Psychological Research

, Volume 83, Issue 1, pp 48–63 | Cite as

On the linear representation of numbers: evidence from a new two-numbers-to-two positions task

  • Hofit BarEmail author
  • Martin H. Fischer
  • Daniel Algom
Original Article


In the number-to-position methodology, a number is presented on each trial and the observer places it on a straight line in a position that corresponds to its felt subjective magnitude. In the novel modification introduced in this study, the two-numbers-to-two-positions method, a pair of numbers rather than a single number is presented on each trial and the observer places them in appropriate positions on the same line. Responses in this method indicate not only the subjective magnitude of each single number but, simultaneously, provide a direct estimation of their subjective numerical distance. The results of four experiments provide strong evidence for a linear representation of numbers and, commensurately, for the linear representation of numerical distances. We attribute earlier results that indicate a logarithmic representation to the ordered nature of numbers and to the task used and not to a truly non-linear underlying representation.



We thank James Townsend, Attila Krajcsi, and an anonymous referee for helpful comments on earlier versions.


No funding was received for this study.

Compliance with ethical standards

Conflict of interest

All authors declare that they do not have a conflict of interest.

Ethical standards

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Research involving human and animal participants

This article does not contain any studies with animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Supplementary material

426_2018_1063_MOESM1_ESM.xlsx (21 kb)
Supplementary material 1 (XLSX 20 KB)
426_2018_1063_MOESM2_ESM.xlsx (80 kb)
Supplementary material 2 (XLSX 80 KB)


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The School of Psychological SciencesTel-Aviv UniversityTel AvivIsrael
  2. 2.Department of PsychologyAchva Academic CollegeArugotIsrael
  3. 3.Department of PsychologyPotsdam UniversityPotsdamGermany

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