Original title: The relationship between numerosity and the Fourier power spectrum of dot arrays
Joonkoo Park, Shimin Hu, Ruoyu Yuan · September 2026
Scientists study how we perceive numbers by showing people images of dot arrays. A common question is whether visual patterns, like repeating light and dark waves across the image, affect this sense of number. Researchers use a math tool called a Fourier power spectrum to measure these visual patterns across frequencies, which are rates of visual detail. In this paper, researchers worked out exact math equations to connect dot counts directly to these visual patterns. The math uses dot number, dot radius, dot spacing, and spatial frequency. By doing this math, the team also showed that a previous study used an unusual way to process these visual measurements, which created a fake link to the number of dots.
Imagine you are trying to measure how many people are in a room by listening to the loudness of their chatter. You notice that the louder the chatter, the more people you think are there. But it turns out that the microphone you are using picks up more noise when placed near a wall, regardless of how many people are talking. In this paper, the Fourier power spectrum is like that microphone, and the specific way of analyzing it creates a false signal that looks like it tracks numerosity, but is actually just a quirk of the measurement method.
Researchers studying how the brain perceives quantity often use dot arrays and analyze their Fourier power spectra. This paper shows that one particular way of distilling those spectra creates a false correlation with the number of dots, which could mislead experiments. Understanding this artifact helps ensure that future studies measure genuine neural responses, not statistical noise.
The paper is purely mathematical and does not include experimental validation. It does not test whether the artifact actually affects real neural or behavioral data. It also only considers arrays of identical dots, not more complex stimuli. The artifact is shown for one specific metric from Paul et al. (2022); other metrics may not have this issue.
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The relationship between numerosity and the Fourier power spectrum of dot arrays — Joonkoo Park, Shimin Hu, Ruoyu Yuan — PsyArXiv — doi:10.31234/osf.io/zs82e_v1
Abstract licence: CC BY
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.