. G. L. Murphy, On metaphoric representation. Cognition 60 (1996),

173–204.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

242 References

358. J. Noble, Mirror-images and the forebrain commisure of the monkey.

Nature 211 (1966), 1263–1266.

359. J. Noble, Paradoxical interocular transfer of mirror-image discrim-

inations in the optic chiasm sectioned monkey. Brain Res ea rch 10

(1968), 120–126.

360. R. Núnez, Do real numbers really move? Language, thought and ges-

ture: the embodied cogniti ve foundations of mathematics. In: 18 Un-

conventional Essays on the Nature of Mathematic s (R. Hersh,

ed.). Springer, 2 005, pp. 160–181.

361. R. Núnez and E. Sweetser, Looking ahead to the past: Convergent

evidence from Aymara language and gesture in the crosslinguistic

comparison of spatial construals of time. Cognitive Science 30 no.

3(2006), 401–450.

362. D. R. Olson, Cognitive Development: The Child’s Acquisition

of Diagonality. Lawrence Erlbaum As sociates Inc., 1996. ISBN-10:

0805823026. ISBN-13: 978-0805823028.

363. A. Ortony, Why metaphors are necessary and not just n ice. Educa-

tional Theory, 25 (19 75), 45–53.

364. W. Paradowski and M. Ginzgerg, Mirror writing and hemipl egia. Per-

ceptual and Motor Skills 32 (1971), 617–618.

365. J. Piaget and B. Inhelder, The Child’s Perception of Space . Rout-

ledge and Kegan Paul, 1956.

366. J. Piaget, Genetic Ep istemology, Columbia University Press, 1970.

ISBN-10: 02310338 69. ISBN-13: 978-0231033862.

367. J. Piaget, Possibility and Necessity , University of Minnesota

Press, 1987. ISBN-10: 0816613680. ISBN-13: 978-08166 13687.

368. P. Pinel, D. Piazza, D. Le Bihan, and S. Dehaene, Distributed and

overlapping cerebral representations of number, size, and luminance

during comparative judgments. Neuron, 41 (2004), 1–20.

369. S. Pinker, How the Mind Works. Norton, New York, 1997.

370. V. Ramachandran, The Emerging Mi nd. P roﬁle Books, 2005. ISBN

1-86197-303-9.

371. F. R estle, Speed of adding and comparing numbers. J. E xperimental

Psychology, 83 (1970), 274–278.

372. S. K. Revkin, M. I. Piazza, L. Cohen, and S. Dehaene, Does subitizing

reﬂect numerical estimation? Psychological Science 19 (2008), 607–

614.

373. I. Rock, Orientation and Form. Acad emic Press, 1973. ISBN 0-12-

591250-1.

374. R. Rodriguez, M. Aguilar, and G. Gonzalez,. Left non-dominant hand

mirror writing. Brain and L anguage 37 (1989), 122–144.

375. E. Rusconi, B. Kwan, B. Giordano, C. Umilta, and B. Butterworth,

Spatial representation of pitch height: The SMARC effect. Cognition

9 (2006), 113–129.

376. J. Sauvy and S. Suavy, The Child’s Discovery of Spac e: From

Hopscotch to Mazes—An Introduction to Intuitive Topol-

ogy. Penguin Books, 1974. ISBN-10: 014080384X. ISBN-13: 978-

0140803846.

377. W. Schaeken, P. N. Johnson-Laird, an d G. dŠYdewalle, Mental models

and temporal reasoning. Cognition 60 (1996), 205–234.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

References 243

378. G. Schott, Some n eurological observati ons on Leonardo da Vinci’s

handwriting. J Neurol. Sci. 42 (1979), 32 1–329 . DOI: 10.1016/ 0022-

510X(79)901 65-5.

379. G. Schott, Mirror movements of the left arm following peripheral

damage to the preferred right arm. J. Neurology, Neurosurgery, and

Psychiatry 43 (1980), 768–773.

380. G. Schott. Mirror writing: Allen’s self observations, Lewis Carroll’s

‘looking glass’ letters, and Leonardo da Vinci’s maps. Lancet 35 4

(1999), 2158–2161. DOI:10.1016/S0140-6736(99)07016-6.

381. G. Schott, Mirror writing: neurological reﬂections on an unusual

phenomenon. J. Neurol. Neurosurg. Psychiatry 78 (2008) , 5–13.

DOI:101136/jnnp2006094870.

382. T. Schubert, Your highness: Vertical positions as perceptual symbols

of power. J. Personality and Social Psychology 89 no. 1 (2005), 1–21.

383. A. Scott, The vertical dimension and time in Mandarin. Australian J.

Linguistics, 9 (1989), 295–314.

384. R. S. Siegler and J. E. Opfer, The d evelopment of numerical esti-

mation: Evidence for multiple representations of numerical quantity.

Psychological Science 14 (20 03), 237–243.

385. M. A. Singer and S. Goldin-Meadow, Chil dren learn when their

teacher’s gestures a nd speech differ, Psychological Science 16 no. 2

(2005), 85–89.

386. A. Sloman, Kantian philosophy of math ematics and young robots.

In Proceedings 7th International Conference on Mathemati-

cal Knowledge Management. Birmingham, UK, 28–3 0 July 2008.

http://events.cs.bham.ac.uk/cicm08/mkm08/.

387. L. Smith, S. Jones, and B. Landau, Naming in young child ren: A

dumb attentional mechanism? Cognition 60 (1996), 143–17 1.

388. R. Sorensen, Mirror imagery and b iological selection, Biology and

Philosophy 17, no. 3 (2002), 409–422.

389. E. S. Spelke, and S. Tsivkin, Language and nu mb er: A bilingual

training study. Cognition 78, no. 1 (2001), 45–48.

390. J. C. Stevens and L. E. Marks, Cross -modality matching of brightness

and loudness. Proc. Nat. Acad. Sci. 54 (1965) , 407– 411.

391. S. S. Stevens, Psychophysics: An Introduction to its Percep-

tual, Neural, and Social Prospects. John Wiley and Sons, New

York, 1975.

392. M. Streiﬂer an d S. Hofman, Sinistral mirror writing and reading

after bra in concussion in a bisystemic (oriento-occidental) polyglot.

Cortex 12 (1976), 356–364 .

393. N. S. Sutherland, Visual dis cri mi nation of orientation and shape by

octopus. Natu re 179 (1957), 11–13. DOI:10.1038/179011a0.

394. L. Ta lmy, Force dynamics in language and cognition. Cognitive Sci-

ence 12 (1988), 49–100.

395. R. Tankle and K. Heilman, Mirror writing in right-handers and left-

handers. Brain and Language 19 (1983), 115–123.

396. T. Tardif, Nouns are not always learned before verbs, but why? Ev-

idence from Mandarin Chinese. Developmental Psychology 32 no. 3

(1996), 492–504.

397. E. L. T raugott, Spatial expressions of tense an d temporal sequencing:

A contribution to the study of semantic ﬁelds. Semiotica 15 (1975),

207–230.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK

244 References

398. L. Trick and Z. Pylyshyn, What enumeration studies can show us

about spatial attention: Evidence for limited capacity preattentive

processing, J. Exp. Psych.: Huma n Perception and Performance 19

(1993), 331–351.

399. R. Trueman, Mirror wri ting. Postgraduate Medicine 38 (1965) , 469–

476.

400. S. W. Tuholski, R. W. Engle, and G. C. Baylis, Individual differences in

working memory capacity an d enumeration, Memory and Cognition

29 (2001), 484–492.

401. O. H. Turnbull a nd R. A. McCarthy, Fa ilure to discriminate between

mirror-i mage objects: a case of viewpoint-independent object recogni-

tion? N eurocas e 2 (1996), 63–72.

402. B. Tversky, S. Kugelmass, and A. Winter, Cross-cultural and devel-

opmental trends in graphic productions. Cognitive Psychology 23

(1991), 515

U-557.

403. E. Vurpillot, The Visual World of the Child. Allen and Unwin ,

London, 1976.

404. L. S. Vygotsky, T hought and Language. John Wiley Inc., New York,

1962.

405. J. Wade and R. Hart, Mirror phenomena in language and non- verbal

activities: a case report. J Clin. Exp. Neuropsychol. 13 (1991), 299–

308. DOI:10.1080/01688639108401045.

406. S. Wagner, H. Nusbaum, and S. Goldin-Meadow, Probing the men-

tal representation of gesture: Is handwaving spati al? J. Memory and

Language 50 (2004), 395–407.

407. V. Walsh, A theory of magnitude: Common cortical metrics of time,

space and qu antity. Trends in Cognitive Science, 7 no. 11 (2003), 483–

488.

408. Wang X-de, Mirror writing of Chin ese characters in children and neu-

rological patients. Chin. Med. J. 105 (1992): 306–311.

409. S. Waxman and T. Kosowski, Nouns mark category relations: Tod-

dlers’ and Preschoolers’ word-learning biases. Child Development 61

(1990), 1461–1473.

410. S. Wheelwright and S. Baron-Cohen, The li nk between autism and

skills such as engineering, maths, physics, and computing: A reply to

Jarrold and Routh. Autism 5 (2001), 223–227.

411. J. Winawer, N. Witthoft, M. C. Frank, L. Wu, A. R. Wade, and L.

Boroditsky, Russian blues reveal effects of langu age on color discrim-

ination. Proc. Nat. Acad. Sci. 104 no. 19 (May 8, 2007), 7780–7785.

www.pnas.org/cgi/doi/10.1073/pnas.0701644104.

412. J. Wood and E. Spelke, Infants’ enumeration of actions: Numeri-

cal discriminati on and its signature limits. Developmental Science

8 (2005), 173–181.

413. K. Wynn, Children’s understanding of counting. Cognition 36 (1990),

155–193.

414. K. Wynn, Addition and subtraction by human infants. Nature 358

(1992), 749–750.

415. K. Wynn, Children’s acqu isition of number words and the counting

system. Cognitive Psychology 24 (19 92), 220–251.

416. K. Wynn, Psychological foundati ons of number: Numerical compe-

tence in huma n infants. Trends in Cogniti ve Sciences 2 (1998), 296–

303.

SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19

 ALEXANDRE V. BOROVIK