The statistical shape of geometric reasoning

Scientific Reports
Yuval HartL Mahadevan

Abstract

Geometric reasoning has an inherent dissonance: its abstract axioms and propositions refer to perfect, idealized entities, whereas its use in the physical world relies on dynamic perception of objects. How do abstract Euclidean concepts, dynamics, and statistics come together to support our intuitive geometric reasoning? Here, we address this question using a simple geometric task - planar triangle completion. An analysis of the distribution of participants' errors in localizing a fragmented triangle's missing corner reveals scale-dependent deviations from a deterministic Euclidean representation of planar triangles. By considering the statistical physics of the process characterized via a correlated random walk with a natural length scale, we explain these results and further predict participants' estimates of the missing angle, measured in a second task. Our model also predicts the results of a categorical reasoning task about changes in the triangle size and shape even when such completion strategies need not be invoked. Taken together, our findings suggest a critical role for noisy physical processes in our reasoning about elementary Euclidean geometry.

References

Jan 1, 1987·Biological cybernetics·J J Koenderink, A J van Doorn
Feb 19, 1971·Science·R N Shepard, J Metzler
Dec 1, 1984·Perception & Psychophysics·P Wenderoth, M Johnson
Dec 1, 1984·Cognition·S Ullman
Feb 1, 1983·Perception & Psychophysics·L Mitrani, N Yakimoff
Sep 9, 1994·Science·C BustamanteS Smith
Jun 1, 1996·Vision Research·S Chen, D M Levi
Nov 1, 1996·Vision Research·D W Heeley, H M Buchanan-Smith
Sep 2, 1998·Nature·C M Harris, D M Wolpert
Jun 6, 2000·Current Biology : CB·J M GoldA B Sekuler
Jan 5, 2002·Perception & Psychophysics·J Feldman
May 22, 2002·Nature Neuroscience·Yair WeissEdward H Adelson
Apr 8, 2003·Journal of Vision·James H Elder, Richard M Goldberg
May 23, 2003·Journal of Experimental Psychology. Human Perception and Performance·Brett R Fajen, William H Warren
May 1, 1954·Psychological Review·F ATTNEAVE
Oct 17, 2003·Journal of Neurophysiology·Robert J van BeersDaniel M Wolpert
Jan 6, 2005·Psychological Review·Jacob Feldman, Manish Singh
Jan 21, 2006·Science·Stanislas DehaeneElizabeth Spelke
Nov 17, 2006·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Micah M MurrayJohn J Foxe
May 24, 2007·Biological cybernetics·Allen CheungMandyam V Srinivasan
Aug 21, 2007·Nature Reviews. Neuroscience·Michael D Fox, Marcus E Raichle
Sep 11, 2008·Biological cybernetics·Allen CheungMandyam V Srinivasan
Aug 1, 2008·Philosophical Psychology·Véronique IzardStanislas Dehaene
May 25, 2011·Proceedings of the National Academy of Sciences of the United States of America·Véronique IzardStanislas Dehaene
Jan 22, 2013·Topics in Cognitive Science·Kevin A Smith, Edward Vul
Oct 23, 2013·Proceedings of the National Academy of Sciences of the United States of America·Peter W BattagliaJoshua B Tenenbaum
Aug 7, 2016·Royal Society Open Science·O Peleg, L Mahadevan
Sep 7, 2016·Cognition·Jessica B HamrickJoshua B Tenenbaum
Jun 29, 2017·Trends in Cognitive Sciences·Tomer D UllmanJoshua B Tenenbaum
Mar 30, 2018·Developmental Psychology·Moira R Dillon, Elizabeth S Spelke

❮ Previous
Next ❯

Citations

Aug 29, 2020·Infancy : the Official Journal of the International Society on Infant Studies·Moira R DillonElizabeth S Spelke
Apr 20, 2021·Cognitive Science·Yacin HamamiMarie Amalric

❮ Previous
Next ❯

Software Mentioned

Amazon
Mechanical

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

IEEE Transactions on Visualization and Computer Graphics
G Farin
Developmental Psychology
Moira R Dillon, Elizabeth S Spelke
Malawi Medical Journal : the Journal of Medical Association of Malawi
S White
© 2022 Meta ULC. All rights reserved