Franciscus Donders

Introduction

Franciscus Cornelis Donders (27 May 1818 – 24 March 1889) was a Dutch physiologist and ophthalmologist who did something that most of his contemporaries believed impossible: he measured how long a thought takes. In an 1868 paper he argued that if a second task requires everything a first task requires plus one additional mental operation, then subtracting the reaction time of the first from the reaction time of the second yields the duration of that operation. The subtraction method, as it came to be called, turned reaction time into a tool for inferring the architecture of the mind, and it is the ancestor of both modern mental chronometry and the subtraction logic used in brain imaging. Donders was not a psychologist in any modern sense — he had no laboratory of psychology, no students of psychology, and no interest in founding the discipline. He was a professor of physiology and an internationally known eye specialist who spent a few years on a side problem. The fact that a side problem from 1868 still shapes how cognitive psychologists design experiments is the measure of it.

Early Life and Education

Donders was born in Tilburg, in the southern province of North Brabant, the son of Jan Franz Donders and Agnes Elizabeth Hegh, and the only boy after eight older sisters. He was educated at Duizel and at seminaries in Tilburg and Boxmeer, and began studying medicine at seventeen at the School of Military Medicine in Utrecht, where he came to prefer experimental work to clinical routine. He served briefly as a junior military surgeon and received his medical doctorate from the University of Leiden in 1840.

After about two years as a medical officer in The Hague, he was appointed in 1842 as lecturer in physiology and anatomy at the Utrecht military medical school. Five years later he became an associate professor at Utrecht University, and in 1862 a full professor of physiology, a chair he held for the rest of his career. He was elected a corresponding member of the Royal Netherlands Academy of Arts and Sciences in 1847 and a full member in 1851.

Academic and Professional Career

Donders's reputation in his own lifetime rested on the eye. In 1858 he founded the Netherlands Hospital for Eye Patients, the first eye hospital in the country, where his assistant was Herman Snellen, later known for the Snellen acuity chart. He was among the first practitioners of the ophthalmoscope, introduced prismatic and cylindrical lenses for the treatment of astigmatism in 1860, and is credited with an impression tonometer in 1862. His 1864 treatise On the Anomalies of Accommodation and Refraction of the Eye set out what amounted to a complete doctrine of refraction and corrective lenses, and made scientific correction of refractive error a practical discipline. With Albrecht von Graefe and Hermann von Helmholtz he is counted among the founders of scientific ophthalmology.

This is the standing that makes the 1868 paper legible. Donders was, by the 1860s, one of the most internationally connected medical scientists in Europe, running a physiology laboratory in Utrecht that drew foreign visitors, and publishing in several languages. When he turned to reaction time he did so as someone entitled to be heard on any physiological question — which is part of why a short paper in a Dutch laboratory report series came to matter so much.

His interests ranged well beyond the eye. He studied eye movements and formulated what is still called Donders' law — that the orientation of the eye is determined by the direction of the line of sight and not by the path taken to reach it. He worked on colour vision, cerebral circulation, and the oxygen consumption of the brain. In an 1870 monograph on the physiology of Dutch speech sounds he gave a detailed account of articulation and acoustics and, using a phonautograph and a tuning fork to mark onset times, made the first measurements of how long it takes to name a stimulus aloud.

Major Contributions to Psychology

Mental chronometry and the subtraction method

The central idea appeared in Over de snelheid van psychische processen ("On the speed of mental processes"), published in 1868 in the report series of the Utrecht physiological laboratory. Donders began the reaction-time experiments in the early 1860s together with his student De Jaager. His reasoning, in his own words, was that he should "interpose into the process of physiological time some new components of mental action" and see how much this lengthened it. He defined three tasks:

  • Task A, the simple reaction — one stimulus, one response. The participant presses a button when a light appears.
  • Task B, the choice reaction — several stimuli, each with its own response. The participant must press the button corresponding to whichever light appeared.
  • Task C, the go/no-go reaction — several stimuli, but only one response, which must be given to one stimulus and withheld for the others.

The comparisons are often misdescribed. Donders did not estimate "decision time" by subtracting the simple reaction from the choice reaction. He estimated stimulus discrimination by subtracting Task A from Task C, since C adds discrimination but not response selection, and response selection by subtracting Task C from Task B, since B adds selection on top of discrimination. The difference between the two subtractions gives the two components separately, and only their sum is the full cost of choosing over merely reacting.

The first measurement of naming

Separately from the ABC tasks, Donders measured the time to name a syllable aloud and to repeat one, using a phonautograph to record onsets against a reference oscillation. This was the first measurement of speech-production latency and an early instance of using chronometry on a task with no obvious motor baseline.

The oxygen consumption subtraction

The same logic that Donders applied to mental stages he applied to cerebral metabolism, comparing the oxygen content of blood entering and leaving the brain. He noted that oxygen had been consumed. That measurement, together with the subtraction method, is the direct ancestor of positron emission tomography and functional magnetic resonance imaging, both of which subtract a baseline condition from an active one.

Major Publications

  • Donders, F. C. (1864). On the Anomalies of Accommodation and Refraction of the Eye: With a Preliminary Essay on Physiologic Dioptrics. London: The New Sydenham Society.
  • Donders, F. C. (1868). Over de snelheid van psychische processen. Onderzoekingen gedaan in het physiologisch laboratorium der Utrechtsche Hoogeschool, 2, 92–120. English translation by W. G. Koster in W. G. Koster (Ed.), Attention and Performance II (1969), Amsterdam: North-Holland.
  • Donders, F. C. (1870). De physiologie der spraakklanken, in het bijzonder van die der Nederlandsche taal (The Physiology of Speech Sounds, in particular those of the Dutch Language).

Impact and Legacy

Donders's subtraction method was taken up with enthusiasm by experimental psychologists, because it promised something that had seemed unavailable: a way to identify and time the internal stages of a task. Wilhelm Wundt carried reaction-time measurement into the first psychological laboratory, and the whole tradition of chronometric inference in cognitive psychology descends from the 1868 paper. The Radboud University institute for brain, cognition and behaviour, and a chair at Utrecht, are named for him.

The method's weakness is as famous as its influence, and it is called the assumption of pure insertion. Subtraction gives the duration of an inserted stage only if adding that stage leaves every other stage untouched. Critics argued early and often that it does not: Külpe held on introspective grounds that increasing a task's complexity always alters the other stages qualitatively, and Boring made the same point in his 1929 history. The objection was formalised by Saul Sternberg, who in 1969 proposed the additive-factors method precisely to avoid inserting or deleting stages — instead of comparing tasks, one manipulates factors within a task and reads stage structure off the pattern of additivity and interaction. Sternberg also showed that subtraction estimates are unreliable in practice, sometimes yielding stage durations that are implausibly short or even negative, and Ilan and Miller provided a direct demonstration in 1994 that inserting a mental rotation requirement changes the choice reaction itself rather than adding a separable stage. Underneath all of this sits a second assumption Donders made, that stages are discrete, serial, and non-overlapping, which cascaded and parallel models have since questioned.

The original data were also thin. Donders worked with a handful of participants — De Jaager among them — over numbers of trials and sessions that would not now support the inferences he drew, and his own estimates for the same components moved around considerably between subjects. The method was elegant and the measurement was not yet adequate to it. That is not unusual for a first demonstration, but it is worth recording that the 1868 paper's authority rested on its logic rather than on its numbers.

There is a defence, and it is worth stating. Gottsdanker and Shragg's 1985 verification found that under carefully matched conditions the subtraction method can recover stage durations consistent with independent estimates, and Donders's distinction between discrimination and response selection has survived in substance even where his arithmetic has not.

It is also worth noting how the paper reached the field that now owns it. For most of the eighty years after publication it was an obscure Dutch laboratory report; its English translation appeared in 1969, in the second volume of Attention and Performance, the series that grew out of the symposium held in the Netherlands in 1968 to mark the centenary of the 1868 paper. Cognitive psychology's rediscovery of mental chronometry and its rediscovery of Donders were the same event, which is why the paper reads as a founding document only from the 1960s onward.

The assumption has had a long afterlife in neuroimaging, where cognitive subtraction remains routine: activity in a control condition is subtracted from activity in an experimental condition and the difference is attributed to the targeted process. Researchers in that field have made the same criticism from the inside. Pure insertion, they point out, is an a priori assumption with no physiological validation, and because neural dynamics are nonlinear and richly interactive, the implementation of two putatively separate components will almost always show interactions that a factorial design can reveal directly. Whether this invalidates neuroimaging subtraction or merely bounds it remains unsettled, in much the same way that Donders's own inferences were unsettled a century after he made them.

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References

  • Donders, F. C. (1969). On the speed of mental processes. Acta Psychologica, 30, 412-431. (Original work published 1868)

Last updated: 2026-10-20

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