Graphical representations of number (i.e. numerals) come in many diverse forms, historically predate written language, and are a powerful cognitive tool for transmitting abstract concepts about number. How did they emerge? This repo contains 3 experiments investigating how people create graphical representations of number within communicative contexts.
Some examples of different numerals:
 WWII airforce pilot, representing a 1-to-1 tally using marks that correspond to each type of event. (source) |
 Mesopotamian administrative tablet representing object-types (barley) and quantities in separate graphical forms, ca. 5,000 yBP. (source) |
 Numerals invented by Iñupiaq students in the 1990s to represent a base-20 system. (source) |
Partners played a reference game in which one person used graphical tools to communicate numerical information to their partner, using graphical tools.
- In Experiment 1, we asked whether and how people would distill numerical information from arrays of objects to create a specifically numerical representation.
- In Experiment 2, we asked whether objects arranged in predictable, regular arrays made it easier to develop graphical conventions about number that transcended the use of 1-to-1 correspondence.
- In Experiment 3, we asked how the presence of existing symbols might be used to create representations of number in a left-to-right communicative medium.
Cartoon of the methods used in each experiment.
- Available as PDFs under
/osf/.
- Source code for communication tasks is in
/experiments/, in directories that contain "draw_number". - Source code for recognition tasks is in
/experiments/, in directories that contain "classify_iternum". - Source code for stimulus generation is in
/stimuli/, in directories with names that match those in/experiments/. - Some additional tools used in the above are in
/utils/.
- An R script for our pre-registered statistical models can be found in
/analysis/analyses.R. - A python notebook for manuscript figures and some simple descriptive statistics can be found in
/analysis/main_analyses.ipynb/. - One additional supplementary analysis can be found in
/analysis/supplementary_analysis.ipynb/. - Helper functions can be found in
/analysis/utils/.
/analysis/results/csv/contains CSVs of all processed experimental data. It also contains/extra/, with raw data, as well as/features/and/classifier/, generated in the supplementary analysis./analysis/results/plots/contains Jupyter notebook output that was used to create the figures in the manuscript./analysis/results/bare_sketches/contains sketch results from each experiment, to be processed in our supplementary analysis./analysis/results/bare_targets/contains target images for the above sketches./analysis/results/sketch/contains sketches annotated with correct / incorrect viewer response, and the corresponding target image./analysis/results/sketch_galleries/contains all of the above sketches, arranged into galleries that show all trials from a given game. Below are two examples of sketch galleries from Experiments 1 and 2, with a key for how to read them.
Qualitative data from a game in Experiment 1. Trials progress from left to right, 32 trials per game. Target images are rendered below and Sketchers' sketches rendered above. The bar in between targets and sketches is green if the Viewer guessed correctly, or red otherwise.
Qualitative data from a game in Experiment 2. Trials are NOT in order, but arranged according to trial blocks (early-game above, late-game below), the cardinality of sets (6 trials for each cardinality over the whole game), and the animal quantified by each set (3 animals per cardinality x 2 trial blocks).