Atomism (from Greek ἄτομον, atomon, i.e. "uncuttable, indivisible") is a natural philosophy proposing that the physical universe is composed of fundamental indivisible components known as atoms.
References to the concept of atomism and its atoms appeared in both ancient Greek and ancient Indian philosophical traditions. The ancient Greek atomists theorized that nature consists of two fundamental principles: atom and void. Clusters of different shapes, arrangements, and positions give rise to the various macroscopic substances in the world.
The particles of chemical matter for which chemists and other natural philosophers of the early 19th century found experimental evidence were thought to be indivisible, and therefore were given by John Dalton the name "atom", long used by the atomist philosophy. Although the connection to historical atomism is at best tenuous, elementary particles have become a modern analogue of philosophical atoms.
Reductionism
Philosophical atomism is a reductive argument, proposing not only that everything is composed of atoms and void, but that nothing they compose really exists: the only things that really exist are atoms ricocheting off each other mechanistically in an otherwise empty void. Atomism stands in contrast to a substance theory wherein a prime material continuum remains qualitatively invariant under division (for example, the ratio of the four classical elements would be the same in any portion of a homogeneous material).
Indian Buddhists, such as Dharmakirti (fl. c. 6th or 7th century) and others, developed distinctive theories of atomism, for example, involving momentary (instantaneous) atoms (kalapas) that flash in and out of existence.
History
Antiquity
Greek atomism
In the 5th century BCE, Leucippus and his pupil Democritus proposed that all matter was composed of small indivisible particles called atoms. Nothing whatsoever is known about Leucippus except that he was the teacher of Democritus. Democritus, by contrast, was a prolific writer, who wrote over eighty known treatises, none of which have survived to the present day complete. However, a massive number of fragments and quotations of his writings have survived. These are the main source of information on his teachings about atoms. Democritus's argument for the existence of atoms hinged on the idea that it is impossible to keep dividing matter for infinity and that matter must therefore be made up of extremely tiny particles. The atomistic theory aimed to remove the "distinction which the Eleatic school drew between the Absolute, or the only real existence, and the world of change around us."
Democritus believed that atoms are too small for human senses to detect, they are infinitely many, they come in infinitely many varieties, and that they have always existed. They float in a vacuum, which Democritus called the "void", and they vary in form, order, and posture. Some atoms, he maintained, are convex, others concave, some shaped like hooks, and others like eyes. They are constantly moving and colliding into each other. Democritus wrote that atoms and void are the only things that exist and that all other things are merely said to exist by social convention. The objects humans see in everyday life are composed of many atoms united by random collisions and their forms and materials are determined by what kinds of atom make them up. Likewise, human perceptions are caused by atoms as well. Bitterness is caused by small, angular, jagged atoms passing across the tongue; whereas sweetness is caused by larger, smoother, more rounded atoms passing across the tongue.
Parmenides denied the existence of motion, change and void. He believed all existence to be a single, all-encompassing and unchanging mass (a concept known as monism), and that change and motion were mere illusions. He explicitly rejected sensory experience as the path to an understanding of the universe and instead used purely abstract reasoning. He believed there is no such thing as void, equating it with non-being. This in turn meant that motion is impossible, because there is no void to move into. Parmenides doesn't mention or explicitly deny the existence of the void, stating instead that what is not does not exist. He also wrote all that is must be an indivisible unity, for if it were manifold, then there would have to be a void that could divide it. Finally, he stated that the all encompassing Unity is unchanging, for the Unity already encompasses all that is and can be.
Democritus accepted most of Parmenides' arguments, except for the idea that change is an illusion. He believed change was real, and if it was not then at least the illusion had to be explained. He thus supported the concept of void, and stated that the universe is made up of many Parmenidean entities that move around in the void. The void is infinite and provides the space in which the atoms can pack or scatter differently. The different possible packings and scatterings within the void make up the shifting outlines and bulk of the objects that organisms feel, see, eat, hear, smell, and taste. While organisms may feel hot or cold, hot and cold actually have no real existence. They are simply sensations produced in organisms by the different packings and scatterings of the atoms in the void that compose the object that organisms sense as being "hot" or "cold".
The work of Democritus only survives in secondhand reports, some of which are unreliable or conflicting. Much of the best evidence of Democritus' theory of atomism is reported by Aristotle in his discussions of Democritus' and Plato's contrasting views on the types of indivisibles composing the natural world.
Geometry and atoms
| Element | Polyhedron | Number of Faces | Number of Triangles | |
|---|---|---|---|---|
| Fire | Tetrahedron |
|
4 | 24 |
| Air | Octahedron |
|
8 | 48 |
| Water | Icosahedron |
|
20 | 120 |
| Earth | Cube |
|
6 | 24 |
| Geometrical simple bodies according to Plato | ||||
Plato (c. 427 – c. 347 BCE), if he had been familiar with the atomism of Democritus, would have objected to its mechanistic materialism. He argued that atoms just crashing into other atoms could never produce the beauty and form of the world. In Plato's Timaeus (28b–29a) the character of Timeaus insisted that the cosmos was not eternal but was created, although its creator framed it after an eternal, unchanging model.
One part of that creation were the four simple bodies of fire, air, water, and earth. But Plato did not consider these corpuscles to be the most basic level of reality, for in his view they were made up of an unchanging level of reality, which was mathematical. These simple bodies were geometric solids, the faces of which were, in turn, made up of triangles. The square faces of the cube were each made up of four isosceles right-angled triangles and the triangular faces of the tetrahedron, octahedron, and icosahedron were each made up of six right-angled triangles.
He postulated the geometric structure of the simple bodies of the four elements as summarized in the adjacent table. The cube, with its flat base and stability, was assigned to earth; the tetrahedron was assigned to fire because its penetrating points and sharp edges made it mobile. The points and edges of the octahedron and icosahedron were blunter and so these less mobile bodies were assigned to air and water. Since the simple bodies could be decomposed into triangles, and the triangles reassembled into atoms of different elements, Plato's model offered a plausible account of changes among the primary substances.
Rejection in Aristotelianism
Sometime before 330 BC Aristotle asserted that the elements of fire, air, earth, and water were not made of atoms, but were continuous. Aristotle considered the existence of a void, which was required by atomic theories, to violate physical principles. Change took place not by the rearrangement of atoms to make new structures, but by transformation of matter from what it was in potential to a new actuality. A piece of wet clay, when acted upon by a potter, takes on its potential to be an actual drinking mug. Aristotle has often been criticized for rejecting atomism, but in ancient Greece the atomic theories of Democritus remained "pure speculations, incapable of being put to any experimental test."
Minima naturalia were theorized by Aristotle as the smallest parts into which a homogeneous natural substance (e.g., flesh, bone, or wood) could be divided and still retain its essential character. Unlike the atomism of Democritus, the Aristotelian "natural minimum" was not conceptualized as physically indivisible. Instead, the concept was rooted in Aristotle's hylomorphic worldview, which held that every physical thing is a compound of matter (Greek hyle) and an immaterial substantial form (Greek morphe) that imparts its essential nature and structure. For instance, a rubber ball for a hylomorphist like Aristotle would be rubber (matter) structured by spherical shape (form). Aristotle's intuition was that there is some smallest size beyond which matter could no longer be structured as flesh, or bone, or wood, or some other such organic substance that for Aristotle, living before the microscope, could be considered homogeneous. For instance, if flesh were divided beyond its natural minimum, what would be left might be a large amount of the element water, and smaller amounts of the other elements. But whatever water or other elements were left, they would no longer have the "nature" of flesh: in hylomorphic terms, they would no longer be matter structured by the form of flesh; instead the remaining water, e.g., would be matter structured by the form of water, not the form of flesh.
Later ancient atomism
Epicurus (341–270 BCE) studied atomism with Nausiphanes who had been a student of Democritus. Although Epicurus was certain of the existence of atoms and the void, he was less sure we could adequately explain specific natural phenomena such as earthquakes, lightning, comets, or the phases of the Moon (Lloyd 1973, 25–6). Few of Epicurus' writings survive and those that do reflect his interest in applying Democritus' theories to assist people in taking responsibility for themselves and for their own happiness—since he held there are no gods around that can help them. He understood gods' role as moral ideals.
His ideas are also represented in the works of his Roman follower Lucretius, who wrote On the Nature of Things. This Classical Latin scientific work in poetic form illustrates several segments of Epicurean theory on how the universe came into its current stage and it shows that the phenomena we perceive are actually composite forms. The atoms and the void are eternal and in constant motion. Atomic collisions create objects, which are still composed of the same eternal atoms whose motion for a while is incorporated into the created entity. Human sensations and meteorological phenomena are also explained by Lucretius in terms of atomic motion.
Atomism and ethics
Some later philosophers attributed the idea that man created gods and that gods did not create man to Democritus. For example, Sextus Empiricus noted:
- Some people think that we arrived at the idea of gods from the remarkable things that happen in the world. Democritus ... says that the people of ancient times were frightened by happenings in the heavens such as thunder, lightning, ..., and thought that they were caused by gods.
Three hundred years after Epicurus, Lucretius in his epic poem On the Nature of Things would depict him as the hero who crushed the monster Religion through educating the people in what was possible in the atoms and what was not possible in the atoms. However, Epicurus expressed a non-aggressive attitude characterized by his statement: "The man who best knows how to meet external threats makes into one family all the creatures he can; and those he can not, he at any rate does not treat as aliens; and where he finds even this impossible, he avoids all dealings, and, so far as is advantageous, excludes them from his life."
Indian atomism
In ancient Indian philosophy, preliminary instances of atomism are found in the works of Vedic sage Aruni, who lived in the 8th century BCE, especially his proposition that "particles too small to be seen mass together into the substances and objects of experience" known as kaṇa. Later, the Charvaka, and Ajivika schools of atomism originated as early as the 7th century BCE. Bhattacharya posits that Charvaka may have been one of several atheistic, materialist schools that existed in ancient India. Kanada founded the Vaisheshika school of Indian philosophy that also represents the earliest Indian natural philosophy. The Nyaya and Vaisheshika schools developed theories on how kaṇas combined into more complex objects.
Several of these doctrines of atomism are, in some respects, "suggestively similar" to that of Democritus. McEvilley (2002) assumes that such similarities are due to extensive cultural contact and diffusion, probably in either direction.
The Nyaya–Vaisesika school developed one of the earliest forms of atomism; scholars date the Nyaya and Vaisesika texts from the 9th to 4th centuries BCE. Vaisesika atomists posited the four elemental atom types, but in Vaisesika physics atoms had 25 different possible qualities, divided between general extensive properties and specific (intensive) properties. The Nyaya–Vaisesika atomists had elaborate theories of how atoms combine. In Vaisesika atomism, atoms first combine in pairs (dyads), and then group into trios of pairs (triads), which are the smallest visible units of matter.
The Buddhist atomists had very qualitative, Aristotelian-style atomic theory. According to ancient Buddhist atomism, which probably began developing before the 4th century BCE, there are four kinds of atoms, corresponding to the standard elements. Each of these elements has a specific property, such as solidity or motion, and performs a specific function in mixtures, such as providing support or causing growth. Like the Hindus, the Buddhists were able to integrate a theory of atomism with their theological presuppositions. Later Indian Buddhist philosophers, such as Dharmakirti and Dignāga, considered atoms to be point-sized, durationless, and made of energy.
Some of the canonical texts make reference to matter and atoms (called paramāṇu, a term already used in Yajnavalkya, Lalitha Sahasranama and Yoga Sutra), including Pancastikayasara, Kalpasutra and Tattvarthasutra. The Jains envisioned the world as consisting wholly of atoms, except for souls. Atoms were considered as the basic building blocks of all matter. Each atom had "one kind of taste, one smell, one color, and two kinds of touch", though it is unclear what was meant by "kind of touch". Atoms can exist in one of two states: subtle, in which case they can fit in infinitesimally small spaces, and gross, in which case they have extension and occupy a finite space. The texts also give "detailed theories" of how atoms could combine, react, vibrate, move, and perform other actions, all of which were thoroughly deterministic.
Middle Ages
Medieval Hinduism
Ajivika is a "Nastika" school of thought whose metaphysics included a theory of atoms or atomism which was later adapted in the Vaiśeṣika school, which postulated that all objects in the physical universe are reducible to paramāṇu (atoms), and one's experiences are derived from the interplay of substance (a function of atoms, their number and their spatial arrangements), quality, activity, commonness, particularity and inherence. Everything was composed of atoms, qualities emerged from aggregates of atoms, but the aggregation and nature of these atoms was predetermined by cosmic forces. His traditional name Kanada means 'atom eater', and he is known for developing the foundations of an atomistic approach to physics and philosophy in the Sanskrit text Vaiśeṣika Sūtra. His text is also known as Kanada Sutras, or Aphorisms of Kanada.
Medieval Buddhism
Medieval Buddhist atomism, flourishing in ca. the 7th century, was very different from the atomist doctrines taught in early Buddhism. Medieval Buddhist philosophers Dharmakirti and Dignāga considered atoms to be point-sized, durationless, and made of energy. In discussing the two systems, Fyodor Shcherbatskoy (1930) stresses their commonality, the postulate of "absolute qualities" (guna-dharma) underlying all empirical phenomena.
Still later, the Abhidhammattha-sangaha, a text dated to the 11th or 12th century, postulates the existence of rupa-kalapa, imagined as the smallest units of the physical world, of varying elementary composition. Invisible under normal circumstances, the rupa-kalapa are said to become visible as a result of meditative samadhi.
Medieval Islam
Atomistic philosophies are found very early in Islamic philosophy and was influenced by earlier Greek and to some extent Indian philosophy. Like both the Greek and Indian versions, Islamic atomism was a charged topic that had the potential for conflict with the prevalent religious orthodoxy, but it was instead more often favoured by orthodox Islamic theologians. It was such a fertile and flexible idea that, as in Greece and India, it flourished in some leading schools of Islamic thought.
The most successful form of Islamic atomism was in the Asharite school of Islamic theology, most notably in the work of the theologian al-Ghazali (1058–1111). In Asharite atomism, atoms are the only perpetual, material things in existence, and all else in the world is "accidental" meaning something that lasts for only an instant. Nothing accidental can be the cause of anything else, except perception, as it exists for a moment. Contingent events are not subject to natural physical causes, but are the direct result of God's constant intervention, without which nothing could happen. Thus nature is completely dependent on God, which meshes with other Asharite Islamic ideas on causation, or the lack thereof (Gardet 2001). Al-Ghazali also used the theory to support his theory of occasionalism. In a sense, the Asharite theory of atomism has far more in common with Indian atomism than it does with Greek atomism.
Other traditions in Islam rejected the atomism of the Asharites and expounded on many Greek texts, especially those of Aristotle. An active school of philosophers in Al-Andalus, including the noted commentator Averroes (1126–1198 CE) explicitly rejected the thought of al-Ghazali and turned to an extensive evaluation of the thought of Aristotle. Averroes commented in detail on most of the works of Aristotle and his commentaries became very influential in Jewish and Christian scholastic thought.
Medieval Christendom
While Aristotelian philosophy eclipsed the importance of the atomists in late Roman and medieval Europe, their work was still preserved and exposited through commentaries on the works of Aristotle. In the 2nd century, Galen (AD 129–216) presented extensive discussions of the Greek atomists, especially Epicurus, in his Aristotle commentaries. According to historian of atomism Joshua Gregory, there was no serious work done with atomism from the time of Galen until Isaac Beeckman, Gassendi and Descartes resurrected it in the 17th century; "the gap between these two 'modern naturalists' and the ancient Atomists marked "the exile of the atom" and "it is universally admitted that the Middle Ages had abandoned Atomism, and virtually lost it."
However, although the ancient atomists' works were unavailable, Scholastic thinkers still had Aristotle's critiques of atomism. In medieval universities there were expressions of atomism. For example, in the 14th century Nicholas of Autrecourt considered that matter, space, and time were all made up of indivisible atoms, points, and instants and that all generation and corruption took place by the rearrangement of material atoms. The similarities of his ideas with those of al-Ghazali suggest that Nicholas may have been familiar with Ghazali's work, perhaps through Averroes' refutation of it (Marmara, 1973–74).
Although the atomism of Epicurus had fallen out of favor in the centuries of Scholasticism, the minima naturalia of Aristotelianism received extensive consideration. Speculation on minima naturalia provided philosophical background for the mechanistic philosophy of early modern thinkers such as Descartes, and for the alchemical works of Geber and Daniel Sennert, who in turn influenced the corpuscularian alchemist Robert Boyle, one of the founders of modern chemistry.
A chief theme in late Roman and Scholastic commentary on this concept is reconciling minima naturalia with the general Aristotelian principle of infinite divisibility. Commentators like John Philoponus and Thomas Aquinas reconciled these aspects of Aristotle's thought by distinguishing between mathematical and "natural" divisibility. With few exceptions, much of the curriculum in the universities of Europe was based on such Aristotelianism for most of the Middle Ages.
Atomist renaissance
In the 17th century, a renewed interest arose in Epicurean atomism and corpuscularianism as a hybrid or an alternative to Aristotelian physics. The main figures in the rebirth of atomism were Isaac Beeckman, René Descartes, Pierre Gassendi, and Robert Boyle, as well as other notable figures.
One of the first groups of atomists in England was a cadre of amateur scientists known as the Northumberland circle, led by Henry Percy, 9th Earl of Northumberland (1564–1632). Although they published little of account, they helped to disseminate atomistic ideas among the burgeoning scientific culture of England, and may have been particularly influential to Francis Bacon, who became an atomist around 1605, though he later rejected some of the claims of atomism. Though they revived the classical form of atomism, this group was among the scientific avant-garde: the Northumberland circle contained nearly half of the confirmed Copernicans prior to 1610 (the year of Galileo's The Starry Messenger). Other influential atomists of late 16th and early 17th centuries include Giordano Bruno, Thomas Hobbes (who also changed his stance on atomism late in his career), and Thomas Hariot. A number of different atomistic theories were blossoming in France at this time, as well (Clericuzio 2000).
Galileo Galilei (1564–1642) was an advocate of atomism in his 1612, Discourse on Floating Bodies (Redondi 1969). In The Assayer, Galileo offered a more complete physical system based on a corpuscular theory of matter, in which all phenomena—with the exception of sound—are produced by "matter in motion". Galileo identified some basic problems with Aristotelian physics through his experiments. He utilized a theory of atomism as a partial replacement, but he was never unequivocally committed to it. For example, his experiments with falling bodies and inclined planes led him to the concepts of circular inertial motion and accelerating free-fall. The current Aristotelian theories of impetus and terrestrial motion were inadequate to explain these. While atomism did not explain the law of fall either, it was a more promising framework in which to develop an explanation because motion was conserved in ancient atomism (unlike Aristotelian physics).
René Descartes' (1596–1650) "mechanical" philosophy of corpuscularism had much in common with atomism, and is considered, in some senses, to be a different version of it. Descartes thought everything physical in the universe to be made of tiny vortices of matter. Like the ancient atomists, Descartes claimed that sensations, such as taste or temperature, are caused by the shape and size of tiny pieces of matter. The main difference between atomism and Descartes' concept was the existence of the void. For him, there could be no vacuum, and all matter was constantly swirling to prevent a void as corpuscles moved through other matter. Another key distinction between Descartes' view and classical atomism is the mind/body duality of Descartes, which allowed for an independent realm of existence for thought, soul, and most importantly, God. Gassendi's concept was closer to classical atomism, but with no atheistic overtone.
Pierre Gassendi (1592–1655) was a Catholic priest from France who was also an avid natural philosopher. He was particularly intrigued by the Greek atomists, so he set out to "purify" atomism from its heretical and atheistic philosophical conclusions (Dijksterhius 1969). Gassendi formulated his atomistic conception of mechanical philosophy partly in response to Descartes; he particularly opposed Descartes' reductionist view that only purely mechanical explanations of physics are valid, as well as the application of geometry to the whole of physics (Clericuzio 2000).
Johann Chrysostom Magnenus (c. 1590 – c. 1679) published his Democritus reviviscens in 1646. Magnenus was the first to arrive at a scientific estimate of the size of an "atom" (i.e. of what would today be called a molecule). Measuring how much incense had to be burned before it could be smelled everywhere in a large church, he calculated the number of molecules in a grain of incense to be of the order 1018, only about one order of magnitude below the actual figure.
Corpuscularianism
Corpuscularianism is similar to atomism, except that where atoms were supposed to be indivisible, corpuscles could in principle be divided. In this manner, for example, it was theorized that mercury could penetrate into metals and modify their inner structure, a step on the way towards transmutative production of gold. Corpuscularianism was associated by its leading proponents with the idea that some of the properties that objects appear to have are artifacts of the perceiving mind: 'secondary' qualities as distinguished from 'primary' qualities. Not all corpuscularianism made use of the primary-secondary quality distinction, however. An influential tradition in medieval and early modern alchemy argued that chemical analysis revealed the existence of robust corpuscles that retained their identity in chemical compounds (to use the modern term). William R. Newman has dubbed this approach to matter theory "chymical atomism," and has argued for its significance to both the mechanical philosophy and to the chemical atomism that emerged in the early 19th century. Corpuscularianism stayed a dominant theory over the next several hundred years and retained its links with alchemy in the work of scientists such as Robert Boyle and Isaac Newton in the 17th century. It was used by Newton, for instance, in his development of the corpuscular theory of light. The form that came to be accepted by most English scientists after Robert Boyle (1627–1692) was an amalgam of the systems of Descartes and Gassendi. In The Sceptical Chymist (1661), Boyle demonstrates problems that arise from chemistry, and offers up atomism as a possible explanation. The unifying principle that would eventually lead to the acceptance of a hybrid corpuscular–atomism was mechanical philosophy, which became widely accepted by physical sciences.
Modern atomic theory
By the late 18th century, the useful practices of engineering and technology began to influence philosophical explanations for the composition of matter. Those who speculated on the ultimate nature of matter began to verify their "thought experiments" with some repeatable demonstrations, when they could.
Roger Boscovich provided the first general mathematical theory of atomism, based on the ideas of Newton and Leibniz but transforming them so as to provide a programme for atomic physics.
In 1808, John Dalton assimilated the known experimental work of many people to summarize the empirical evidence on the composition of matter. He noticed that distilled water everywhere analyzed to the same elements, hydrogen and oxygen. Similarly, other purified substances decomposed to the same elements in the same proportions by weight.
- Therefore we may conclude that the ultimate particles of all homogeneous bodies are perfectly alike in weight, figure, etc. In other words, every particle of water is like every other particle of water; every particle of hydrogen is like every other particle of hydrogen, etc.
Furthermore, he concluded that there was a unique atom for each element, using Lavoisier's definition of an element as a substance that could not be analyzed into something simpler. Thus, Dalton concluded the following.
- Chemical analysis and synthesis go no farther than to the separation of particles one from another, and to their reunion. No new creation or destruction of matter is within the reach of chemical agency. We might as well attempt to introduce a new planet into the solar system, or to annihilate one already in existence, as to create or destroy a particle of hydrogen. All the changes we can produce, consist in separating particles that are in a state of cohesion or combination, and joining those that were previously at a distance.
And then he proceeded to give a list of relative weights in the compositions of several common compounds, summarizing:
- 1st. That water is a binary compound of hydrogen and oxygen, and the relative weights of the two elementary atoms are as 1:7, nearly;
- 2nd. That ammonia is a binary compound of hydrogen and azote nitrogen, and the relative weights of the two atoms are as 1:5, nearly...
Dalton concluded that the fixed proportions of elements by weight suggested that the atoms of one element combined with only a limited number of atoms of the other elements to form the substances that he listed.
Dalton's atomic theory remained controversial throughout the 19th century. Whilst the Law of definite proportion was accepted, the hypothesis that this was due to atoms was not so widely accepted. For example, in 1826 when Sir Humphry Davy presented Dalton the Royal Medal from the Royal Society, Davy said that the theory only became useful when the atomic conjecture was ignored. Sir Benjamin Collins Brodie in 1866 published the first part of his Calculus of Chemical Operations as a non-atomic alternative to the Atomic Theory. He described atomic theory as a 'Thoroughly materialistic bit of joiners work'. Alexander Williamson used his Presidential Address to the London Chemical Society in 1869 to defend the Atomic Theory against its critics and doubters. This in turn led to further meetings at which the positivists again attacked the supposition that there were atoms. The matter was finally resolved in Dalton's favour in the early 20th century with the rise of atomic physics.
Atoms and molecules had long been theorized as the constituents of matter, and Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules, making one of his first big contributions to science. This explanation of Brownian motion served as convincing evidence that atoms and molecules exist, and was further verified experimentally by Jean Perrin in 1908. Perrin was awarded the Nobel Prize in Physics in 1926 "for his work on the discontinuous structure of matter". The direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion.
