Mind-bending geometry: Children’s and adults’ intuitions about linearity on spheres.
Bibliographic record
Abstract
Humans appear to intuitively grasp definitions foundational to formal geometry, like definitions that describe points as infinitely small and lines as infinitely long. Nevertheless, previous studies exploring human's intuitive natural geometry have consistently focused on geometric principles in planar Euclidean contexts and thus may not comprehensively characterize humans' capacity for geometric reasoning. The present study explores whether children and adults can reason about linearity in spherical contexts. We showed 48 children (age range: 6-8 years) and 48 adults from the U.S. Northeast two different paths between the same two points on pictures of spheres and asked them to judge which path was the most efficient for an actor to get from a starting point to a goal object. In one kind of trial, both paths looked curved in the pictures, and in another kind of trial, the correct curved-looking path was paired with an incorrect straight-looking path. Adults were successful on both kinds of trials, and although children often chose the incorrect straight-looking path, they were surprisingly successful at identifying the efficient path when comparing two that were curved. Children thus may build on a natural geometry that gives us humans intuitions that are not limited to the formal axioms of Euclidean geometry or even to the Euclidean plane. (PsycInfo Database Record (c) 2023 APA, all rights reserved).
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.007 |
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; both teacher heads agree on what is shown here.
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".