Editing Gustav Fechner (section)

== Contributions ==

Fechner published chemical and physical papers, and translated chemical works by [[Jean-Baptiste Biot]] and [[Louis Jacques Thénard]] from [[French language|French]]. He also wrote several poems and humorous pieces, such as the ''Vergleichende Anatomie der Engel'' (1825), written under the pseudonym of '''"Dr. Mises."'''<ref name="EB1911"/>

=== Elemente der Psychophysik ===

Fechner's epoch-making work was his ''Elemente der Psychophysik'' (1860). He started from the [[Monism|monistic]] thought that bodily facts and conscious facts, though not reducible one to the other, are different sides of one reality. His originality lies in trying to discover an exact mathematical relation between them. The most famous outcome of his inquiries is the law known as ''Fechner's Law'', which may be expressed as follows:<ref name="EB1911"/>

:"In order that the intensity of a sensation may increase in arithmetical progression, the stimulus must increase in geometrical progression."

The law has been found to be immensely useful, but to fail for very faint and for very strong sensations. Within its useful range, Fechner's law is that sensation is a logarithmic function of physical intensity. [[Stanley Smith Stevens|S. S. Stevens]] pointed out that such a law does not account for the fact that perceived relationships among stimuli (e.g., papers coloured black, dark grey, grey, light grey, and white) are unchanged with changes in overall intensity (i.e., in the level of illumination of the papers). He proposed, in his famous [[Stevens' power law|1961 paper]] entitled "To Honor Fechner and Repeal His Law", that intensity of stimulation is related to perception via a power-law.

Fechner's general formula for getting at the number of units in any sensation is ''S'' =&nbsp;''c''&nbsp;log&nbsp;''R'', where ''S'' stands for the sensation, ''R'' for the stimulus numerically estimated, and ''c'' for a constant that must be separately determined by experiment in each particular order of sensibility. Fechner's reasoning has been criticized on the grounds that although stimuli are composite, sensations are not. "Every sensation," says [[William James]], "presents itself as an indivisible unit; and it is quite impossible to read any clear meaning into the notion that they are masses of units combined."<ref name="EB1911"/>

=== The Fechner color effect ===
[[Image:Benham's Disc.svg|thumb|right|250px|A sample of a Benham's disk]]
In 1838, he also studied the still-mysterious perceptual illusion of what is still called the [[Fechner color|Fechner color effect]], whereby colors are seen in a moving pattern of black and white. The English journalist and amateur scientist [[Charles Benham]], in 1894, enabled English-speakers to learn of the effect through the invention of the spinning top that bears his name, Benham's top. Whether Fechner and Benham ever actually met face to face is not known.

=== The median ===
In his ''Vorschule der Aesthetik'' (1876) he used the method of extreme ranks for subjective judgements. Two years later he published a paper which developed the notion of the [[median]] and is generally credited with introducing the median into the formal analysis of data.<ref name="keynesProb">Keynes, John Maynard; ''A Treatise on Probability'' (1921), Pt II Ch XVII §5 (p 201).</ref> He later explored [[experimental aesthetics]] and attempted to determine the shapes and dimensions of aesthetically pleasing objects, using as a database the sizes of paintings.<ref>{{cite web |url=http://statprob.com/encyclopedia/gustavtheodorfechner.html |title=Gustav Theodor Fechner |author=Michael Heidelberger |publisher=/statprob.com |access-date=5 January 2014 |url-status=dead |archive-url=https://web.archive.org/web/20160304053646/http://statprob.com/encyclopedia/gustavtheodorfechner.html |archive-date=4 March 2016 }}</ref>

=== Synesthesia ===
In 1871, Fechner reported the first empirical survey of coloured letter photisms among 73 [[synesthesia|synesthetes]].<ref>Fechner, G. (1876) ''Vorschule der Aesthetik''. Leipzig: Breitkopf und Hartel. Website: [https://archive.org/details/vorschulederaest12fechuoft chuoft.pdf]</ref><ref>Campen, Cretien van (1996). De verwarring der zintuigen. Artistieke en psychologische experimenten met synesthesie. ''Psychologie & Maatschappij'', vol. 20, nr. 1, pp. 10–26.</ref> His work was followed in the 1880s by that of [[Francis Galton]].<ref name="galton1880b">{{cite journal |author=Galton F |title=Visualized Numerals |journal=Nature |volume=21 |issue= 543|pages=494–5 |year=1880 |doi= 10.1038/021494e0|bibcode=1880Natur..21..494G |url=https://zenodo.org/record/1429243|doi-access=free }}</ref><ref name="galton1880a">{{cite journal |author=Galton F |title=Visualized Numerals |journal=Nature |volume=21 |issue= 533|pages=252–6 |year=1880 |doi= 10.1038/021252a0|bibcode=1880Natur..21..252G |doi-access=free }}</ref><ref name="galton1883">{{cite book |author=Galton F. |title=Inquiries into Human Faculty and Its Development |publisher=Macmillan |year=1883 |url=https://galton.org/books/human-faculty/ |access-date=2008-06-17}}</ref>

=== Corpus callosum split ===
One of Fechner's speculations about consciousness dealt with brain. During his time, it was known that the brain is bilaterally symmetrical and that there is a deep division between the two halves that are linked by a connecting band of fibers called the [[corpus callosum]]. Fechner speculated that if the [[Corpus callosotomy|corpus callosum were split]], two separate streams of consciousness would result - the mind would become two. Yet, Fechner believed that his theory would never be tested; he was incorrect. During the mid-twentieth century, [[Roger Wolcott Sperry|Roger Sperry]] and [[Michael Gazzaniga]] worked on epileptic patients with sectioned corpus callosum and observed that Fechner's idea was correct.<ref>[Gazzinga, M.S (1970). The bisected brain. New York: Appleton-Century-Crofts]</ref>

=== Golden section hypothesis ===
Fechner constructed ten rectangles with different ratios of width to length and asked numerous observers to choose the "best" and "worst" rectangle shape. He was concerned with the visual appeal of rectangles with different proportions. Participants were explicitly instructed to disregard any associations that they have with the rectangles, e.g. with objects of similar ratios. The rectangles chosen as "best" by the largest number of participants and as "worst" by the fewest participants had a ratio of 0.62 (21:34).<ref>{{Cite book|title=Vorschule der Ästhetik|last=Fechner|first=Gustav|publisher=Breitkopf & Härtel|year=1876|location=Leipzig|pages=190–202}}</ref> This ratio is known as the "golden section" (or [[golden ratio]]) and referred to the ratio of a rectangle's width to length that is most appealing to the eye. [[Carl Stumpf]] was a participant in this study.

However, there has been some ongoing dispute on the experiment itself, as the fact that Fechner deliberately discarded results of the study ill-fitting to his needs became known, with many mathematicians, including [[Mario Livio]], refuting the result of the experiment.<ref>{{Cite book |last=Livio |first=Mario |url=https://www.worldcat.org/oclc/49226115 |title=The Golden Ratio: The Story of Phi, the World's Most Astonishing Number |date=2002 |publisher=Broadway Books |isbn=0-7679-0815-5 |edition=1st |location=New York |oclc=49226115}}</ref>

=== The two-piece normal distribution ===
In his posthumously published ''Kollektivmasslehre'' (1897), Fechner introduced the Zweiseitige Gauss'sche Gesetz or [[Split normal distribution|two-piece normal distribution]], to accommodate the asymmetries he had observed in empirical frequency distributions in many fields. The distribution has been independently rediscovered by several authors working in different fields.<ref>Wallis, K.F. (2014). "The two-piece normal, binormal, or double Gaussian distribution: its origin and rediscoveries". ''[[Statistical Science]]'', Vol. 29, No. 1, pp.106-112. DOI: 10.1214/13-STS417 {{ArXiv|1405.4995}}</ref>

=== Fechner's paradox<!--'Fechner's paradox' redirects here--> ===

In 1861, Fechner reported that if he looked at a light with a darkened piece of glass over one eye then closed that eye, the light appeared to become brighter, even though less light was coming into his eyes.<ref name=Levelt1965>Levelt, W. J. M. (1965). Binocular brightness averaging and contour information. [[British Journal of Psychology]], 56, 1-13. https://dx.doi.org/10.1111/j.2044-8295.1965.tb00939.x</ref> This phenomenon has come to be called '''Fechner's paradox'''<!--boldface per WP:R#PLA-->.<ref>Robinson, T. R. (1896). Light intensity and depth perception. [[American Journal of Psychology]], 7, 518-532. https://dx.doi.org/10.2307/1411847</ref> It has been the subject of numerous research papers, including in the 2000s.<ref>Ding, J., & Levi, D. M. (2017). Binocular combination of luminance profiles. [[Journal of Vision]], 17(13, 4), 1-32. https://dx.doi.org/10.1167/17.13.4</ref> It occurs because the perceived brightness of the light with both eyes open is similar to the average brightness of each light viewed with one eye.<ref name=Levelt1965 />