Gustav Fechner

Introduction

Gustav Theodor Fechner (19 April 1801 – 18 November 1887) posed a question that most of his contemporaries thought was nonsense, and answered it in a way that made experimental psychology possible: how much does a sensation increase when the stimulus that causes it gets stronger?

The question presupposes that a sensation has a magnitude, and that the magnitude can be related by a law to a physical quantity. Neither was obvious in 1850. The mind was understood to have ideas, and ideas were not the sort of thing that could be measured against grams or candlepower. Fechner's claim was that they could — not directly, but through the measurable capacity of a person to discriminate. You cannot ask someone how bright a light feels. You can ask them whether two lights differ. And from a long series of such yes/no judgments, a lawful relation between the physical and the mental can be recovered.

He published the result as Elemente der Psychophysik (1860) and called the discipline psychophysics. It is the first body of work in which mental quantities are measured systematically, and it is the reason Wilhelm Wundt could found a laboratory nineteen years later with instruments and methods already to hand.

Fechner was, by training and by profession until he was fifty, a physicist. He came to the question by way of a mystical conviction about the unity of mind and matter, and his answer was later shown to be wrong in its specific form. What survived is the question, the methods he invented to pursue it, and the demonstration — which nobody before him had made — that the relation between the physical world and experience is a lawful, measurable thing.

Early Life and Education

Fechner was born in Groß Särchen, a village in Lower Lusatia (now Żarki Wielkie in Poland), where his father was the pastor. He was educated at the Sorau gymnasium, and then read medicine at the University of Leipzig from 1817, taking his degree in 1822.

He never practised. Leipzig had no physics chair he could hope for, so he lived by writing and translating scientific textbooks — a multi-volume physics dictionary, a popular astronomy book — while working privately on electricity and on the physics of the nervous system. He was appointed to a lectureship in physics at Leipzig in 1824 and to the professorship in 1834, and he spent the 1830s producing a long series of experimental papers on electric currents and on the physiology of vision.

Academic and Professional Career

The illness and the turn

In 1839 Fechner damaged his eyes badly, studying afterimages by staring at the sun through coloured glass. The injury was followed by a severe nervous collapse: he was unable to work, unable to read, in almost total darkness and in acute pain, and for three years he was effectively incapacitated. He resigned his chair. He considered suicide.

He recovered suddenly, in 1843, in an episode he experienced as a kind of illumination — and the recovery produced a philosophical conversion. Fechner concluded that the physical and the mental are not two substances but two appearances of one reality, that the world is everywhere animate, and that consciousness is not confined to animals with brains. He spent the 1840s and early 1850s writing this up in works that modern readers find hard to take: Nanna, oder über das Seelenleben der Pflanzen (Nanna, or the Soul-Life of Plants, 1848), which argued for plant sentience, and Zend-Avesta (1851), a three-volume cosmological treatise.

He called the scientific description of the world the night view (Nachtansicht) and the animating, spiritual interpretation the day view (Tagesansicht), and he regarded the second as the truer one. His scientific contemporaries found the mysticism embarrassing and largely ignored it. It is, however, the motive for the psychophysics: he wanted to demonstrate the mind–body relation quantitatively, because he believed the demonstration mattered metaphysically.

The idea of 1850

The technical breakthrough came in the early hours of 22 October 1850 — an occasion he recorded, and which is often called Fechner's "morning dream" (Morgentraum). His colleague at Leipzig, the physiologist Ernst Heinrich Weber, had established that the smallest detectable difference between two stimuli is not a fixed amount but a fixed proportion of the stimulus: you can detect a one-gram difference between two 100-gram weights but not between two 1000-gram weights. That is Weber's law, and Fechner named it as such, which is why the result carries Weber's name rather than his own.

Fechner's insight on that morning was that Weber's law could be integrated. If each just-noticeable step adds the same proportional increment, and if each such step adds the same amount of sensation, then sensation must grow as the logarithm of stimulus intensity:

S = k · log I

where S is sensation, I is stimulus intensity, and k a constant fixed by the modality. Doubling a light's physical intensity does not double its apparent brightness. To make a light seem twice as bright, you have to multiply its physical intensity many times over.

He spent the next decade testing it, and published Elemente der Psychophysik in 1860. He was fifty-nine.

Later years

Fechner was appointed professor of philosophy at Leipzig in 1846, and held the post for the rest of his life. He continued to work on psychophysics and, in the 1870s, on experimental aesthetics — Vorschule der Aesthetik (1876), the first attempt to study aesthetic preference empirically rather than philosophically, using measured judgments about rectangles, proportions and the golden section.

He died in Leipzig on 18 November 1887.

Major Contributions to Psychology

Psychophysics, and the three classical methods

Fechner's durable achievement is not the logarithmic law but the instrument he built to test it. To measure a threshold you need a procedure, and he devised three, all of which are still in use:

Method of limits (just-noticeable differences) — the stimulus is varied continuously, ascending and descending, until the observer reports a change; the threshold is taken as the average of the crossover points. He also identified the errors it produces: habituation (the observer anticipates) and expectation (the observer commits early).
Method of constant stimuli — a fixed set of comparison stimuli is presented many times in random order; the threshold is the value detected on a defined proportion of trials. This is the most reliable of the three, and it is the direct ancestor of modern psychometric function fitting.
Method of adjustment (average error) — the observer adjusts the comparison stimulus until it matches the standard; the threshold is the variability of the settings.

Alongside these he introduced the two-point threshold as a measure of tactile sensitivity, and the method of right and wrong cases, which he used to correct for guessing.

Outer and inner psychophysics

Fechner distinguished two problems. Outer psychophysics is the relation between the physical stimulus and the sensation — accessible, because both ends are measurable or at least orderable. Inner psychophysics is the relation between the underlying neural activity and the sensation — inaccessible in his day, and, as he argued, only partly accessible now.

The distinction matters because it is what makes his method indirect. He did not claim to measure sensation; he claimed to measure the sensitivity of the discriminating system, and to derive a scale of sensation from it.

Signal detection, and what came after

The next hundred years corrected Fechner in two ways, and both corrections are now standard material.

The first is S. S. Stevens' power law (1957–61), which replaced the logarithm with a power function, S = a·Iⁿ, where the exponent varies by modality — about 0.33 for brightness, about 0.6 for loudness, above 1 for electric shock, meaning that for some modalities sensation grows faster than the stimulus. The log law fitted the narrow middle range of intensities Fechner could test and fails outside it.

The second is signal detection theory (Green and Swets, 1966), which showed that every judgment in a psychophysical task depends on two independent things: the observer's sensitivity and the observer's response criterion — their willingness to say "yes". Fechner's methods confound them. A cautious observer and an impulsive one produce different thresholds from the same sensory apparatus, and once you separate the two you find that "threshold" is not a property of the senses alone.

Experimental aesthetics

Fechner's Vorschule der Aesthetik is the first empirical study of aesthetic preference, and it introduced the method of asking large numbers of people to choose between stimuli — the method still used in the field. His specific finding — that the golden section rectangle is preferred — has not survived systematic replication, and is usually regarded as an artefact of his procedure. The method lasted; the result did not.

He is also credited with introducing the median as a statistical summary, and with early work on the "Fechner paradox" in binocular vision.

Major Publications

Elemente der Psychophysik / Elements of Psychophysics (1860) — the founding text of the discipline
Nanna, oder über das Seelenleben der Pflanzen (1848) — the panpsychist work
Zend-Avesta, oder über die Dinge des Himmels und des Jenseits (1851) — the cosmological treatise
Über die physische und philosophische Atomenlehre (1855) — the atomism argument
Vorschule der Aesthetik (1876) — experimental aesthetics
In Sachen der Psychophysik (1877) — his reply to critics, including von Kries and Mach

Impact and Legacy

Fechner's legacy is a demonstration rather than a law. He showed that a mental quantity could be put into a functional relation with a physical one, and that the relation could be measured experimentally with repeatable methods and stated as mathematics. That demonstration is what made psychology a quantitative science, and it is why Wundt — who came to it as a physiologist looking for a method — had a discipline to institutionalise.

The methods are his most direct bequest. The method of constant stimuli and the psychometric function are used everywhere: in vision and hearing research, in the measurement of pain, in drug discrimination studies, in the fitting of psychometric curves in modern cognitive neuroscience. Signal detection theory, which replaced his account of the threshold, is built directly on the experimental apparatus he invented.

And there is a conceptual legacy worth stating. Before Fechner, the mind's contents were qualities; after him, they were quantities on scales, and the business of mapping a stimulus to a response — which is what much of experimental psychology still does — had a template.

Criticism

The logarithmic law is wrong. Stevens' power law superseded it, and even Stevens' law is now treated as an approximation. Fechner's data covered a narrow intensity range in which the logarithm and the power function are hard to distinguish, and his extrapolation to all intensities does not hold.

His scale does not measure what he said it did. Fechner claimed to have measured sensation. What he measured was discriminability — the observer's capacity to detect a difference — and his "sensation scale" is a scale of sensitivity, not of felt intensity. It is, in modern terms, ordinal rather than interval. The criticism was made in his own lifetime, notably by Georg Elias Müller and by Carl Stumpf, and it is now accepted.

His method confounds sensitivity with response bias. This is signal detection theory's central point, and it is decisive against the classical threshold concept. Two observers with identical hearing can report different thresholds depending on how willing they are to say they heard something. Fechner knew that his observers' "expectation" and "habituation" introduced errors and tried to correct for them by counterbalancing; what he could not do was model the decision, because the framework did not exist yet.

The metaphysics motivated the science, and coloured it. Fechner was not trying to build psychophysics for its own sake; he was trying to demonstrate the mind–body identity, and specifically to refute materialism by showing that the mental has its own lawful structure. That is a strange goal for a founder of quantitative psychology, and his contemporaries — Helmholtz among them — regarded Zend-Avesta as evidence that he had lost his way. The science survived the motive, but the two should not be separated when reading him.

And his later experimental work was weak. The aesthetics programme is historically important as a first attempt and empirically poor by any standard; the golden-section result is generally regarded as an artefact, and his stimulus sets and procedures would not be acceptable now. His work on plant sentience was never science at all.

Associated Figures

Ernst Heinrich Weber — his Leipzig colleague, whose law of the just-noticeable difference Fechner named, generalised and integrated
Wilhelm Wundt — who founded the first experimental psychology laboratory on the psychophysical methods Fechner established
Hermann von Helmholtz — his contemporary, and a critic of his metaphysics
S. S. Stevens — who replaced the logarithmic law with the power law
Georg Elias Müller — among the first to object that Fechner's scale measured discrimination rather than sensation

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References

Fechner, G. T. (1860). Elemente der Psychophysik. Breitkopf & Härtel.