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The time-intensity uncertainty principle in vision.

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The authors' code

R · 90 lines · 2 KB · no license

  1. #Experiment 1
  2. par(mfrow=c(1,2),cex=0.8, oma=c(0,0,0,0), mar=c(5,5,5,5))
  3. # Parameters
  4. sigma = sqrt(sqrt(0.00707))
  5. Rmax = 10000
  6. K = 100
  7. n = 1.03
  8. st = c(5,10, 20, 40, 80, 160, 320, 640, 1280,1280*2) / 1000
  9. sb = 3.33
  10. options(scipen=10)
  11. # Naka-Rushton firing rate
  12. lambda = function(L) Rmax * (L^n) / (L^n + K^n)
  13. l = lambda(sb)
  15. # Common Weber fraction for both methods
  16. wf = sqrt(1/(l * st) + sigma^2) # = sqrt(1/μ + σ²)
  18. # Exact method
  19. Rup = l + (wf * l)
  20. Rdown = l - (wf * l)
  21. iNRup = K * ( (Rup / (Rmax - Rup))^(1/n) )
  22. iNRdown = K * ( (Rdown / (Rmax - Rdown))^(1/n) )
  23. DL_L_exact = (iNRup - iNRdown) / 2
  25. # Correct approximation
  26. DL_L_approx = wf * (sb * (sb^n + K^n)) / (n * K^n)
  28. # Compare
  29. data.frame(
  30. Time = st,
  31. Exact = DL_L_exact,
  32. Approx = DL_L_approx,
  33. Ratio = DL_L_exact / DL_L_approx
  34. )
  36. #store error
  37. meanerror1=mean(DL_L_exact / DL_L_approx)
  38. sderror1=sd(DL_L_exact / DL_L_approx)
  40. plot(st,DL_L_approx,log='xy', main="Apprx. DL_L Exp1",xlab="t", ylab="DL_L", type="b", pch=17)
  41. plot(st,DL_L_exact,log='xy', main="Exact DL_L Exp1",xlab="t", ylab="DL_L",type="b", pch=16)
  44. #Experiment 2
  46. # Parameters
  47. sigma = sqrt(sqrt(0.00338))
  48. Rmax = 15000
  49. K = 100
  50. n = 0.73
  51. st = c(240) / 20
  52. sb=c(0.03,0.06,0.12,0.24,0.48,0.96,1.92,3.84)
  53. # Naka-Rushton firing rate
  54. lambda = function(L) Rmax * (L^n) / (L^n + K^n)
  55. l = lambda(sb)
  57. # Common Weber fraction for both methods
  58. wf = sqrt(1/(l * st) + sigma^2) # = sqrt(1/μ + σ²)
  60. # Exact method
  61. Rup = l + (wf * l)
  62. Rdown = l - (wf * l)
  63. iNRup = K * ( (Rup / (Rmax - Rup))^(1/n) )
  64. iNRdown = K * ( (Rdown / (Rmax - Rdown))^(1/n) )
  65. DL_L_exact = (iNRup - iNRdown) / 2
  67. # Correct approximation
  68. DL_L_approx = wf * (sb * (sb^n + K^n)) / (n * K^n)
  70. # Compare
  71. data.frame(
  72. Time = st,
  73. Exact = DL_L_exact,
  74. Approx = DL_L_approx,
  75. Ratio = DL_L_exact / DL_L_approx
  76. )
  78. #store error
  79. meanerror2=mean(DL_L_exact / DL_L_approx)
  80. sderror2=sd(DL_L_exact / DL_L_approx)
  82. #very accurate for exp1
  83. meanerror1
  84. sderror1
  86. #and exp2
  87. meanerror2
  88. sderror2

DL_L_TwoMethods.R, no license · at the source

Overview

Authors: Robert C. G. Johansson1, Karin M. Bausenhart1, Rolf Ulrich1, Paul Kelber1
ORCID iDs: Robert C. G. Johansson, Paul Kelber
  1. Department of Psychology, University of Tübingen,Schleichstraße 4, Tübingen, 72076 Germany
Institutions: University of Tübingen (Germany)
Journal: Attention, perception & psychophysics, volume 88, issue 4, article 106
Dates: received 6 November 2025; accepted 6 March 2026; published online 14 April 2026; in print 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.3758/s13414-026-03249-0 · PMID 41979719 · PMCID PMC13079518 · OpenAlex W7154383216
Open access: hybrid, a free copy (OpenAlex)
Preprint: osf.io/zt6jw
Status: code verified
Categories: behavior only (modality), human (organism), cognitive (subfield)
Methods: Connectivity, Statistics, Single-unit activity, calcium imaging
Keywords: Uncertainty principle, Sensory processing, Time perception, Brightness perception, Visual psychophysics
MeSH: Contrast Sensitivity*, Time Perception*, Visual Perception*, Discrimination, Psychological, Humans, Pattern Recognition, Visual, Psychophysics, Uncertainty, Visual Cortex (* major topic)
Topic: Visual perception and processing mechanisms (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Deutsche Forschungsgemeinschaft (DFG) (381713393)
Citations: not cited yet (Europe PMC); 74 references in the paper

Abstract

The relationship between time perception and brightness perception remains poorly understood. Here we present a computational account linking the two domains, grounded in established principles of neural information processing in visual cortex. A nonlinear transducer maps luminance to population spike rate, while correlated gain fluctuations impose an upper bound on achievable signal-to-noise ratios. Perceptual magnitudes in both domains are decoded from the same spike-count statistics, yielding a reciprocal trade-off in perceptual resolution: brighter stimuli improve temporal precision but impair brightness sensitivity, whereas longer stimuli enhance brightness sensitivity but degrade temporal resolution. We tested this conjectured trade-off in two psychophysical experiments manipulating stimulus duration and luminance. Model predictions closely matched the behavioral data, revealing a fundamental coding limit in vision: the time–intensity uncertainty principle. This limit provides a unified explanation for near-miss relations to Weber’s law for time perception and intensity perception, Bloch-like temporal summation effects governing brightness discrimination sensitivity, and luminance-dependent shifts in duration discrimination sensitivity.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above.

OSF zt6jw

License: none: the authors keep all their rights
State: the link answers, verified on 29 September 2026
Evidence: files inventoried
Languages: R (2)
Size: 4 files, 2 scripts
Software Heritage: not checked
Found in: “Code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: lme4 (3 files), tidyverse (2 files)
Availability: 1 check, the latest on 29 September 2026: the link answers (HTTP 200)
  • 29 September 2026: the link answers (HTTP 200)
4 files
At the source: osf.io/zt6jw

Code availability

Analysis scripts are available at https://osf.io/zt6jw.

Reproduced under the paper's license (CC BY), from the paper cited above.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 4 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Availability of data and materials

Raw data are available at https://osf.io/zt6jw.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 1, 29 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 5 keywords, 9 MeSH terms, 1 funder, 70 references.

Cite

This paper

Johansson, R. C. G., Bausenhart, K. M., Ulrich, R., & Kelber, P. (2026). The time-intensity uncertainty principle in vision. Attention, perception & psychophysics, 88(4), 106. https://doi.org/10.3758/s13414-026-03249-0

BibTeX

@article{johansson2026time,
author = {Johansson, Robert C. G. and Bausenhart, Karin M. and Ulrich, Rolf and Kelber, Paul},
title = {{The time-intensity uncertainty principle in vision}},
journal = {Attention, perception \& psychophysics},
year = {2026},
month = apr,
volume = {88},
number = {4},
pages = {106},
publisher = {Springer Science+Business Media},
issn = {1943-3921},
doi = {10.3758/s13414-026-03249-0},
url = {https://doi.org/10.3758/s13414-026-03249-0},
pmid = {41979719},
pmcid = {PMC13079518}
}

RIS

TY - JOUR
AU - Johansson, Robert C. G.
AU - Bausenhart, Karin M.
AU - Ulrich, Rolf
AU - Kelber, Paul
TI - The time-intensity uncertainty principle in vision
T2 - Attention, perception & psychophysics
J2 - Atten Percept Psychophys
PY - 2026
DA - 2026/04/14
VL - 88
IS - 4
SP - 106
SN - 1943-3921
PB - Springer Science+Business Media
DO - 10.3758/s13414-026-03249-0
UR - https://doi.org/10.3758/s13414-026-03249-0
LA - en
ER -

CSL-JSON

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"container-title-short": "Atten Percept Psychophys",
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"page": "106",
"DOI": "10.3758/s13414-026-03249-0",
"PMID": "41979719",
"PMCID": "PMC13079518",
"ISSN": "1943-3921",
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