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In
philosophy,
panpsychism is the view that consciousness, mind or soul (
psyche) is a universal and primordial feature of all things. Panpsychists see themselves as minds in a world of mind.
Panpsychism is one of the oldest philosophical theories, and has been ascribed to philosophers like
Thales,
Parmenides,
Plato,
Averroes,
Spinoza,
Leibniz and
William James. Panpsychism can also be seen in ancient philosophies such as
Stoicism,
Taoism,
Vedanta and
Mahayana Buddhism. During the 19th century, panpsychism was the default theory in
philosophy of mind, but it saw a decline during the middle years of the 20th century with the rise of
logical positivism.
[1][2] The recent interest in the
hard problem of consciousness has revived interest in panpsychism.
[1]
Etymology
The term "panpsychism" has its origins with the
Greek term
pan (
πᾶν : "all, everything, whole") and
psyche (
ψυχή: "soul, mind") as the unifying center of the mental life of us humans and other living creatures."
[3] Psyche comes from the Greek word ψύχω (
psukhō, "I blow") and can mean life, soul, mind, spirit, heart and 'life-breath'. The use of
psyche is controversial due to it being synonymous with
soul, a term usually taken to have some sort of supernatural quality; more common terms now found in the literature include
mind,
mental properties, mental aspect, and
experience.
History
Ancient philosophy
Two
iwakura — a rock where a
kami or spirit is said to reside in the religion of
Shinto.
Early forms of panpsychism can be found in pre-modern
animistic beliefs in religions such as
Shinto,
Taoism,
Paganism and
shamanism. Panpsychist views are also a staple theme in
pre-Socratic Greek philosophy.
[1] According to
Aristotle,
Thales (c. 624 – 545 BCE) the first Greek philosopher, posited a theory which held "that everything is full of gods."
[4] Thales believed that this was demonstrated by magnets. This has been interpreted as a panpsychist doctrine.
[1] Other Greek thinkers that have been associated with Panpsychism include
Anaxagoras (who saw the underlying principle or
arche as
nous or mind),
Anaximenes (who saw the
arche as
pneuma or spirit) and
Heraclitus (who said "The thinking faculty is common to all").
[5]
Plato argues for Panpsychism in his
Sophist, in which he writes that all things participate in the
form of Being and that it must have a psychic aspect of mind and soul (psyche).
[5] In the
Philebus and
Timaeus,
Plato argues for the idea of a world soul or
anima mundi. According to
Plato:
This world is indeed a living being endowed with a soul and
intelligence ... a single visible living entity containing all other
living entities, which by their nature are all related.[6]
Stoicism developed a cosmology which held that the natural world was infused with a divine fiery essence called
Pneuma, which was directed by a universal intelligence called
Logos. The relationship of the individual Logos of beings with the universal Logos was a central concern of the Roman Stoic
Marcus Aurelius. The
Metaphysics of Stoicism was based on
Hellenistic philosophies such as
Neoplatonism and
Gnosticism also made use of the Platonic idea of the
Anima mundi.
Renaissance
Illustration of the Cosmic order by Robert Fludd, the
World Soul is depicted as a woman.
After the closing of
Plato's Academy by the Emperor Justinian in 529 CE,
Neoplatonism declined. Though there were mediaeval Christian thinkers who ventured what might be called panpsychist ideas (such as
John Scotus Eriugena), it was not a dominant strain in
Christian thought. In the
Italian Renaissance, however, Panpsychism enjoyed something of an intellectual revival, in the thought of figures such as
Gerolamo Cardano,
Bernardino Telesio,
Francesco Patrizi,
Giordano Bruno, and
Tommaso Campanella.
Cardano argued for the view that soul or anima was a fundamental part
of the world and Patrizi introduced the actual term "panpsychism" into
the philosophical vocabulary. According to Giordano Bruno: "There is
nothing that does not possess a soul and that has no vital principle."
[5] Platonist ideas like the
anima mundi also resurfaced in the work of
esoteric thinkers like
Paracelsus,
Robert Fludd and
Cornelius Agrippa.
Modern philosophy
In the 17th century, two
rationalists can be said to be panpsychists,
Baruch Spinoza and
Gottfried Leibniz.
[1]
In Spinoza's monism, the one single infinite and eternal substance is
"God, or Nature" (Deus sive Natura) which has the aspects of mind
(thought) and matter (extension). Leibniz' view is that there are an
infinite number of absolutely simple mental substances called
monads which make up the fundamental structure of the universe. The Idealist philosophy of
George Berkeley is also a form of pure panpsychism and technically all idealists can be said to be panpsychists by default.
[1]
In the 19th century, Panpsychism was at its zenith. Philosophers like
Arthur Schopenhauer,
C.S Peirce,
Josiah Royce,
William James,
Eduard von Hartmann,
F.C.S. Schiller,
Ernst Haeckel and
William Kingdon Clifford as well as psychologists like
Gustav Fechner,
Wilhelm Wundt and
Rudolf Hermann Lotze all promoted Panpsychist ideas.
[1]
Arthur Schopenhauer argued for a two-sided view of reality which was both
Will
and Representation (Vorstellung). According to Schopenhauer: "All
ostensible mind can be attributed to matter, but all matter can likewise
be attributed to mind".
Josiah Royce,
the leading American absolute idealist held that reality was a "world
self", a conscious being that comprised everything, though he didn't
necessarily attribute mental properties to the smallest constituents of
mentalistic "systems". The American Pragmatist philosopher
Charles Sanders Peirce espoused a sort of Psycho-physical
Monism which the universe as suffused with mind which he associated with spontaneity and freedom. Following Pierce,
William James also espoused a form of panpsychism.
[7] In his lecture notes, James wrote:
Our only intelligible notion of an object in itself is that it should be an object for itself, and this lands us in panpsychism and a belief that our physical perceptions are effects on us of 'psychical' realities[5]
A diagram with neutral monism compared to Cartesian dualism, physicalism and idealism.
In 1893,
Paul Carus
proposed his own philosophy similar to panpsychism known as
'panbiotism', which he defined as "everything is fraught with life; it
contains life; it has the ability to live."
[8]
In the 20th century, the most significant proponent of the Panpsychist view is arguably
Alfred North Whitehead (1861-1947).
[1] Whitehead's
ontology
saw the basic nature of the world as made up of events and the process
of their creation and extinction. These elementary events (which he
called occasions) are in part mental.
[1] According to Whitehead: "we should conceive mental operations as among the factors which make up the constitution of nature."
[5] Bertrand Russell's
neutral monist views also tended towards panpsychism.
[5]
The psychologist
Carl Jung, who is known for his idea of the
collective unconscious,
wrote that "psyche and matter are contained in one and the same world,
and moreover are in continuous contact with one another", and that it
was probable that "psyche and matter are two different aspects of one
and the same thing".
[9] The psychologists
James Ward and
Charles Augustus Strong also endorsed variants of panpsychism.
[10][11][12]
Sewall Wright
endorsed a version of panpsychism. He believed that the birth of
consciousness was not due to a mysterious property of increasing
complexity, but rather an inherent property, therefore implying these
properties were in the most elementary particles.
[13]
Contemporary
The panpsychist doctrine has recently been making a comeback in the American
philosophy of mind. Prominent defenders include
Christian de Quincey,
Leopold Stubenberg,
David Ray Griffin, and
David Skrbina.
[1] In 1990, the physicist
David Bohm
published a paper named "A New theory of the relationship of mind and
matter" promoting a panpsychist theory of consciousness based on Bohm's
interpretation of quantum mechanics. Bohm has a number of followers among philosophers of mind both in United States (e.g.
Quentin Smith) and internationally (e.g.
Paavo Pylkkänen). In the United Kingdom the case for panpsychism has been made in recent decades by
Galen Strawson,
[14] Gregg Rosenberg and
Timothy Sprigge.
In the philosophy of mind, panpsychism is one possible solution to the so-called
hard problem of consciousness.
[15] The doctrine has also been applied in the field of environmental philosophy through the work of Australian philosopher
Freya Mathews.
[16] David Chalmers has provided a sympathetic account of it in
The Conscious Mind (1996). In addition, neuroscientist
Christof Koch has proposed a "scientifically refined version" of panpsychism.
[17]
Arguments for
Non-emergentism
The problems found with
emergentism are often cited by panpsychists as grounds to reject
physicalism. This argument can be traced back to the Ancient Greek philosopher
Parmenides, who argued that
ex nihilo nihil fit — nothing comes from nothing and thus the mental cannot arise from the non-mental.
In his 1979 article
Panpsychism,
Thomas Nagel
tied panpsychism to the failure of emergentism to deal with
metaphysical relation: "There are no truly emergent properties of
complex systems. All properties of complex systems that are not
relations between it and something else derive from the properties of
its constituents and their effects on each other when so combined."
[1]
Thus he denies that mental properties can arise out of complex
relationships between physical matter. Opposing Nagel, emergentist
philosophers
Roberto Mangabeira Unger in
The Religion of The Future and
Alexander Bard &
Jan Söderqvist in
Syntheism - Creating God in The Internet Age
have argued that the reality of time enables complex systems to have
truly emergent (as in irreversible and irreproducible) properties,
thereby replacing any need for panpsychism with a chronocentric, strong
emergentism.
Evolutionary
The most popular empirically based argument for panpsychism stems from
Darwinism and is a form of the non-emergence argument. This argument begins with the assumption that
evolution is a process that creates complex systems out of pre-existing properties but yet cannot make "entirely novel" properties.
[1] William Kingdon Clifford argued that:
[...] we cannot suppose that so enormous a jump from one creature to
another should have occurred at any point in the process of evolution as
the introduction of a fact entirely different and absolutely separate
from the physical fact. It is impossible for anybody to point out the
particular place in the line of descent where that event can be supposed
to have taken place. The only thing that we can come to, if we accept
the doctrine of evolution at all, is that even in the very lowest
organism, even in the Amoeba which swims about in our own blood, there
is something or other, inconceivably simple to us, which is of the same
nature with our own consciousness [...][18]
Thomas Nagel
In his book titled
Mortal Questions,
Thomas Nagel defines panpsychism as, "the view that the basic physical constituents of the universe have mental properties,"
[19] effectively claiming the panpsychist thesis to be a type of
property dualism. Nagel argues that panpsychism follows from four premises:
-
- (1) "Material composition", or commitment to materialism.
- (2) "Non-reductionism", or the view that mental properties cannot be reduced to physical properties.
- (3) "Realism" about mental properties.
- (4) "Non-emergence", or the view that "there are no truly emergent properties of complex systems".
Nagel notes that new physical properties are discovered through
explanatory inference from known physical properties; following a
similar process, mental properties would seem to derive from properties
of matter not included under the label of "physical properties", and so
they must be additional properties of matter. Also, he argues that, "the
demand for an account of how mental states necessarily appear in
physical organisms cannot be satisfied by the discovery of uniform
correlations between mental states and physical brain states."
[20] Furthermore, Nagel argues mental states are real by appealing to the inexplicability of subjective experience, or
qualia, by physical means.
Quantum physics
Philosophers such as
Alfred North Whitehead have drawn on the
indeterminacy observed by
quantum physics
to defend panpsychism. A similar line of argument has been repeated
subsequently by a number of thinkers including the physicist
David Bohm, anesthesiologist
Stuart Hameroff and philosophers such as
Quentin Smith,
Paavo Pylkkänen,
Shan Gao,
[21] and
David Chalmers who, in his more recent work, has revisited his formerly negative views concerning
quantum-theories of consciousness, and expressed sympathy towards the idea that consciousness be identified with the
collapse of the wave-function.
The advocates of panpsychist quantum consciousness theories see quantum
indeterminacy and informational but non-causal relations between
quantum elements as the key to explaining consciousness.
[1] Recent work on this approach has been also undertaken by
William Lycan (1996) and
Michael Lockwood (1991).
Intrinsic nature
These
arguments are based on the idea that everything must have an intrinsic
nature. They argue that while the objects studied by physics are
described in a dispositional way, these dispositions must be based on
some non-dispositional intrinsic attributes, which Whitehead called the
"mysterious reality in the background, intrinsically unknowable".
[1]
While we have no way of knowing what these intrinsic attributes are
like, we can know the intrinsic nature of conscious experience which
possesses irreducible and intrinsic characteristics.
Arthur Schopenhauer
argued that while the world appears to us as representation, there must
be 'an object that grounds' representation, which he called the 'inner
essence' (
das innere Wesen) and 'natural force' (
Naturkraft), which lies outside of what our understanding perceives as natural law.
[22]
Philosophers such as
Galen Strawson,
Roger Penrose (1989),
John Searle (1991),
Thomas Nagel (1979, 1986, 1999) and
Noam Chomsky (1999) have said that a revolutionary change in physics may be needed to solve the problem of consciousness.
[1]
Galen Strawson has also called for a revised "realistic physicalism"
arguing that "the experiential considered specifically as such — the
portion of reality we have to do with when we consider experiences
specifically and solely in respect of the experiential character they
have for those who have them as they have them — that ‘just is’
physical".
[1]
Arguments against
One criticism of panpsychism is the simple lack of evidence that the physical entities have any mental attributes.
John Searle
states that panpsychism is an "absurd view" and that thermostats lack
"enough structure even to be a remote candidate for consciousness"
(Searle, 1997, p. 48).
Physicalists also could
[original research?]
argue against panpsychism by denying proposition (2) of Nagel's
argument. If mental properties are reduced to physical properties of a
physical system, then it does not follow that all matter has mental
properties: it is in virtue of the structural or functional organization
of the physical system that the system can be said to have a mind, not
simply that it is made of matter. This is the common
Functionalist
position. This view allows for certain man-made systems that are
properly organized, such as some computers, to be said to have minds.
This may cause problems when (4) is taken into account. Also,
qualia seem to undermine the reduction of mental properties to brain properties.
[citation needed]
Some have argued that the only properties shared by all
qualia are that they are not precisely
describable, and thus are of
indeterminate
meaning within any philosophy which relies upon precise definition
according to these critics (that is, it tends to presuppose a definition
for mentality without describing it in any real detail). The need to
define better the terms used within the thesis of panpsychism is
recognized by panpsychist David Skrbina,
[23]
and he resorts to asserting some sort of hierarchy of mental terms to
be used. This is motivation to argue for panexperientialism rather than
panpsychism, since only the most fundamental meaning of mind is what is
present in all matter, namely, subjective experience.
The panpsychist answers both these challenges in the same way: we already know what
qualia
are through direct, introspective apprehension; and we likewise know
what conscious mentality is by virtue of being conscious. For someone
like
Alfred North Whitehead,
third-person description takes second place to the intimate connection
between every entity and every other which is, he says, the very fabric
of reality. To take a mere
description as having primary reality is to commit the "
fallacy of misplaced concreteness".
[citation needed]
One response is to separate the
phenomenal, non-cognitive aspects of consciousness—particularly
qualia, the essence of the
hard problem of consciousness—from cognition. Thus panpsychism is transformed into panexperientialism.
[citation needed]
However, this strategy of division generates problems of its own: what
is going on causally in the head of someone who is thinking—cognitively
of course—about their qualia?
[original research?]
In relation to other metaphysical positions
Panpsychism can be understood as related to a number of other metaphysical positions.
Idealism
Panpsychism agrees with
idealism that in a sense everything is mental, but whereas idealism treats most things as
mental content or ideas, panpsychism treats them as
mind-like,
in some sense, and as having their own reality. Also, in contrast to
many forms of idealism, it holds that there is for all minds, there is a
single, external, spatio-temporal world.
In contrast to "idealism", as this term is often used, panpsychism is
not a doctrine of the unreality of the spatio-temporal world perceived
through the senses, or its reduction to mere "ideas" in the human or
divine mind. The constituents of this world are, for panpsychists, just
as real as human minds or as any mind. Indeed, they are minds, though,
in large part, of an extremely low, subhuman order. Thus panpsychism is
panpsychical realism; realistic both in the sense of admitting the
reality of nature, and in the sense of avoiding an exaggerated view of
the qualities of its ordinary constituents. "Souls" may be very humble
sorts of entities––for example, the soul of a frog––and panpsychists
usually suppose that multitudes of units of nature are on a much lower
level of psychic life even than that.
[24]
Dualism
Panpsychists
and dualists agree that mental properties cannot be reduced to physical
properties. The difference is that dualists consider mental and
physical properties to be
qualitatively different, to belong to
different categories with virtually nothing in common (for instance,
Descartes' characterisation of matter and mind as "extension" and
"thought"), whereas panpsychists view physical properties as lesser
quantities
of mental properties. For instance, a panpsychist would interpret the
ability of a stone to move under an impact to be a highly diminished
form of sensitivity, with no element of volition. This distinction also
separates
dual aspect theory
from panpsychism: although dual aspect theorists can agree with
panpsychists that everything has some mental properties, they also hold
that everything has some physical properties, whereas panpsychists hold
that physical properties
are (lessened) mental properties.
Neutral monism
There are also varieties of
monism that don't presuppose (like materialism and idealism do) that mind and matter are fundamentally separable. An example is
neutral monism first introduced by
Spinoza and later propounded by
William James.
Neutral monism is often coupled with dual aspect theory which maintains
that mental and physical are two perspectives on a reality that is
neither mental nor physical. Panpsychism, on the other hand, holds that
the physical is the (attenuated) mental.
Physicalism and materialism
Reductive physicalism, a form of
monism, is normally assumed to be incompatible with panpsychism.
Materialism,
if held to be distinct from physicalism, is compatible with panpsychism
insofar as mental properties are attributed to physical matter, which
is the only basic substance.
Holism
Panpsychism is related to the more
holistic view that the whole
Universe is an organism that possesses a mind (
cosmic consciousness). It is claimed to be distinct from
animism or
hylozoism, which hold that all things have a soul or are alive, respectively.
Gustav Theodor Fechner
claimed in "Nanna" and "Zend-Avesta" that the Earth is a living
organism whose parts are the people, the animals and the plants.
Panpsychism, as a view that the universe has "
universal consciousness", is shared by some forms of religious thought such as
theosophy,
pantheism,
cosmotheism,
non-dualism,
new age thought and
panentheism. The
hundredth monkey effect exemplifies the threshold for this applied
cosmic consciousness. The
Tiantai Buddhist view is that "when one attains it, all attain it".
[25]
Hylopathism
Hylopathism
argues for a similarly universal attribution of sentience to matter.
Few writers would advocate a hylopathic materialism, although the idea
is not new; it has been formulated as "whatever underlies consciousness
in a material sense, i.e., whatever it is about the brain that gives
rise to consciousness, must necessarily be present to some degree in any
other material thing". A compound state of mind does not consist of
compounded psychic atoms. The concept of awareness "being in itself"
allows for the idea of self-aware matter. Attempts have been made to
conceptualize this primitive level of existence prior to associative
learning and memory. In the way that the collection of self-aware matter
constitutes a cognitive being, the collection of cognitive beings as a
conglomerate entity, reflects panpsychism. Consciousness was not
"nascent" but emergent due to a lack of abandon during the evolution of
material awareness.
[26]
Similar ideas have been attributed to Australian philosopher
David Chalmers,
who assumes that consciousness is a fundamental feature of the
Universe, what he refers to as the First Datum in the study of the mind.
In the practice of non-reductionism this feature may not be
attributable to any base monad but instead radically emergent on the
level of physical complexity at which it demonstrates itself. Complex
elegance is the further development of awareness that is self-aware.
This we can call "post-intelligence" where "intelligence" is simple
processing. The element of superiority might be that the
post-intelligence is proto-experiential. These phenomenal properties are
called "the internal aspects of information".
[26]:162–170
Emergentism
In
philosophy, emergentism is the belief in
emergence, particularly as it involves
consciousness and the
philosophy of mind, and as it contrasts (or not) with
reductionism. A property of a
system
is said to be emergent if it is a new outcome of some other properties
of the system and their interaction, while it is itself different from
them.
[27]
Emergent properties are not identical with, reducible to, or deducible
from the other properties. The different ways in which this independence
requirement can be satisfied lead to variant types of emergence.
Panexperientialism
Panexperientialism
(or "panprotopsychism"), and "panprotoexperientialism" are related
concepts. Panexperientialism is associated with the philosophies of
Charles Hartshorne and
Alfred North Whitehead, although the term itself was invented by
David Ray Griffin in order to distinguish the
process philosophical view from other varieties of panpsychism.
Whitehead's metaphysics incorporated a scientific worldview similar to
Einstein’s
theory of relativity into the development of his philosophical system. His
process philosophy
argues that the fundamental elements of the universe are "occasions of
experience," which can together create something as complex as a human
being. This experience is not consciousness; there is no mind-body
duality under this system, since mind is seen as a particularly
developed kind of experience. Whitehead was not a subjective idealist,
and while his occasions of experience (or "actual occasions") resemble
Leibniz's
monads, they are described as constitutively interrelated. He embraced
panentheism,
with God encompassing all occasions of experience and yet still
transcending them. Whitehead believed that these occasions of experience
are the smallest element in the universe—even smaller than
subatomic particles.
Panprotoexperientialism is a theory found in the works of
Gregg Rosenberg. For his part, process philosopher
Michel Weber argues for a pancreativism.
[28]
The ecological phenomenology carefully developed in the writings of the American cultural ecologist and philosopher,
David Abram, is often (and quite appropriately) described as a form of panexperientialism,
[29][30] as is the "poetic biology" developed by Abram's close associate, the German biologist Andreas Weber.
[31]
In eastern philosophy
According to Graham Parkes: "Most of traditional Chinese, Japanese
and Korean philosophy would qualify as panpsychist in nature. For the
philosophical schools best known in the west —
Neo-confucianism and
Japanese Buddhism — the world is a dynamic force field of energies known as
qi or bussho (
Buddha nature) and classifiable in western terms as
psychophysical."
[32]
East Asian Buddhism
According to D. S. Clarke, panpsychist and panexperientialist aspects can be found in the
Huayan and
Tiantai (Jpn.
Tendai) Buddhist doctrines of
Buddha nature, which was often attributed to inanimate objects such as lotus flowers and mountains.
[33] Tiantai patriarch
Zhanran argued that "even non-sentient beings have
Buddha nature."
[32]
Who, then, is "animate" and who "inanimate"? Within the assembly of
the Lotus, all are present without division. In the case of grass, trees
and the soil...whether they merely lift their feet or energetically
traverse the long path, they will all reach Nirvana.[32]
The Tiantai school was transmitted to Japan by
Saicho, who spoke of the "buddha-nature of trees and rocks".
[32]
According to the 9th-century Shingon Buddhist thinker
Kukai, the
Dharmakaya
is nothing other than the physical universe and natural objects like
rocks and stones are included as part of the supreme embodiment of the
Buddha.
[32] The
Soto Zen master
Dogen also argued for the universality of
Buddha nature. According to Dogen, "fences, walls, tiles, and pebbles" are also "mind" (心,
shin).
Dogen also argued that "insentient beings expound the teachings" and
that the words of the eternal Buddha "are engraved on trees and on rocks
. . . in fields and in villages". This is the message of his "Mountains
and Waters Sutra" (Sansui kyô).
[32]
Dzogchen
According to a common misunderstanding, in the Buddhist
Dzogchen tradition
[citation needed], particularly Dzogchen
Semde or "mind series" the principal text of which is the
Kulayarāja Tantra,
there is nothing which is non-sentient, i.e. everything is sentient.
Moreover, two of the English scholars that opened the discourse of the
Bardo literature of the
Nyingma Dzogchen tradition,
Evans-Wentz &
Jung (1954, 2000: p. 10) specifically with their partial translation and commentary of the
Bardo Thodol
into the English language write of the "One Mind" (Tibetan: sems nyid
gcig; Sanskrit: *ekacittatva; *ekacittata; where * denotes a possible
Sanskrit back-formation) thus:
The One Mind, as Reality, is the Heart which pulsates for ever,
sending forth purified the blood-streams of existence, and taking them
back again; the Great Breath, the Inscrutable Brahman, the Eternally
Unveiled Mystery of the Mysteries of Antiquity, the Goal of all
Pilgrimages, the End of all Existence.[34]
It should be borne in mind, that Evans-Wentz never studied the
Tibetan language and that the lama who did the main translation work for
him was of the Gelukpa Sect and is not known to have actually studied
or practiced Dzogchen.
According to the translation with commentary, "Self-Liberation Through Seeing with Naked Awareness", by
John Myrdhin Reynolds,
the phrase, "It is the single nature of mind which encompasses all of
Samsara and Nirvana," occurs only once in the text and it refers not to
"some sort of
Neo-Platonic hypostasis, a universal
Nous,
of which all individual minds are but fragments or appendages", but to
the teaching that, "whether one finds oneself in the state of Samsara or
in the state of Nirvana, it is the nature of the mind which reflects
with awareness all experiences, no matter what may be their nature."
This can be found in Appendix I, on pages 80–81. Reynolds elucidates
further with the analogy of a mirror. To say that a single mirror can
reflect ugliness or beauty, does not constitute an allegation that all
ugliness and beauty is one single mirror.
) yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury (e = 0.2056), one must simply calculate the inverse sine
to find the projection angle of 11.86 degrees. Next, tilt any circular
object (such as a coffee mug viewed from the top) by that angle and the
apparent ellipse projected to your eye will be of that same eccentricity.
