- Spencer Caplan scaplan@gc.cuny.edu
- Karthik Durvasula karthikd@msu.edu
- Bash tested on GNU bash, version 3.2.57(1)-release (arm64-apple-darwin23)
- Python tested on version 3.9.6 with no external libraries.
- R scripts have been tested on version 4.4.1. The following R packages are required to create the plots and run statistical analysis.
dplyr, tidyr, stringr, ggplot2, Hmisc, scales, multimode, Matrix, tibble, lme4, reshape2, tidyverse, cowplot, ggpubr, ggrepel, xtable, broom, devtools, ggridges, diptest, transport- The scripts will attempt to install them automatically, though in my experimence it is far preferred to ensure that these are present and available on the local system ahead of time.
No other setup is required.
n.b. a number of scripts assume a Unix-style directory stucture (already satisfied on Linux or Mac OS systems). You may need to make some manual adjustments if running on Windows (or, perhaps easier, would be to run using "linux subsystem for windows" if this applies to you).
The following script runs all generation and analysis:
$ runall.sh
Among the foundational questions for cognition is whether perceptual systems encode sensory input as continuous values or transform it into discrete mental representations. Speech—long a model system for probing the nature of perceptual representation—offers a critical testing ground. Yet the literature routinely conflates the content of representations (cue-based vs. category-based) with their granularity (continuous vs. discrete). Likewise, the well-known observation that incrementally varied stimuli often elicit graded behavioral responses, particularly when averaged across trials, is commonly taken as evidence for continuous internal representations. We challenge this assumption and synthesize the surrounding debate by introducing the Discrete Sampling (DS) framework, a novel theory under which listeners map continuous input into discrete, category-based internal states via a biologically plausible sampling procedure. We formalize a specific instantiation of DS computationally and demonstrate how it accounts for a wide range of core phenomena. We compare DS to a general class of continuous alternatives using data from 575 subjects across three experimental paradigms, with precise, differentiating predictions confirmed by the results. DS provides a single cognitive architecture for a parameter-independent derivation of binary and scalar categorization responses, concave reaction-time patterns centered on category boundaries, the joint modulation of categorization slope and processing speed by task demands and noise, and the distribution of inter-listener variability. We show how sampling from discrete categories can produce behavior traditionally taken to imply continuity, offering a unified reinterpretation of decades of evidence and reframing how uncertainty and apparent gradience are represented in perceptual and psychological systems more broadly.