Philosophy of war

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Philosophy_of_war 

The philosophy of war is the area of philosophy devoted to examining issues such as the causes of war, the relationship between war and human nature, and the ethics of war. Certain aspects of the philosophy of war overlap with the philosophy of history, political philosophy, international relations and the philosophy of law.

Works about the philosophy of war

Carl von Clausewitz, painting by Karl Wilhelm Wach.

Perhaps the greatest and most influential work in the philosophy of war is Carl von Clausewitz's On War, published in 1832. It combines observations on strategy with questions about human nature and the purpose of war. Clausewitz especially examines the teleology of war: whether war is a means to an end outside itself or whether it can be an end in itself. He concludes that the latter cannot be so, and that war is "politics by different means"; i.e. that war must not exist only for its own sake. It must serve some purpose for the state.

Leo Tolstoy's 1869 novel War and Peace contains frequent philosophical digressions on the philosophy of war (and broader metaphysical speculations derived from Christianity and from Tolstoy's observations of the Napoleonic Wars). It was influential on later thought about war. Tolstoy's Christian-centered philosophy of war (especially his essays "A Letter to a Hindu" (1908) and "The Kingdom of God is Within You" (1894)) directly influenced Gandhi's Hinduism-centered non-violent resistance philosophy.

Writing in 1869, Genrikh Leer [ru] emphasized the favorable effects of war on nations: "[...] war emerges as a powerful tool in the matter of improving the internal, moral and material life of peoples [...]."^[1]

While Sun Tzu's The Art of War (5th century BCE), focuses mostly on weaponry and strategy instead of on philosophy, various commentators have broadened his observations into philosophies applied in situations extending well beyond war itself such as competition or management (see the main Wikipedia article on The Art of War for a discussion of the application of Sun Tzu's philosophy to areas other than war). In the early 16th century, parts of Niccolò Machiavelli's masterpiece The Prince (as well as his Discourses) and parts of Machiavelli's own work titled The Art of War discuss some philosophical points relating to war, though neither book could be said to be a work in the philosophy of war.

Just War Theory

The Indian Hindu epic, the Mahabharata, offers the first written discussions of a "just war" (dharma-yuddha or "righteous war"). In it, one of five ruling brothers (Pandavas) asks if the suffering caused by war can ever be justified. A long discussion then ensues between the siblings, establishing criteria like proportionality (chariots cannot attack cavalry, only other chariots; no attacking people in distress), just means (no poisoned or barbed arrows), just cause (no attacking out of rage), and fair treatment of captives and the wounded. The philosophy of just war theorizes what aspects of war are justifiable according to morally acceptable principles. Just war theory is based upon four core criteria to be followed by those determined to go to war. The four principles are as follows: just authority; just cause; right intention; last resort.

Just authority

The criterion of just authority refers to the determined legality of going to war, and whether the concept of war and the pursuit of it has been legally processed and justified.

Just cause

Just cause is a justifiable reason that war is the appropriate and necessary response. If war can be avoided, that must be determined first, according to the philosophy of just war theory.

Right intention

To go to war, one must determine if the intentions of doing so are right according to morality. Right intention criterion requires the determination of whether or not a war response is a measurable way to the conflict being acted upon.

Last resort

War is a last resort response, meaning that if there is a conflict between disagreeing parties, all solutions must be attempted before resorting to war.

Traditions of thought

Since the philosophy of war is often treated as a subset of another branch of philosophy (for example, political philosophy or the philosophy of law) it would be difficult to define any clear-cut schools of thought in the same sense that, e.g., Existentialism or Objectivism can be described as distinct movements. The Stanford Encyclopedia of Philosophy refers to Carl von Clausewitz as "the only (so-called) philosopher of war", implying that he is the only (major) philosophical writer who develops a philosophical system focusing exclusively on war. However, discernible traditions of thought on war have developed over time, so that some writers have been able to distinguish broad categories (if somewhat loosely).

Teleological categories

Anatol Rapoport's introduction to his edition of the J. J. Graham translation of Clausewitz's On War identifies three main teleological traditions in the philosophy of war: the cataclysmic, the eschatological, and the political. (On War, Rapoport's introduction, 13). These are not the only possible teleological philosophies of war, but only three of the most common. As Rapoport says,

To put it metaphorically, in political philosophy war is compared to a game of strategy (like chess); in eschatological philosophy, to a mission or the dénouement of a drama; in cataclysmic philosophy, to a fire or an epidemic.

These do not, of course, exhaust the views of war prevailing at different times and at different places. For example, war has at times been viewed as a pastime or an adventure, as the only proper occupation for a nobleman, as an affair of honor (for example, the days of chivalry), as a ceremony (e.g. among the Aztecs), as an outlet of aggressive instincts or a manifestation of a "death wish", as nature's way of ensuring the survival of the fittest, as an absurdity (e.g. among Eskimos), as a tenacious custom, destined to die out like slavery, and as a crime. (On War, Rapoport's introduction, 17)

• The Cataclysmic school of thought, which was espoused by Leo Tolstoy in his epic novel War and Peace, sees war as a bane on humanity – whether avoidable or inevitable – which serves little purpose outside of causing destruction and suffering, and which may cause drastic change to society, but not in any teleological sense. Tolstoy's view may be placed under the subcategory of global cataclysmic philosophy of war. Another subcategory of the cataclysmic school of thought is the ethnocentric cataclysmic, in which this view is focused specifically on the plight of a specific ethnicity or nation, for example the view in Judaism of war as a punishment from God on the Israelites in certain books of the Tenakh (Old Testament). As the Tenakh (in certain books) sees war as an ineluctable act of God, so Tolstoy especially emphasizes war as something that befalls man and is in no way under the influence of man's "free will", but is instead the result of irresistible global forces. (On War, Rapoport's introduction 16)
• The Eschatological school of thought sees all wars (or all major wars) as leading to some goal, and asserts that some final conflict will someday resolve the path followed by all wars and result in a massive upheaval of society and a subsequent new society free from war (in varying theories the resulting society may be either a utopia or a dystopia). There are two subsets of this view: the Messianic and the Global theory. The Marxist concept of a communist world ruled by the proletariat after a final worldwide revolution is an example of the global theory, and the Christian concept of an Armageddon war which will usher in the second coming of Christ and the final defeat of Satan is an example of a theory that could fall under Global or Messianic. (On War, Rapoport's introduction, 15) The messianic eschatological philosophy is derived from the Jewish-Christian concept of a Messiah, and sees wars as culminating in unification of humanity under a single faith or a single ruler. Crusades, Jihads, the Nazi concept of a Master Race and the 19th century American concept of Manifest Destiny may also fall under this heading. (On War, Rapoport's introduction, 15) (See main articles for more information: Christian eschatology, Jewish eschatology)
• The Political school of thought, of which Clausewitz was a proponent, sees war as a tool of the state. On page 13 Rapoport says,

Clausewitz views war as a rational instrument of national policy. The three words "rational", "instrument" and "national" are the key concepts of his paradigm. In this view, the decision to wage war "ought" to be rational, in the sense that it ought to be based on estimated costs and gains of war. Next, war "ought" to be instrumental, in the sense that it ought to be waged in order to achieve some goal, never for its own sake; and also in the sense that strategy and tactics ought to be directed towards just one end, namely towards victory. Finally, war "ought" to be national, in the sense that its objective should be to advance the interests of a national state and that the entire effort of the nation ought to be mobilized in the service of the military objective.

He later characterizes the philosophy behind the Vietnam War and other Cold War conflicts as "Neo-Clausewitzian". Rapoport also includes Machiavelli as an early example of the political philosophy of war (On War, Rapoport's introduction, 13). Decades after his essay, the War on Terrorism and the Iraq War begun by the United States under President George W. Bush in 2001 and 2003 have often been justified under the doctrine of preemption, a political motivation stating that the United States must use war to prevent further attacks such as the September 11, 2001 attacks.

Ethical categories

Another possible system for categorizing different schools of thought on war can be found in the Stanford Encyclopedia of Philosophy (see external links, below), based on ethics. The SEP describes three major divisions in the ethics of war: the realist, the pacifist, and the just war Theory. In a nutshell:

• Realists will typically hold that systems of morals and ethics which guide individuals within societies cannot realistically be applied to societies as a whole to govern the way they, as societies, interact with other societies. Hence, a state's purposes in war is simply to preserve its national interest. This kind of thinking is similar to Machiavelli's philosophy, and Thucydides and Hobbes may also fall under this category.
• Pacifism however, maintains that a moral evaluation of war is possible, and that war is always found to be immoral. Generally, there are two kinds of modern secular pacifism to consider: (1) a more consequentialist form of pacifism (or CP), which maintains that the benefits accruing from war can never outweigh the costs of fighting it; and (2) a more deontological form of pacifism (or DP), which contends that the very activity of war is intrinsically wrong, since it violates foremost duties of justice, such as not killing human beings. Eugene Victor Debs and others were famous advocates of pacifistic diplomatic methods instead of war.
• Just war theory, along with pacifism, holds that morals do apply to war. However, unlike pacifism, according to just war theory it is possible for a war to be morally justified. The concept of a morally justified war underlies much of the concept international law, such as the Geneva Conventions. Aristotle, Cicero, Augustine, Aquinas, and Hugo Grotius are among the philosophers who have espoused some form of a just war philosophy. One common just war theory evaluation of war is that war is only justified if 1.) waged in a state or nation's self-defense, or 2.) waged in order to end gross violations of human rights. Political philosopher John Rawls advocated these criteria as justification for war.

The Art of War

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/The_Art_of_War

 

The Art of War

Author	Sun Tzu (traditional)
Country	China
Language	Classical Chinese
Subject	Military art
Publication date	5th century BC
Original text	The Art of War at Chinese Wikisource
Translation	The Art of War at Wikisource

The Art of War
Traditional Chinese	孫子兵法
Simplified Chinese	孙子兵法
Literal meaning	"Master Sun's Military Methods"

The Art of War (Chinese: 孫子兵法; lit. 'Sun Tzu's Military Method', pinyin: Sūnzǐ bīngfǎ) is an ancient Chinese military treatise dating from the Late Spring and Autumn Period (roughly 5th century BC). The work, which is attributed to the ancient Chinese military strategist Sun Tzu ("Master Sun"), is composed of 13 chapters. Each one is devoted to a different set of skills or art related to warfare and how it applies to military strategy and tactics. For almost 1,500 years it was the lead text in an anthology that was formalized as the Seven Military Classics by Emperor Shenzong of Song in 1080. The Art of War remains the most influential strategy text in East Asian warfare and has influenced both East Asian and Western military theory and thinking and has found a variety of applications in a myriad of competitive non-military endeavors across the modern world including espionage, culture, politics, business, and sports.

The book contains a detailed explanation and analysis of the 5th-century BC Chinese military, from weapons, environmental conditions, and strategy to rank and discipline. Sun also stressed the importance of intelligence operatives and espionage to the war effort. Considered one of history's finest military tacticians and analysts, his teachings and strategies formed the basis of advanced military training for millennia to come.

The book was translated into French and published in 1772 (re-published in 1782) by the French Jesuit Jean Joseph Marie Amiot. A partial translation into English was attempted by British officer Everard Ferguson Calthrop in 1905 under the title The Book of War. The first annotated English translation was completed and published by Lionel Giles in 1910. Military and political leaders such as the Chinese communist revolutionary Mao Zedong, Japanese daimyō Takeda Shingen, Vietnamese general Võ Nguyên Giáp, and American military generals Douglas MacArthur and Norman Schwarzkopf Jr. are all cited as having drawn inspiration from the book.

History

Text and commentaries

The Art of War is traditionally attributed to an ancient Chinese military general known as Sun Tzu (now Romanized "Sunzi") meaning "Master Sun". Sun Tzu was traditionally said to have lived in the 6th century BC, but The Art of War's earliest parts probably date to at least 100 years later.

Sima Qian's Records of the Grand Historian, the first of China's 24 dynastic histories, records an early Chinese tradition that a text on military matters was written by one "Sun Wu" (孫武) from the State of Qi, and that this text had been read and studied by King Helü of Wu (r. 514 BC – 495 BC). This text was traditionally identified with the received Master Sun's Art of War. The conventional view was that Sun Wu was a military theorist from the end of the Spring and Autumn period (776–471 BC) who fled his home state of Qi to the southeastern kingdom of Wu, where he is said to have impressed the king with his ability to quickly train even court women in military discipline and to have made Wu's armies powerful enough to challenge their western rivals in the state of Chu. This view is still widely held in China.

The strategist, poet, and warlord Cao Cao in the early 3rd century AD authored the earliest known commentary to the Art of War. Cao's preface makes clear that he edited the text and removed certain passages, but the extent of his changes were unclear historically. The Art of War appears throughout the bibliographical catalogs of the Chinese dynastic histories, but listings of its divisions and size varied widely.

Authorship

Fragments of The Art of War discovered as a part of the Yinqueshan Han Slips, showing the version of The Art of War that was popular in Han Dynasty (206 BC – 220 AD)

Beginning around the 12th century, some Chinese scholars began to doubt the historical existence of Sun Tzu, primarily on the grounds that he is not mentioned in the historical classic The Commentary of Zuo (Zuo Zhuan), which mentions most of the notable figures from the Spring and Autumn period. The name "Sun Wu" (孫武) does not appear in any text prior to the Records of the Grand Historian, and has been suspected to be a made-up descriptive cognomen meaning "the fugitive warrior", glossing the surname "Sun" as the related term "fugitive" (xùn 遜), while "Wu" is the ancient Chinese virtue of "martial, valiant" (wǔ 武), which corresponds to Sunzi's role as the hero's doppelgänger in the story of Wu Zixu. In the early 20th century, the Chinese writer and reformer Liang Qichao theorized that the text was actually written in the 4th century BC by Sun Tzu's purported descendant Sun Bin, as a number of historical sources mention a military treatise he wrote. Unlike Sun Wu, Sun Bin appears to have been an actual person who was a genuine authority on military matters, and may have been the inspiration for the creation of the historical figure "Sun Tzu" through a form of euhemerism.

In 1972, the Yinqueshan Han slips were discovered in two Han dynasty (206 BC – 220 AD) tombs near the city of Linyi in Shandong Province. Among the many bamboo slip writings contained in the tombs, which had been sealed between 134 and 118  BC, respectively were two separate texts, one attributed to "Sun Tzu", corresponding to the received text, and another attributed to Sun Bin, which explains and expands upon the earlier The Art of War by Sunzi. The Sun Bin text's material overlaps with much of the "Sun Tzu" text, and the two may be "a single, continuously developing intellectual tradition united under the Sun name". This discovery showed that much of the historical confusion was due to the fact that there were two texts that could have been referred to as "Master Sun's Art of War", not one. The content of the earlier text is about one-third of the chapters of the modern The Art of War, and their text matches very closely. It is now generally accepted that the earlier The Art of War was completed sometime between 500 and 430 BC.

Cultural influence

The beginning of The Art of War in a classical bamboo book from the reign of the Qianlong Emperor

Military and intelligence applications

Across East Asia, The Art of War was part of the syllabus for potential candidates of military service examinations.

During the Sengoku period (c. 1467–1568), the Japanese daimyō Takeda Shingen (1521–1573) is said to have become almost invincible in all battles without relying on guns, because he studied The Art of War. The book even gave him the inspiration for his famous battle standard "Fūrinkazan" (Wind, Forest, Fire and Mountain), meaning fast as the wind, silent as a forest, ferocious as fire and immovable as a mountain.

The translator Samuel B. Griffith offers a chapter on "Sun Tzu and Mao Tse-Tung" where The Art of War is cited as influencing Mao's On Guerrilla Warfare, On the Protracted War and Strategic Problems of China's Revolutionary War, and includes Mao's quote: "We must not belittle the saying in the book of Sun Wu Tzu, the great military expert of ancient China, 'Know your enemy and know yourself and you can fight a thousand battles without disaster.'"

During the Vietnam War, some Viet Cong officers extensively studied The Art of War and reportedly could recite entire passages from memory. General Võ Nguyên Giáp successfully implemented tactics described in The Art of War during the Battle of Dien Bien Phu ending major French involvement in Indochina and leading to the accords which partitioned Vietnam into North and South. General Giáp, later the main PVA military commander in the Vietnam War, was an avid student and practitioner of Sun Tzu's ideas.

Outside East Asia

The United States' defeat in the Vietnam War, more than any other event, brought Sun Tzu to the attention of leaders of U.S. military theory. The Department of the Army in the United States, through its Command and General Staff College, lists The Art of War as one example of a book that may be kept at a military unit's library. The Art of War is listed on the US Marine Corps Professional Reading Program (formerly known as the Commandant's Reading List). It is recommended reading for all United States Military Intelligence personnel. The Art of War is also used as instructional material at the US Military Academy at West Point, in the course Military Strategy (470), and it is also recommended reading for Officer cadets at the Royal Military Academy, Sandhurst. Some notable military leaders have stated the following about Sun Tzu and The Art of War:

"I always kept a copy of The Art of War on my desk." – General Douglas MacArthur, 5 Star General & Supreme Commander for the Allied Powers.

"I have read The Art of War by Sun Tzu. He continues to influence both soldiers & politicians." – General Colin Powell, Chairman of the Joint Chiefs of Staff, National Security Advisor, and Secretary of State.

According to some authors, the strategy of deception from The Art of War was studied and widely used by the KGB: "I will force the enemy to take our strength for weakness, and our weakness for strength, and thus will turn his strength into weakness".

Finnish Field Marshal Mannerheim and general Aksel Airo were avid readers of Art of War; Airo kept the book on his bedside table in his quarters.

Application outside the military

The Art of War has been applied to many fields outside of the military. Much of the text is about how to outsmart one's opponent without actually having to engage in physical battle. As such, it has found application as a training guide for many competitive endeavors that do not involve actual combat.

The Art of War is mentioned as an influence in the earliest known Chinese collection of stories about fraud (mostly in the realm of commerce), Zhang Yingyu's The Book of Swindles (Du pian xin shu, 杜騙新書, c. 1617), which dates to the late Ming dynasty.

Many business books have applied the lessons taken from the book to office politics and corporate business strategy. Many Japanese companies make the book required reading for their key executives. The book is also popular among Western business circles citing its utilitarian values regarding management practices. Many entrepreneurs and corporate executives have turned to it for inspiration and advice on how to succeed in competitive business situations. The book has also been applied to the field of education.

The Art of War has been the subject of legal books and legal articles on the trial process, including negotiation tactics and trial strategy.

The book The 48 Laws of Power by Robert Greene employs philosophies covered in The Art of War.

The Art of War has also been applied in sports. National Football League coach Bill Belichick, record holder of the most Super Bowl wins in history, has stated on multiple occasions his admiration for The Art of War. Brazilian association football coach Luiz Felipe Scolari actively used The Art of War for Brazil's successful 2002 World Cup campaign. During the tournament Scolari put passages of The Art of War underneath his players' doors at night.

The Art of War is often quoted while developing tactics and/or strategy in esports. "Play To Win" by David Sirlin analyses applications of the ideas from The Art of War in modern esports. The Art of War was released in 2014 as an e-book companion alongside the Art of War DLC for Europa Universalis IV, a PC strategy game by Paradox Development Studios, with a foreword by Thomas Johansson.

The Art of War has also been featured in the 2019 video game Age of Empires II: Definitive Edition from Microsoft.

Film and television

The Art of War and Sun Tzu have been referenced and quoted in many movies and television shows, including in the 1987 movie Wall Street, in which Gordon Gekko (Michael Douglas) frequently references it. The 20th James Bond film, Die Another Day (2002) also references The Art of War as the spiritual guide shared by Colonel Moon and his father. In The Sopranos, season 3, episode 8 ("He Is Risen"), Dr. Melfi suggests to Tony Soprano that he read the book.

In the Star Trek: The Next Generation first-season episode "The Last Outpost", first officer William Riker quotes The Art of War: "Fear is the true enemy, the only enemy". Captain Captain Picard expressed pleasure that Sun Tzu was still taught at Starfleet Academy. Later in the episode, a survivor from a long-dead nonhuman empire noted common aspects between his own people's wisdom and The Art of War with regard to knowing when and when not to fight.

The Art of War is a 2000 action spy film directed by Christian Duguay and starring Wesley Snipes, Michael Biehn, Anne Archer and Donald Sutherland.

Notable translations

Running Press miniature edition of the 1994 Ralph D. Sawyer translation, printed in 2003

• Sun Tzu on the Art of War. Translated by Lionel Giles. London: Luzac and Company. 1910.
• The Art of War. Translated by Samuel B. Griffith. Oxford: Oxford University Press. 1963. ISBN 978-0-19-501476-1. Part of the UNESCO Collection of Representative Works.
• Sun Tzu, The Art of War. Translated by Thomas Cleary. Boston: Shambhala Dragon Editions. 1988. ISBN 978-0877734529.
• The Art of Warfare. Translated by Roger Ames. Random House. 1993. ISBN 978-0-345-36239-1.
• The Art of War. Translated by John Minford. New York: Viking. 2002. ISBN 978-0-670-03156-6.
• The Art of War: Sunzi's Military Methods. Translated by Victor H. Mair. New York: Columbia University Press. 2007. ISBN 978-0-231-13382-1.
• The Art of War. Translated by Peter Harris. Everyman's Library. 2018. ISBN 978-1101908006.
• The Science of War: Sun Tzu's Art of War re-translated and re-considered. Translated by Christopher MacDonald. Hong Kong: Earnshaw Books. 2018. ISBN 978-988-8422-69-2.
• The Art of War. Translated by Michael Nylan. W.W. Norton & Company, Inc. 2020. ISBN 9781324004899.
• The Art of War. Translated by Thomas Huynh. Skylight Paths Publishing. 2008. ISBN 9781594732447.

Criticality accident

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Criticality_accident 

A criticality accident is an accidental uncontrolled nuclear fission chain reaction. It is sometimes referred to as a critical excursion, critical power excursion, or divergent chain reaction. Any such event involves the unintended accumulation or arrangement of a critical mass of fissile material, for example enriched uranium or plutonium. Criticality accidents can release potentially fatal radiation doses, if they occur in an unprotected environment.

Under normal circumstances, a critical or supercritical fission reaction (one that is self-sustaining in power or increasing in power) should only occur inside a safely shielded location, such as a reactor core or a suitable test environment. A criticality accident occurs if the same reaction is achieved unintentionally, for example in an unsafe environment or during reactor maintenance.

Though dangerous and frequently lethal to humans within the immediate area, the critical mass formed would not be capable of producing a massive nuclear explosion of the type that fission bombs are designed to produce. This is because all the design features needed to make a nuclear warhead cannot arise by chance. In some cases, the heat released by the chain reaction will cause the fissile (and other nearby) materials to expand. In such cases, the chain reaction can either settle into a low power steady state or may even become either temporarily or permanently shut down (subcritical).

In the history of atomic power development, at least 60 criticality accidents have occurred, including 22 in process environments, outside nuclear reactor cores or experimental assemblies, and 38 in small experimental reactors and other test assemblies. Although process accidents occurring outside reactors are characterized by large releases of radiation, the releases are localized. Nonetheless, fatal radiation exposures have occurred to persons close to these events, resulting in more than 20 fatalities. In a few reactor and critical experiment assembly accidents, the energy released has caused significant mechanical damage or steam explosions.

Physical basis

Criticality occurs when sufficient fissile material (a critical mass) accumulates in a small volume such that each fission, on average, produces a neutron that in turn strikes another fissile atom causing another fission; this causes the chain reaction to become self-sustaining within the mass of material. In other words, in a critical mass the number of neutrons emitted, over time, exactly equals the number of neutrons captured by another nucleus or lost to the environment. If the mass is supercritical, the number of neutrons emitted per unit time exceeds those absorbed or lost, resulting in a cascade of nuclear fissions at increasing rate.

Criticality can be achieved by using metallic uranium or plutonium, liquid solutions, or powder slurries. The chain reaction is influenced by range of parameters noted by the acronyms MAGIC MERV (for mass, absorption, geometry, interaction, concentration, moderation, enrichment, reflection, and volume) and MERMAIDS (for mass, enrichment, reflection, moderation, absorption, interaction, density, and shape). Temperature is also a factor.

Calculations can be performed to determine the conditions needed for a critical state, mass, geometry, concentration etc. Where fissile materials are handled in civil and military installations, specially trained personnel are employed to carry out such calculations, and to ensure that all reasonably practicable measures are used to prevent criticality accidents, during both planned normal operations and any potential process upset conditions that cannot be dismissed on the basis of negligible likelihoods (reasonably foreseeable accidents).

The assembly of a critical mass establishes a nuclear chain reaction, resulting in an exponential rate of change in the neutron population over space and time leading to an increase in neutron flux. This increased flux and attendant fission rate produces radiation that contains both a neutron and gamma ray component and is extremely dangerous to any unprotected nearby life-form. The rate of change of neutron population depends on the neutron generation time, which is characteristic of the neutron population, the state of "criticality", and the fissile medium.

A nuclear fission creates approximately 2.5 neutrons per fission event on average. Hence, to maintain a stable, exactly critical chain reaction, 1.5 neutrons per fission event must either leak from the system or be absorbed without causing further fissions.

For every 1,000 neutrons released by fission, a small number, typically no more than about 7, are delayed neutrons which are emitted from the fission product precursors, called delayed neutron emitters. This delayed neutron fraction, on the order of 0.007 for uranium, is crucial for the control of the neutron chain reaction in reactors. It is called one dollar of reactivity. The lifetime of delayed neutrons ranges from fractions of seconds to almost 100 seconds after fission. The neutrons are usually classified in 6 delayed neutron groups. The average neutron lifetime considering delayed neutrons is approximately 0.1 sec, which makes the chain reaction relatively easy to control over time. The remaining 993 prompt neutrons are released very quickly, approximately 1 μs after the fission event.

In steady-state operation, nuclear reactors operate at exact criticality. When at least one dollar of reactivity is added above the exact critical point (where the neutron production rate balances the rate of neutron losses, from both absorption and leakage) then the chain reaction does not rely on delayed neutrons. In such cases, the neutron population can rapidly increase exponentially, with a very small time constant, known as the prompt neutron lifetime. Thus there is a very large increase in neutron population over a very short time frame. Since each fission event contributes approximately 200 MeV per fission, this results in a very large energy burst as a "prompt-critical spike". This spike can be easily detected by radiation dosimetry instrumentation and "criticality accident alarm system" detectors that are properly deployed.

Accident types

Criticality accidents are divided into one of two categories:

• Process accidents, where controls in place to prevent any criticality are breached;
• Reactor accidents, which occur due to operator errors or other unintended events (e.g., during maintenance or fuel loading) in locations intended to achieve or approach criticality, such as nuclear power plants, nuclear reactors, and nuclear experiments.

Excursion types can be classified into four categories depicting the nature of the evolution over time:

1. Prompt criticality excursion
2. Transient criticality excursion
3. Exponential excursion
4. Steady-state excursion

The prompt-critical excursion is characterized by a power history with an initial prompt-critical spike as previously noted, which either self-terminates or continues with a tail region that decreases over an extended period of time. The transient critical excursion is characterized by a continuing or repeating spike pattern (sometimes known as "chugging") after the initial prompt-critical excursion. The longest of the 22 process accidents occurred at Hanford Works in 1962 and lasted for 37.5 hours. The 1999 Tokaimura nuclear accident remained critical for about 20 hours, until it was shut down by active intervention. The exponential excursion is characterized by a reactivity of less than one dollar added, where the neutron population rises as an exponential over time, until either feedback effects or intervention reduce the reactivity. The exponential excursion can reach a peak power level, then decrease over time, or reach a steady-state power level, where the critical state is exactly achieved for a "steady-state" excursion.

The steady-state excursion is also a state which the heat generated by fission is balanced by the heat losses to the ambient environment. This excursion has been characterized by the Oklo natural reactor that was naturally produced within uranium deposits in Gabon, Africa about 1.7 billion years ago.

Known incidents

A Los Alamos report (McLaughlin et al) recorded 60 criticality accidents between 1945 and 1999. These caused 21 deaths: seven in the United States, ten in the Soviet Union, two in Japan, one in Argentina, and one in Yugoslavia. Nine have been due to process accidents, and the others from research reactor accidents.

Criticality accidents have occurred in the context of production and testing of fissile material for both nuclear weapons and nuclear reactors.

• 

  The sphere of plutonium surrounded by neutron-reflecting tungsten carbide blocks in a re-enactment of Harry Daghlian's 1945 experiment.

• 

  A re-creation of the Slotin incident. The inside hemisphere with the thumb-hole next to the hand is beryllium (replacing the uranium tamper in a Fat Man bomb), with an external larger metal sphere under it, of aluminium. The 3.5-inch-diameter (89 mm) plutonium "demon core" (the same as in the Daghlian incident) was inside at the time of the accident, and would not be visible. However, its dimensions are comparable with the two small half-spheres shown resting nearby.

• 

  Image of the Lady Godiva assembly in the scrammed (safe) configuration.

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  Image of the Lady Godiva assembly, showing the damage caused to the supporting rods after the excursion of February 1954. Note the images are of different assemblies.

There was speculation although not confirmed within criticality accident experts, that Fukushima 3 suffered a criticality accident. Based on incomplete information about the 2011 Fukushima I nuclear accidents, Dr. Ferenc Dalnoki-Veress speculates that transient criticalities may have occurred there. Noting that limited, uncontrolled chain reactions might occur at Fukushima I, a spokesman for the International Atomic Energy Agency (IAEA) "emphasized that the nuclear reactors won't explode." By 23 March 2011, neutron beams had already been observed 13 times at the crippled Fukushima nuclear power plant. While a criticality accident was not believed to account for these beams, the beams could indicate nuclear fission is occurring. On 15 April, TEPCO reported that nuclear fuel had melted and fallen to the lower containment sections of three of the Fukushima I reactors, including reactor three. The melted material was not expected to breach one of the lower containers, which could cause a massive radioactivity release. Instead, the melted fuel is thought to have dispersed uniformly across the lower portions of the containers of reactors No. 1, No. 2 and No. 3, making the resumption of the fission process, known as a "recriticality", most unlikely.

Observed effects

Image of a 60-inch cyclotron, circa 1939, showing an external beam of accelerated ions (perhaps protons or deuterons) ionizing the surrounding air and causing an ionized-air glow. Due to the similar mechanism of production, the blue glow is thought to resemble the "blue flash" seen by Harry Daghlian and other witnesses of criticality accidents.

Blue glow

See also: Ionized-air glow

It has been observed that many criticality accidents emit a blue flash of light.

The blue glow of a criticality accident results from the fluorescence of the excited ions, atoms and molecules of the surrounding medium falling back to unexcited states. This is also the reason electrical sparks in air, including lightning, appear electric blue. The smell of ozone was said to be a sign of high ambient radioactivity by Chernobyl liquidators.

This blue flash or "blue glow" can also be attributed to Cherenkov radiation, if either water is involved in the critical system or when the blue flash is experienced by the human eye. Additionally, if ionizing radiation directly transects the vitreous humor of the eye, Cherenkov radiation can be generated and perceived as a visual blue glow/spark sensation.

It is a coincidence that the color of Cherenkov light and light emitted by ionized air are a very similar blue; their methods of production are different. Cherenkov radiation does occur in air for high-energy particles (such as particle showers from cosmic rays) but not for the lower energy charged particles emitted from nuclear decay.

Heat effects

Some people reported feeling a "heat wave" during a criticality event. It is not known whether this may be a psychosomatic reaction to the realization of what has just occurred (i.e. the high probability of inevitable impending death from a fatal radiation dose), or if it is a physical effect of heating (or non-thermal stimulation of heat sensing nerves in the skin) due to radiation emitted by the criticality event.

A review of all of the criticality accidents with eyewitness accounts indicates that the heat waves were only observed when the fluorescent blue glow (the non-Cherenkov light, see above) was also observed. This would suggest a possible relationship between the two, and indeed, one can be potentially identified. In dense air, over 30% of the emission lines from nitrogen and oxygen are in the ultraviolet range, and about 45% are in the infrared range. Only about 25% are in the visible range. Since the skin feels light (visible or otherwise) through its heating of the skin surface, it is possible that this phenomenon can explain the heat wave perceptions. However, this explanation has not been confirmed and may be inconsistent with the intensity of light reported by witnesses compared to the intensity of heat perceived. Further research is hindered by the small amount of data available from the few instances where humans have witnessed these incidents and survived long enough to provide a detailed account of their experiences and observations.

Approximate number system

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Approximate_number_system 

The approximate number system (ANS) is a cognitive system that supports the estimation of the magnitude of a group without relying on language or symbols. The ANS is credited with the non-symbolic representation of all numbers greater than four, with lesser values being carried out by the parallel individuation system, or object tracking system. Beginning in early infancy, the ANS allows an individual to detect differences in magnitude between groups. The precision of the ANS improves throughout childhood development and reaches a final adult level of approximately 15% accuracy, meaning an adult could distinguish 100 items versus 115 items without counting. The ANS plays a crucial role in development of other numerical abilities, such as the concept of exact number and simple arithmetic. The precision level of a child's ANS has been shown to predict subsequent mathematical achievement in school. The ANS has been linked to the intraparietal sulcus of the brain.

History

Piaget's theory

Jean Piaget was a Swiss developmental psychologist who devoted much of his life to studying how children learn. A book summarizing his theories on number cognition, The Child's Conception of Number, was published in 1952. Piaget's work supported the viewpoint that children do not have a stable representation of number until the age of six or seven. His theories indicate that mathematical knowledge is slowly gained and during infancy any concept of sets, objects, or calculation is absent.

Challenging the Piagetian viewpoint

Piaget's ideas pertaining to the absence of mathematical cognition at birth have been steadily challenged. The work of Rochel Gelman and C. Randy Gallistel among others in the 1970s suggested that preschoolers have intuitive understanding of the quantity of a set and its conservation under non cardinality-related changes, expressing surprise when objects disappear without an apparent cause.

Current theory

Beginning as infants, people have an innate sense of approximate number that depends on the ratio between sets of objects. Throughout life the ANS becomes more developed, and people are able to distinguish between groups having smaller differences in magnitude. The ratio of distinction is defined by Weber's law, which relates the different intensities of a sensory stimulus that is being evaluated. In the case of the ANS, as the ratio between the magnitudes increases, the ability to discriminate between the two quantities increases.

Today, some theorize that the ANS lays the foundation for higher-level arithmetical concepts. Research has shown that the same areas of the brain are active during non-symbolic number tasks in infants and both non-symbolic and more sophisticated symbolic number tasks in adults. These results could suggest that the ANS contributes over time to the development of higher-level numerical skills that activate the same part of the brain.

However, longitudinal studies do not necessarily find that non-symbolic abilities predict later symbolic abilities. Conversely, early symbolic number abilities have been found to predict later non-symbolic abilities, not vice versa as predicted. In adults for example, non-symbolic number abilities do not always explain mathematics achievement.

Neurological basis

Brain imaging studies have identified the parietal lobe as being a key brain region for numerical cognition. Specifically within this lobe is the intraparietal sulcus which is "active whenever we think about a number, whether spoken or written, as a word or as an Arabic digit, or even when we inspect a set of objects and think about its cardinality". When comparing groups of objects, activation of the intraparietal sulcus is greater when the difference between groups is numerical rather than an alternative factor, such as differences in shape or size. This indicates that the intraparietal sulcus plays an active role when the ANS is employed to approximate magnitude.

Parietal lobe brain activity seen in adults is also observed during infancy during non-verbal numerical tasks, suggesting that the ANS is present very early in life. A neuroimaging technique, functional Near-Infrared Spectroscopy, was performed on infants revealing that the parietal lobe is specialized for number representation before the development of language. This indicates that numerical cognition may be initially reserved to the right hemisphere of the brain and becomes bilateral through experience and the development of complex number representation.

It has been shown that the intraparietal sulcus is activated independently of the type of task being performed with the number. The intensity of activation is dependent on the difficulty of the task, with the intraparietal sulcus showing more intense activation when the task is more difficult. In addition, studies in monkeys have shown that individual neurons can fire preferentially to certain numbers over others. For example, a neuron could fire at maximum level every time a group of four objects is seen, but will fire less to a group three or five objects.

Pathology

Damage to intraparietal sulcus

Damage done to parietal lobe, specifically in the left hemisphere, can produce difficulties in counting and other simple arithmetic. Damage directly to the intraparietal sulcus has been shown to cause acalculia, a severe disorder in mathematical cognition. Symptoms vary based the location of damage, but can include the inability to perform simple calculations or to decide that one number is larger than another. Gerstmann syndrome, a disease resulting in lesions in the left parietal and temporal lobes, results in acalculia symptoms and further confirms the importance of the parietal region in the ANS.

Developmental delays

A syndrome known as dyscalculia is seen in individuals who have unexpected difficulty understanding numbers and arithmetic despite adequate education and social environments.^[13] This syndrome can manifest in several different ways from the inability to assign a quantity to Arabic numerals to difficulty with times tables. Dyscalculia can result in children falling significantly behind in school, regardless of having normal intelligence levels.

In some instances, such as Turner syndrome, the onset of dyscalculia is genetic. Morphological studies have revealed abnormal lengths and depths of the right intraparietal sulcus in individuals suffering from Turner syndrome. Brain imaging in children exhibiting symptoms of dyscalculia show less gray matter or less activation in the intraparietal regions stimulated normally during mathematical tasks. Additionally, impaired ANS acuity has been shown to differentiate children with dyscalculia from their normally-developing peers with low maths achievement.

Further research and theories

Impact of the visual cortex

The intraparietal region relies on several other brain systems to accurately perceive numbers. When using the ANS we must view the sets of objects in order to evaluate their magnitude. The primary visual cortex is responsible for disregarding irrelevant information, such as the size or shape of the objects. Certain visual cues can sometimes affect how the ANS functions.

Arranging the items differently can alter the effectiveness of the ANS. One arrangement proven to influence the ANS is visual nesting, or placing the objects within one another. This configuration affects the ability to distinguish each item and add them together at the same time. The difficulty results in underestimation of the magnitude present in the set or a longer amount of time needed to perform an estimate.

Another visual representation that affects the ANS is the spatial-numerical association response code, or the SNARC effect. The SNARC effect details the tendency of larger numbers to be responded to faster by the right hand and lower numbers by the left hand, suggesting that the magnitude of a number is linked to a spatial representation. Dehaene and other researchers believe this effect is caused by the presence of a “mental number line” in which small numbers appear on the left and increase as you move right. The SNARC effect indicates that the ANS works more effectively and accurately if the larger set of objects is on the right and the smaller on the left.

Development and mathematical performance

Although the ANS is present in infancy before any numerical education, research has shown a link between people's mathematical abilities and the accuracy in which they approximate the magnitude of a set. This correlation is supported by several studies in which school-aged children's ANS abilities are compared to their mathematical achievements. At this point the children have received training in other mathematical concepts, such as exact number and arithmetic. More surprisingly, ANS precision before any formal education accurately predicts better math performance. A study involving 3- to 5-year-old children revealed that ANS acuity corresponds to better mathematical cognition while remaining independent of factors that may interfere, such as reading ability and the use of Arabic numerals.

ANS in animals

Main article: Number sense in animals

Many species of animals exhibit the ability to assess and compare magnitude. This skill is believed to be a product of the ANS. Research has revealed this capability in both vertebrate and non-vertebrate animals including birds, mammals, fish, and even insects. In primates, implications of the ANS have been steadily observed through research. One study involving lemurs showed that they were able to distinguish groups of objects based only on numerical differences, suggesting that humans and other primates utilize a similar numerical processing mechanism.

In a study comparing students to guppies, both the fish and students performed the numerical task almost identically. The ability for the test groups to distinguish large numbers was dependent on the ratio between them, suggesting the ANS was involved. Such results seen when testing guppies indicate that the ANS may have been evolutionarily passed down through many species.

Applications in society

Implications for the classroom

Understanding how the ANS affects students' learning could be beneficial for teachers and parents. The following tactics have been suggested by neuroscientists to utilize the ANS in school:

• Counting or abacus games
• Simple board games
• Computer-based number association games
• Teacher sensitivity and different teaching methods for different learners

Such tools are most helpful in training the number system when the child is at an earlier age. Children coming from a disadvantaged background with risk of arithmetic problems are especially impressionable by these tactics.