Origins of the brain networks for advanced mathematics in expert mathematicians

Origins of the brain networks for advanced mathematics in expert mathematicians Amalric Dehaene

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Origins of the brain networks for advanced mathematics in expert mathematicians 2016 Proceedings of the National Academy of Sciences 10.1073/pnas.1603205113 Amalric2016-origins-of-the-brain-networks-for-advanced-m Amalric2016-origins-of-the-brain-networks-for-advanced-m.txt, the project's staged copy ef83c308095a0a39a404004b950ca0eea83d69ec not-redistributable neuroscience

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them whether advanced mathematical thought rests on the language faculty or on evolutionarily older circuits for number and space Quotation withheld because this record is not cleared for redistribution. which brain areas professional mathematicians engage when judging advanced mathematical statements, and whether they are language areas or number areas Quotation withheld because this record is not cleared for redistribution. shows a bilateral parietal, inferior temporal and prefrontal network active for all four branches of mathematics in experts only, sparing language areas and overlapping the circuits for numerals and arithmetic Quotation withheld because this record is not cleared for redistribution. existence Quotation withheld because this record is not cleared for redistribution. high-level mathematical reasoning in expert mathematicians Quotation withheld because this record is not cleared for redistribution. fmri fmri Quotation withheld because this record is not cleared for redistribution. mechanisms Prolonged exposure to mathematical symbols reshapes ventral visual cortex, amplifying symbol responses and displacing face responses, in the same way reading expertise does for letters Quotation withheld because this record is not cleared for redistribution. mechanisms Because advanced mathematics and basic arithmetic share the same cortical circuit, early number skills and later mathematical achievement are developmentally linked through that shared substrate Quotation withheld because this record is not cleared for redistribution. expertise amplifies responses at sites that already respond to numerals and formulas in non-experts, rather than recruiting new territory Quotation withheld because this record is not cleared for redistribution. the ventral visual change mirrors literacy, where learning to read shifts responses toward letters and away from faces Quotation withheld because this record is not cleared for redistribution. the enhanced formula response reflects a genuine increase in activated cortical volume, not just tighter anatomical alignment in the expert group Quotation withheld because this record is not cleared for redistribution. the caudate shifts its engagement to whichever domain the subject is expert in, consistent with a role in motivation and attention Quotation withheld because this record is not cleared for redistribution. language contributes transiently at the angular gyrus during sentence comprehension, and that area is deactivated during the reflection itself Quotation withheld because this record is not cleared for redistribution. The group differences in ventral visual responses (formulas, tools, faces) cannot yet be tied to behaviour or shown to be caused by mathematical training. what this limits: the ventral visual group differences: THESE INTRIGUING DIFFERENCES MUST BE CONSIDERED WITH CAUTION BECAUSE THEIR BEHAVIORAL IMPACT AND CAUSAL LINK TO MATHEMATICAL TRAINING REMAINS PRESENTLY UNKNOWN Quotation withheld because this record is not cleared for redistribution. The design cannot rule out a transient role of language areas during the acquisition of mathematical concepts; only learning studies could settle it. what this limits: the claim that language areas are not involved: a transient role during acquisition is not excluded, and IMAGING STUDIES OF THE LEARNING PROCESS WOULD BE NEEDED TO RESOLVE THIS POINT Quotation withheld because this record is not cleared for redistribution. Mathematicians and controls may differ on uncontrolled dimensions such as IQ or musical talent, which the authors argue is irrelevant to the within-group dissociation but is not measured. what this limits: the between-group comparison but not the within-mathematician one: MATHEMATICIANS AND CONTROLS MAY STILL DIFFER ON DIMENSIONS SUCH AS IQ, MUSICAL TALENT, HOBBIES ... SUCH PUTATIVE DIFFERENCES ARE IRRELEVANT TO OUR MAIN CONCLUSION OF A DISSOCIATION ... WITHIN THE MATHEMATICIANS Quotation withheld because this record is not cleared for redistribution. the authors flag the ventral visual group differences as needing caution, since their behavioural impact and causal link to mathematical training are unknown what this limits: the same scope as limitations[0] - the ventral visual differences are flagged by the authors as needing caution Quotation withheld because this record is not cleared for redistribution. a small language-area overlap in left BA44 appeared only in smoothed group images and failed to reach significance in single subjects what this limits: the language-overlap result: THIS SMALL OVERLAP WAS PRESENT ONLY IN SMOOTHED GROUP IMAGES AND FAILED TO REACH SIGNIFICANCE IN HIGHER RESOLUTION analyses Quotation withheld because this record is not cleared for redistribution. controls were near chance on the mathematical statements, so the expertise interaction rests on a group that could not do the task what this limits: any expertise contrast that uses the control group's maths performance: THEY FELL CLOSE TO CHANCE LEVEL WITH MATH (37% CORRECT, CHANCE LEVEL = 33%) ... COULD NOT IDENTIFY THEIR TRUTH VALUE (d' = 0.38, n.s.) Quotation withheld because this record is not cleared for redistribution. objective performance was matched but each group rated its own domain as more comfortable what this limits: the matched-performance argument: OBJECTIVE PERFORMANCE ON NONMATH PROBLEMS DID NOT DIFFER ... their SUBJECTIVE RATINGS ... REVEALED THAT EACH GROUP FELT MORE COMFORTABLE WITH ITS RESPECTIVE EXPERTISE DOMAIN Quotation withheld because this record is not cleared for redistribution. the expertise-driven ventral visual shift toward symbols and away from faces, transposed from literacy to mathematics Quotation withheld because this record is not cleared for redistribution. representational similarity, used to test whether math, arithmetic and numeral viewing share an activation topography within each subject Quotation withheld because this record is not cleared for redistribution. an eighth stimulus category of circular checkerboards, built so that its retinotopic extent EXCEEDED that of every other category eliminates: a difference in retinotopic extent between conditions - the checkerboard is built to exceed every other category, so any area responding to sheer visual extent is exposed rather than counted as mathematical · outcome (stated by the tagger, no quotation): absent-not-in-staged-text · would have ruled out, had it been run: low-level visual drive as the explanation of category-selective responses - a region that answers to mathematical formulas more than to a checkerboard covering MORE of the visual field is not responding to retinotopic extent Quotation withheld because this record is not cleared for redistribution. meaningful versus meaningless is the paper's second, ORTHOGONAL criterion - it holds lexical content constant and so tests the same claim without the math-versus-nonmath comparison Quotation withheld because this record is not cleared for redistribution. difficulty here has an objective form (percent correct, matched) and a subjective form (rated, slightly higher for math), and the paper's controls address the second Quotation withheld because this record is not cleared for redistribution. the visual number form area is defined by responding to Arabic numerals more than letters or pictures, and was previously hard to detect because it sits near a zone of fMRI signal loss Quotation withheld because this record is not cleared for redistribution. the multiple demand system is the rival account: a set of areas active in any hard task, which overlaps the math network and is why difficulty had to be excluded Quotation withheld because this record is not cleared for redistribution. language areas here are defined by an independent localiser in the same subjects, not by anatomy, so the sparing claim is about functionally identified voxels Quotation withheld because this record is not cleared for redistribution. method: auditory statement judgement in the scanner with matched non-mathematical statements, plus independent localisers for sentences, calculation and visual categories a second reading DIFFERING from the recorded value. Recorded: fmri — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. phenomenon: the cortical network engaged during reflection on advanced mathematical statements a second reading DIFFERING from the recorded value. Recorded: high-level mathematical reasoning in expert mathematicians — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. replicates → earlier observations of number-sense and number-form areas (cited as references 16, 18, 37) Quotation withheld because this record is not cleared for redistribution. contradicts → the hypothesis that mathematics is an offshoot of language syntax, attributed in the article to Noam Chomsky (reference 1) Quotation withheld because this record is not cleared for redistribution. contradicts → the hypothesis that mathematical capacity is an abstraction from linguistic operations Quotation withheld because this record is not cleared for redistribution. supports → the account grounding mathematics in ancient nonlinguistic intuitions of number and space Quotation withheld because this record is not cleared for redistribution. extends → arithmetic imaging work, by answering the objection that number concepts are too simple to represent advanced mathematics Quotation withheld because this record is not cleared for redistribution. confirms → prior reports of visual number form areas, using a sequence that overcomes the signal loss which made them hard to detect Quotation withheld because this record is not cleared for redistribution. qualifies → its own language-independence claim, by noting a transient angular gyrus contribution during comprehension Quotation withheld because this record is not cleared for redistribution. t-test t-test Quotation withheld because this record is not cleared for redistribution. ANOVA ANOVA Quotation withheld because this record is not cleared for redistribution. F-test F-test Quotation withheld because this record is not cleared for redistribution. signal-detection sensitivity index signal-detection sensitivity index Quotation withheld because this record is not cleared for redistribution. correction for multiple comparisons correction for multiple comparisons Quotation withheld because this record is not cleared for redistribution. correlation correlation Quotation withheld because this record is not cleared for redistribution. Student t tests Student t tests Quotation withheld because this record is not cleared for redistribution. F-test F-test Quotation withheld because this record is not cleared for redistribution. cluster P < 0.05 corrected cluster P < 0.05 corrected Quotation withheld because this record is not cleared for redistribution. The activations evoked by mathematical reflection spared areas related to language and to general-knowledge semantics. Quotation withheld because this record is not cleared for redistribution. The same math network was engaged by all four tested branches of mathematics and even transiently by meaningless mathematical statements. Quotation withheld because this record is not cleared for redistribution. Non-mathematical general-knowledge reflection recruited a separate anterior temporal and angular gyrus semantic network. Quotation withheld because this record is not cleared for redistribution. A region-of-interest analysis of language areas showed mathematics engaged them no more, and often less, than general semantic reasoning did. Quotation withheld because this record is not cleared for redistribution. The high-level mathematics network overlapped the parietal and inferior temporal sites activated by simple calculation and by the mere sight of numerals, and this overlap survived removal of statements containing any numerical reference. Quotation withheld because this record is not cleared for redistribution. The math network was active even during simple mathematical reflection, and its greater activation for math than nonmath held irrespective of task difficulty. Quotation withheld because this record is not cleared for redistribution. Mathematical expertise was accompanied by expanded number and formula responses in the left visual number form area. Quotation withheld because this record is not cleared for redistribution. mathematicians performed equally on math and non-math statements, 63% against 65% correct Quotation withheld because this record is not cleared for redistribution. controls matched mathematicians on non-math but were near chance on math Quotation withheld because this record is not cleared for redistribution. all four domains of mathematics activated the math-responsive regions, in a significant intersection Quotation withheld because this record is not cleared for redistribution. the network stayed active for about fifteen seconds after a math statement and deactivated for non-math Quotation withheld because this record is not cleared for redistribution. in controls the math contrast landed on the sites for meaningless statements Quotation withheld because this record is not cleared for redistribution. essentially no intersection between the math and general-knowledge semantic networks, and none in perisylvian language cortex even at a lenient threshold Quotation withheld because this record is not cleared for redistribution. language regions defined by an independent localiser were engaged no more by math than by general reasoning, and often less Quotation withheld because this record is not cleared for redistribution. the math network overlapped the areas for arithmetic and for merely viewing numerals Quotation withheld because this record is not cleared for redistribution. responses to written formulas were larger in mathematicians, as extra activated volume rather than tighter alignment Quotation withheld because this record is not cleared for redistribution. face responses were reduced in right inferior temporal cortex in mathematicians Quotation withheld because this record is not cleared for redistribution. the caudate responded to whichever domain each group was expert in Quotation withheld because this record is not cleared for redistribution. CONFOUND REVERSED: easy math contrasted against difficult non-math still produced the same sites Quotation withheld because this record is not cleared for redistribution. CONTROL NULL: contrasting difficult against easy statements within each domain revealed no significant sites at all Quotation withheld because this record is not cleared for redistribution. ORTHOGONAL REPLICATION: the meaningful-versus-meaningless math contrast, which holds words constant, reproduced the whole result Quotation withheld because this record is not cleared for redistribution. CONTENT REANALYSIS: excluding statements with any indirect numerical reference left the activation virtually unchanged Quotation withheld because this record is not cleared for redistribution. HAZARD NAMED ABOUT THEIR OWN RESULT: group-level overlap can arise from intersubject averaging, so the overlap was retested within subjects Quotation withheld because this record is not cleared for redistribution. the within-subject pattern analyses confirmed that advanced math, arithmetic and numeral viewing share cortical sites in trained individuals Quotation withheld because this record is not cleared for redistribution. visual number form area visual number form area Quotation withheld because this record is not cleared for redistribution. multiple demand system multiple demand system Quotation withheld because this record is not cleared for redistribution. immediacy immediacy Quotation withheld because this record is not cleared for redistribution. multiple demand system multiple demand system Quotation withheld because this record is not cleared for redistribution. VNFA VNFA Quotation withheld because this record is not cleared for redistribution. core knowledge core knowledge Quotation withheld because this record is not cleared for redistribution. task difficulty task difficulty Quotation withheld because this record is not cleared for redistribution. meaningless meaningless Quotation withheld because this record is not cleared for redistribution. imageability imageability Quotation withheld because this record is not cleared for redistribution. topology topology Quotation withheld because this record is not cleared for redistribution. 15 and 15 — sample size: professional mathematicians and academically matched humanities controls scanned with fMRI Quotation withheld because this record is not cleared for redistribution. 63% and 65% correct — mathematicians' accuracy on math and on nonmath statements, showing the two problem types were matched in objective difficulty Quotation withheld because this record is not cleared for redistribution. 37% correct, chance level = 33%; P = 0.014 — control subjects' accuracy on mathematical statements, barely above chance Quotation withheld because this record is not cleared for redistribution. ∼15 s — duration for which the fMRI signal stayed elevated in the math network after a mathematical statement Quotation withheld because this record is not cleared for redistribution. 52.4 ± 3.4 versus 40.0 ± 4.5; t = 2.4, P = 0.03 — mathematicians' subjective difficulty ratings (0–100 scale) for math versus nonmath statements Quotation withheld because this record is not cleared for redistribution. t = 4.72 — whole-brain effect size for reduced face responses in right inferior temporal cortex in mathematicians relative to controls Quotation withheld because this record is not cleared for redistribution. 72 and 18 — number of mathematical statements (18 per domain) and of nonmathematical statements presented in the auditory runs Quotation withheld because this record is not cleared for redistribution. 15 and 15 — professional mathematicians and non-mathematician controls of equal academic standing Quotation withheld because this record is not cleared for redistribution. 63% and 65% — mathematicians' accuracy on math and non-math, the basis for calling the two matched in difficulty Quotation withheld because this record is not cleared for redistribution. 37% against 33% chance — controls' accuracy on mathematical statements Quotation withheld because this record is not cleared for redistribution. 52.4 against 40.0 — subjective difficulty for math and non-math on a 0-100 scale, the only difficulty difference found Quotation withheld because this record is not cleared for redistribution. about 15 s — how long the math network stayed active after a statement Quotation withheld because this record is not cleared for redistribution.

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