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Chaos
In culture, chaos, from the Greek Χάος, refers to utter confusion, an unorganized state, or a system in disorder. [1] In thermodynamic modern colloquial terms, when queried, people tend to associate entropy with chaos. [2] This, however, is late 20th century metaphor-crossover effect. None of the original founders of thermodynamics, such as Clausius, Maxwell, Gibbs, Boltzmann, Planck, etc., for instance, used the term “chaos”. [3]
Mythology
In reference to the etymology of the word chaos, the opening sentence of the 1600 version of the Bible, i.e. the first paragraph of the Genesis section of the Pentateuch, reads: “In the beginning God created the heaven and the earth. And the earth was without form, and void; and the darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.” In etymology of this myth, the Hebrew scribes borrowed the Egyptian Hermopolitan creation scheme, from the ancient city of Hermopolis, to describe the state of the universe before creation begins.
In Hermopolis mythology, between c. 3100 BC - 2100 BC, the primeval universe was considered to be comprised of four basic elements, each element having a male and female counterpart. These elements or gods were known as the Ogdoad or “group of eight”. The deities and their associations were Nun and Naunet, the primordial water; Huh and Hauhet, space or infinity (also considered as the flood force); Kuk and Kauket, darkness; and Amen and Amenent, the invisibility of the winds. [15] At some point the eight elements interacted to create a burst of energy, allowing creation to take place. [17]
Hence, through etymological-evolution, the words translated as “without form and void” appear in the original Hebrew as “tohu” and “bohu”, and those two words sometimes appear in popular writing as an idiomatic way of expressing chaos or disorder, as in “all was tohu and bohu”. [16]
In short, in the biblical-version, the four male deities have been omitted from the story but their essential characteristics have been retained. Subsequently, the origin of the word “chaos” derives from the Egyptian frog headed god Huh, and his consort the snake-headed goddess Hauhet, personifying the “formless and infinity”. [17] He is often represented anthropomorphically holding in each hand a notched palm-rib branch (as shown adjacent), the hieroglyph for ‘year’ symbolizing the passing of time (or "rib-of-time" analgous to arrow of time), where each notch represents one year.
Interestingly, then, in modern terms, we have come, unknowingly, to symbolize both chaos and the passage of time by one entity, that of “entropy”, symbol S, in place of older Egyptian-deity/palm-rib combination. One can only imagine, what we will use in another 5,000-years from now?
By the year 1440, the term “chaos” had come to be known as "gaping void," from Latin chaos, from Greek khaos "abyss, that which gapes wide open, is vast and empty" and chaos meaning "utter confusion" (1606) is extended from theological use of chaos for "the void at the beginning of creation" in Vulgate version of Genesis. [7]
Chemistry
In 1632, Flemish physician and chemist Jan Baptista van Helmont coined the concept of “gas”, as type of air having distinct physical and chemical properties, from the Greek word “chaos”. [8] He wrote: “I call Gas, not far different from the Chaos of the ancients”. [9] The particles of a gas, or of a gas, were in chaos, and gas could be a wild spirit because of its habit of escaping from chemical reactions. [10] Van Helmont called “this Spirit, unknown hitherto, by the new name of Gas, which can neither be constrained by Vessels, nor reduced into a visible body.” [11]
Into the late 17th century, debates on the overlap of science and religion, in relation to chaos (of Genesis) and the new gas theories, were beginning to erupt. In 1663, for instance, British clergyman Richard Bentley argued that: “The Atoms or Particles, which now constitute Heaven and Earth, being once separate and diffused in Mundane Space, like the supposed Chaos, could never without a God by their Mechanical affections have convened into this present Frame of Things or any other like it.”
Thermodynamics
In 1895, Ludwig Boltzmann finished is famous Vorlesungen über Gastheorie (Lectures on Gas Theory), in which he outlined a statistical thermodynamic interpretation of “molar-ordered” [molar-geordnete] and “molar-disordered” distributions of gas molecules in containers. In this work, originally published in two parts, 1896 (Part I) and 1898 (Part II), through a bit of derivation related to the logarithms of the probabilities of the arrangements of molecules and distributions of states among them in several gases, Boltzmann then concludes that:
Hence, although Boltzmann never actually equated entropy with chaos, by way of these statements, most have come to attribute the molecular chaos/ entropy logic to the theories of Boltzmann. In the 1964 Translator’s Introduction to Boltzmann’s Gas Theory, for instance, physics historian Stephen Brush, comments that: “Boltzmann was able to deduce immediately a very important result from his equation, which was not at all obvious from Maxwell’s original formulation: a quantity called H, which can be identified with the negative of the entropy, must always decrease or remain constant, if one assumes that the velocity distributions of two colliding molecules are uncorrelated. The molecular interpretation of the law of increasing entropy is thus intimately related to the assumption of molecular chaos and the relation between entropy and probability.” He continues, “H remains constant only when the gas attains a special velocity distribution which had previously been deduced by Maxwell (1859) in a less convincing manner.” [12]
To elaborate further on the association of the logic of Boltzmann with chaos, a key insight applied by Boltzmann was to determine the collision term resulting solely from two-body collisions between particles that are assumed to be uncorrelated prior to the collision. This assumption was referred to by Boltzmann as the 'Stosszahl Ansatz', and is now known as the Boltzmann chaos assumption or 'molecular chaos assumption'. The Boltzmann chaos assumption, roughly speaking, postulates the non-correlation of velocities of particles which are about to collide. [13] The translation of these terms into the loose public idea that “entropy = chaos” and that the second law states that “everything tends to chaos”, however, did not involve a quantitative rigorous development, but rather a haphazard dumbing-down of the technicalities and stipulations involved in favor ball-park understanding.
One of the earliest references to the supposed equality of entropy and chaos is found in the 1920 A System of Physical Chemistry by William Lewis and James Rice, who state that “the molecules of a gas are in a continuous disordered movement, a gas being in fact a molecular chaos”. [4] They refer to American mathematical physicist Willard Gibbs description of entropy as mixed-up-ness and state that “this definition of entropy will be understood to a certain extent if we think of a substance as a molecular chaos … owing to collisions between the molecules their motion tends to become more and more disordered until a final stage of disorder is reached.” The section heading “entropy as mixed-up-ness" by Gibbs, however, was a planned, but never finished, chapter heading found in the unpublished fragments of Gibbs papers. [5] In any event, they incorrectly state that “Gibbs considered that the degree of the disorder was identical with entropy” and that “when the disorder or chaos is greatest the entropy of a substance is likewise a maximum”. Gibbs, however, never once used the words “disorder” or “chaos”.
In the 1967 book Order and Chaos - Laws of Energy and Entropy, authors Stanley Angrist and Loren Hepler attempt to show how the laws of thermodynamics apply to technology, culture, and life processes. [19] By 1971, “chaos theory” was beginning to be correlated with entropy and the second law of thermodynamics. [18] Belgian thermodynamicist Ilya Prigogine, having been greatly influenced by Boltzmann in his early days, was a great promoter of the word “chaos”. His most popular book is the 1984 Order Out of Chaos, in which he set out to show that events called bifurcations and fluctuations, in non-equilibrium thermodynamic processes, can create “order out of chaos” in accordance with second law of thermodynamics, albeit with a modified version of internal entropy synthesized by him. [20] Another is this 1996 The End of Certainty - Time, Chaos, and the New Laws of Nature. [21]
References
1. (a) Chaos (definition) - Oxford Illustrated American Dictionary, 1998.
(b) Chaos (definition) - Merriam-Webster Collegiate Dictionary, 2000.
2. Schmitz, John E.J. (2007). The Second Law of Life: Energy, Technology, and the Future of Earth as We Know It, (pg. 6). William Andrew Publishing.
3. Examples include: Rudolf Clausius, Mechanical Theory of Heat (1865), James Maxwell, Theory of Heat (1871), Willard Gibbs, On the Equilibrium of Heterogeneous Substances (1876), Ludwig Boltzmann, Lectures on Gas Theory (1895), Max Planck, Treatise on Thermodynamics (1897), etc., all checked using Google book keyword search (and physical index searching).
4. Lewis, William and Rice, James. (1920). A System of Physical Chemistry, (pg. 48). Longmans and Green.
5. Mixed-up-ness (in the collected Scientific Papers of J. Willard Gibbs (Longmans), the reader will find on page 418 of the first volume a number of unpublished fragments, one subject bearing the title: Entropy as mixed-up-ness, a planned, but never finished, chapter).
6. Jordon, Michael. (1993). Encyclopedia of Gods, (pg. 55). New York: Facts on File, Inc.
7. Chaos (etymology) - Online Etymology Dictionary.
8. Perrot, Pierre. (1998). A to Z of Thermodynamics, (pg. 123). Oxford: Oxford University Press.
9. Lerner, Lawrence S. (1997). Physics for Scientist and Engineers, (pg. 411). Jones & Barlett Publisher.
10. Levere, Trevor H. (2001). Transforming Mater: A History of Chemistry from Alchemy to the Buckyball, (pg. 51). JHU Press.
11. Van Helmont, J.R. (1663). Oriatrike, pg. 106. London.
12. Boltzmann, Ludwig. (1964). Lectures on Gas Theory, (pgs. 9, 74). New York: Dover.
13. Villani, Cédric. (2003). Topics in Optimal Transportation, (pg. 224). AMS Bookstore.
14. Bentley, Richard. (1963). A Confutation of Atheism from the Origin and Frame of the World, Part II, 7. (as found in the 2005 Oxford Dictionary of Scientific Quotations).
15. Greenberg, Gary. (2000). 101 Myths of the Bible - How the Ancient Scribes Invented Biblical History. Naperville, Illinois: SourceBooks, Inc.
16. (a) Ibid, Greenberg, section: “Myth #1: In the beginning everything was without form and void”, (pgs. 11-12).
(b) O’Grady, John, F. (2005). Men in the Bible: The Good, the Bad, and the Ugly, (pgs. 3-4). Paulist Press.
17. (a) Oakes, Lorna and Gahlin, Lucia. (2002). Ancient Egypt - an Illustrated Reference to the Myths, Religions, Pyramids, and Temples of the Land of the Pharaohs, (pg. 286, 300). Hermes House.
(b) Image of the god Heh: as he kneels on the hieroglyphic sign for gold, and clutches notched palm branches, symbolizing the passing of time, 18th Dynasty (1550-1292 BC); as found on the back of one of Tutankhamun’s thrones.
18. Quote: Today, the theory of chaos can help with the answer. The second law of thermodynamics is, according to Arthur Eddington, the "supreme law of Nature". ... (Source: New Scientist, 1971, pg. 41).
19. Angrist, Stanley W. and Helper, Loren G. (1967). Order and Chaos – Laws of Energy and Entropy. New York: Basic Books.
20. Prigogine, Ilya. (1984). Order Out of Chaos – Man’s New Dialogue with Nature. New York: Bantam Books.
21. Prigogine, Illya. (1996). The End of Certainty - Time, Chaos, and the New Laws of Nature. New York: The Free Press.
Mythology
See main: Comparative mythology and religionThe etymology of the term chaos, in ancient origins, stems from early 4,000 BC mythological conceptions, primarily Egyptian, of a primordial deity (or set of deities) that personified the empty space or void that existed before the formation of the cosmos. [6] In particular, according to what is called the “documentary hypothesis”, when the Pentateuch, a Greek word meaning “five scrolls”, was written, between 1,000-500 BC, the Israelite authors, estimated to be four plus an editor, incorporated much of Egyptian and Babylonian mythology, from the places they had lived in, into the construction of the Bible. [15]
In reference to the etymology of the word chaos, the opening sentence of the 1600 version of the Bible, i.e. the first paragraph of the Genesis section of the Pentateuch, reads: “In the beginning God created the heaven and the earth. And the earth was without form, and void; and the darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.” In etymology of this myth, the Hebrew scribes borrowed the Egyptian Hermopolitan creation scheme, from the ancient city of Hermopolis, to describe the state of the universe before creation begins.
In Hermopolis mythology, between c. 3100 BC - 2100 BC, the primeval universe was considered to be comprised of four basic elements, each element having a male and female counterpart. These elements or gods were known as the Ogdoad or “group of eight”. The deities and their associations were Nun and Naunet, the primordial water; Huh and Hauhet, space or infinity (also considered as the flood force); Kuk and Kauket, darkness; and Amen and Amenent, the invisibility of the winds. [15] At some point the eight elements interacted to create a burst of energy, allowing creation to take place. [17]
Hence, through etymological-evolution, the words translated as “without form and void” appear in the original Hebrew as “tohu” and “bohu”, and those two words sometimes appear in popular writing as an idiomatic way of expressing chaos or disorder, as in “all was tohu and bohu”. [16]In short, in the biblical-version, the four male deities have been omitted from the story but their essential characteristics have been retained. Subsequently, the origin of the word “chaos” derives from the Egyptian frog headed god Huh, and his consort the snake-headed goddess Hauhet, personifying the “formless and infinity”. [17] He is often represented anthropomorphically holding in each hand a notched palm-rib branch (as shown adjacent), the hieroglyph for ‘year’ symbolizing the passing of time (or "rib-of-time" analgous to arrow of time), where each notch represents one year.
Interestingly, then, in modern terms, we have come, unknowingly, to symbolize both chaos and the passage of time by one entity, that of “entropy”, symbol S, in place of older Egyptian-deity/palm-rib combination. One can only imagine, what we will use in another 5,000-years from now?
By the year 1440, the term “chaos” had come to be known as "gaping void," from Latin chaos, from Greek khaos "abyss, that which gapes wide open, is vast and empty" and chaos meaning "utter confusion" (1606) is extended from theological use of chaos for "the void at the beginning of creation" in Vulgate version of Genesis. [7]
Chemistry
In 1632, Flemish physician and chemist Jan Baptista van Helmont coined the concept of “gas”, as type of air having distinct physical and chemical properties, from the Greek word “chaos”. [8] He wrote: “I call Gas, not far different from the Chaos of the ancients”. [9] The particles of a gas, or of a gas, were in chaos, and gas could be a wild spirit because of its habit of escaping from chemical reactions. [10] Van Helmont called “this Spirit, unknown hitherto, by the new name of Gas, which can neither be constrained by Vessels, nor reduced into a visible body.” [11]
Into the late 17th century, debates on the overlap of science and religion, in relation to chaos (of Genesis) and the new gas theories, were beginning to erupt. In 1663, for instance, British clergyman Richard Bentley argued that: “The Atoms or Particles, which now constitute Heaven and Earth, being once separate and diffused in Mundane Space, like the supposed Chaos, could never without a God by their Mechanical affections have convened into this present Frame of Things or any other like it.”
Thermodynamics
In 1895, Ludwig Boltzmann finished is famous Vorlesungen über Gastheorie (Lectures on Gas Theory), in which he outlined a statistical thermodynamic interpretation of “molar-ordered” [molar-geordnete] and “molar-disordered” distributions of gas molecules in containers. In this work, originally published in two parts, 1896 (Part I) and 1898 (Part II), through a bit of derivation related to the logarithms of the probabilities of the arrangements of molecules and distributions of states among them in several gases, Boltzmann then concludes that:
“The fact that in nature the entropy tends to a maximum shows that for all interactions (diffusion, heat conduction, etc.) of actual gases the individual molecules behave according to the laws of probability in their interactions, or at least that the actual gas behaves like the molecular-disordered gas which we have in mind”
Hence, although Boltzmann never actually equated entropy with chaos, by way of these statements, most have come to attribute the molecular chaos/ entropy logic to the theories of Boltzmann. In the 1964 Translator’s Introduction to Boltzmann’s Gas Theory, for instance, physics historian Stephen Brush, comments that: “Boltzmann was able to deduce immediately a very important result from his equation, which was not at all obvious from Maxwell’s original formulation: a quantity called H, which can be identified with the negative of the entropy, must always decrease or remain constant, if one assumes that the velocity distributions of two colliding molecules are uncorrelated. The molecular interpretation of the law of increasing entropy is thus intimately related to the assumption of molecular chaos and the relation between entropy and probability.” He continues, “H remains constant only when the gas attains a special velocity distribution which had previously been deduced by Maxwell (1859) in a less convincing manner.” [12]
To elaborate further on the association of the logic of Boltzmann with chaos, a key insight applied by Boltzmann was to determine the collision term resulting solely from two-body collisions between particles that are assumed to be uncorrelated prior to the collision. This assumption was referred to by Boltzmann as the 'Stosszahl Ansatz', and is now known as the Boltzmann chaos assumption or 'molecular chaos assumption'. The Boltzmann chaos assumption, roughly speaking, postulates the non-correlation of velocities of particles which are about to collide. [13] The translation of these terms into the loose public idea that “entropy = chaos” and that the second law states that “everything tends to chaos”, however, did not involve a quantitative rigorous development, but rather a haphazard dumbing-down of the technicalities and stipulations involved in favor ball-park understanding.
One of the earliest references to the supposed equality of entropy and chaos is found in the 1920 A System of Physical Chemistry by William Lewis and James Rice, who state that “the molecules of a gas are in a continuous disordered movement, a gas being in fact a molecular chaos”. [4] They refer to American mathematical physicist Willard Gibbs description of entropy as mixed-up-ness and state that “this definition of entropy will be understood to a certain extent if we think of a substance as a molecular chaos … owing to collisions between the molecules their motion tends to become more and more disordered until a final stage of disorder is reached.” The section heading “entropy as mixed-up-ness" by Gibbs, however, was a planned, but never finished, chapter heading found in the unpublished fragments of Gibbs papers. [5] In any event, they incorrectly state that “Gibbs considered that the degree of the disorder was identical with entropy” and that “when the disorder or chaos is greatest the entropy of a substance is likewise a maximum”. Gibbs, however, never once used the words “disorder” or “chaos”.
In the 1967 book Order and Chaos - Laws of Energy and Entropy, authors Stanley Angrist and Loren Hepler attempt to show how the laws of thermodynamics apply to technology, culture, and life processes. [19] By 1971, “chaos theory” was beginning to be correlated with entropy and the second law of thermodynamics. [18] Belgian thermodynamicist Ilya Prigogine, having been greatly influenced by Boltzmann in his early days, was a great promoter of the word “chaos”. His most popular book is the 1984 Order Out of Chaos, in which he set out to show that events called bifurcations and fluctuations, in non-equilibrium thermodynamic processes, can create “order out of chaos” in accordance with second law of thermodynamics, albeit with a modified version of internal entropy synthesized by him. [20] Another is this 1996 The End of Certainty - Time, Chaos, and the New Laws of Nature. [21]
References
1. (a) Chaos (definition) - Oxford Illustrated American Dictionary, 1998.
(b) Chaos (definition) - Merriam-Webster Collegiate Dictionary, 2000.
2. Schmitz, John E.J. (2007). The Second Law of Life: Energy, Technology, and the Future of Earth as We Know It, (pg. 6). William Andrew Publishing.
3. Examples include: Rudolf Clausius, Mechanical Theory of Heat (1865), James Maxwell, Theory of Heat (1871), Willard Gibbs, On the Equilibrium of Heterogeneous Substances (1876), Ludwig Boltzmann, Lectures on Gas Theory (1895), Max Planck, Treatise on Thermodynamics (1897), etc., all checked using Google book keyword search (and physical index searching).
4. Lewis, William and Rice, James. (1920). A System of Physical Chemistry, (pg. 48). Longmans and Green.
5. Mixed-up-ness (in the collected Scientific Papers of J. Willard Gibbs (Longmans), the reader will find on page 418 of the first volume a number of unpublished fragments, one subject bearing the title: Entropy as mixed-up-ness, a planned, but never finished, chapter).
6. Jordon, Michael. (1993). Encyclopedia of Gods, (pg. 55). New York: Facts on File, Inc.
7. Chaos (etymology) - Online Etymology Dictionary.
8. Perrot, Pierre. (1998). A to Z of Thermodynamics, (pg. 123). Oxford: Oxford University Press.
9. Lerner, Lawrence S. (1997). Physics for Scientist and Engineers, (pg. 411). Jones & Barlett Publisher.
10. Levere, Trevor H. (2001). Transforming Mater: A History of Chemistry from Alchemy to the Buckyball, (pg. 51). JHU Press.
11. Van Helmont, J.R. (1663). Oriatrike, pg. 106. London.
12. Boltzmann, Ludwig. (1964). Lectures on Gas Theory, (pgs. 9, 74). New York: Dover.
13. Villani, Cédric. (2003). Topics in Optimal Transportation, (pg. 224). AMS Bookstore.
14. Bentley, Richard. (1963). A Confutation of Atheism from the Origin and Frame of the World, Part II, 7. (as found in the 2005 Oxford Dictionary of Scientific Quotations).
15. Greenberg, Gary. (2000). 101 Myths of the Bible - How the Ancient Scribes Invented Biblical History. Naperville, Illinois: SourceBooks, Inc.
16. (a) Ibid, Greenberg, section: “Myth #1: In the beginning everything was without form and void”, (pgs. 11-12).
(b) O’Grady, John, F. (2005). Men in the Bible: The Good, the Bad, and the Ugly, (pgs. 3-4). Paulist Press.
17. (a) Oakes, Lorna and Gahlin, Lucia. (2002). Ancient Egypt - an Illustrated Reference to the Myths, Religions, Pyramids, and Temples of the Land of the Pharaohs, (pg. 286, 300). Hermes House.
(b) Image of the god Heh: as he kneels on the hieroglyphic sign for gold, and clutches notched palm branches, symbolizing the passing of time, 18th Dynasty (1550-1292 BC); as found on the back of one of Tutankhamun’s thrones.
18. Quote: Today, the theory of chaos can help with the answer. The second law of thermodynamics is, according to Arthur Eddington, the "supreme law of Nature". ... (Source: New Scientist, 1971, pg. 41).
19. Angrist, Stanley W. and Helper, Loren G. (1967). Order and Chaos – Laws of Energy and Entropy. New York: Basic Books.
20. Prigogine, Ilya. (1984). Order Out of Chaos – Man’s New Dialogue with Nature. New York: Bantam Books.
21. Prigogine, Illya. (1996). The End of Certainty - Time, Chaos, and the New Laws of Nature. New York: The Free Press.
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| Started By | Thread Subject | Replies | Last Post | ||
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| SdogV | Choas | 0 | Jul 18 2008, 2:46 PM EDT by SdogV | ||
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Thread started: Jul 18 2008, 2:46 PM EDT
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I always liked the definition, "Chaos is the state of things where chance is supreme!" which implies a different dimension on its relation to entropy..
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