Atomic theory

From Wikipedia, the free encyclopedia

The current theoretical model of the atom involves a dense nucleus surrounded by a probabilistic "cloud" of electrons

In chemistry and physics, atomic theory is a scientific theory of the nature of matter, which states that matter is composed of discrete units called atoms. It began as a philosophical concept in ancient Greece and entered the scientific mainstream in the early 19th century when discoveries in the field of chemistry showed that matter did indeed behave as if it were made up of atoms.

The word atom comes from the Ancient Greek adjective atomos, meaning "indivisible".^[1] 19th century chemists began using the term in connection with the growing number of irreducible chemical elements. While seemingly apropos, around the turn of the 20th century, through various experiments with electromagnetism and radioactivity, physicists discovered that the so-called "uncuttable atom" was actually a conglomerate of various subatomic particles (chiefly, electrons, protons and neutrons) which can exist separately from each other. In fact, in certain extreme environments, such as neutron stars, extreme temperature and pressure prevents atoms from existing at all.

Since atoms were found to be divisible, physicists later invented the term "elementary particles" to describe the "uncuttable", though not indestructible, parts of an atom. The field of science which studies subatomic particles is particle physics, and it is in this field that physicists hope to discover the true fundamental nature of matter.

History

Philosophical atomism

The idea that matter is made up of discrete units is a very old one, appearing in many ancient cultures such as Greece and India. The word "atom" was coined by the ancient Greek philosophers Leucippus and his pupil Democritus.^[2][3] However, these ideas were founded in philosophical and theological reasoning rather than evidence and experimentation. Because of this, they could not convince everybody, so atomism was but one of a number of competing theories on the nature of matter. It was not until the 19th century that the idea was embraced and refined by scientists, as the blossoming science of chemistry produced discoveries that could easily be explained using the concept of atoms.

John Dalton

Near the end of the 18th century, two laws about chemical reactions emerged without referring to the notion of an atomic theory. The first was the law of conservation of mass, formulated by Antoine Lavoisier in 1789, which states that the total mass in a chemical reaction remains constant (that is, the reactants have the same mass as the products).^[4] The second was the law of definite proportions. First proven by the French chemist Joseph Louis Proust in 1799,^[5] this law states that if a compound is broken down into its constituent elements, then the masses of the constituents will always have the same proportions, regardless of the quantity or source of the original substance.

John Dalton studied and expanded upon this previous work and developed the law of multiple proportions: if two elements can be combined to form a number of possible compounds, then the ratios of the masses of the second element which combine with a fixed mass of the first element will be ratios of small whole numbers. For example: Proust had studied tin oxides and found that their masses were either 88.1% tin and 11.9% oxygen or 78.7% tin and 21.3% oxygen (these were tin(II) oxide and tin dioxide respectively). Dalton noted from these percentages that 100g of tin will combine either with 13.5g or 27g of oxygen; 13.5 and 27 form a ratio of 1:2. Dalton found that an atomic theory of matter could elegantly explain this common pattern in chemistry. In the case of Proust's tin oxides, one tin atom will combine with either one or two oxygen atoms.^[6]

Dalton believed atomic theory could explain why water absorbed different gases in different proportions - for example, he found that water absorbed carbon dioxide far better than it absorbed nitrogen.^[7] Dalton hypothesized this was due to the differences in mass and complexity of the gases' respective particles. Indeed, carbon dioxide molecules (CO₂) are heavier and larger than nitrogen molecules (N₂).

Dalton proposed that each chemical element is composed of atoms of a single, unique type, and though they cannot be altered or destroyed by chemical means, they can combine to form more complex structures (chemical compounds). This marked the first truly scientific theory of the atom, since Dalton reached his conclusions by experimentation and examination of the results in an empirical fashion.

Various atoms and molecules as depicted in John Dalton's A New System of Chemical Philosophy (1808).

In 1803 Dalton orally presented his first list of relative atomic weights for a number of substances. This paper was published in 1805, but he did not discuss there exactly how he obtained these figures.^[7] The method was first revealed in 1807 by his acquaintance Thomas Thomson, in the third edition of Thomson's textbook, A System of Chemistry. Finally, Dalton published a full account in his own textbook, A New System of Chemical Philosophy, 1808 and 1810.

Dalton estimated the atomic weights according to the mass ratios in which they combined, with the hydrogen atom taken as unity. However, Dalton did not conceive that with some elements atoms exist in molecules—e.g. pure oxygen exists as O₂. He also mistakenly believed that the simplest compound between any two elements is always one atom of each (so he thought water was HO, not H₂O).^[8] This, in addition to the crudity of his equipment, flawed his results. For instance, in 1803 he believed that oxygen atoms were 5.5 times heavier than hydrogen atoms, because in water he measured 5.5 grams of oxygen for every 1 gram of hydrogen and believed the formula for water was HO. Adopting better data, in 1806 he concluded that the atomic weight of oxygen must actually be 7 rather than 5.5, and he retained this weight for the rest of his life. Others at this time had already concluded that the oxygen atom must weigh 8 relative to hydrogen equals 1, if one assumes Dalton's formula for the water molecule (HO), or 16 if one assumes the modern water formula (H₂O).^[9]

Avogadro

The flaw in Dalton's theory was corrected in principle in 1811 by Amedeo Avogadro. Avogadro had proposed that equal volumes of any two gases, at equal temperature and pressure, contain equal numbers of molecules (in other words, the mass of a gas's particles does not affect the volume that it occupies).^[10] Avogadro's law allowed him to deduce the diatomic nature of numerous gases by studying the volumes at which they reacted. For instance: since two liters of hydrogen will react with just one liter of oxygen to produce two liters of water vapor (at constant pressure and temperature), it meant a single oxygen molecule splits in two in order to form two particles of water. Thus, Avogadro was able to offer more accurate estimates of the atomic mass of oxygen and various other elements, and made a clear distinction between molecules and atoms.

Brownian Motion

In 1827, the British botanist Robert Brown observed that dust particles inside pollen grains floating in water constantly jiggled about for no apparent reason. In 1905, Albert Einstein theorized that this Brownian motion was caused by the water molecules continuously knocking the grains about, and developed a hypothetical mathematical model to describe it.^[11] This model was validated experimentally in 1908 by French physicist Jean Perrin, thus providing additional validation for particle theory (and by extension atomic theory).

Discovery of subatomic particles

Atoms were thought to be the smallest possible division of matter until 1897 when J.J. Thomson discovered the electron through his work on cathode rays.^[12]
A Crookes tube is a sealed glass container in which two electrodes are separated by a vacuum. When a voltage is applied across the electrodes, cathode rays are generated, creating a glowing patch where they strike the glass at the opposite end of the tube. Through experimentation, Thomson discovered that the rays could be deflected by an electric field (in addition to magnetic fields, which was already known). He concluded that these rays, rather than being a form of light, were composed of very light negatively charged particles he called "corpuscles" (they would later be renamed electrons by other scientists). He measured the mass-to-charge ratio and discovered it was 1800 times smaller than that of hydrogen, the smallest atom. These corpuscles were a particle unlike any other previously known.

Thomson suggested that atoms were divisible, and that the corpuscles were their building blocks.^[13] To explain the overall neutral charge of the atom, he proposed that the corpuscles were distributed in a uniform sea of positive charge; this was the plum pudding model^[14] as the electrons were embedded in the positive charge like plums in a plum pudding (although in Thomson's model they were not stationary).

Discovery of the nucleus

The Geiger-Marsden experiment
Left: Expected results: alpha particles passing through the plum pudding model of the atom with negligible deflection.
Right: Observed results: a small portion of the particles were deflected by the concentrated positive charge of the nucleus.

Thomson's plum pudding model was disproved in 1909 by one of his former students, Ernest Rutherford, who discovered that most of the mass and positive charge of an atom is concentrated in a very small fraction of its volume, which he assumed to be at the very center.

In the Geiger–Marsden experiment, Hans Geiger and Ernest Marsden (colleagues of Rutherford working at his behest) shot alpha particles at thin sheets of metal and measured their deflection through the use of a fluorescent screen.^[15] Given the very small mass of the electrons, the high momentum of the alpha particles, and the low concentration of the positive charge of the plum pudding model, the experimenters expected all the alpha particles to pass through the metal foil without significant deflection. To their astonishment, a small fraction of the alpha particles experienced heavy deflection. Rutherford concluded that the positive charge of the atom must be concentrated in a very tiny volume to produce an electric field sufficiently intense to deflect the alpha particles so strongly.

This led Rutherford to propose a planetary model in which a cloud of electrons surrounded a small, compact nucleus of positive charge. Only such a concentration of charge could produce the electric field strong enough to cause the heavy deflection.^[16]

First steps toward a quantum physical model of the atom

The planetary model of the atom had two significant shortcomings. The first is that, unlike planets orbiting a sun, electrons are charged particles. An accelerating electric charge is known to emit electromagnetic waves according to the Larmor formula in classical electromagnetism. An orbiting charge should steadily lose energy and spiral toward the nucleus, colliding with it in a small fraction of a second. The second problem was that the planetary model could not explain the highly peaked emission and absorption spectra of atoms that were observed.

The Bohr model of the atom

Quantum theory revolutionized physics at the beginning of the 20th century, when Max Planck and Albert Einstein postulated that light energy is emitted or absorbed in discrete amounts known as quanta (singular, quantum). In 1913, Niels Bohr incorporated this idea into his Bohr model of the atom, in which an electron could only orbit the nucleus in particular circular orbits with fixed angular momentum and energy, its distance from the nucleus (i.e., their radii) being proportional to its energy.^[17] Under this model an electron could not spiral into the nucleus because it could not lose energy in a continuous manner; instead, it could only make instantaneous "quantum leaps" between the fixed energy levels.^[17] When this occurred, light was emitted or absorbed at a frequency proportional to the change in energy (hence the absorption and emission of light in discrete spectra).^[17]

Bohr's model was not perfect. It could only predict the spectral lines of hydrogen; it couldn't predict those of multielectron atoms. Worse still, as spectrographic technology improved, additional spectral lines in hydrogen were observed which Bohr's model couldn't explain. In 1916, Arnold Sommerfeld added elliptical orbits to the Bohr model to explain the extra emission lines, but this made the model very difficult to use, and it still couldn't explain more complex atoms.

Discovery of isotopes

While experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one element at each position on the periodic table.^[18] The term isotope was coined by Margaret Todd as a suitable name for these elements.
That same year, J.J. Thomson conducted an experiment in which he channeled a stream of neon ions through magnetic and electric fields, striking a photographic plate at the other end. He observed two glowing patches on the plate, which suggested two different deflection trajectories. Thomson concluded this was because some of the neon ions had a different mass.^[19] The nature of this differing mass would later be explained by the discovery of neutrons in 1932.

Discovery of nuclear particles

In 1917 Rutherford bombarded nitrogen gas with alpha particles and observed hydrogen nuclei being emitted from the gas (Rutherford recognized these, because he had previously obtained them bombarding hydrogen with alpha particles, and observing hydrogen nuclei in the products). Rutherford concluded that the hydrogen nuclei emerged from the nuclei of the nitrogen atoms themselves (in effect, he had split a nitrogen).^[20]

From his own work and the work of his students Bohr and Henry Moseley, Rutherford knew that the positive charge of any atom could always be equated to that of an integer number of hydrogen nuclei. This, coupled with the atomic mass of many elements being roughly equivalent to an integer number of hydrogen atoms - then assumed to be the lightest particles - led him to conclude that hydrogen nuclei were singular particles and a basic constituent of all atomic nuclei. He named such particles protons. Further experimentation by Rutherford found that the nuclear mass of most atoms exceeded that of the protons it possessed; he speculated that this surplus mass was composed of previously-unknown neutrally charged particles, which were tentatively dubbed "neutrons".

In 1928, Walter Bothe observed that beryllium emitted a highly penetrating, electrically neutral radiation when bombarded with alpha particles. It was later discovered that this radiation could knock hydrogen atoms out of paraffin wax. Initially it was thought to be high-energy gamma radiation, since gamma radiation had a similar effect on electrons in metals, but James Chadwick found that the ionization effect was too strong for it to be due to electromagnetic radiation, so long as energy and momentum were conserved in the interaction. In 1932, Chadwick exposed various elements, such as hydrogen and nitrogen, to the mysterious "beryllium radiation", and by measuring the energies of the recoiling charged particles, he deduced that the radiation was actually composed of electrically neutral particles which could not be massless like the gamma ray, but instead were required to have a mass similar to that of a proton. Chadwick now claimed these particles as Rutherford's neutrons.^[21] For his discovery of the neutron, Chadwick received the Nobel Prize in 1935.

Quantum physical models of the atom

The five filled atomic orbitals of a neon atom separated and arranged in order of increasing energy from left to right, with the last three orbitals being equal in energy. Each orbital holds up to two electrons, which most probably exist in the zones represented by the colored bubbles. Each electron is equally present in both orbital zones, shown here by color only to highlight the different wave phase.

In 1924, Louis de Broglie proposed that all moving particles—particularly subatomic particles such as electrons—exhibit a degree of wave-like behavior. Erwin Schrödinger, fascinated by this idea, explored whether or not the movement of an electron in an atom could be better explained as a wave rather than as a particle. Schrödinger's equation, published in 1926,^[22] describes an electron as a wavefunction instead of as a point particle. This approach elegantly predicted many of the spectral phenomena that Bohr's model failed to explain. Although this concept was mathematically convenient, it was difficult to visualize, and faced opposition.^[23] One of its critics, Max Born, proposed instead that Schrödinger's wavefunction described not the electron but rather all its possible states, and thus could be used to calculate the probability of finding an electron at any given location around the nucleus.^[24] This reconciled the two opposing theories of particle versus wave electrons and the idea of wave–particle duality was introduced. This theory stated that the electron may exhibit the properties of both a wave and a particle. For example, it can be refracted like a wave, and has mass like a particle.^[25]

A consequence of describing electrons as waveforms is that it is mathematically impossible to simultaneously derive the position and momentum of an electron. This became known as the Heisenberg uncertainty principle after the theoretical physicist Werner Heisenberg, who first described it and published it in 1927.^[26] This invalidated Bohr's model, with its neat, clearly defined circular orbits. The modern model of the atom describes the positions of electrons in an atom in terms of probabilities. An electron can potentially be found at any distance from the nucleus, but, depending on its energy level, exists more frequently in certain regions around the nucleus than others; this pattern is referred to as its atomic orbital. The orbitals come in a variety of shapes-sphere, dumbbell, torus, etc.-with the nucleus in the middle.^[27]

Orbital eccentricity

From Wikipedia, the free encyclopedia

An elliptic, parabolic, and hyperbolic Kepler orbit:
  elliptic (eccentricity = 0.7)
  parabolic (eccentricity = 1)
  hyperbolic orbit (eccentricity = 1.3)

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy.

Definition

e=0

e=0.5

Orbits in a two-body system for two values of the eccentricity, e.

In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape.

The eccentricity may take the following values:

• circular orbit: e = 0
• elliptic orbit: 0 < e < 1 (see ellipse)
• parabolic trajectory: e = 1 (see parabola)
• hyperbolic trajectory: e > 1 (see hyperbola)

The eccentricity e is given by

${\displaystyle e={\sqrt {1+{\frac {2EL^{2}}{m_{\text{red}}\alpha ^{2}}}}}}$

where E is the total orbital energy, L is the angular momentum, m_red is the reduced mass, and α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics:

${\displaystyle F={\frac {\alpha }{r^{2}}}}$

(α is negative for an attractive force, positive for a repulsive one; see also Kepler problem)

or in the case of a gravitational force:

${\displaystyle e={\sqrt {1+{\frac {2\varepsilon h^{2}}{\mu ^{2}}}}}}$

where ε is the specific orbital energy (total energy divided by the reduced mass), μ the standard gravitational parameter based on the total mass, and h the specific relative angular momentum (angular momentum divided by the reduced mass).

For values of e from 0 to 1 the orbit's shape is an increasingly elongated (or flatter) ellipse; for values of e from 1 to infinity the orbit is a hyperbola branch making a total turn of 2 arccsc e, decreasing from 180 to 0 degrees. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola.

Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1 (or in the parabolic case, remains 1).

For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable.

For elliptical orbits, a simple proof shows that arcsin(${\displaystyle e}$) 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.

Etymology

The word "eccentricity" comes from Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros "out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center". "Eccentric" first appeared in English in 1551, with the definition "a circle in which the earth, sun. etc. deviates from its center".^{[citation needed]} By five years later, in 1556, an adjectival form of the word had developed.

Calculation

The eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector:

${\displaystyle e=\left|\mathbf {e} \right|}$

where:

• e is the eccentricity vector.

For elliptical orbits it can also be calculated from the periapsis and apoapsis since r_p = a(1 − e) and r_a = a(1 + e), where a is the semimajor axis.

${\displaystyle {\begin{aligned}e&={{r_{\text{a}}-r_{\text{p}}} \over {r_{\text{a}}+r_{\text{p}}}}\\&=1-{\frac {2}{{\frac {r_{\text{a}}}{r_{\text{p}}}}+1}}\end{aligned}}}$

where:

• r_a is the radius at apoapsis (i.e., the farthest distance of the orbit to the center of mass of the system, which is a focus of the ellipse).
• r_p is the radius at periapsis (the closest distance).

The eccentricity of an elliptical orbit can also be used to obtain the ratio of the periapsis to the apoapsis:

${\displaystyle {{r_{\text{p}}} \over {r_{\text{a}}}}={{1-e} \over {1+e}}}$

For Earth, orbital eccentricity ≈ 0.0167, apoapsis= aphelion = apogee and periapsis= perihelion = perigee relative to sun.

For Earth's annual orbit path, r_a/r_p ratio = longest_radius / shortest_radius ≈ 1.034 relative to center point of path.

Examples

Gravity Simulator plot of the changing orbital eccentricity of Mercury, Venus, Earth, and Mars over the next 50,000 years. The arrows indicate the different scales used. The 0 point on this plot is the year 2007.

 

Eccentricities of Solar System bodies

Object	eccentricity
Triton	0.00002
Venus	0.0068
Neptune	0.0086
Earth	0.0167
Titan	0.0288
Uranus	0.0472
Jupiter	0.0484
Saturn	0.0541
Moon	0.0549
1 Ceres	0.0758
4 Vesta	0.0887
Mars	0.0934
10 Hygiea	0.1146
Makemake	0.1559
Haumea	0.1887
Mercury	0.2056
2 Pallas	0.2313
Pluto	0.2488
3 Juno	0.2555
324 Bamberga	0.3400
Eris	0.4407
Nereid	0.7507
Sedna	0.8549
Halley's Comet	0.9671
Comet Hale-Bopp	0.9951
Comet Ikeya-Seki	0.9999
ʻOumuamua	1.20[a]

The eccentricity of the Earth's orbit is currently about 0.0167; the Earth's orbit is nearly circular. Venus and Neptune have even lower eccentricities. Over hundreds of thousands of years, the eccentricity of the Earth's orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets (see graph).^[1]

The table lists the values for all planets and dwarf planets, and selected asteroid, comets and moons. Mercury has the greatest orbital eccentricity of any planet in the Solar System (e = 0.2056). Such eccentricity is sufficient for Mercury to receive twice as much solar irradiation at perihelion compared to aphelion. Before its demotion from planet status in 2006, Pluto was considered to be the planet with the most eccentric orbit (e = 0.248). Other Trans-Neptunian objects have significant eccentricity, notably the dwarf planet Eris (0.44). Even further out, Sedna, has an extremely high eccentricity of 0.855 due to its estimated aphelion of 937 AU and perihelion of about 76 AU.

Most of the Solar System's asteroids have orbital eccentricities between 0 and 0.35 with an average value of 0.17.^[2] Their comparatively high eccentricities are probably due to the influence of Jupiter and to past collisions.

The Moon's value is 0.0549, the most eccentric of the large moons of the Solar System. The four Galilean moons have eccentricity < 0.01. Neptune's largest moon Triton has an eccentricity of 1.6×10⁻⁵ (0.000016),^[3] the smallest eccentricity of any known body in the Solar System;^{[citation needed]} its orbit is as close to a perfect circle as can be currently^[when?] measured. However, smaller moons, particularly irregular moons, can have significant eccentricity, such as Neptune's third largest moon Nereid (0.75).

Comets have very different values of eccentricity. Periodic comets have eccentricities mostly between 0.2 and 0.7,^[4] but some of them have highly eccentric elliptical orbits with eccentricities just below 1, for example, Halley's Comet has a value of 0.967. Non-periodic comets follow near-parabolic orbits and thus have eccentricities even closer to 1. Examples include Comet Hale–Bopp with a value of 0.995^[5] and comet C/2006 P1 (McNaught) with a value of 1.000019.^[6] As Hale–Bopp's value is less than 1, its orbit is elliptical and it will in fact return.^[5] Comet McNaught has a hyperbolic orbit while within the influence of the planets, but is still bound to the Sun with an orbital period of about 10⁵ years.^[7] As of a 2010 Epoch, Comet C/1980 E1 has the largest eccentricity of any known hyperbolic comet with an eccentricity of 1.057,^[8] and will leave the Solar System indefinitely.

ʻOumuamua is the first interstellar object found passing through the Solar System. Its orbital eccentricity of 1.20 indicates that ʻOumuamua has never been gravitationally bound to our sun. It was discovered 0.2 AU (30,000,000 km; 19,000,000 mi) from Earth and is roughly 200 meters in diameter. It has an interstellar speed (velocity at infinity) of 26.33 km/s (58,900 mph).

Mean eccentricity

The mean eccentricity of an object is the average eccentricity as a result of perturbations over a given time period. Neptune currently has an instant (current epoch) eccentricity of 0.0113,^[9] but from 1800 to 2050 has a mean eccentricity of 0.00859.^[10]

Climatic effect

Orbital mechanics require that the duration of the seasons be proportional to the area of the Earth's orbit swept between the solstices and equinoxes, so when the orbital eccentricity is extreme, the seasons that occur on the far side of the orbit (aphelion) can be substantially longer in duration. Today, northern hemisphere fall and winter occur at closest approach (perihelion), when the earth is moving at its maximum velocity—while the opposite occurs in the southern hemisphere. As a result, in the northern hemisphere, fall and winter are slightly shorter than spring and summer—but in global terms this is balanced with them being longer below the equator. In 2006, the northern hemisphere summer was 4.66 days longer than winter, and spring was 2.9 days longer than fall due to the Milankovitch cycles.^[11][12]

Apsidal precession also slowly changes the place in the Earth's orbit where the solstices and equinoxes occur. Note that this is a slow change in the orbit of the Earth, not the axis of rotation, which is referred to as axial precession (see Precession § Astronomy). Over the next 10,000 years, the northern hemisphere winters will become gradually longer and summers will become shorter. However, any cooling effect in one hemisphere is balanced by warming in the other, and any overall change will be counteracted by the fact that the eccentricity of Earth's orbit will be almost halved.^[13] This will reduce the mean orbital radius and raise temperatures in both hemispheres closer to the mid-interglacial peak.

Exoplanets

Of the many exoplanets discovered, most have a higher orbital eccentricity than planets in our solar system. Exoplanets found with low orbital eccentricity, near circular orbits, are very close to their star and are tidally locked to the star. All eight planets in the Solar System have near-circular orbits. The exoplanets discovered show that the solar system, with its unusually low eccentricity, is rare and unique.^[14] One theory attributes this low eccentricity to the high number of planets in the Solar System; another suggests it arose because of its unique asteroid belts. A few other multiplanetary systems have been found, but none resemble the Solar System. The Solar System has unique planetesimal systems, which led the planets to have near-circular orbits. Solar planetesimal systems include the asteroid belt, Hilda family, Kuiper belt, Hills cloud, and the Oort cloud. The exoplanet systems discovered have either no planetesimal systems or one very large one. Low eccentricity is needed for habitability, especially advanced life.^[15] High multiplicity planet systems are much more likely to have habitable exoplanets.^[16][17] The grand tack hypothesis of the Solar System also helps understand its near-circular orbits and other unique features.

Panpsychism

From Wikipedia, the free encyclopedia

Illustration of the Neoplatonic concept of the World Soul emanating from The Absolute

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

In the art of the Japanese rock garden, the artist must be aware of the rocks' "ishigokoro" ('heart', or 'mind')^[32]

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.