Symbolic and non-symbolic representations of numerical zero in the human brain
Bibliographic record
Abstract
Representing the quantity zero as a symbolic concept is considered a unique achievement of abstract human thought.1Bialystok E. Codd J. Representing quantity beyond whole numbers: Some, none, and part.Can. J. Exp. Psychol. 2000; 54: 117-128https://doi.org/10.1037/h0087334Crossref PubMed Scopus (42) Google Scholar,2Nieder A. Representing Something Out of Nothing: The Dawning of Zero.Trends Cogn. Sci. 2016; 20: 830-842https://doi.org/10.1016/j.tics.2016.08.008Abstract Full Text Full Text PDF PubMed Scopus (51) Google Scholar To conceptualize zero, one must abstract away from the (absence of) sensory evidence to construct a representation of numerical absence: creating “something” out of “nothing.”2Nieder A. Representing Something Out of Nothing: The Dawning of Zero.Trends Cogn. Sci. 2016; 20: 830-842https://doi.org/10.1016/j.tics.2016.08.008Abstract Full Text Full Text PDF PubMed Scopus (51) Google Scholar,3Butterworth B. The mathematical brain 1. Macmillan, 1999Google Scholar,4Wellman H.M. Miller K.F. Thinking about nothing: Development of concepts of zero.Br. J. Dev. Psychol. 1986; 4: 31-42https://doi.org/10.1111/j.2044-835X.1986.tb00995.xCrossref Google Scholar Previous investigations of the neural representation of natural numbers reveal distinct numerosity-selective neural populations that overlap in their tuning curves with adjacent numerosities.5Kutter E.F. Bostroem J. Elger C.E. Mormann F. Nieder A. Single Neurons in the Human Brain Encode Numbers.Neuron. 2018; 100: 753-761.e4https://doi.org/10.1016/j.neuron.2018.08.036Abstract Full Text Full Text PDF PubMed Scopus (81) Google Scholar,6Piazza M. Izard V. Pinel P. Le Bihan D. Dehaene S. Tuning curves for approximate numerosity in the human intraparietal sulcus.Neuron. 2004; 44: 547-555https://doi.org/10.1016/j.neuron.2004.10.014Abstract Full Text Full Text PDF PubMed Scopus (836) Google Scholar Importantly, a component of this neural code is thought to be invariant across non-symbolic and symbolic numerical formats.7Damarla S.R. Cherkassky V.L. Just M.A. Modality-independent representations of small quantities based on brain activation patterns.Hum. Brain Mapp. 2016; 37: 1296-1307https://doi.org/10.1002/hbm.23102Crossref PubMed Scopus (14) Google Scholar,8Eger E. Sterzer P. Russ M.O. Giraud A.-L. Kleinschmidt A. A supramodal number representation in human intraparietal cortex.Neuron. 2003; 37: 719-725https://doi.org/10.1016/s0896-6273(03)00036-9Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar,9Eger E. Michel V. Thirion B. Amadon A. Dehaene S. Kleinschmidt A. Deciphering Cortical Number Coding from Human Brain Activity Patterns.Curr. Biol. 2009; 19: 1608-1615https://doi.org/10.1016/j.cub.2009.08.047Abstract Full Text Full Text PDF PubMed Scopus (159) Google Scholar,10Piazza M. Pinel P. Le Bihan D. Dehaene S. A Magnitude Code Common to Numerosities and Number Symbols in Human Intraparietal Cortex.Neuron. 2007; 53: 293-305https://doi.org/10.1016/j.neuron.2006.11.022Abstract Full Text Full Text PDF PubMed Scopus (652) Google Scholar,11Teichmann L. Grootswagers T. Carlson T. Rich A.N. Decoding Digits and Dice with Magnetoencephalography: Evidence for a Shared Representation of Magnitude.J. Cogn. Neurosci. 2018; 30: 999-1010https://doi.org/10.1162/jocn_a_01257Crossref PubMed Scopus (15) Google Scholar Although behavioral evidence indicates that zero occupies a place at the beginning of this mental number line,12Dehaene S. Bossini S. Giraux P. The mental representation of parity and number magnitude.J. Exp. Psychol. Gen. 1993; 122: 371-396https://doi.org/10.1037/0096-3445.122.3.371Crossref Scopus (2061) Google Scholar,13Zagury Y. Zaks-Ohayon R. Tzelgov J. Pinhas M. Sometimes nothing is simply nothing: Automatic processing of empty sets.Q. J. Exp. Psychol. 2022; 75: 1810-1827https://doi.org/10.1177/17470218211066436Crossref Scopus (1) Google Scholar,14Pinhas M. Tzelgov J. Expanding on the mental number line: Zero is perceived as the “smallest”.J. Exp. Psychol. Learn. Mem. Cogn. 2012; 38: 1187-1205https://doi.org/10.1037/a0027390Crossref PubMed Scopus (41) Google Scholar in humans zero is also associated with unique behavioral and developmental profiles compared to natural numbers,4Wellman H.M. Miller K.F. Thinking about nothing: Development of concepts of zero.Br. J. Dev. Psychol. 1986; 4: 31-42https://doi.org/10.1111/j.2044-835X.1986.tb00995.xCrossref Google Scholar,15Krajcsi A. Kojouharova P. Lengyel G. Development of Preschoolers’ Understanding of Zero.Front. Psychol. 2021; 12: 583734https://doi.org/10.3389/FPSYG.2021.583734Crossref Google Scholar,16Merritt D.J. Brannon E.M. Nothing to it: Precursors to a zero concept in preschoolers.Behav. Processes. 2013; 93: 91-97https://doi.org/10.1016/j.beproc.2012.11.001Crossref PubMed Scopus (33) Google Scholar,17Brysbaert M. Arabic Number Reading: On the Nature of the Numerical Scale and the Origin of Phonological Recoding.J. Exp. Psychol. Gen. 1995; 124: 434-452https://doi.org/10.1037/0096-3445.124.4.434Crossref Scopus (243) Google Scholar suggestive of a distinct neural basis for zero. We characterized the neural representation of zero in the human brain by employing two qualitatively different numerical tasks18Kriegeskorte N. Diedrichsen J. Peeling the Onion of Brain Representations.Annu. Rev. Neurosci. 2019; 42: 407-432https://doi.org/10.1146/annurev-neuro-080317-061906Crossref PubMed Scopus (65) Google Scholar,19Luyckx F. Nili H. Spitzer B. Summerfield C. Neural structure mapping in human probabilistic reward learning.Elife. 2019; 8e42816https://doi.org/10.7554/eLife.42816Crossref Scopus (37) Google Scholar in concert with magnetoencephalography (MEG) recordings. We assay both neural representations of non-symbolic numerosities (dot patterns), including zero (empty sets), and symbolic numerals, including symbolic zero. Our results reveal that neural representations of zero are situated along a graded neural number line shared with other natural numbers. Notably, symbolic representations of zero generalized to predict non-symbolic empty sets. We go on to localize abstract representations of numerical zero to posterior association cortex, extending the purview of parietal cortex in human numerical cognition to encompass representations of zero.10Piazza M. Pinel P. Le Bihan D. Dehaene S. A Magnitude Code Common to Numerosities and Number Symbols in Human Intraparietal Cortex.Neuron. 2007; 53: 293-305https://doi.org/10.1016/j.neuron.2006.11.022Abstract Full Text Full Text PDF PubMed Scopus (652) Google Scholar,20Harvey B.M. Dumoulin S.O. A network of topographic numerosity maps in human association cortex.Nat. Hum. Behav. 2017; 10036https://doi.org/10.1038/s41562-016-0036Crossref Scopus (77) Google Scholar
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".