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									                                           Cruise Scientific    Visual Statistics Studio    Visual Statistics Illustra

Mueller-Lyer Apparatus

Anyone who attended college could not have missed seeing the Mueller-Lyer perceptual
illusion. It typically occupies the front pages of introductory psychology textbooks, next
to the alternating vase-human face figure, the Necker cube, and in old psychology
textbook next to alternating pictures of human skull and two young ladies. Its typical
rendering shows two lines of the same length, one terminated by arrows and the other by
the inverted arrows, where the second line appears to be longer than the first one. Few
people know that the original Mueller-Lyer illusion was not a drawing, but an apparatus.
The author first encountered the original Mueller-Lyer apparatus at the University of
Muenster, Germany. The instrument was located in a rather dusty display window.
Mounted on a dark brown oak board, its movable arrow was operated by a pair of worn
out strings. The eerie feeling the contraption conveyed was heightened by the
surroundings. Muenster is an old Hanseatic city. The medieval walls of its university still
echo with the footsteps of mendicant friars and goliardic verses composed by its student
body. Nevertheless, this encounter with the real Mueller-Lyer apparatus was disquieting.
Prior to visiting Germany, the author saw hundreds of Mueller-Lyer figures: horizontal
and vertical, aligned on a line or separated by white space, with parallels or shifted edges.
Some were printed in black on white, others were colored or redesigned by graphic
artists. But all were petrified in two-dimensional fields, immovable and static. The story
of the Mueller-Lyer illusion is included here to illustrate that sometimes, the plausibility
of narratives changes over time.

The apparatus

The apparatus was mounted on a wooden block and consisted of a brass plate, a beam,
and vertical bars. The middle pair vertical bar was attached to a pair of strings. Subjects,
sitting at a distance from the apparatus, could move the bars by pulling the strings.

On the backside of the brass plate were engravings of protractors and rulers. During the
experimental phase of the experiment, the angular separation of the vertical bars was
typically set to 45 and 135 degrees. During the control phase of the experiment, the
angular separation of all vertical bars was 90 degrees. During both phases of the
experiment, the researcher recorded the discrepancies between the physical and estimated
middle of the beam. This technical description of the Mueller-Lyer device may leave the
reader baffled as to why is it discussed here. The point we try to make is that the original
meaning of the Mueller-Lyer illusion was quite different from the meaning subsequent
generations ascribed to this illusion.

Individual differences
At the time of inception of the Mueller-Lyer apparatus, one of the issues generating
attention of the scientific community was the problem of variability of subjective
estimates while matching lighted surfaces to the brightness of starts. These practical
difficulties lead Bessel (1784-1846) to formulate the personal equation problem that is
basically the problem of measurement of individual differences. Fechner (1801-1887),
using the data provided by Mueller-Lyer apparatus, introduced the notion of constant and
variable errors and provided a general solution to the problem of measurement of
individual differences.
Idealists and realists
Around the turn of the century, the Mueller-Lyer illusion was used in debates between
philosophical idealists and realists that continued the classical controversy between John
Locke and George Berkeley. Locke maintained the view that material objects exist
independently of the mind. Berkeley believed that the Lockean view leads to atheism and
postulated that nothing exists apart from the mind. His doctrine is frequently summarized
by the expression esse est percipi, (to be is to be perceived), frequently illustrated by
parable of a falling tree in a forest with no-one perceiving its fall. Bishop Berkeley
further reasoned that since a given object is likely to be perceived by different individuals
as being the same, the individuals' mind had to be created by a divine being. Realists
asserted that objects in the external world exist independently of what is thought about
them. Idealists' counterargument was that this view fails to explain perceptual mistakes
and illusions, and supported this contention by using the Mueller-Lyer illusion.

...And beyond
In the 1920s, Gestalt psychologists saw the perceptual phenomena reflected by the
Mueller-Lyer figure as illustrating their doctrine of the primacy of the whole. Gestalt
translates from German approximately as ‘pattern,’ ‘form,’ or ‘configuration.’ Gestalt
psychologists such as Kurt Koffka, Wolfgang Kohler, and Max Wertheimer argued that
relationships among components of an object rather than properties of its components
determine what is perceived.

During the ascendancy of Skinner’s operant conditioning theory in the 1950s,
conditioned stimuli provided by the Mueller-Lyer configurations of bars and arrows led
to the conclusion that even ‘chickens react in a manner which suggests that they
experience an illusion.
                                       In the 1960s, the figure was interpreted within the
context of research pertaining to perceptual differences between ‘civilized’ people
growing up in the rectangular, ‘carpentered’ world and ‘primitive’ people growing up in
an oblique world of thatched huts and hogans. It was hypothesized that rectangular
environment provides different cues than oblique environment and the Mueller-Lyer
illusion was used to support this argument

 For a while it seemed that the Mueller-Lyer illusion was finally laid to rest when, in the
1970s, the American Psychologist published the article: ‘Liar’s Illusion’. Measuring
actual lengths of the Mueller-Lyer arrows in about a dozen introductory psychology
textbooks, the line bordered by arrows was actually shorter, this difference in length
being statistically significant. Over the time, graphic artists repeatedly rendering this
illusion for countless PSY101 textbooks also succumbed to its deceptiveness.

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