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Sunday, November 10, 2024

Gestalt psychology

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Gestalt_psychology
 
Gestalt psychology, gestaltism, or configurationism is a school of psychology and a theory of perception that emphasises the processing of entire patterns and configurations, and not merely individual components. It emerged in the early twentieth century in Austria and Germany as a rejection of basic principles of Wilhelm Wundt's and Edward Titchener's elementalist and structuralist psychology.

Gestalt psychology is often associated with the adage, "The whole is greater than the sum of its parts". In Gestalt theory, information is perceived as wholes rather than disparate parts which are then processed summatively. As used in Gestalt psychology, the German word Gestalt (/ɡəˈʃtælt, -ˈʃtɑːlt/ gə-SHTA(H)LT, German: [ɡəˈʃtalt] ; meaning "form") is interpreted as "pattern" or "configuration".

It differs from Gestalt therapy, which is only peripherally linked to Gestalt psychology.

Origin and history

Max Wertheimer, Kurt Koffka, and Wolfgang Köhler founded Gestalt psychology in the early 20th century. The dominant view in psychology at the time was structuralism, exemplified by the work of Hermann von Helmholtz, Wilhelm Wundt, and Edward B. Titchener. Structuralism was rooted firmly in British empiricism and was based on three closely interrelated theories:

  1. "atomism," also known as "elementalism," the view that all knowledge, even complex abstract ideas, is built from simple, elementary constituents
  2. "sensationalism," the view that the simplest constituents—the atoms of thought—are elementary sense impressions
  3. "associationism," the view that more complex ideas arise from the association of simpler ideas.

Together, these three theories give rise to the view that the mind constructs all perceptions and abstract thoughts strictly from lower-level sensations, which are related solely by being associated closely in space and time. The Gestaltists took issue with the widespread atomistic view that the aim of psychology should be to break consciousness down into putative basic elements.

In contrast, the Gestalt psychologists believed that breaking psychological phenomena down into smaller parts would not lead to understanding psychology. Instead, they viewed psychological phenomena as organized, structured wholes. They argued that the psychological "whole" has priority and that the "parts" are defined by the structure of the whole, rather than the other way round. Gestalt theories of perception are based on human nature being inclined to understand objects as an entire structure rather than the sum of its parts.

Wertheimer had been a student of Austrian philosopher, Christian von Ehrenfels, a member of the School of Brentano. Von Ehrenfels introduced the concept of Gestalt to philosophy and psychology in 1890, before the advent of Gestalt psychology as such. Von Ehrenfels observed that a perceptual experience, such as perceiving a melody or a shape, is more than the sum of its sensory components. He claimed that, in addition to the sensory elements of the perception, there is something additional that is an element in its own right, despite in some sense being derived from the organization of the component sensory elements. He called it Gestalt-qualität or "form-quality." It is this Gestalt-qualität that, according to von Ehrenfels, allows a tune to be transposed to a new key, using completely different notes, while still retaining its identity. The idea of a Gestalt-qualität has roots in theories by David Hume, Johann Wolfgang von Goethe, Immanuel Kant, David Hartley, and Ernst Mach. Both von Ehrenfels and Edmund Husserl seem to have been inspired by Mach's work Beiträge zur Analyse der Empfindungen (Contributions to the Analysis of Sensations, 1886), in formulating their very similar concepts of gestalt and figural moment, respectively.

By 1914, the first published references to Gestalt theory could be found in a footnote of Gabriele von Wartensleben's application of Gestalt theory to personality. She was a student at Frankfurt Academy for Social Sciences, who interacted deeply with Wertheimer and Köhler.

Through a series of experiments, Wertheimer discovered that a person observing a pair of alternating bars of light can, under the right conditions, experience the illusion of movement between one location and the other. He noted that this was a perception of motion absent any moving object. That is, it was pure phenomenal motion. He dubbed it phi ("phenomenal") motion. Wertheimer's publication of these results in 1912 marks the beginning of Gestalt psychology. In comparison to von Ehrenfels and others who had used the term "gestalt" earlier in various ways, Wertheimer's unique contribution was to insist that the "gestalt" is perceptually primary. The gestalt defines the parts from which it is composed, rather than being a secondary quality that emerges from those parts. Wertheimer took the more radical position that one hears the melody first and only then may perceptually divide it up into notes. Similarly, in vision, one sees the form of the circle first, with its apprehension not mediated by a process of part-summation. Only after this primary apprehension might one notice that it is made up of lines or dots or stars.

The two men who served as Wertheimer's subjects in the phi experiments were Köhler and Koffka. Köhler was an expert in physical acoustics, having studied under physicist Max Planck, but had taken his degree in psychology under Carl Stumpf. Koffka was also a student of Stumpf's, having studied movement phenomena and psychological aspects of rhythm. In 1917, Köhler published the results of four years of research on learning in chimpanzees. Köhler showed, contrary to the claims of most other learning theorists, that animals can learn by "sudden insight" into the "structure" of a problem, over and above the associative and incremental manner of learning that Ivan Pavlov and Edward Lee Thorndike had demonstrated with dogs and cats, respectively.

In 1921, Koffka published a Gestalt-oriented text on developmental psychology, Growth of the Mind. With the help of American psychologist Robert Ogden, Koffka introduced the Gestalt point of view to an American audience in 1922 by way of a paper in Psychological Bulletin. It contains criticisms of then-current explanations of a number of problems of perception, and the alternatives offered by the Gestalt school. Koffka moved to the United States in 1924, eventually settling at Smith College in 1927. In 1935, Koffka published his Principles of Gestalt Psychology. This textbook laid out the Gestalt vision of the scientific enterprise as a whole. Science, he said, is not the simple accumulation of facts. What makes research scientific is the incorporation of facts into a theoretical structure. The goal of the Gestaltists was to integrate the facts of inanimate nature, life, and mind into a single scientific structure. This meant that science would have to accommodate not only what Koffka called the quantitative facts of physical science but the facts of two other "scientific categories": questions of order and questions of Sinn, a German word which has been variously translated as significance, value, and meaning. Without incorporating the meaning of experience and behavior, Koffka believed that science would doom itself to trivialities in its investigation of human beings.

Having survived the Nazis up to the mid-1930s, all the core members of the Gestalt movement were forced out of Germany to the United States by 1935. Köhler published another book, Dynamics in Psychology, in 1940 but thereafter the Gestalt movement suffered a series of setbacks. Koffka died in 1941 and Wertheimer in 1943. Wertheimer's long-awaited book on mathematical problem-solving, Productive Thinking, was published posthumously in 1945, but Köhler was left to guide the movement without his two long-time colleagues.

Gestalt therapy

Gestalt psychology differs from Gestalt therapy, which is only peripherally linked to Gestalt psychology. The founders of Gestalt therapy, Fritz and Laura Perls, had worked with Kurt Goldstein, a neurologist who had applied principles of Gestalt psychology to the functioning of the organism. Laura Perls had been a Gestalt psychologist before she became a psychoanalyst and before she began developing Gestalt therapy together with Fritz Perls. The extent to which Gestalt psychology influenced Gestalt therapy is disputed. On one hand, Laura Perls preferred not to use the term "Gestalt" to name the emerging new therapy, because she thought that the Gestalt psychologists would object to it; on the other hand, Fritz and Laura Perls clearly adopted some of Goldstein's work.

Mary Henle noted in her presidential address to Division 24 at the meeting of the American Psychological Association: "What Perls has done has been to take a few terms from Gestalt psychology, stretch their meaning beyond recognition, mix them with notions—often unclear and often incompatible—from the depth psychologies, existentialism, and common sense, and he has called the whole mixture gestalt therapy. His work has no substantive relation to scientific Gestalt psychology. To use his own language, Fritz Perls has done 'his thing'; whatever it is, it is not Gestalt psychology."

One form of psychotherapy that, unlike Gestalt therapy, is actually consistently based on Gestalt psychology is Gestalt theoretical psychotherapy.

Theoretical framework and methodology

The Gestalt psychologists practiced a set of theoretical and methodological principles that attempted to redefine the approach to psychological research. This is in contrast to investigations developed at the beginning of the 20th century, based on traditional scientific methodology, which divided the object of study into a set of elements that could be analyzed separately with the objective of reducing the complexity of this object.

The principle of totality asserts that conscious experience must be considered globally by taking into account all the physical and mental aspects of the individual simultaneously, because the nature of the mind demands that each component be considered as part of a system of dynamic relationships. Thus, holism as fundamental aspect of Gestalt psychology. Moreover, the perception of the nature of a part depends upon the whole in which it is embedded. The maxim that the whole is more than the sum of its parts is not a precise description of the Gestaltist view. Rather, as Koffka writes, "The whole is something else than the sum of its parts, because summing is a meaningless procedure, whereas the whole-part relationship is meaningful."

The principle of psychophysical isomorphism hypothesizes that there is a correlation between conscious experience and cerebral activity.

Based on the principles, phenomenon experimental analysis was derived, which asserts that any psychological research should take phenomena as a starting point and not be solely focused on sensory qualities. A related principle is that of the biotic experiment, which establishes the need to conduct real experiments that sharply contrasted with and opposed classic laboratory experiments. This signified experimenting in natural situations, developed in real conditions, in which it would be possible to reproduce, with higher fidelity, what would be habitual for a subject.

Principles

The Gestaltists were the first to document and demonstrate empirically many facts about perception—including facts about the perception of movement, the perception of contour, perceptual constancy, and perceptual illusions. Wertheimer's discovery of the phi phenomenon is one example of such a contribution.

Properties

The key principles of gestalt systems are emergence, reification, multistability and invariance. These principles are not necessarily separable modules to model individually, but they could be different aspects of a single unified dynamic mechanism.

Reification

Reification

Reification is the constructive or generative aspect of perception, by which the experienced object of perception contains more explicit spatial information than the sensory stimulus on which it is based. For instance, a triangle is perceived in picture A, though no triangle is there. In pictures B and D the eye recognizes disparate shapes as "belonging" to a single shape, in C a complete three-dimensional shape is seen, where in actuality no such thing is drawn.

Reification can be explained by progress in the study of illusory contours, which are treated by the visual system as "real" contours.

Multistability

The Necker cube and the Rubin vase, two examples of multistability

Multistability (or multistable perception) is the tendency of ambiguous perceptual experiences to pop back and forth between two or more alternative interpretations. This is seen, for example, in the Necker cube and Rubin's Figure/Vase illusion. Other examples include the three-legged blivet, artist M. C. Escher's artwork, and the appearance of flashing marquee lights moving first one direction and then suddenly the other.

Invariance

Invariance

Invariance is the property of perception whereby simple geometrical objects are recognized independent of rotation, translation, and scale, as well as several other variations such as elastic deformations, different lighting, and different component features. For example, the objects in A in the figure are all immediately recognized as the same basic shape, which is immediately distinguishable from the forms in B. They are even recognized despite perspective and elastic deformations as in C, and when depicted using different graphic elements as in D. Computational theories of vision, such as those by David Marr, have provided alternate explanations of how perceived objects are classified.

Perceptual organisation forms

Perceptual grouping

Like figure-ground organization, perceptual grouping (sometimes called perceptual segregation) is a form of perceptual organization. Perceptual grouping is the process that determines how organisms perceive some parts of their perceptual fields as being more related than others, using such information for object detection.

The Gestaltists were the first psychologists to systematically study perceptual grouping. According to Gestalt psychologists, the fundamental principle of perceptual grouping is the law of Prägnanz, also known as the law of good Gestalt. Prägnanz is a German word that directly translates to "pithiness" and implies salience, conciseness, and orderliness. The law of Prägnanz says that people tend to experience things as regular, orderly, symmetrical, and simple.

Gestalt psychologists attempted to discover refinements of the law of Prägnanz, which involved writing down laws that predict the interpretation of sensation. Wertheimer defined a few principles that explain the ways humans perceive objects based on similarity, proximity, and continuity.

Law of proximity

Law of proximity

The law of proximity states that when an individual perceives an assortment of objects, they perceive objects that are close to each other as forming a group. For example, in the figure illustrating the law of proximity, there are 72 circles, but we perceive the collection of circles in groups. Specifically, we perceive that there is a group of 36 circles on the left side of the image and three groups of 12 circles on the right side of the image. This law is often used in advertising logos to emphasize which aspects of events are associated.

Law of similarity

Law of similarity

The law of similarity states that elements within an assortment of objects are perceptually grouped together if they are similar to each other. This similarity can occur in the form of shape, colour, shading or other qualities. For example, the figure illustrating the law of similarity portrays 36 circles all equal distance apart from one another forming a square. In this depiction, 18 of the circles are shaded dark, and 18 of the circles are shaded light. We perceive the dark circles as grouped together and the light circles as grouped together, forming six horizontal lines within the square of circles. This perception of lines is due to the law of similarity.

Law of closure

Law of closure

Gestalt psychologists believed that humans tend to perceive objects as complete rather than focusing on the gaps that the object might contain. For example, a circle has good Gestalt in terms of completeness. However, we will also perceive an incomplete circle as a complete circle. That tendency to complete shapes and figures is called closure. The law of closure states that individuals perceive objects such as shapes, letters, pictures, etc., as being whole when they are not complete. Specifically, when parts of a whole picture are missing, our perception fills in the visual gap. Research shows that the reason the mind completes a regular figure that is not perceived through sensation is to increase the regularity of surrounding stimuli. For example, the figure that depicts the law of closure portrays what we perceive as a circle on the left side of the image and a rectangle on the right side of the image. However, gaps are present in the shapes. If the law of closure did not exist, the image would depict an assortment of different lines with different lengths, rotations, and curvatures—but with the law of closure, we perceptually combine the lines into whole shapes.

Law of symmetry

The law of symmetry states that the mind perceives objects as being symmetrical and forming around a center point. It is perceptually pleasing to divide objects into an even number of symmetrical parts. Therefore, when two symmetrical elements are unconnected the mind perceptually connects them to form a coherent shape. Similarities between symmetrical objects increase the likelihood that objects are grouped to form a combined symmetrical object. For example, the figure depicting the law of symmetry shows a configuration of square and curled brackets. When the image is perceived, we tend to observe three pairs of symmetrical brackets rather than six individual brackets.

Law of common fate

The law of common fate states that objects are perceived as lines that move along the smoothest path. Experiments using the visual sensory modality found that the movement of elements of an object produces paths that individuals perceive that the objects are on. We perceive elements of objects to have trends of motion, which indicate the path that the object is on. The law of continuity implies the grouping together of objects that have the same trend of motion and are therefore on the same path. For example, if there is an array of dots and half the dots are moving upward while the other half are moving downward, we would perceive the upward moving dots and the downward moving dots as two distinct units.

Law of continuity

Law of continuity

The law of continuity (also known as the law of good continuation) states that elements of objects tend to be grouped together, and therefore integrated into perceptual wholes if they are aligned within an object. In cases where there is an intersection between objects, individuals tend to perceive the two objects as two single uninterrupted entities. Stimuli remain distinct even with overlap. We are less likely to group elements with sharp abrupt directional changes as being one object. For example, the figure depicting the law of continuity shows a configuration of two crossed keys. When the image is perceived, we tend to perceive the key in the background as a single uninterrupted key instead of two separate halves of a key.

Law of past experience

The law of past experience implies that under some circumstances visual stimuli are categorized according to past experience. If objects tend to be observed within close proximity, or small temporal intervals, the objects are more likely to be perceived together. For example, the English language contains 26 letters that are grouped to form words using a set of rules. If an individual reads an English word they have never seen, they use the law of past experience to interpret the letters "L" and "I" as two letters beside each other, rather than using the law of closure to combine the letters and interpret the object as an uppercase U.

Music

An example of the Gestalt movement in effect, as it is both a process and result, is a music sequence. People are able to recognise a sequence of perhaps six or seven notes, despite them being transposed into a different tuning or key. An early theory of gestalt grouping principles in music was composer-theorist James Tenney's Meta+Hodos (1961). Auditory Scene Analysis as developed by Albert Bregman further extends a gestalt approach to the analysis of sound perception.

Figure-ground organization

Figure-ground organization is a form of perceptual organization, which interprets perceptual elements in terms of their shapes and relative locations in the layout of surfaces in the 3-D world. Figure-ground organization structures the perceptual field into a figure (standing out at the front of the perceptual field) and a background (receding behind the figure). Pioneering work on figure-ground organization was carried out by the Danish psychologist Edgar Rubin. The Gestalt psychologists demonstrated that people tend to perceive as figures those parts of our perceptual fields that are convex, symmetric, small, and enclosed.

Problem solving and insight

Gestalt psychology contributed to the scientific study of problem solving. In fact, the early experimental work of the Gestaltists in Germany marks the beginning of the scientific study of problem solving. Later this experimental work continued through the 1960s and early 1970s with research conducted on relatively simple laboratory tasks of problem solving.

Max Wertheimer distinguished two kinds of thinking: productive thinking and reproductive thinking. Productive thinking is solving a problem based on insight—a quick, creative, unplanned response to situations and environmental interaction. Reproductive thinking is solving a problem deliberately based on previous experience and knowledge. Reproductive thinking proceeds algorithmically—a problem solver reproduces a series of steps from memory, knowing that they will lead to a solution—or by trial and error.

Karl Duncker, another Gestalt psychologist who studied problem solving, coined the term functional fixedness for describing the difficulties in both visual perception and problem solving that arise from the fact that one element of a whole situation already has a (fixed) function that has to be changed in order to perceive something or find the solution to a problem.

Legacy

Gestalt psychology struggled to precisely define terms like Prägnanz, to make specific behavioural predictions, and to articulate testable models of underlying neural mechanisms. It was criticized as being merely descriptive. These shortcomings led, by the mid-20th century, to growing dissatisfaction with Gestaltism and a subsequent decline in its impact on psychology. Despite this decline, Gestalt psychology has formed the basis of much further research into the perception of patterns and objects and of research into behaviour, thinking, problem solving and psychopathology.

Support from cybernetics and neurology

In the 1940s and 1950s, laboratory research in neurology and what became known as cybernetics on the mechanism of frogs' eyes indicate that perception of 'gestalts' (in particular gestalts in motion) is perhaps more primitive and fundamental than 'seeing' as such:

A frog hunts on land by vision... He has no fovea, or region of greatest acuity in vision, upon which he must centre a part of the image... The frog does not seem to see or, at any rate, is not concerned with the detail of stationary parts of the world around him. He will starve to death surrounded by food if it is not moving. His choice of food is determined only by size and movement. He will leap to capture any object the size of an insect or worm, providing it moves like one. He can be fooled easily not only by a piece of dangled meat but by any moving small object... He does remember a moving thing provided it stays within his field of vision and he is not distracted.
The lowest-level concepts related to visual perception for a human being probably differ little from the concepts of a frog. In any case, the structure of the retina in mammals and in human beings is the same as in amphibians. The phenomenon of distortion of perception of an image stabilised on the retina gives some idea of the concepts of the subsequent levels of the hierarchy. This is a very interesting phenomenon. When a person looks at an immobile object, "fixes" it with his eyes, the eyeballs do not remain absolutely immobile; they make small involuntary movements. As a result, the image of the object on the retina is constantly in motion, slowly drifting and jumping back to the point of maximum sensitivity. The image "marks time" in the vicinity of this point.

Use in contemporary social psychology

The halo effect can be explained through the application of Gestalt theories to social information processing. The constructive theories of social cognition are applied to the expectations of individuals. They have been perceived in this manner and the person judging the individual is continuing to view them in this positive manner. Gestalt's theories of perception enforces that individual's tendency to perceive actions and characteristics as a whole rather than isolated parts, therefore humans are inclined to build a coherent and consistent impression of objects and behaviors in order to achieve an acceptable shape and form. The halo effect is what forms patterns for individuals, the halo effect being classified as a cognitive bias which occurs during impression formation. The halo effect can also be altered by physical characteristics, social status and many other characteristics. As well, the halo effect can have real repercussions on the individual's perception of reality, either negatively or positively, meaning to construct negative or positive images about other individuals or situations, something that could lead to self-fulfilling prophesies, stereotyping, or even discrimination.

Contemporary cognitive and perceptual psychology

Some of the central criticisms of Gestaltism are based on the preference Gestaltists are deemed to have for theory over data, and a lack of quantitative research supporting Gestalt ideas. This is not necessarily a fair criticism as highlighted by a recent collection of quantitative research on Gestalt perception. Researchers continue to test hypotheses about the mechanisms underlying Gestalt principles such as the principle of similarity.

Other important criticisms concern the lack of definition and support for the many physiological assumptions made by gestaltists and lack of theoretical coherence in modern Gestalt psychology.

In some scholarly communities, such as cognitive psychology and computational neuroscience, gestalt theories of perception are criticized for being descriptive rather than explanatory in nature. For this reason, they are viewed by some as redundant or uninformative. For example, a textbook on visual perception states that, "The physiological theory of the gestaltists has fallen by the wayside, leaving us with a set of descriptive principles, but without a model of perceptual processing. Indeed, some of their 'laws' of perceptual organisation today sound vague and inadequate. What is meant by a 'good' or 'simple' shape, for example?"

One historian of psychology, David J. Murray, has argued that Gestalt psychologists first discovered many principles later championed by cognitive psychology, including schemas and prototypes. Another psychologist has argued that the Gestalt psychologists made a lasting contribution by showing how the study of illusions can help scientists understand essential aspects of how the visual system normally functions, not merely how it breaks down.

Use in design

Several grouping principles are employed in this map: similarity allows the reader to selectively isolate cities, rivers, or state boundaries; closure allows the dashed boundary lines to be perceived as continuous borders; proximity makes the collection of river segments appear as a single watershed; and continuity helps the reader "see" whole states even when boundaries are obscured under rivers.

The gestalt laws are used in several visual design fields, such as user interface design and cartography. The laws of similarity and proximity can, for example, be used as guides for placing radio buttons. They may also be used in designing computers and software for more intuitive human use. Examples include the design and layout of a desktop's shortcuts in rows and columns.

In map design, principles of Prägnanz or grouping are crucial for implying a conceptual order to the portrayed geographic features, thus facilitating the intended use of the map. The Law of Similarity is employed by selecting similar map symbols for similar kinds of features or features with similar properties; the Law of Proximity is crucial to identifying geographic patterns and regions; and the Laws of Closure and Continuity allow users to recognize features that may be obscured by other features (such as when a road goes over a river).

As above, so below

From Wikipedia, the free encyclopedia
The Magician, from the 1909 Rider–Waite tarot deck, often thought to represent the concept of "as above, so below".

"As above, so below" is a popular modern paraphrase of the second verse of the Emerald Tablet, a short Hermetic text which first appeared in an Arabic source from the late eighth or early ninth century. The paraphrase is based on one of several existing Latin translations of the Emerald Tablet, in which the second verse appears as follows:

Quod est superius est sicut quod inferius, et quod inferius est sicut quod est superius.

That which is above is like to that which is below, and that which is below is like to that which is above.

The paraphrase is peculiar to this Latin version, and differs from the original Arabic, which reads "from" rather than "like to".

Following its use by prominent modern occultists such as Helena P. Blavatsky (1831–1891, co-founder of the Theosophical Society) and the anonymous author of the Kybalion (often taken to be William W. Atkinson, 1862–1932, a pioneer of the New Thought movement), the paraphrase started to take on a life of its own, becoming an often cited motto in New Age circles.

Scholarly interpretations

Man as a microcosm; illustrated in Robert Fludd's Utrisque Cosmi, 1619.

Among historians of philosophy and science, the verse is often understood as a reference to the supposed effects of celestial mechanics upon terrestrial events. This would include the effects of the Sun upon the change of seasons, or those of the Moon upon the tides, but also more elaborate astrological effects.

According to another common interpretation, the verse refers to the structural similarities (or 'correspondences') between the macrocosm (from Greek makros kosmos, "the great world"; the universe as a whole, understood as a great living being) and the microcosm (from Greek mikros kosmos, "the small world"; the human being, understood as a miniature universe). This type of view is found in many philosophical systems world-wide, the most relevant here being ancient Greek and Hellenistic philosophy, where notable proponents included Anaximander (c. 610 – c. 546 BCE), Plato (c. 428 or 424 – c. 348 BCE), the Hippocratic authors (late fifth or early fourth century BCE and onwards), and the Stoics (third century BCE and onwards).

Occultist interpretations

Helena P. Blavatsky's Isis Unveiled (1877)

The occultists who were responsible for the popularization of the paraphrase generally understood it in the context of Emanuel Swedenborg's (1688–1772) doctrine of the correspondence between different planes of existence, a strongly elaborated version of the classical macrocosm–microcosm analogy. This interpretation was pioneered by Helena P. Blavatsky (1831–1891), whose works contain some of the earliest occurrences of the phrase as an independent axiom. Generally writing from a perennialist perspective, Blavatsky associated the phrase with a number of historically unrelated thought systems such as Pythagoreanism, Kabbalah and Buddhism.

Helena P. Blavatsky (1831–1891)

From Blavatsky's Isis Unveiled (1877):

His [sc. Swedenborg's] doctrine of correspondence, or Hermetic symbolism, is that of Pythagoras and of the kabalists—"as above, so below." It is also that of the Buddhist philosophers, who, in their still more abstract metaphysics, inverting the usual mode of definition given by our erudite scholars, call the invisible types the only reality, and everything else the effects of the causes, or visible prototypes—illusions.

There is no prominent character in all the annals of sacred or profane history whose prototype we cannot find in the half-fictitious and half-real traditions of bygone religions and mythologies. As the star, glimmering at an immeasurable distance above our heads, in the boundless immensity of the sky, reflects itself in the smooth waters of a lake, so does the imagery of men of the antediluvian ages reflect itself in the periods we can embrace in an historical retrospect. "As above, so it is below. That which has been, will return again. As in heaven, so on earth."

The spirit of a mineral, plant, or animal, may begin to form here, and reach its final development millions of ages hereafter, on other planets, known or unknown, visible or invisible to astronomers. For, who is able to controvert the theory previously suggested, that the earth itself will, like the living creatures to which it has given birth, ultimately, and after passing through its own stage of death and dissolution, become an etherealized astral planet ? "As above, so below;" harmony is the great law of nature.

The Kybalion (1908)

Though retaining the interpretation of the phrase in terms of Swedenborg's doctrine of correspondence, it was somewhat more closely associated with the philosophical mentalism (the primacy of mind as the active cause of things) of the ancient Greek Hermetica by the anonymous author of the Kybalion (1908, 'Three Initiates', perhaps William W. Atkinson, 1862–1932). What follows are some literal quotes from the book:

William W. Atkinson (1862–1932), often thought to be the author of the Kybalion.
Emanuel Swedenborg (1688–1772), major advocate of the doctrine of correspondence.

II. The Principle of Correspondence.

"As above, so below; as below, so above"– The Kybalion.

This Principle embodies the truth that there is always a Correspondence between the laws and phenomena of the various planes of Being and Life. The old Hermetic axiom ran in these words: "As above, so below; as below, so above." [...] This Principle is of universal application and manifestation, on the various planes of the material, mental, and spiritual universe– it is an Universal Law. [...] Just as a knowledge of the Principles of Geometry enables man to measure distant suns and their movements, while seated in his observatory, so a knowledge of the Principle of Correspondence enables Man to reason intelligently from the Known to the Unknown. [...]

The Planes of Correspondence.

"As above, so below; as below, so above."—The Kybalion.

The great Second Hermetic Principle embodies the truth that there is a harmony, agreement, and correspondence between the several planes of Manifestation, Life and Being. This truth is a truth because all that is included in the Universe emanates from the same source, and the same laws, principles, and characteristics apply to each unit, or combination of units of activity, as each manifests its own phenomena upon its own plane. [...]

[...] The old Hermetic axiom, "As above so below," may be pressed into service at this point. Let us endeavor to get a glimpse of the workings on higher planes by examining those on our own. The Principle of Correspondence must apply to this as well as to other problems. Let us see! On his own plane of being, how does Man create? Well, first, he may create by making something out of outside materials. But this will not do, for there are no materials outside of THE ALL with which it may create. Well, then, secondly, Man pro-creates or reproduces his kind by the process of begetting, which is self-multiplication accomplished by transferring a portion of his substance to his offspring. But this will not do, because THE ALL cannot transfer or subtract a portion of itself, nor can it reproduce or multiply itself— in the first place there would be a taking away, and in the second case a multiplication or addition to THE ALL, both thoughts being an absurdity. Is there no third way in which MAN creates? Yes, there is—he CREATES MENTALLY! And in so doing he uses no outside materials, nor does he reproduce himself, and yet his Spirit pervades the Mental Creation. Following the Principle of Correspondence, we are justified in considering that THE ALL creates the Universe MENTALLY, in a manner akin to the process whereby Man creates Mental Images. [...]

[...] The student will, of course, realize that the illustrations given above are necessarily imperfect and inadequate, for they represent the creation of mental images in finite minds, while the Universe is a creation of Infinite Mind—and the difference between the two poles separates them. And yet it is merely a matter of degree—the same Principle is in operation—the Principle of Correspondence manifests in each—"As above, so Below; as Below, so above." And, in the degree that Man realizes the existence of the Indwelling Spirit immanent within his being, so will he rise in the spiritual scale of life. This is what spiritual development means—the recognition, realization, and manifestation of the Spirit within us. Try to remember this last definition—that of spiritual development. It contains the Truth of True Religion.

Difference from the original Arabic

It may be noted that the original Arabic of the verse in the Emerald Tablet itself does not mention that what is above and what is below are "as" or "like" each other, but rather that they are "from" each other:

Arabic: إن الأعلى من الأسفل والأسفل من الأعلى (Inna al-aʿlā min al-asfal wa-l-asfal min al-aʿlā)

Latin translation by Hugo of Santalla: Superiora de inferioribus, inferiora de superioribus

English translation of the Arabic: That which is above is from that which is below, and that which is below is from that which is above.

The phrase has also been adopted as a title for various works of art, such as the 2014 found-footage horror film As Above, So Below, as well as a number of musical works listed at As above, so below (disambiguation).

Seven heavens

From Wikipedia, the free encyclopedia
Wood carving 1475; pointing to 7 celestial bodies consisted 5 planets that can be seen with naked eye, the Sun and the Moon, each floating in a heaven layer, (Arabic Felaq in ancient cosmology)

In mythological or religious cosmology, the seven heavens refer to seven levels or divisions of the Heavens. The concept, also found in the ancient Mesopotamian religions, can be found in Judaism and Islam; the Christian Bible does not mention seven levels of heaven. Some of these traditions, including Jainism, also have a concept of seven earths or seven underworlds both with the metaphysical realms of deities and with observed celestial bodies such as the classical planets and fixed stars.

Beliefs in the plurality of the heavens were not restricted to the belief in seven heavens. Ancient near eastern cosmology largely accepted the existence of three heavens. In Jewish cosmologies (albeit absent from the Hebrew Bible), the number of heavens could range from 3 to 365, with 7 being the most popular figure.

Origins

The notion or belief in a cosmos structured or tiered into seven heavens likely originates or derives from the seven visible heavenly bodies (Mercury, Venus, Mars, Jupiter, Saturn, the Moon, and the Sun).

Greek astronomy and cosmology

Each of the seven heavens corresponds to one of the seven classical planets known in antiquity. Ancient observers noticed that these heavenly objects (the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn) moved at different paces in the sky both from each other and from the fixed stars beyond them. Unlike comets, which appeared in the sky with no warning, they moved in regular patterns that could be predicted. They also observed that objects in the sky influenced objects on Earth as when movements of the sun affect the behavior of plants or movements of the Moon affect ocean tides.

Mesopotamian cosmology

The concept of seven heavens as developed in ancient Mesopotamia where it took on a symbolic or magical meaning as opposed to a literal one. The concept of a seven-tiered was likely In the Sumerian language, the words for heavens (or sky) and Earth are An and Ki. The ancient Mesopotamians regarded the sky as a series of domes (usually three, but sometimes seven) covering the flat Earth. Each dome was made of a different kind of precious stone. The lowest dome of the heavens was made of jasper and was the home of the stars. The middle dome of heaven was made of saggilmut stone and was the abode of the Igigi. The highest and outermost dome of the heavens was made of luludānītu stone and was personified as An, the god of the sky. The celestial bodies were equated with specific deities as well. The planet Venus was believed to be Inanna, the goddess of love, sex, and war. The Sun was her brother Utu, the god of justice and the Moon was their father Nanna. Ordinary mortals could not go to the heavens because it was the abode of the gods alone. Instead, after a person died, his or her soul went to Kur (later known as Irkalla), a dark shadowy underworld, located deep below the surface of the Earth. Sumerian incantations of the late second millennium BCE make references to seven heavens and seven earths. One such incantation is: "an-imin-bi ki-imin-bi" (the heavens are seven, the earths are seven.)

The understanding that the heavens can influence things on Earth lent heavenly, magical properties to the number seven itself, as in stories of seven demons, seven churches, seven spirits, or seven thrones. The number seven appears frequently in Babylonian magical rituals. The seven Jewish and the seven Islamic heavens may have had their origin in Babylonian astronomy.

In general, the heavens is not a place for humans in Mesopotamian religion. As Gilgamesh says to his friend Enkidu, in the Epic of Gilgamesh: "Who can go up to the heavens, my friend? Only the gods dwell with Shamash forever". Along with the idea of seven heavens, the idea of three heavens was also common in ancient Mesopotamia.

Abrahamic religions

Judaism

In the Talmud, it is suggested that the upper part of the universe is made up of seven heavens (Hebrew: shamayim):

  1. Vilon (וילון), see (Isa 40:22)
  2. Raki'a (רקיע), see (Gen 1:17)
  3. Shehaqim (שחקים), see (Ps 78:23, Midr. Teh. to Ps. xix. 7)
  4. Zebul (זבול), see (Isa 63:15, 1 Kings 8:13)
  5. Ma'on (מעון), see (Deut 26:15, Ps 42:9)
  6. Machon (מכון), see (1 Kings 8:39, Deut 28:12)
  7. Araboth (ערבות), The seventh Heaven where ophanim, the seraphim, and the hayyoth and the Throne of God are located.

The Jewish Merkavah and Hekhalot literature was devoted to discussing the details of these heavens, sometimes in connection with traditions relating to Enoch, such as the Third Book of Enoch.

Apocryphal texts

The Second Book of Enoch, also written in the first century CE, describes the mystical ascent of the patriarch Enoch through a hierarchy of Ten Heavens. Enoch passes through the Garden of Eden in the Third Heaven on his way to meet the Lord face-to-face in the Tenth (chapter 22). Along the way, he encounters vividly described populations of angels who torment wrongdoers; he sees homes, olive oil, and flowers.

The book's depiction of ten heavens represented an expansion of the ancient seven-heaven model. This expanded cosmology was developed further in medieval Christianity.

Christianity

La materia della Divina commedia di Dante Alighieri, Plate VI: "The Ordering of Paradise" by Michelangelo Caetani (1804–1882)

The New Testament does not refer to the concept of seven heavens. However, an explicit reference to a third heaven appears in the Second Epistle to the Corinthians, penned in Macedonia around 55 CE. It describes the following mystical experience:

I know a person in Christ who fourteen years ago was caught up to the third heaven—whether in the body or out of the body I do not know; God knows. And I know that such a person—whether in the body or out of the body I do not know; God knows—was caught up into Paradise and heard things that are not to be told, that no mortal is permitted to repeat.

— (2 Corinthians 12.2–4 NRSV)

The description is usually taken as an oblique reference by the author to himself. The passage appears to reflect first-century beliefs among Jews and Christians that the realm of Paradise existed in a different heaven than the highest one—an impression that may find support in the original Greek wording (closer to "caught away" than "caught up").

In the second century, Irenaeus also knows seven heavens (see his Demonstration of Apostolic Preaching 9; cf. Against Heresies 1.5.2).

Over the course of the Middle Ages, Christian thinkers expanded the ancient Mesopotamian seven-heaven model into a system of ten heavens. This cosmology, taught in the first European universities by the Scholastics, reached its supreme literary expression in The Divine Comedy by Dante Alighieri. The idea of seven heavens is carried over into the esoteric Christian cabala.

Islam

A Persian miniature depicting Seven Heavens from The History of Mohammed, Bibliothèque nationale de France, Paris.

The Quran and Hadith frequently mention the existence of seven samāwāt (سماوات), the plural of samāʾ (سماء), meaning 'heaven, sky, celestial sphere', and cognate with Hebrew shamāyim (שמים). Some of the verses in the Quran mentioning the samaawat are Q41:12, Q65:12 and Q71:15. The seven heavens are not final destinations for the dead after the Day of Judgment, but regions distinct from the earth, guarded by angels and inhabited by souls whose abode depends on their good deeds (fasting, jihad, Hajj, charity), with the highest layer, the closest to God. According to Quran and Hadiths, each of the skies has its own Qibla or a structure which became direction of prayer, similar to Kaaba of the mortal world, where the Qibla of highest heaven is called Bayt al-Ma'mur, while the Qibla building for the lowest sky is called Bayt al-Izza.

In other sources, the concept is presented in metaphorical terms. Each of the seven heavens is depicted as being composed of a different material, and Islamic prophets are resident in each. The names are taken from Suyuti's Al-Hay’a as-samya fi l-hay’a as-sunmya:

  1. Raqi'a (رقيعاء): The first heaven is described as being made of water and is the home of Adam and Eve, as well as the angels of each star. According to some narratives, Muhammad encountered the angel Habib here.
  2. Araqlun (أرفلون): The second heaven is described as being made of white pearls and is the home of Yahya (John the Baptist) and Isa (Jesus).
  3. Qaydum (قيدوم): The third heaven is described as being made of iron (alternatively pearls or other dazzling stones); Joseph and the Angel of Death (named Azrael) are resident there.
  4. Maʿuna (ماعونا): The fourth heaven is described as being made of brass (alternatively white gold); Idris (conventionally identified with Enoch) and the "Angel of Tears" reside there.
  5. Di'a (ريقا): The fifth heaven is described as being made of silver; Aaron holds court over this heaven. Sometimes, the guardian of hellfire is assigned to this place.
  6. Daqua (دقناء): The sixth heaven is described as being composed of gold (alternatively garnets and rubies); Moses can be found here.
  7. ʿAriba (عريبا): The seventh heaven, which borrows some concepts from its Jewish counterpart, is depicted as being composed of divine light incomprehensible to the mortal man (alternatively emerald). Abraham is a resident there and Sidrat al-Muntaha, a large enigmatic Lote tree, marks the end of the seventh heaven and the utmost extremity for all of God's creatures and heavenly knowledge.

There are two interpretations of using the number "seven". One viewpoint is that the number "seven" here simply means "many" and is not to be taken literally (the number is often used to imply that in the Arabic language). But many other commentators use the number literally.

One modern interpretation of "heavens" is that all the stars and galaxies (including the Milky Way) are all part of the "first heaven", and "beyond that six still bigger worlds are there," which have yet to be discovered by scientists.

Gnosticism

The Gnostic text On the Origin of the World states that seven heavens were created in Chaos by Yaldabaoth below the higher realms, and each of them are ruled over by an Archon. During the end times, these heavens will collapse on each and the heaven of Yaldabaoth will split in two, causing its stars to fall upon the Earth, therefore causing it to sink into the Abyss.

In the Coptic Apocalypse of Paul, the apostle Paul ascends through the lower Seven Heavens. At the seventh heaven, he meets an old man who opens the gate to the realm beyond the material universe, and Paul then ascends to the eighth, ninth, and tenth heavens.

In Mandaeism, a series of maṭartas, or "toll houses," are located between the World of Light (alma ḏ-nhūra) from Tibil (Earth). The term maṭarta has variously been translated as "watch-station", "toll-station", "way-station", or "purgatory". Maṭartas are guarded by various uthras (celestial beings from the World of Light) and demons. In the Ginza Rabba, seven maṭartas are listed and described in Chapter 3 in Book 5 of the Right Ginza. However, the number of maṭartas is not always seven; Book 6 of the Right Ginza (also known as the "Book of Dinanukht") lists six, and Chapter 4 in Book 1 of the Left Ginza lists eight. Alternatively, the Seven Heavens can also be seen as corresponding to the Seven Planets, who form part of the entourage of Ruha in the World of Darkness.

Hinduism

According to all Puranas, the Brahmanda is divided into fourteen worlds known as lokas. Seven are upper worlds: Bhuloka (the Earth and sky), Bhuvarloka, Svargaloka, Maharloka, Janarloka, Tapaloka and Satyaloka; and seven are lower worlds: Atala, Vitala, Sutala, Talatala, Mahatala, Rasatala and Patala.

Celestial spheres

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Celestial_spheres
Geocentric celestial spheres; Peter Apian's Cosmographia (Antwerp, 1539)

The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed stars and planets are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element (quintessence), like gems set in orbs. Since it was believed that the fixed stars did not change their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.

In modern thought, the orbits of the planets are viewed as the paths of those planets through mostly empty space. Ancient and medieval thinkers, however, considered the celestial orbs to be thick spheres of rarefied matter nested one within the other, each one in complete contact with the sphere above it and the sphere below. When scholars applied Ptolemy's epicycles, they presumed that each planetary sphere was exactly thick enough to accommodate them. By combining this nested sphere model with astronomical observations, scholars calculated what became generally accepted values at the time for the distances to the Sun: about 4 million miles (6.4 million kilometres), to the other planets, and to the edge of the universe: about 73 million miles (117 million kilometres). The nested sphere model's distances to the Sun and planets differ significantly from modern measurements of the distances, and the size of the universe is now known to be inconceivably large and continuously expanding.

Albert Van Helden has suggested that from about 1250 until the 17th century, virtually all educated Europeans were familiar with the Ptolemaic model of "nesting spheres and the cosmic dimensions derived from it". Even following the adoption of Copernicus's heliocentric model of the universe, new versions of the celestial sphere model were introduced, with the planetary spheres following this sequence from the central Sun: Mercury, Venus, Earth-Moon, Mars, Jupiter and Saturn.

Mainstream belief in the theory of celestial spheres did not survive the Scientific Revolution. In the early 1600s, Kepler continued to discuss celestial spheres, although he did not consider that the planets were carried by the spheres but held that they moved in elliptical paths described by Kepler's laws of planetary motion. In the late 1600s, Greek and medieval theories concerning the motion of terrestrial and celestial objects were replaced by Newton's law of universal gravitation and Newtonian mechanics, which explain how Kepler's laws arise from the gravitational attraction between bodies.

History

Early ideas of spheres and circles

In Greek antiquity the ideas of celestial spheres and rings first appeared in the cosmology of Anaximander in the early 6th century BC. In his cosmology both the Sun and Moon are circular open vents in tubular rings of fire enclosed in tubes of condensed air; these rings constitute the rims of rotating chariot-like wheels pivoting on the Earth at their centre. The fixed stars are also open vents in such wheel rims, but there are so many such wheels for the stars that their contiguous rims all together form a continuous spherical shell encompassing the Earth. All these wheel rims had originally been formed out of an original sphere of fire wholly encompassing the Earth, which had disintegrated into many individual rings. Hence, in Anaximanders's cosmogony, in the beginning was the sphere, out of which celestial rings were formed, from some of which the stellar sphere was in turn composed. As viewed from the Earth, the ring of the Sun was highest, that of the Moon was lower, and the sphere of the stars was lowest.

Following Anaximander, his pupil Anaximenes (c. 585 – c. 528/4) held that the stars, Sun, Moon, and planets are all made of fire. But whilst the stars are fastened on a revolving crystal sphere like nails or studs, the Sun, Moon, and planets, and also the Earth, all just ride on air like leaves because of their breadth. And whilst the fixed stars are carried around in a complete circle by the stellar sphere, the Sun, Moon and planets do not revolve under the Earth between setting and rising again like the stars do, but rather on setting they go laterally around the Earth like a cap turning halfway around the head until they rise again. And unlike Anaximander, he relegated the fixed stars to the region most distant from the Earth. The most enduring feature of Anaximenes' cosmos was its conception of the stars being fixed on a crystal sphere as in a rigid frame, which became a fundamental principle of cosmology down to Copernicus and Kepler.

After Anaximenes, Pythagoras, Xenophanes and Parmenides all held that the universe was spherical. And much later in the fourth century BC Plato's Timaeus proposed that the body of the cosmos was made in the most perfect and uniform shape, that of a sphere containing the fixed stars. But it posited that the planets were spherical bodies set in rotating bands or rings rather than wheel rims as in Anaximander's cosmology.

Emergence of the planetary spheres

Instead of bands, Plato's student Eudoxus developed a planetary model using concentric spheres for all the planets, with three spheres each for his models of the Moon and the Sun and four each for the models of the other five planets, thus making 26 spheres in all. Callippus modified this system, using five spheres for his models of the Sun, Moon, Mercury, Venus, and Mars and retaining four spheres for the models of Jupiter and Saturn, thus making 33 spheres in all. Each planet is attached to the innermost of its own particular set of spheres. Although the models of Eudoxus and Callippus qualitatively describe the major features of the motion of the planets, they fail to account exactly for these motions and therefore cannot provide quantitative predictions. Although historians of Greek science have traditionally considered these models to be merely geometrical representations, recent studies have proposed that they were also intended to be physically real or have withheld judgment, noting the limited evidence to resolve the question.

In his Metaphysics, Aristotle developed a physical cosmology of spheres, based on the mathematical models of Eudoxus. In Aristotle's fully developed celestial model, the spherical Earth is at the centre of the universe and the planets are moved by either 47 or 55 interconnected spheres that form a unified planetary system, whereas in the models of Eudoxus and Callippus each planet's individual set of spheres were not connected to those of the next planet. Aristotle says the exact number of spheres, and hence the number of movers, is to be determined by astronomical investigation, but he added additional spheres to those proposed by Eudoxus and Callippus, to counteract the motion of the outer spheres. Aristotle considers that these spheres are made of an unchanging fifth element, the aether. Each of these concentric spheres is moved by its own god—an unchanging divine unmoved mover, and who moves its sphere simply by virtue of being loved by it.

Ptolemaic model of the spheres for Venus, Mars, Jupiter, and Saturn with epicycle, eccentric deferent and equant point. Georg von Peuerbach, Theoricae novae planetarum, 1474.

In his Almagest, the astronomer Ptolemy (fl. c. 150 AD) developed geometrical predictive models of the motions of the stars and planets and extended them to a unified physical model of the cosmos in his Planetary hypotheses. By using eccentrics and epicycles, his geometrical model achieved greater mathematical detail and predictive accuracy than had been exhibited by earlier concentric spherical models of the cosmos. In Ptolemy's physical model, each planet is contained in two or more spheres, but in Book 2 of his Planetary Hypotheses Ptolemy depicted thick circular slices rather than spheres as in its Book 1. One sphere/slice is the deferent, with a centre offset somewhat from the Earth; the other sphere/slice is an epicycle embedded in the deferent, with the planet embedded in the epicyclical sphere/slice. Ptolemy's model of nesting spheres provided the general dimensions of the cosmos, the greatest distance of Saturn being 19,865 times the radius of the Earth and the distance of the fixed stars being at least 20,000 Earth radii.

The planetary spheres were arranged outwards from the spherical, stationary Earth at the centre of the universe in this order: the spheres of the Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. In more detailed models the seven planetary spheres contained other secondary spheres within them. The planetary spheres were followed by the stellar sphere containing the fixed stars; other scholars added a ninth sphere to account for the precession of the equinoxes, a tenth to account for the supposed trepidation of the equinoxes, and even an eleventh to account for the changing obliquity of the ecliptic. In antiquity the order of the lower planets was not universally agreed. Plato and his followers ordered them Moon, Sun, Mercury, Venus, and then followed the standard model for the upper spheres. Others disagreed about the relative place of the spheres of Mercury and Venus: Ptolemy placed both of them beneath the Sun with Venus above Mercury, but noted others placed them both above the Sun; some medieval thinkers, such as al-Bitruji, placed the sphere of Venus above the Sun and that of Mercury below it.

Middle Ages

The Earth within seven celestial spheres, from Bede, De natura rerum, late 11th century

Astronomical discussions

A series of astronomers, beginning with the Muslim astronomer al-Farghānī, used the Ptolemaic model of nesting spheres to compute distances to the stars and planetary spheres. Al-Farghānī's distance to the stars was 20,110 Earth radii which, on the assumption that the radius of the Earth was 3,250 miles (5,230 kilometres), came to 65,357,500 miles (105,182,700 kilometres). An introduction to Ptolemy's Almagest, the Tashil al-Majisti, believed to be written by Thābit ibn Qurra, presented minor variations of Ptolemy's distances to the celestial spheres. In his Zij, Al-Battānī presented independent calculations of the distances to the planets on the model of nesting spheres, which he thought was due to scholars writing after Ptolemy. His calculations yielded a distance of 19,000 Earth radii to the stars.

Around the turn of the millennium, the Arabic astronomer and polymath Ibn al-Haytham (Alhacen) presented a development of Ptolemy's geocentric models in terms of nested spheres. Despite the similarity of this concept to that of Ptolemy's Planetary Hypotheses, al-Haytham's presentation differs in sufficient detail that it has been argued that it reflects an independent development of the concept. In chapters 15–16 of his Book of Optics, Ibn al-Haytham also said that the celestial spheres do not consist of solid matter.

Near the end of the twelfth century, the Spanish Muslim astronomer al-Bitrūjī (Alpetragius) sought to explain the complex motions of the planets without Ptolemy's epicycles and eccentrics, using an Aristotelian framework of purely concentric spheres that moved with differing speeds from east to west. This model was much less accurate as a predictive astronomical model, but it was discussed by later European astronomers and philosophers.

In the thirteenth century the astronomer al-'Urḍi proposed a radical change to Ptolemy's system of nesting spheres. In his Kitāb al-Hayáh, he recalculated the distance of the planets using parameters which he redetermined. Taking the distance of the Sun as 1,266 Earth radii, he was forced to place the sphere of Venus above the sphere of the Sun; as a further refinement, he added the planet's diameters to the thickness of their spheres. As a consequence, his version of the nesting spheres model had the sphere of the stars at a distance of 140,177 Earth radii.

About the same time, scholars in European universities began to address the implications of the rediscovered philosophy of Aristotle and astronomy of Ptolemy. Both astronomical scholars and popular writers considered the implications of the nested sphere model for the dimensions of the universe. Campanus of Novara's introductory astronomical text, the Theorica planetarum, used the model of nesting spheres to compute the distances of the various planets from the Earth, which he gave as 22,612 Earth radii or 73,387,747+100660 miles (118,106,130.55 km). In his Opus Majus, Roger Bacon cited Al-Farghānī's distance to the stars of 20,110 Earth radii, or 65,357,700 miles (105,183,000 km), from which he computed the circumference of the universe to be 410,818,517+37 miles (661,148,316.1 km). Clear evidence that this model was thought to represent physical reality is the accounts found in Bacon's Opus Majus of the time needed to walk to the Moon and in the popular Middle English South English Legendary, that it would take 8,000 years to reach the highest starry heaven. General understanding of the dimensions of the universe derived from the nested sphere model reached wider audiences through the presentations in Hebrew by Moses Maimonides, in French by Gossuin of Metz, and in Italian by Dante Alighieri.

Philosophical and theological discussions

Philosophers were less concerned with such mathematical calculations than with the nature of the celestial spheres, their relation to revealed accounts of created nature, and the causes of their motion.

Adi Setia describes the debate among Islamic scholars in the twelfth century, based on the commentary of Fakhr al-Din al-Razi about whether the celestial spheres are real, concrete physical bodies or "merely the abstract circles in the heavens traced out… by the various stars and planets." Setia points out that most of the learned, and the astronomers, said they were solid spheres "on which the stars turn… and this view is closer to the apparent sense of the Qur'anic verses regarding the celestial orbits." However, al-Razi mentions that some, such as the Islamic scholar Dahhak, considered them to be abstract. Al-Razi himself, was undecided, he said: "In truth, there is no way to ascertain the characteristics of the heavens except by authority [of divine revelation or prophetic traditions]." Setia concludes: "Thus it seems that for al-Razi (and for others before and after him), astronomical models, whatever their utility or lack thereof for ordering the heavens, are not founded on sound rational proofs, and so no intellectual commitment can be made to them insofar as description and explanation of celestial realities are concerned."

Christian and Muslim philosophers modified Ptolemy's system to include an unmoved outermost region, the empyrean heaven, which came to be identified as the dwelling place of God and all the elect. Medieval Christians identified the sphere of stars with the Biblical firmament and sometimes posited an invisible layer of water above the firmament, to accord with Genesis. An outer sphere, inhabited by angels, appeared in some accounts.

Edward Grant, a historian of science, has provided evidence that medieval scholastic philosophers generally considered the celestial spheres to be solid in the sense of three-dimensional or continuous, but most did not consider them solid in the sense of hard. The consensus was that the celestial spheres were made of some kind of continuous fluid.

Later in the century, the mutakallim Adud al-Din al-Iji (1281–1355) rejected the principle of uniform and circular motion, following the Ash'ari doctrine of atomism, which maintained that all physical effects were caused directly by God's will rather than by natural causes. He maintained that the celestial spheres were "imaginary things" and "more tenuous than a spider's web". His views were challenged by al-Jurjani (1339–1413), who maintained that even if the celestial spheres "do not have an external reality, yet they are things that are correctly imagined and correspond to what [exists] in actuality".

Medieval astronomers and philosophers developed diverse theories about the causes of the celestial spheres' motions. They attempted to explain the spheres' motions in terms of the materials of which they were thought to be made, external movers such as celestial intelligences, and internal movers such as motive souls or impressed forces. Most of these models were qualitative, although a few incorporated quantitative analyses that related speed, motive force and resistance. By the end of the Middle Ages, the common opinion in Europe was that celestial bodies were moved by external intelligences, identified with the angels of revelation. The outermost moving sphere, which moved with the daily motion affecting all subordinate spheres, was moved by an unmoved mover, the Prime Mover, who was identified with God. Each of the lower spheres was moved by a subordinate spiritual mover (a replacement for Aristotle's multiple divine movers), called an intelligence.

Renaissance

Thomas Digges' 1576 Copernican heliocentric model of the celestial orbs

Early in the sixteenth century Nicolaus Copernicus drastically reformed the model of astronomy by displacing the Earth from its central place in favour of the Sun, yet he called his great work De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres). Although Copernicus does not treat the physical nature of the spheres in detail, his few allusions make it clear that, like many of his predecessors, he accepted non-solid celestial spheres. Copernicus rejected the ninth and tenth spheres, placed the orb of the Moon around the Earth, and moved the Sun from its orb to the center of the universe. The planetary orbs circled the center of the universe in the following order: Mercury, Venus, the great orb containing the Earth and the orb of the Moon, then the orbs of Mars, Jupiter, and Saturn. Finally he retained the eighth sphere of the stars, which he held to be stationary.

The English almanac maker, Thomas Digges, delineated the spheres of the new cosmological system in his Perfit Description of the Caelestiall Orbes … (1576). Here he arranged the "orbes" in the new Copernican order, expanding one sphere to carry "the globe of mortalitye", the Earth, the four classical elements, and the Moon, and expanding the sphere of stars infinitely to encompass all the stars and also to serve as "the court of the Great God, the habitacle of the elect, and of the coelestiall angelles."

Johannes Kepler's diagram of the celestial spheres, and of the spaces between them, following the opinion of Copernicus (Mysterium Cosmographicum, 2nd ed., 1621)

In the sixteenth century, a number of philosophers, theologians, and astronomers—among them Francesco Patrizi, Andrea Cisalpino, Peter Ramus, Robert Bellarmine, Giordano Bruno, Jerónimo Muñoz, Michael Neander, Jean Pena, and Christoph Rothmann—abandoned the concept of celestial spheres. Rothmann argued from observations of the comet of 1585 that the lack of observed parallax indicated that the comet was beyond Saturn, while the absence of observed refraction indicated the celestial region was of the same material as air, hence there were no planetary spheres.

Tycho Brahe's investigations of a series of comets from 1577 to 1585, aided by Rothmann's discussion of the comet of 1585 and Michael Maestlin's tabulated distances of the comet of 1577, which passed through the planetary orbs, led Tycho to conclude that "the structure of the heavens was very fluid and simple." Tycho opposed his view to that of "very many modern philosophers" who divided the heavens into "various orbs made of hard and impervious matter." Edward Grant found relatively few believers in hard celestial spheres before Copernicus and concluded that the idea first became common sometime between the publication of Copernicus's De revolutionibus in 1542 and Tycho Brahe's publication of his cometary research in 1588.

In his early Mysterium Cosmographicum, Johannes Kepler considered the distances of the planets and the consequent gaps required between the planetary spheres implied by the Copernican system, which had been noted by his former teacher, Michael Maestlin. Kepler's Platonic cosmology filled the large gaps with the five Platonic polyhedra, which accounted for the spheres' measured astronomical distance. In Kepler's mature celestial physics, the spheres were regarded as the purely geometric spatial regions containing each planetary orbit rather than as the rotating physical orbs of the earlier Aristotelian celestial physics. The eccentricity of each planet's orbit thereby defined the radii of the inner and outer limits of its celestial sphere and thus its thickness. In Kepler's celestial mechanics, the cause of planetary motion became the rotating Sun, itself rotated by its own motive soul. However, an immobile stellar sphere was a lasting remnant of physical celestial spheres in Kepler's cosmology.

Literary and visual expressions

"Because the medieval universe is finite, it has a shape, the perfect spherical shape, containing within itself an ordered variety....
"The spheres ... present us with an object in which the mind can rest, overwhelming in its greatness but satisfying in its harmony."

C. S. Lewis, The Discarded Image, p. 99.

Dante and Beatrice gaze upon the highest Heaven; from Gustave Doré's illustrations to the Divine Comedy, Paradiso Canto 28, lines 16–39.

In Cicero's Dream of Scipio, the elder Scipio Africanus describes an ascent through the celestial spheres, compared to which the Earth and the Roman Empire dwindle into insignificance. A commentary on the Dream of Scipio by the Roman writer Macrobius, which included a discussion of the various schools of thought on the order of the spheres, did much to spread the idea of the celestial spheres through the Early Middle Ages.

Nicole Oresme, Le livre du Ciel et du Monde, Paris, BnF, Manuscrits, Fr. 565, f. 69 (1377)

Some late medieval figures noted that the celestial spheres' physical order was inverse to their order on the spiritual plane, where God was at the center and the Earth at the periphery. Near the beginning of the fourteenth century Dante, in the Paradiso of his Divine Comedy, described God as a light at the center of the cosmos. Here the poet ascends beyond physical existence to the Empyrean Heaven, where he comes face to face with God himself and is granted understanding of both divine and human nature. Later in the century, the illuminator of Nicole Oresme's Le livre du Ciel et du Monde, a translation of and commentary on Aristotle's De caelo produced for Oresme's patron, King Charles V, employed the same motif. He drew the spheres in the conventional order, with the Moon closest to the Earth and the stars highest, but the spheres were concave upwards, centered on God, rather than concave downwards, centered on the Earth. Below this figure Oresme quotes the Psalms that "The heavens declare the Glory of God and the firmament showeth his handiwork."

The late-16th-century Portuguese epic The Lusiads vividly portrays the celestial spheres as a "great machine of the universe" constructed by God. The explorer Vasco da Gama is shown the celestial spheres in the form of a mechanical model. Contrary to Cicero's representation, da Gama's tour of the spheres begins with the Empyrean, then descends inward toward Earth, culminating in a survey of the domains and divisions of earthly kingdoms, thus magnifying the importance of human deeds in the divine plan.

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