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Mathematical sociology is the area of sociology that uses mathematics to construct social theories.  Mathematical sociology aims to take sociological theory, which is strong in intuitive content but weak from a formal point of view, and to express it in formal terms.  The benefits of this approach include increased clarity and the ability to use mathematics to derive implications of a theory that cannot be arrived at intuitively.  In mathematical sociology, the preferred style is encapsulated in the phrase "constructing a mathematical model."   This means making specified assumptions about some social phenomenon, expressing them in formal mathematics, and providing an empirical interpretation for the ideas.  It also means deducing properties of the model and comparing these with relevant empirical data.  Social network analysis is the best-known contribution of this subfield to sociology as a whole and to the scientific community at large. The models typically used in mathematical sociology allow sociologists to understand how predictable local interactions are and they are often able to elicit global patterns of social structure.[1]
History
Starting in the early 1940s, Nicolas Rashevsky,[2][3] and subsequently in the late 1940s, Anatol Rapoport and others, developed a relational and probabilistic approach to the characterization of large social networks in which the nodes are persons and the links are acquaintanceship. During the late 1940s, formulas were derived that connected local parameters such as closure of contacts – if A is linked to both B and C, then there is a greater than chance probability that B and C are linked to each other – to the global network property of connectivity.[4]
Moreover, acquaintanceship is a positive tie, but what about negative ties such as animosity among persons?  To tackle this problem, graph theory, which is the mathematical study of abstract representations of networks of points and lines, can be extended to include these two types of links and thereby to create models that represent both positive and negative sentiment relations, which are represented as signed graphs.  A signed graph is called balanced if the product of the signs of all relations in every cycle (links in every graph cycle) is positive.  Through formalization by mathematician Frank Harary this work produced the fundamental theorem of this theory.  It says that if a network of interrelated positive and negative ties is balanced, e.g. as illustrated by the psychological principle that "my friend's enemy is my enemy", then it consists of two subnetworks such that each has positive ties among its nodes and there are only negative ties between nodes in distinct subnetworks.[5]  The imagery here is of a social system that splits into two cliques. There is, however, a special case where one of the two subnetworks is empty, which might occur in very small networks.
In another model, ties have relative strengths. 'Acquaintanceship' can be viewed as a 'weak' tie and 'friendship' is represented as a strong tie.  Like its uniform cousin discussed above, there is a concept of closure, called strong triadic closure.  A graph satisfies strong triadic closure If A is strongly connected to B, and B is strongly connected to C, then A and C must have a tie (either weak or strong).
n these two developments we have mathematical models bearing upon the analysis of structure.  Other early influential developments in mathematical sociology pertained to process.  For instance, in 1952 Herbert A. Simon produced a mathematical formalization of a published theory[6] of social groups by constructing a model consisting of a deterministic system of differential equations.  A formal study of the system led to theorems about the dynamics and the implied equilibrium states of any group.
The emergence of mathematical models in the social sciences was part of the zeitgeist in the 1940s and 1950s in which a variety of new interdisciplinary scientific innovations occurred, such as information theory, game theory, cybernetics and mathematical model building in the social and behavioral sciences.[7]
Further developments
In 1954, a critical expository analysis of Rashevsky's social behavior models was written by sociologist James S. Coleman.[8] Rashevsky's models and as well as the model constructed by Simon raise a question: how can one connect such theoretical models to the data of sociology, which often take the form of surveys in which the results are expressed in the form of proportions of people believing or doing something.  This suggests deriving the equations from assumptions about the chances of an individual changing state in a small interval of time, a procedure well known in the mathematics of stochastic processes.
Coleman embodied this idea in his 1964 book Introduction to Mathematical Sociology, which showed how stochastic processes in social networks could be analyzed in such a way as to enable testing of the constructed model by comparison with the relevant data. The same idea can and has been applied to processes of change in social relations, an active research theme in the study of social networks, illustrated by an empirical study appearing in the journal Science.[9]
In other work, Coleman employed mathematical ideas drawn from economics, such as general equilibrium theory, to argue that general social theory should begin with a concept of purposive action and, for analytical reasons, approximate such action by the use of rational choice models (Coleman, 1990).  This argument is similar to viewpoints expressed by other sociologists in their efforts to use rational choice theory in sociological analysis although such efforts have met with substantive and philosophical criticisms.[10]
Meanwhile, structural analysis of the type indicated earlier received a further extension to social networks based on institutionalized social relations, notably those of kinship.  The linkage of mathematics and sociology here involved abstract algebra, in particular, group theory.[11]  This, in turn, led to a focus on a data-analytical version of homomorphic reduction of a complex social network (which along with many other techniques is presented in Wasserman and Faust 1994[12]).
In regard to Rapoport's random and biased net theory, his 1961 study of a large sociogram, co-authored with Horvath turned out to become a very influential paper. [13] There was early evidence of this influence. In 1964, Thomas Fararo and a co-author analyzed another large friendship sociogram using a biased net model.[14] Later in the 1960s, Stanley Milgram described the small world problem and undertook a field experiment dealing with it.[15] [16] A highly fertile idea was suggested and applied by Mark Granovetter in which he drew upon Rapoport's 1961 paper to suggest and apply a distinction between weak and strong ties. The key idea was that there was "strength" in weak ties. [17]
Some programs of research in sociology employ experimental methods to study social interaction processes.  Joseph Berger and his colleagues initiated such a program in which the central idea is the use of the theoretical concept "expectation state" to construct theoretical models to explain interpersonal processes, e.g., those linking external status in society to differential influence in local group decision-making. Much of this theoretical work is linked to mathematical model building, especially after the late 1970s adoption of a graph theoretic representation of social information processing, as Berger (2000) describes in looking back upon the development of his program of research. In 1962 he and his collaborators explained model building by reference to the goal of the model builder, which could be explication of a concept in a theory, representation of a single recurrent social process, or a broad theory based on a theoretical construct, such as, respectively, the concept of balance in psychological and social structures, the process of conformity in an experimental situation, and stimulus sampling theory.[18]
The generations of mathematical sociologists that followed Rapoport, Simon, Harary, Coleman, White and Berger, including those entering the field in the 1960s such as Thomas Fararo, Philip Bonacich, and Tom Mayer, among others, drew upon their work in a variety of ways.
Present research

Mathematical sociology remains a small subfield within the discipline, but it has succeeded in spawning a number of other subfields which share its goals of formally modeling social life.  The foremost of these fields is social network analysis, which has become among the fastest growing areas of sociology in the 21st century.[19]  The other major development in the field is the rise of computational sociology, which expands the mathematical toolkit with the use of computer simulations, artificial intelligence and advanced statistical methods.  The latter subfield also makes use of the vast new data sets on social activity generated by social interaction on the internet.
One important indicator of the significance of mathematical sociology is that the general interest journals in the field, including such central journals as The American Journal of Sociology and The American Sociological Review, have published mathematical models that became influential in the field at large.
More recent trends in mathematical sociology are evident in contributions to The Journal of Mathematical Sociology (JMS).  Several trends stand out: the further development of formal theories that explain experimental data dealing with small group processes, the continuing interest in structural balance as a major mathematical and theoretical idea, the interpenetration of mathematical models oriented to theory and innovative quantitative techniques relating to methodology, the use of computer simulations to study problems in social complexity, interest in micro–macro linkage and the problem of emergence, and ever-increasing research on networks of social relations.
Thus, topics from the earliest days, like balance and network models, continue to be of contemporary interest. The formal techniques employed remain many of the standard and well-known methods of mathematics: differential equations, stochastic processes and game theory. Newer tools like agent-based models used in computer simulation studies are prominently represented. Perennial substantive problems still drive research: social diffusion, social influence, social status origins and consequences, segregation, cooperation, collective action, power, and much more.
Research programs
Many of the developments in mathematical sociology, including formal theory, have exhibited notable decades-long advances that began with path-setting contributions by leading mathematical sociologists and formal theorists.  This provides another way of taking note of recent contributions but with an emphasis on continuity with early work through the use of the idea of “research program,” which is a coherent series of theoretical and empirical studies based on some fundamental principle or approach.  There are more than a few of these programs and what follows is no more than a brief capsule description of leading exemplars of this idea in which there is an emphasis on the originating leadership in each program and its further development over decades.
(1) Rational Choice Theory and James S. Coleman: After his 1964 pioneering Introduction to Mathematical Sociology, Coleman continued to make contributions to social theory and mathematical model building and his 1990 volume, Foundations of Social Theory was the major theoretical work of a career that spanned the period from 1950s to 1990s and included many other research-based contributions..[20]  The Foundation book combined accessible examples of how rational choice theory could function in the analysis of such sociological topics as authority, trust, social capital and the norms (in particular, their emergence).  In this way, the book showed how rational choice theory could provide an effective basis for making the transition from micro to macro levels of sociological explanation.  An important feature of the book is its use of mathematical ideas in generalizing the rational choice model to include interpersonal sentiment relations as modifiers of outcomes and doing so such that the generalized theory captures the original more self-oriented theory as a special case, as point emphasized in a later analysis of the theory.[21] The rationality presupposition of the theory led to debates among sociological theorists[22].  Nevertheless, many sociologists drew upon Coleman’s formulation of a general template for micro-macro transition to gain leverage on the continuation of topics central to his and the discipline's explanatory focus on a variety of macrosocial phenomena in which rational choice simplified the micro level in the interest of combining individual actions to account for macro outcomes of social processes.[23]
(2) Structuralism (Formal) and Harrison C. White: In the decades since his earliest contributions, Harrison White has led the field in putting social structural analysis on a mathematical and empirical basis, including the 1970 publication of Chains of Opportunity: System Models of Mobility in Organization</i>s which set out and applied to data a vacancy chain model for mobility in and across organizations.   His very influential other work includes the operational concepts of blockmodel and structural equivalence which start from a body of social relational data to produce analytical results using these procedures and concepts.   These ideas and methods were developed in collaboration with his former students François Lorraine, Ronald Breiger, and Scott Boorman. These three are among the more than 30 students who earned their doctorates under White in the period 1963-1986. [24]  The theory and application of blockmodels has been set out in detail in a recent monograph.[25]. White's later contributions include a structuralist approach to markets[26] and, in 1992, a general theoretical framework[27], later appearing in a revised edition[28].
(3) Expectation states theory and Joseph Berger: Under Berger’s intellectual and organizational leadership, Expectation States Theory branched out into a large number of specific programs of research on specific problems, each treated in terms of the master concept of expectation states.  He and his colleague and frequent collaborator Morris Zelditch Jr not only produced work of their own but created a doctoral program at Stanford University that led to an enormous outpouring of research by notable former students, including Murray Webster, David Wagner, and Hamit Fisek.  Collaboration with mathematician Robert Z. Norman led to the use of mathematical graph theory as a way of representing and analyzing social information processing in self-other(s) interactions.  Berger and Zelditch also advanced work in formal theorizing and mathematical model building as early as 1962 with a collaborative expository analysis of types of models.[29]  Berger and Zelditch stimulated advances in other theoretical research programs by providing outlets for the publication of new work, culminating in a 2002 edited volume[30] that  includes a chapter that presents an authoritative overview of Expectation states theory as a program of cumulative research dealing with group processes.
(4) Formalization in Theoretical Sociology and Thomas J. Fararo: Many of this sociologist’s contributions have been devoted to bringing mathematical thinking into greater contact with sociological theory.[31]  He organized a symposium attended by sociological theorists in which formal theorists delivered papers that were subsequently published in 2000.[32]  Through collaborations with students and colleagues his own theoretical research program dealt with such topics as macrostructural theory and E-state structuralism (both with former student John Skvoretz), subjective images of stratification[33] (with former student Kenji Kosaka), tripartite structural analysis (with colleague Patrick Doreian)[34] and computational sociology (with colleague Norman P. Hummon)[35].[36] Two of his books are extended treatments of his approach to theoretical sociology.[37][38]
(5) Social Network Analysis and Linton C. Freeman:  In the early 1960s Freeman directed a sophisticated empirical study of community power structure.  In 1978 he established the journal Social Networks.  It rapidly became a major outlet for original research papers that used mathematical techniques to analyze network data.  The journal also publishes conceptual and theoretical contributions, including his paper “Centrality in Social Networks: Conceptual Clarification.” The paper has been cited more than 13,000 times[39].  In turn, the mathematical concept defined in that paper led to further elaborations of the ideas, to experimental tests, and to numerous applications in empirical studies.[40]  He is the author of a study of the history and sociology of the field of social network analysis.[41]
(6) Quantitative Methodology and Kenneth C. Land: Kenneth Land has been on the frontier of quantitative methodology in sociology as well as formal theoretical model building.  The influential yearly volume Sociological Methodology has been one of Land’s favorite outlets for the publication of papers that often lie in the intersection of quantitative methodology and mathematical sociology.  Two of his theoretical papers appeared early in this journal: “Mathematical Formalization of Durkheim's Theory of Division of Labor” (1970) and “Formal Theory” (1971).  His decades-long research program includes contributions relating to numerous special topics and methods, including social statistics, social indicators, stochastic processes, mathematical criminology, demography and social forecasting.  Thus Land brings to these fields the skills of a statistician, a mathematician and a sociologist, combined.
(7) Affect Control Theory and David R. Heise:  In 1979, Heise published a groundbreaking formal and empirical study in the tradition of interpretive sociology, especially symbolic interactionism,Understanding Events: Affect and the Construction of Social Action. It was the origination of a research program that has included his further theoretical and empirical studies and those of other sociologists, such as  Lynn Smith-Lovin, Dawn Robinson and Neil MacKinnon. Definition of the situation and self-other definitions are two of the leading concepts in affect control theory. The formalism used by Heise and other contributors uses a validated form of measurement and a cybernetic control mechanism in which immediate feelings and compared with fundamental sentiments in such a way as to generate an effort to bring immediate feelings in a situation into correspondence with sentiments. In the simplest models, each person in an interactive pair, is represented in terms of one side of a role relationship in which fundamental sentiments associated with each role guide the process of immediate interaction.  A higher level of the control process can be activated in which the definition of the situation is transformed. This research program comprises several of the key chapters in a  2006 volume[42] of contributions to control systems theory (in the sense of Powers 1975 [43]) in sociology.
(8) "Distributive Justice Theory" and Guillermina Jasso: Since 1980, Jasso has treated problems of distributive justice with an original theory that uses mathematical methods.[44] She has elaborated upon and applied this theory to a wide range of social phenomena.[45]  Her most general mathematical apparatus – with the theory of distributive justice as a special case -- deals with any subjective comparison between some actual state and some reference level for it, e.g., a comparison of an actual reward with an expected reward.  In her justice theory, she starts with a very simple premise, the justice evaluation function (the natural logarithm of the ratio of actual to just reward) and then derives numerous empirically testable implications.[46]
(9) Collaborative research and John Skvoretz. A major feature of modern science is collaborative research in which the distinctive skills of the participants combine to produce original research.  Skvoretz, in addition to this other contributions, has been a frequent collaborator in a variety of theoretical research programs, often using mathematical expertise as well as skills in experimental design, statistical data analysis and simulation methods.  Some examples are: (1) Collaborative work on theoretical, statistical and mathematical problems in biased net theory.[47]  (2) Collaborative contributions to Expectation States Theory.[48] (3) Collaborative contributions to Elementary Theory.[49] (4) Collaboration with Bruce Mayhew in a structuralist research program.[50] From the early 1970s, Skvoretz has been one of the most prolific of contributors to the advance of mathematical sociology.[51]
The above discussion could be expanded to include many other programs and individuals including European sociologists such as Peter Abell and the late Raymond Boudon.
Awards in mathematical sociology
The Mathematical Sociology section of The American Sociological Association in 2002 initiated awards for contributions to the field, including The James S. Coleman Distinguished Career Achievement Award. (Coleman had died in 1995 before the section had been established.)  Given every other year, the awardees include some of those just listed in terms of their career-long research programs:
2018: Ronald Breiger, University of Arizona
2017: Lynn Smith-Lovin, Duke University.
2014: Philip Bonacich, University of California, Los Angeles.
2012: John Skvoretz, University of South Florida.
2010: David R. Heise, Indiana University.
2008: Scott Boorman, Yale University.
2006: Linton Freeman, University of California, Irvine.
2004: Thomas Fararo, University of Pittsburgh.
2002: Harrison White, Columbia University.
The section's other categories of awards and their recipients are listed at
Texts and journals
Mathematical sociology textbooks cover a variety of models, usually explaining the required mathematical background before discussing important work in the literature (Fararo 1973, Leik and Meeker 1975, Bonacich and Lu 2012). An earlier text by Otomar Bartos (1967) is still of relevance. Of wider scope and mathematical sophistication is the text by Rapoport (1983).  A very reader-friendly and imaginative introduction to explanatory thinking leading to models is Lave and March (1975, reprinted 1993). The Journal of Mathematical Sociology (started in 1971) has been open to papers covering a broad spectrum of topics employing a variety of types of mathematics, especially through frequent special issues. Other journals in sociology who publish papers with substantial use of mathematics are , ,
Articles in Social Networks, a journal devoted to social structural analysis, very often employ mathematical models and related structural data analyses.  In addition – importantly indicating the penetration of mathematical model building into sociological research – the major comprehensive journals in sociology, especially The American Journal of Sociology and The American Sociological Review, regularly publish articles featuring mathematical formulations.
See also
Isaac Asimov's Foundation series, based on a massive expansion of the premise
Positivism
Statistics
Computational sociology
Peter Blau
Harrison White
Nicolas Rashevsky
Society for Mathematical Biology
Interpersonal ties
Duncan Watts
James Samuel Coleman
James D. Montgomery
Thomas Fararo
Social network
Network Science
Barabasi-Albert Model

Further reading
Bartos, Otomar. 1967. "Simple Models of Group Behavior." Columbia University Press.
Berger, Joseph. 2000. "Theory and Formalization: Some Reflections on Experience." Sociological Theory 18(3):482-489.
Berger, Joseph, Bernard P. Cohen, J. Laurie Snell, and Morris Zelditch, Jr. 1962. Types of Formalization in Small Group Research. Houghton-Mifflin.
Berger, Joseph and Morris Zelditch Jr. 2002. New Directions in Contemporary Sociological Theory Rowman and Littlefield.
Bonacich, Philip and Philip Lu. Introduction to Mathematical Sociology. Princeton University Press.
Coleman, James S. 1964. An Introduction to Mathematical Sociology. Free Press.
_____. 1990. Foundations of Social Theory. Harvard University Press.
Doreian, Patrick, Vladimir Batagelj, and Anuska Ferligoj. 2004. Generalized Blockmodeling. Cambridge University Press.
Edling, Christofer R. 2002. "Mathematics in Sociology," Annual Review of Sociology.
Fararo, Thomas J. 1973. Mathematical Sociology. Wiley. Reprinted by Krieger, 1978.
_____. 1984. Editor. Mathematical Ideas and Sociological Theory. Gordon and Breach.
_____. 1989. The Meaning of General Theoretical Sociology: Tradition and Formalization. Cambridge University Press.
Freeman, Linton C. 2004. The Development of Social Network Analysis. Empirical Press.
Heise, David R. 1979. Understanding Events: Affect and the Construction of Social Action. Cambridge University Press.
Helbing, Dirk. 1995. Quantitative Sociodynamics. Kluwer Academics.
Lave, Charles and James March. 1975. An Introduction to Models in the Social Sciences. Harper and Row.
Leik, Robert K. and Barbara F. Meeker. 1975. Mathematical Sociology. Prentice-Hall.
Rapoport, Anatol. 1983. Mathematical Models in the Social and Behavioral Sciences. Wiley.
Nicolas Rashevsky.: 1965, The Representation of Organisms in Terms of Predicates, Bulletin of Mathematical Biophysics 27: 477-491.
Nicolas Rashevsky.: 1969, Outline of a Unified Approach to Physics, Biology and Sociology., Bulletin of Mathematical Biophysics 31: 159-198.
Rosen, Robert. 1972. "Tribute to Nicolas Rashevsky 1899-1972." Progress in Theoretical Biology 2.
Leik, Robert K. and Barbara F. Meeker. 1975. Mathematical Sociology. Prentice-Hall.
Simon, Herbert A. 1952. "A Formal Theory of Interaction in Social Groups." American Sociological Review 17:202-212.
Wasserman, Stanley and Katherine Faust. 1994. Social Network Analysis: Methods and Applications. Cambridge University Press.
White, Harrison C. 1963. An Anatomy of Kinship. Prentice-Hall.
_____. 1970. Chains of Opportunity. Harvard University Press.
_____. 1992. Identity and Control: A Structural Theory of Action. Princeton University Press.
_____. 2008. Identity and Control: How Social Formations Emerge. 2nd Ed. (Revised) Princeton University Press.

What are the benefits to understanding sociology?


The Burnley Tunnel is a tollway tunnel in Melbourne, in Victoria, Australia, which carries traffic eastbound from the West Gate Freeway to the Monash Freeway. It is part of the CityLink Tollway operated by Transurban. Running under the Yarra River and the inner suburbs of Richmond and Burnley, the tunnel provides a bypass of the central business district.
History
The tunnel was constructed between 1996 and 2000 by Transfield–Obayashi Corporation Joint Venture. Prior to its opening to traffic, the tunnel was opened to the public to walk through from Southbank to Burnley, on 16 December 2000.
The tunnel was opened to traffic on 22 December 2000. The first known person to enter the tunnel as a paying client was Ben Johnstone during which time the whole process was played out live on 3AW.  In February 2001 it was found that a wall panel was cracked with 5 litres of water a second entering the tunnel.[1] The cause was later found to be floor sections lifting from water pressure, and modifications to correct this being approved in November 2001. Also in 2001 Transfield Obayashi Joint Venture agreed to pay Transurban $157 million in damages in an out-of-court settlement over late completion of the tunnel.[2]
Transurban launched further legal action against the Transfield Obayashi Joint Venture in 2007, after radar tests indicated the tunnel walls were thinner than that specified in the contract, possibly resulting in the tunnel not lasting for the proposed 100-year design life.[3] Further tunnel leaks were also discovered in 2007, but were unrelated to the tunnel fire.[4] When Transurban hands the tunnel over to the Victorian government in 2034, after 34 years in service, it must do so with the tunnel in the condition that it will have a 66-year operational life.[5]
2007 fire

On 23 March 2007 just before 10 am, a pile-up occurred in the tunnel involving three trucks and four cars.  The crash resulted in an explosion and a subsequent fire which reached temperatures in excess of 1,000°C (1,832°F) according to firefighters,[6] and forced the evacuation of motorists from both the Burnley and nearby Domain tunnels.  Three people died in the accident: Geoff Kennard, 51; Damian McDonald, an Australian cyclist who won a gold medal in the road team time trial at the 1994 Commonwealth Games in Victoria, Canada, and also represented Australia at the 1996 Summer Olympics;[7] and Darren Hartley Sporn, a father of two daughters, who owned a plumbing business.[6] Approximately 400 people were advised by the tunnel's safety system to abandon their cars, to leave their keys in the ignition, and to evacuate the tunnel after the collision.
The accident occurred after a truck suffered a blown tyre and stopped in the left lane.  Safety systems allegedly closed the left lane and a response vehicle was on its way to assist the broken-down truck. Two cars traveling in the left hand lane had come up behind the broken-down truck and were attempting to merge into the center lane.  Another truck traveling in the left lane came up behind them and also attempted to merge to the right, but it failed to either stop behind the stationary vehicles or merge successfully. It then collided with vehicles in both the left and middle lanes, resulting in a multi-vehicle pile up involving 4 cars and three trucks.  It is believed an explosion resulted from the ignition of a ruptured fuel tank of a vehicle involved in the crash.  of the details vary, however.
The following traffic came to a stop and approximately 200 vehicles became stranded inside the tunnel. The Public Address & Radio Rebroadcast Systems advised motorists to turn off their ignition, leave the keys in, and to evacuate the tunnel.  Emergency exits are located throughout the tunnel and lead to separate pedestrian tunnels.  Some motorists walked the 1km back along the roadway to the western tunnel entrance. Approximately 400 people were evacuated, three of whom were taken to hospital.  Hundreds waited at the tunnel's west entrance until emergency services advised it was safe to remove their vehicles. The tunnel suffered some damage to cables and other internal infrastructure, but is believed the structure was undamaged by the fire.
Eighty-four firefighters responded within five minutes of the crash occurring and emergency personnel were able to gain access to the Burnley tunnel on foot via a separate emergency tunnel linking the Burnley to the Domain tunnel.  Fire hoses were carried through to the crash site while emergency vehicles were stationed in the Domain Tunnel. A number of fire appliances were transported contra-flow from the exit portal of the tunnel to the crash site. The deluge system was activated instantly and this was deemed by firefighters to have greatly aided in keeping the fire under control. The smoke extraction system functioned as planned and removed toxic fumes from the tunnel and out into the open air. Smoke was vented to the ventilation stack in Southbank.
Metropolitan Ambulance Service Paramedics were sent in to treat evacuees if required. St John Ambulance Australia emergency medical teams were also put on standby in case the accident was deemed as a major disaster and many more injured and fatalities had arisen.
Design

The Burnley Tunnel is 3.4 kilometres (2.1mi) long and comprises 460 metres (1,509ft) of cut and cover at the west portal, 2.84km (1.76mi) of driven tunnel, and 180m (591ft) of cut and cover at the east portal. The gradient at the west end is 6.2% downhill for traffic, then relatively level until a 5.2% grade out of the tunnel.[8] During construction a shaft located at the midpoint of the tunnel was used to speed up work, as it provided another two working faces for the roadheaders used. The shaft is today used for ventilation and emergency egress, in addition to a 1,420-metre-long (4,659ft) pedestrian tunnel that parallels the eastern part of the tunnel. Eight cross passages link the main and emergency tunnels, two more cross connects provide an emergency exit to the Domain Tunnel, and two emergency refuges are also located in the tunnel.[8] Unlike the shallower and shorter Domain Tunnel, it passes deep under the Yarra River.  It was subject to significant engineering problems and delays during construction due to unexpectedly high water pressures at its maximum depth of 65m (213ft).
A variable speed limit applies to traffic in the tunnel. In normal circumstances the speed limit is 80km/h (50mph), but a 40km/h (25mph) speed limit applies during maintenance.  The speed limit during peak periods is often reduced to 60km/h (37mph) to prevent unnecessary congestion at the Monash Freeway. Regular AM and FM radio transmissions can be received while in the tunnel because the tunnel operator has installed re-broadcast transmitters. Normal radio broadcasts can be interrupted by management announcements over all channels.
See also

Domain Tunnel, the westbound tunnel running parallel to the Burnley Tunnel.

Does the Metro Tunnel in Melbourne go underwater?


Stephen Todd Alford (born November 23, 1964) is an American basketball coach and former professional player who was most recently the head coach of the UCLA Bruins men's basketball team. Born and raised in Indiana, he was a two-time consensus first-team All-American as a college basketball player for the Indiana Hoosiers. He led them to a national championship in 1987. After playing professionally for four years in the National Basketball Association (NBA), he has been a college head coach for almost 30 years.
Alford was named Indiana Mr. Basketball in high school before playing at Indiana University under coach Bobby Knight.
He helped the Hoosiers claim their fifth national championship, and finished his career as Indiana's all-time leading scorer. Alford was selected in the second round of the 1987 NBA draft by the Dallas Mavericks, and played four years in the league with Dallas and the Golden State Warriors. Alford then became a college head coach. He has coached at Manchester University, Southwest Missouri State University, the University of Iowa and the University of New Mexico. He spent 51⁄2 seasons with UCLA before being fired in 2018.
Early life
Alford was born in Franklin, Indiana and grew up in New Castle. He learned to count as a three-year-old by watching the numbers tick off the scoreboard in Monroe City, where his father, Sam Alford, coached the high school team. Sam often moved for various coaching jobs. Steve missed only two of his father's games, once when he had chicken pox and once when he made the regionals of the Elks Club free-throw shooting contest.[1] When Alford was nine years old, he attended a basketball camp put on by Coach Bob Knight.[1] Eventually the Alfords settled in New Castle, Indiana, where Steve played on the New Castle Chrysler High School basketball team with his dad as coach. Alford was known to practice shooting so much that he would wear out six or seven nets a summer and frequently forego social activities.[1]
As a high school freshman Alford barely averaged a point a game, but then averaged 18.7 the next season.[1] By his senior year in 1983, before the three-point line was even implemented, Alford averaged 37.7 points per game and earned the Indiana "Mr. Basketball" award.[2] His team advanced to the state quarterfinal but lost to Connersville in the 1983 state tournament. Later, shortly after Alford won a gold medal as a member of Bob Knight's U.S. Olympic team, he gave the medal to his dad in a tearful ceremony at the high school in tribute to the loss.[1]
College career
Alford decided to play basketball for Bob Knight and the Indiana Hoosiers men's basketball team. At Indiana, he became the university's all-time leading scorer with 2,438 points (a record later eclipsed by Calbert Cheaney, who went on to become the Big Ten's all-time leading scorer). Alford was the first player to be named the team's MVP four times. During his final three seasons, Alford earned first team all-Big Ten honors. In the Legends of College Basketball by The Sporting News Alford was #35 on the list of the 100 greatest Division-I college basketball players. When The Sporting News named its top ten NCAA basketball players of the 1980s in December 1989, Alford was listed at number ten.
As a freshman, Alford quickly earned the favor of Coach Knight. Dan Dakich, Alford's former teammate and later an interim Indiana coach, said "Steve was incredibly mature as a freshman. He was getting thrown out of practice then. If Coach respects you and knows you can handle it, he'll do that. When I was a freshman, only Randy Wittman and Ted Kitchel, the seniors, were thrown out." [1] That year Alford helped lead Indiana to an upset of the Michael Jordan-led North Carolina Tar Heels in the 1984 NCAA tournament.
For the 1984 Summer Olympics Alford, just 19 years old and a sophomore, was selected to play on the U.S. basketball team, coached by Bob Knight. Alford averaged 10.3 points per game, was second in assists, and shot .644 from the field. He and his teammates went on to win the gold medal at the 1984 games. In this game Alford played alongside Michael Jordan, Patrick Ewing, Sam Perkins, Chris Mullin and Wayman Tisdale. Alford has recounted that during the Olympic training camp, Jordan bet him $100 that he would not last four years on Knight's Indiana team.
As a sophomore Alford was named to the 1985 NIT Tournament All-Tournament team after the Hoosiers finished second behind UCLA. As a junior, he and the 1985-86 Hoosiers were profiled in a best-selling book A Season on the Brink. Author John Feinstein was granted unprecedented access to the Indiana basketball program and insights into Knight's coaching style. The book recounts how Knight once criticized Alford's work habits and leadership ability, telling him he couldn't "lead a whore into bed." [1] Knight later admitted Alford was in fact an incredible worker and leader and the comments were just Knight's method of motivating players.[1] The Hoosiers went 21-8 that year and finished second in the Big Ten, with Alford earning All-America and Big Ten Player of the Year honors.
In his senior year, the Alford-led 1986-87 Hoosiers won Indiana's fifth national championship, when the team defeated Syracuse in title game of the
tournament. The game was decided by a game-winning jump shot by Keith Smart with five seconds remaining.[3] Alford shot 7–10 from the three-point line, scored 23 points, including a buzzer-beating three-pointer at the end of the first half that put the Hoosiers ahead by one point to start the second half.
Professional playing career
Alford was drafted 26th in the 1987 NBA draft.[4] Many fans in Indiana expected Alford to be drafted by the Indiana Pacers, but the Pacers selected Reggie Miller and Alford fell to the Dallas Mavericks.[5] Initially the choice angered Indiana fans but ultimately they and even Alford embraced the decision. Years later, Alford said "not only was it a much better draft choice than drafting me... Reggie turned out not to be a great pick, he turned out to be great for the state of Indiana."[2] Alford played in the NBA for four seasons, mostly with the Dallas Mavericks, although he spent a portion of one season with Golden State Warriors. Over his career, he started three games, scored 744 points, had 176 assists and shot free throws with an accuracy of 87 percent.
Player profile
Alford quickly became the face of Indiana basketball and a fan favorite throughout the state. Dan Dakich, Alford's former teammate and later an interim Indiana coach, said of him, "Basically, he owns all of Indiana." [1] Alford's wife Tanya said, "Everybody talks about his hair, his all-American image, how mothers would want him to marry their daughter. Everybody thinks he's so perfect. Well, that's a pretty accurate image. That's exactly what he is." [1]
Alford embodied the "David versus Goliath" image of Indiana basketball popularized in the hit movie Hoosiers (released in 1986 while Alford was at Indiana). He was small for a major-college guard, slow without any compensatory quickness and strong only because he ate and flexed himself up to 185 pounds from 150 as a freshman.[1] According to commentators, Alford owed his success to repetition and work.[1] In his workouts he would pick a spot on the floor and take ten shots. If he did not make eight, he would punish himself with fingertip push-ups or wind sprints. At the end of his college career, Coach Knight said, "He's gotten more out of his abilities offensively than anybody I've seen play college basketball. He's about as good a scorer for being strictly a jump shooter as I've ever seen. He's scored more than 2,400 points that way, and that's incredible, considering he doesn't get any tip-ins, drives or dunks." [1]
Alford is considered one of the best free throw shooters in the history of the game.[1] Alford's free throw percentage of .897 (535-596) is ninth best in the history of the NCAA.[6] His form at the foul line is so routine that it inspired a famous mantra from Indiana fans: "Socks, shorts, 1-2-3 swish". Before releasing a free throw, Alford told himself, "Soft over the front edge of the rim," and some people believed they could see his lips move.[1]
Coaching career
Manchester University Spartans
Alford began his college coaching career in North Manchester, Indiana in 1991 as head coach of the Division III Manchester University's basketball program. During his four seasons with the team, Alford had a record of 78–29. When Alford began coaching that team, the team had lost its first eight games. During his first season there Alford won four of 20 games. In his first full season as coach the team posted a record of 20–8. In the next season Manchester posted a record of 23–4, and in his fourth and final season his team finished 31–1.
In 1994 and 1995 Manchester won conference titles, and in Alford's final three seasons the team competed in the NCAA Division III Tournament. Under Alford, the team won three straight conference tournament titles (1993, 1994, 1995). The team advanced to the Division III championship game in 1995, placing second in the nation after suffering its first defeat in 32 games. The loss to Bo Ryan's University of Wisconsin-Platteville team marked the only title game in NCAA history matching two undefeated squads.
In 1993, 1994, and 1995 Alford was named the Indiana Collegiate Conference Coach of the Year. In the 1994-95 season the Manchester team was inducted into the school Hall of Fame. In 1999 Alford was also inducted into Manchester's Hall of Fame.
Missouri State Bears
Following his time at Manchester, Alford was named the head coach at Southwest Missouri State University. He began his position there in the 1995-96 season, and would remain there until 1999. During his time at Missouri State, his teams posted a 78–48 record. In 1999, the Bears advanced to the Sweet 16 of the NCAA Tournament before losing to Duke.[7]
Iowa Hawkeyes
Steve Alford was named the head coach of the University of Iowa Hawkeyes men's basketball program on March 22, 1999.
Although Alford's first game as coach was a 70–68 victory against the defending national champion Connecticut Huskies at Madison Square Garden, his team went 14-16 during his first season at Iowa. During his second year (2000–01) the Hawkeyes went 23–12 in the regular season and 7–9 in the Big Ten Conference regular season, but they won the Big Ten Conference Men's Basketball Tournament with four straight wins against Northwestern, Ohio State, Penn State, and Indiana. This earned them a #7 seed in the 2001 NCAA Men's Division I Basketball Tournament, where they defeated Creighton in the first round but lost to Kentucky in the second round.
The Hawkeyes' conference record dropped to 5–11 during the 2001–02 season, but they defeated Purdue, Wisconsin, and Indiana in the Big Ten Tournament before losing to Ohio State in the finals. The Hawkeyes played in the National Invitation Tournament that season, but lost to LSU in the first round to finish with a 19–16 record. This was the first of three straight seasons that the Hawkeyes played in the NIT under Alford. They won the first two rounds of the 2003 tournament against Valparaiso and Iowa State before losing to Georgia Tech, finishing with a 17–14 record. That season, leading scorer Pierre Pierce was charged with raping a female Iowa athlete. Alford was adamant about Pierce's innocence.  A plea bargain was reached where Pierce pleaded guilty to a lesser charge. He was suspended from the team and redshirted.[8] In 2004, Iowa lost to St. Louis in the first round of the NIT to finish 16–13 despite a 9–7 conference record (the first winning Big Ten Conference record under Alford).
The Hawkeyes finished 21-12 with a 7-9 conference record in the 2004-2005 regular season, but they won their first two Big Ten Tournament games against Purdue and Michigan State before losing the third game to Wisconsin, 59-56. They earned an at-large invitation to the 2005 NCAA Tournament as a #10 seed, where they lost 76-64 to Cincinnati in the first round. In 2005, Pierce was charged with sexual assault of his girlfriend, and he was dismissed from the team before charges were filed.[8][9] However, Alford's reputation among Iowa fans suffered.[9] Pierce later served 11 months in a correctional facility.[10]
During the 2005–06 season, the Hawkeyes went undefeated at Carver-Hawkeye Arena and finished in a second-place tie with Illinois with an 11-5 conference record, one game behind Ohio State. However, the Hawkeyes defeated Minnesota, Michigan State, and Ohio State to win the Big Ten Tournament and finish 25-8 going into its third NCAA Tournament under Alford. They were seeded #3 in the Atlanta Regional of the 2006 NCAA Tournament, but lost in a first-round upset to #14 seed Northwestern State 64-63, leaving Alford with only one NCAA Tournament win since taking over at Iowa.
During the 2006–2007 season, Alford led the Hawkeyes to an 8–6 non-conference record (losing to in-state rivals Drake and Northern Iowa) and a 9–7 record in the Big Ten Conference (17-14 overall). Iowa failed to make the NCAA tournament or the NIT. It marked the first time since the 1976–1977 season that an Iowa team with a winning record has failed to make either the NCAA tournament or the NIT.
At the conclusion of the 2006–2007 season, Alford resigned from the University of Iowa to accept the coaching position at the University of New Mexico. He led the Hawkeyes to the NCAA Tournament three times, but  had a 61–67 record in the Big Ten, only once finishing higher than fourth in the conference.[7]
New Mexico Lobos

Alford was named head coach at the University of New Mexico on March 23, 2007 replacing the fired Ritchie McKay. In his first year as the Lobos coach Alford posted a record of 24–9, 11–5 in league play. Twenty-four wins is the most for a New Mexico head coach in their first year. The Lobos were led by future 1st round Boston Celtics draft pick J. R. Giddens.  The Lobos were eliminated in the first round of the NIT by Cal.
In his second season, led by seniors Daniel Faris, Tony Danridge and Chad Toppert, Alford guided the Lobos to their first conference championship in 15 years.  He earned the MWC Coach of the Year Award for his team's performance. Alford also set a record for most wins in the first two seasons for a UNM head coach.  Alford and his New Mexico squad fell just short of the NCAA tourney and ended up with their second consecutive NIT bid.  They won a first round home game against Nebraska and lost on a last second buzzer beater on the road to Notre Dame.
His third year, coaching a mostly young, untested team, Alford's Lobos nevertheless won the regular season MWC title for the second year in a row, were ranked in the top 15 for the majority of the year, and earned a #3 seed in the NCAA Tournament, the team's first bid since 2005. In the first round, they survived a tough game against Montana 62–57, but despite Dairese Gary's 28 points, fell in the second round to an upstart Washington side.  At the end of the season Coach Alford received a ten-year contract extension through the 2019–2020 season.
The 2010-2011 season started with Alford's group at 12-4 after non-conference play, but the team struggled to an 8-8 conference regular season record. Drew Gordon and Dairese Gary led a talented team that underachieved much throughout the year into the conference tournament. The team seemed poised to make a run in the MWC conference tournament, but a tragic ACL injury to Gary in the semi-finals against BYU proved to be too much to overcome for this young UNM squad. Their 2010-2011 season ended with an NIT loss to Alabama 74-67. However, with everyone coming back (with the exception of Gary), the following season seemed to hold promise.
The 2011-2012 season began with a rough patch. UNM was picked to win the league for the first time in Alford's five years at the helm, but the team started a questionable 2-2 with losses to home state rival NMSU and a bottom feeder WCC team in Santa Clara. UNM then raced off to a twelve-game win streak and finished the non-conference season at 14-2. UNM then went on to have a 10-4 conference regular season record and a share of the conference title with arch-rival San Diego State. It was only fitting that the regular season co-champions would square off in the MWC tournament title game. With Drew Gordon and Demetrius Walker leading a battle tested UNM team in the championship, Alford and his Lobos prevailed to a 69-58 conference tournament title. UNM received a fifth seed in the NCAA West region, and they defeated Casper Ware and the Long Beach State 49ers in their first game of the NCAA Tournament. The Lobos lost to the Louisville Cardinals in their next game.
In the 2012-2013 season, with a vicious defensive team, Alford led his Lobo squad to a 26-5 regular season record, winning the Mountain West Regular Season conference title. Alford won his third MWC coach of the year honor, and New Mexico garnered another Player of the Year award in Kendall Williams. New Mexico was primed to make a deep run in the NCAA tournament after winning the MWC conference tournament for the second straight year. At 29-5 entering the tournament, New Mexico was an early favorite as a Final Four participant by several analysts and publications, but Alford and his No. 3 seed Lobos were upset by an underdog 14th-seeded Harvard team,[7] who won their first NCAA tournament game in school history.
UCLA Bruins
Consecutive Sweet Sixteens (2013–2015)
On March 30, 2013, Alford signed a seven-year, $18.2-million contract to become the head coach of the UCLA Bruins,[7] joining a program that has won a record 11 national titles.[11] He replaced the fired Ben Howland, who was coming off a blowout loss in the first round of the 2013 NCAA Tournament after UCLA had captured the Pac-12 Conference regular season title with a new up-tempo offense. Overall, he won four conference titles and reached the Final Four three straight times (2006–2008) with the Bruins.[12][13] Alford had a 5-7 NCAA Tournament record,[14] and had only advanced his teams beyond the first weekend of the tournament once before, when he led his Cinderella squad from Southwest Missouri State to the Sweet 16 in 1999.[7]  UCLA tasked Alford with reviving their offense, connecting with a new generation of players, and rejuvenating its fan base.[7][11] He accepted the UCLA position just three days after he had signed a 10-year extension at New Mexico.[15]  At UCLA's introductory news conference, Alford was questioned about his handling of Pierce in Iowa, and he stated that he did "everything that [he] was told to do."[8] Criticism grew over his hiring, especially over his handling of Pierce.  Two weeks after his hiring, Alford apologized for declaring Pierce's innocence "before the legal system had run its course. This was inappropriate, insensitive and hurtful, especially to the young female victim involved, and I apologize for that."[8]

Soon after his hiring, Alford filled his head assistant coaching staff position with good friend and former John Calipari assistant Ed Schilling.  Also hired were David Grace, a rising assistant who spent 2008–2013 on the Oregon State staff, and Duane Broussard, who spent 2008–2013 as Alford's assistant at New Mexico. Tyus Edney, who starred on UCLA's 1995 national championship team, continued as director of operations.[16] In his first season, fans accused Alford of nepotism for playing his son Bryce over fellow freshman Zach LaVine.[11][17][18] The Bruins had rarely sought players who were not four- or five-star recruits,[17] while Bryce was rated a consensus three-star prospect.[19] The coach groomed his son over LaVine to be the team's backup point guard behind starter Kyle Anderson.[20] Alford directed the Bruins to the title in the 2014 Pac-12 Tournament, the school's first conference tournament title in six years.[21] They advanced to the Sweet 16 of the 2014 NCAA Tournament—their first regional semifinal appearance since 2008—before falling to Florida, who improved to 4–0 all-time against UCLA in the NCAA tournament.[22]
After Anderson and LaVine left UCLA for the National Basketball Association (NBA), Bryce became the Bruins' starting point guard in 2014–15.[23][24] Although he was considered more of a shooter than a true point guard,[25][26][27] Alford's son was the team's only legitimate option for the position.[28] The Bruins began the season at 4–0 and ranked No. 22 before losing two of three games at the Battle 4 Atlantis tournament.[29][30] Beginning with their December loss at home to Gonzaga, the Bruins lost five consecutive games, their longest streak since 2009–10.[31] Losses included a 39-point defeat to No. 1 Kentucky—they fell behind 24–0 and trailed 41–7 at halftime—and by 32 points against Utah.[32][33][34] UCLA closed out the regular season with three straight home wins to finish undefeated (9–0) at home in the conference for the first time since 2006–07.[35] The Bruins went 1–1 in the 2015 Pac-12 Tournament,[36] but proved most major projections wrong by receiving an invitation to the 2015 NCAA tournament, earning a No. 11 seed.[36][37] The squad became the lowest-seed UCLA team to ever reach the regional semifinals.[38] They benefitted from a controversial goaltending call and a favorable second-round matchup with No. 14 seed Alabama Birmingham to advance to the Sweet 16,[11] when they lost again to Gonzaga.[39]
Fanbase grows restless (2015–2018)
In 2015–16, UCLA finished with a 15–17 record, the fourth time the program finished with a losing record since 1948, when John Wooden became their coach.[40] They missed the NCAA Tournament for just the third time in 10 years. The Bruins were eliminated from the 2016 Pac-12 Tournament after a 95–71 loss to USC, losing three consecutive times in the same season to their crosstown rivals for the first time in 74 years.[41] One week during the offseason, a plane flew over the UCLA campus on two occasions with a banner urging the school to fire Alford.[42] A week later, Alford apologized for what he called an "unacceptable" season, and he returned a one-year contract extension he had received in 2014.[42][43] He pledged to never allow their defense to rank outside the top 100 nationally.[11] The following year, Alford led a talented squad which featured three eventual NBA first-round draft picks and five future NBA players.[44] The Bruins finished one game out of first place in the Pac-12,[44] and advanced to their third Sweet 16 in four years as freshmen Lonzo Ball and T. J. Leaf led one of the top offensive teams in the nation.[43]
The Bruins in 2017–18 opened their new practice facility, the Mo Ostin Basketball Center.[45] They again struggled defensively.[11] UCLA qualified for the 2018 NCAA Tournament, but lost 65–58 to St. Bonaventure in the First Four for the Bonnies' first tournament win in 48 years. It was the first time in UCLA's history that they had been relegated to a First Four play-in game.[45][46] It was also the first time in the school's four tournament appearances under Alford that they did not advance to the Sweet 16.[47] Another banner was flown over campus, this time reading "Final Fours not First Fours #FireAlford."[11]
In 2018–19 in Alford's sixth year at UCLA,[48] he brought in a top-10 recruiting class which included 7-foot-1-inch (2.16m) center Moses Brown.[49] He also added assistant coach Murry Bartow to improve the team's defense.[11] The Bruins were ranked No. 21 in the preseason AP Poll,[50] and they started the season 4–0 to moved up to No. 17.[51] However, they lost six of the next nine and finished with a 7–6 record in nonconference play, closing it out with four straight losses, the last of which was a 73–58 defeat to Liberty.[51][52] The 15-point setback was the most lopsided home loss in Alford's tenure with UCLA.[52] Combined with an earlier home loss to mid-major program Belmont, it was the first time the Bruins had lost consecutive home games to non-Power Five schools since 2012–13.[53] Four days after Belmont, they lost by 29 at Cincinnati, their largest margin of defeat since 2014–15.[54] Their offense had grown stagnant. As the lossed mounted, Alford increasingly blamed his players.[11] UCLA had not lost four straight since the end of 2015–16, when they finished the season under .500.[54] They had not suffered four consecutive nonconference losses since 2010–11.[55] On December 31, 2018, two days after the Bruins' loss to Liberty, UCLA announced that Alford had been fired[56] It was the first time the program had made a coaching change in the middle of the season.[49]
Alford ended his tenure with a 124–63 overall record and 55–35 in the Pac-12. He guided UCLA to the NCAA Tournament four times in five years, including three times to the Sweet 16.[48] However, he failed to win a Pac-12 regular-season title, and his only Pac-12 Tournament title was in his first season.[50] He never advanced past the Sweet 16. He was only the second coach in UCLA's 100-year history to never win a conference regular-season title; his highest finish was second place in his first season. During his tenure, UCLA had 11 players selected in the NBA draft, including seven first-round picks.[49]
Incidents

During the 2010 season, during a post-game handshake line, Alford had a confrontation with a Brigham Young player in which Alford called him an "extremely vulgar" name, according to the Wall Street Journal.[57]
In 2011, before a home NIT Tournament game against heated rival UTEP, Alford and his staff got into a heated argument with UTEP coach Tim Floyd and his staff, in a dispute over practice time. After this incident, Alford cancelled the historic and long-standing basketball series between New Mexico and UTEP.
Head coaching record

Notes

Personal life
Alford has three children, Kory, Bryce and Kayla. Kory played for the elder Alford at New Mexico and transferred with him to UCLA. Bryce also played under Alford at UCLA, and ended his career as the school's career leader in three-pointers made.[58] He became a professional basketball player.
Alford is a Christian. He has spoken openly about his faith, saying, "I'm a Christian first. I'm a family guy second. As much as I like coaching, as much as I like basketball, it's third, fourth, or fifth down the line."[59]

Career statistics and player information from

When did Stephen Todd Alford become head coach at UCLA?


A view camera is a large format camera in which the lens forms an inverted image on a ground glass screen directly at the plane of the film. The image viewed is exactly the same as the image on the film, which replaces the viewing screen during exposure.[1]
This type of camera was first developed in the era of the daguerreotype[2] (1840s-1850s) and  still in use today, though with many refinements.  It comprises a flexible bellows that forms a light-tight seal between two adjustable standards, one of which holds a lens, and the other a viewfinder or a photographic film holder.[3] There are three general types, the monorail camera, the field camera, and press or technical cameras.
The bellows is a flexible, accordion-pleated box. It encloses the space between the lens and film, and flexes to accommodate the movements of the standards.[4]:p.34 The front standard is a board at the front of the camera that holds the lens and, usually, a shutter.
At the other end of the bellows, the rear standard is a frame that holds a ground glass plate, used for focusing and composing the image before exposure—and is replaced by a holder containing the light-sensitive film, plate, or image sensor for exposure. The front and rear standards can move in various ways relative to each other, unlike most other camera types. This provides control over focus, depth of field, and perspective. The camera is usually used on a tripod or other support.
Types of view camera
Several types of view cameras are used for different purposes, and provide different degrees of movement and portability. They include:

Monorail camera - This is the most common type of studio view camera, with front and rear standards mounted to a single rail that is fixed to a camera support. This design gives the greatest range of movements and flexibility, with both front and rear standards able to tilt, shift, rise, fall, and swing in similar proportion. These are generally made of metal with leather or synthetic bellows, and are difficult to pack for travel. Sinar and Toyo are popular manufacturers of monorail view camera systems. ARCA-Swiss produces monorail cameras for field use in addition to models for the more conventional studio applications. Many manufacturers also offer monorail extensions that move the front or rear standards farther away from each other to facilitate focusing on close objects (macrophotography).
Field camera - These have the front and rear standard mounted on sliding rails fixed to a hinged flat bed that can be attached to a camera support, such as a tripod. These cameras are usually made of wood, or sometimes lightweight and strong composites such as carbon fiber. With the bellows fully retracted, the flat bed folds up, reducing the camera to a relatively small, light, and portable box. The trade off for this portability is that the standards are not as mobile or as adjustable as on a monorail design. The rear standard in particular may be fixed and offer no movement. These large format but transportable cameras are popular with landscape photographers. Tachihara and Wisner are examples of modern field cameras at opposite ends of the price scale.
Extremely large field cameras use 11×14 film and larger, or panoramic film sizes such as 4×10 or 8×20. These are sometimes called banquet cameras, and once were commonly used to photograph large, posed groups of people to mark occasions, such as banquets or weddings.
Studio and salon cameras are similar to field cameras, but do not fold up for portability.
Before the introduction of rollfilm, folding plate cameras with limited movements as described here were often used. An example is the Goerz Taro-Tenax 9x12cm.[5]
Press and technical cameras are true view cameras, as almost all of them have a ground glass integral to the film-holder mechanism that allows critical focus and full use of the sometimes limited movements. More expensive examples had a wide array of movements, as well as focusing and composing aids like rangefinders and viewfinders. They are most often made of metal, designed to fold up quickly for portability, used by press photographers before and during the second world war. Technical cameras have more adjustment capabilities, including some ability to tilt the rear standard, and can be either hand-held or attached to a tripod for support.[4]:p.33
A more modern development is the highly portable  Sinar arTec view camera, which doesn't fit within any of the above criteria. It was designed primarily for architectural photography. It has the novel ability to take panoramic stitched images by means of a built-in step and repeat mechanism.
View cameras use large format sheet film—one sheet per photograph. Standard sizes in inches are: 4×5, 5×7, 4×10, 5×12, 8×10, 11×14, 7×17, 8×20, 12×20, and 20×24. (It is usual to list the short side first in the Americas, and the long side in many other countries, thus 4×5 is the same as 5×4). A similar, but not identical, range of metric sizes is used in many countries; thus 9×12cm is similar to, but not interchangeable with, 4×5inches. The most widely used format is 4×5, followed by 8×10.
A few rollfilm cameras have movements that make them as versatile as a sheet film view camera. Rollfilm and instant film backs are available to use in place of a sheetfilm holder on a single-film camera.
Movements
Photographers use view cameras to control focus and convergence of parallel lines. Image control is done by moving the front and/or rear standards. Movements are the ways the front and rear standards can move to alter perspective and focus. The term can also refer to the mechanisms on the standards that control their position.
Not all cameras have all movements available to both front and rear standards, and some cameras have more movements available than others. Some cameras have mechanisms that facilitate intricate movement combinations.
Some limited view camera–type movements are possible with SLR cameras using various tilt/shift lenses. Also, as use of view cameras declines in favor of digital photography, these movements are simulated using computer software.[6][7]

Rise and fall
Rise and fall are the movements of either the front or rear standard vertically along a line in a plane parallel to the film (or sensor) plane. Rise is a very important movement especially in architectural photography.  Generally, the lens is moved vertically—either up or down—along the lens plane to change the portion of the image captured on the film. In the 35mm format, special shift lenses (sometimes called perspective control lenses) emulate the rise or fall of view cameras.
The main effect of rise is to eliminate converging parallels when photographing tall buildings. If a camera without movements is pointed at a tall building, the top is off. If the camera is tilted upwards to get it all in, the film plane is not parallel to the building, and the building seems narrower at the top than the bottom: lines that are parallel in the object converge in the image.
To avoid this apparent distortion, a wide-angle lens gets more of the building in, but includes more of the foreground and alters the perspective. A camera with rising front lets a normal lens be raised to include the top of the building without tilting the camera.
This requires that the image circle of the lens be larger than is required to cover the film without use of movements. If the lens can produce a circular image just large enough to cover the film, it can't cover the bottom of the film as it rises. Consequently, lens coverage must be larger to accommodate rises (and falls, and shifts).
In Figure a) below (images are upside down, as a photographer would see them on the ground glass of a view camera), the lens is in the “normal” position. Notice that much of the unwanted foreground is included, but not the top of the tower.  In Figure b), the lens has been shifted up: the top of the tower is now inside the area captured on film, at the sacrifice of unwanted green foreground.

Shift

Moving the front standard left or right from its normal position is called lens shift, or simply shift. This movement is similar to rise and fall, but moves the image horizontally rather than vertically. One use for shift is to remove the image of the camera from the final image when photographing a reflective surface.

Tilt

The axis of the lens is normally perpendicular to the film (or sensor). Changing the angle between axis and film by tilting the lens standard backwards or forwards is called lens tilt, or just tilt. Tilt is especially useful in landscape photography. By using the Scheimpflug principle, the “plane of sharp focus” can be changed so that any plane can be brought into sharp focus. When the film plane and lens plane are parallel as is the case for most 35mm cameras, the plane of sharp focus is also parallel to these two planes. If, however, the lens plane is tilted with respect to the film plane, the plane of sharp focus is also tilted according to geometrical and optical properties. The three planes intersect in a line below the camera for downward lens tilt. The tilted plane of sharp focus is useful, in that this plane can be made to coincide with a near and far object. Thus, both near and far objects on the plane are in focus.
This effect is often incorrectly thought of as increasing the depth of field. Depth of field depends on the focal length, aperture, and subject distance. As long as the photographer wants sharpness in a plane that is parallel to the film, tilt is of no use. However, tilt has a strong effect on the depth of field by drastically altering its shape, making it asymmetrical. Without tilt, the limits of near and far acceptable focus are parallel to the plane of sharp focus as well as parallel to the film. With forward tilt, the plane of sharp focus tilts even more and the near and far limits of acceptable focus form a wedge shape (viewed from the side). Thus, the lens still sees a cone shaped portion of whatever is in front of it while the wedge of acceptable focus is now more closely aligned with this cone. Therefore, depending on the shape of the subject, a wider aperture can be used, lessening concerns about camera stability due to slow shutter speed and diffraction due to too-small aperture.
Tilting achieves the desired depth of field using the aperture at which the lens performs best. Too small an aperture risks losses to diffraction and camera/subject motion what is gained from depth of field. Only testing a given scene, or experience, shows whether tilting is better than leaving the standards neutral and relying on the aperture alone to achieve the desired depth of field. If the scene is sharp enough at f/32 with 2 degrees of tilt but would need f/64 with zero tilt, then tilt is the solution. If another scene would need f/45 with or without tilt, then nothing is gained. See Merklinger[8]
and Luong[9]
for extensive discussions on determining the optimal tilt (if any) in challenging situations.
With a forward tilt, the shape of the portion of a scene in acceptable focus is a wedge. Thus, the scene most likely to benefit from tilting is short in the front and expands to a greater height or thickness toward the horizon. A scene consisting of tall trees in the near, middle and far distance may not lend itself to tilting unless the photographer is willing to sacrifice either the top of the near trees and/or the bottom of the far trees.
Assuming lens axis front tilt, here are the trade offs in choosing between a small degree of tilt (say less than 3) and a larger tilt: A small tilt causes a wider or fatter wedge but one that is far off axis from the cone of light seen by the lens. Conversely, a large tilt (say 10 degrees) makes the wedge more aligned with the lens view, but with a narrower wedge. Thus, a modest tilt is often, or even usually, the best starting point.
Small and medium format cameras have fixed bodies that do not allow for misalignment of the film and lens planes, intentionally or not.  Tilt/shift (“TS”) or perspective control (“PC”) lenses that provide limited movements for these cameras can be purchased from a number of lens makers.  High-quality TS or PC lenses are expensive. The price of a new Canon TS-E or Nikon PC-E lens is comparable to that of a good used large-format camera, which offers a much greater range of adjustment.

Swing

Altering the angle of the lens standard in relation to the film plane by swiveling it from side to side is called swing.  Swing is like tilt, but it changes the angle of the focal plane in the horizontal axis instead of the vertical axis. For example, swing can help achieve sharp focus along the entire length of a picket fence that is not parallel to the film plane.

Back tilt/swing
Angular movements of the rear standard change the angle between the lens plane and the film plane just as front standard angular movements do. Though rear standard tilt changes the plane of sharp focus in the same manner as front standard tilt, this is not usually the reason to use rear tilt/swing. When a lens is a certain distance (its focal length) away from the film, distant objects, such as faraway mountains, are in focus. Moving the lens farther from the film brings closer objects into focus. Tilting or swinging the film plane puts one side of the film farther from the lens than the center is and the opposite point of the film is therefore closer to the lens.
One reason to swing or tilt the rear standard is to keep the film plane parallel to the face of the subject. Another reason to swing or tilt the rear standard is to control apparent convergence of lines when shooting subjects at an angle.
It is often incorrectly stated that rear movements can be used to change perspective. The only thing that truly controls perspective is the location of the camera in relation to the objects in the frame. Rear movements can let a photographer shoot a subject from a perspective that puts the camera at an angle to the subject, yet still achieves parallel lines. Thus, rear movements allow a change of perspective by allowing a different camera location, yet no view camera movement actually alters perspective.
Lenses

A view camera lens typically consists of:
A front lens element— sometimes referred to as a cell.
A shutter—an electronic or spring-actuated mechanism that controls exposure duration. Some early shutters were air-actuated. For long exposures, a lens with no shutter (a barrel lens) can be uncovered for the duration of the exposure by removing a lens cap.
The aperture diaphragm
A lensboard—a flat board, typically square in shape and made of metal or wood, that locks securely into the front standard of a particular view camera, with a central hole of the right size to insert a lens and shutter assembly, usually secured and made light-tight by screwing a ring onto a thread on the rear of the lens assembly. Lensboards, complete with lenses, can be removed and fitted quickly.
A rear lens element (or cell).
Almost any lens of the appropriate coverage area may be used with almost any view camera. All that is required is that the lens be mounted on a lensboard compatible with the camera. Not all lensboards work with all models of view camera, though different cameras may be designed to work with a common lensboard type. Lensboards usually come with a hole sized according to the shutter size, often called the Copal Number. Copal is the most popular maker of leaf shutters for view camera lenses.
The lens is designed to split into two pieces, the front and rear elements screwed, usually by a trained technician, into the front and back of the shutter assembly, and the whole fitted in a lensboard.
View camera lenses are designed with both focal length and coverage in mind. A 300mm lens may give a different angle of view (either over 31° or over 57°), depending on whether it was designed to cover a 4×5 or 8×10 image area. Most lenses are designed to cover more than just the image area to accommodate camera movements.
Focusing involves moving the entire front standard with the lens assembly closer to or further away from the rear standard, unlike many lenses on smaller cameras in which one group of lens elements is fixed and another moves.
Very long focus lenses may require that the camera be fitted with special extra-long rails and bellows. Very short focal length wide-angle lenses may require that the standards be closer together than a normal concertina-folded bellows allows. Such a situation requires a bag bellows, a simple light-tight flexible bag. Recessed lensboards are also sometimes used to get the rear element of a wide angle lens close enough to the film plane; they may also be of use with telephoto lenses, since these compressed long-focus lenses may also have very small spacing between the back of the lens and the film plane.
Zoom lenses are not used in view camera photography, as there is no need for rapid and continuous change of focal length with static subjects, and the price, size, weight, and complexity would be excessive. Some lenses are "convertible": the front or rear element only, or both elements, may be used, giving three different focal lengths, though the quality of the single elements is not as good at larger apertures as the combination. These are popular with field photographers who can save weight by carrying one convertible lens rather than two or three lenses of different focal lengths. Older convertible lenses may not be corrected for chromatic aberration, making them unsatisfactory with color film.
Soft focus lenses introduce spherical aberration deliberately into the optical formula for an ethereal effect considered pleasing, and flattering to subjects with less than perfect complexions. The degree of soft-focus effect is determined by either aperture size or special disks that fit into the lens to modify the aperture shape. Some antique lenses, and some modern SLR soft focus lenses, provide a lever that controls the softening effect by altering the optical formula.
Film
View cameras use sheet film but can use roll film (generally 120/220 size) by using special roll film holders.  Popular "normal" image formats for the 4×5 camera are 6×6, 6×7, and 6×9cm. 6×12 and 6×17cm are suited to panoramic photography.
With an inexpensive modification of the darkslide, and no modification to the camera, half a sheet of film can be exposed at a time. While this technique could be used for economy where a larger image is not required, it is almost always used with the intention of obtaining a panoramic format so that, for example, a 4×5 camera can take two 2×5 photos, an 8×10 can take two 4×10s etc. This is popular for landscape photography, and in the past was common for group photographs (hence, half-frame panorama formats such as 4x10 are commonly referred to as "Banquet formats")
Digital camera backs are available for view cameras to create digital images instead of using film. Prices are high compared to smaller digital cameras.
Operation

The camera must be set up in a suitable position. In some cases the subject can also be manipulated, as in a studio. In others the camera must be positioned to photograph subjects such as landscapes. The camera must be mounted in a way that prevents camera motion for the duration of the exposure. Usually a tripod is used—a camera with a long bellows extension may require two.
To operate the view camera, the photographer opens the shutter on the lens to focus and compose the image on a ground glass plate on the rear standard. The rear standard holds the ground glass in the same plane that the film later occupies—so that an image focused on the ground glass is focused on the film.  The ground glass image can be somewhat dim and difficult to view in bright light. Photographers often use a focusing cloth or "dark cloth" over their heads and the rear of the camera. The dark cloth shrouds the viewing area and keeps environmental light from obscuring the image.  In the dark space created by the dark cloth, the image appears as bright as it can, so the photographer can view, focus, and compose the image.
Often, a photographer uses a magnifying lens, usually a high quality loupe, to critically focus the image. An addition over the ground glass called a Fresnel lens can considerably brighten the ground glass image (with a slight loss of focusing accuracy).  The taking lens may be stopped down to help gauge depth of field effects and vignetting, but the photographer generally opens the lens to its widest setting for focusing.
The ground glass and frame assembly, known as the spring back, is held in place by springs that pull and hold the ground glass firmly into the plane of focus during the focusing and composition process. Once focusing is complete, the same springs act as a flexible clamping mechanism to press the film holder into the same plane of focus that the ground glass occupied.
To take the photograph, the photographer pulls back the ground glass and slides the film holder into its place. The shutter is then closed and cocked, the shutter speed and aperture set. The photographer removes the darkslide that covers the sheet of film in the film holder, and triggers the shutter to make the exposure. Finally, the photographer replaces the darkslide and removes the film holder with the exposed film.
Sheet film holders are generally interchangeable between various brands and models of view cameras, adhering to de facto standards. The largest cameras and more uncommon formats are less standardized.
Special film holders and accessories can fit in place of standard film holders for specific purposes. A Grafmatic, for example, can fit six sheets of film in the space of an ordinary two-sheet holder, and some light meters have an attachment that inserts into the film holder slot on the camera back so the photographer can measure light that falls at a specific point on the film plane. The entire film holder/back assembly is often an industry standard Graflex back, removable so accessories like roll-film holders and digital imagers can be used without altering focus.
Pros and cons compared to medium and 35mm formats
Advantages
The ability to skew the plane of critical focus: In a camera without movements the film plane is always parallel to the lens plane. A camera with tilts and swings lets the photographer skew the plane of focus away from the parallel in any direction, which in many cases can bring the image of a subject that is not parallel to the lens plane into near-to-far focus without stopping down the aperture excessively. Both standards can be tilted through the horizontal or swung through the vertical axes to change the plane of focus. Tilts and swings of the front standard alone do not alter or distort shapes or converging lines in the image; tilts and swings of the rear standard do affect these things, as well as the plane of focus: if the plane of focus must be skewed without altering shapes in the image, front movements alone must be used. The Scheimpflug principle explains the relationship between lens tilts and swings, and the plane of sharp focus.
The ability to distort the shape of the image by skewing the film plane: This is most often to reduce or eliminate, or deliberately exaggerate, convergence of lines that are parallel in the subject. If a camera with parallel film and lens planes is pointed at an angle to a plane subject with parallel lines, the lines appear to converge in the image, becoming closer to each other the further away from the camera they are. With a view camera the rear standard can be swung toward the wall to reduce this convergence. If the standard is parallel to the wall, convergence is entirely eliminated. Moving the rear standard this way skews the plane of focus, which can be corrected with a front swing in the same direction as the rear swing.
Improved image quality for a print of a given size: The larger a piece of film is, the less detail is lost at a given print size because the larger film requires less enlargement for the same size print. In other words, the same scene photographed on a large-format camera provides a better-quality image and allows greater enlargement than the same image in a smaller format. Additionally, the larger a piece of film is, the more subtle and varied the tonal palette and gradations are at a given print size. A large film size also allows same-size contact printing.
Shallow depth of field: view cameras require longer focal length lenses than smaller format cameras, especially for the larger sizes, with shallower depth of field, letting the photographer focus solely on the subject.
Smaller apertures can be used: much smaller apertures can be used than with smaller format cameras before diffraction becomes significant for a given print size.
Low resale value is an advantage for buyers, but not for sellers. A top-of-the-line 8×10 camera that cost $8,000 new can often be bought in excellent condition, with additional accessories, for $1,500.
Disadvantages
Lack of automation: most view cameras are fully manual, requiring time, and allowing even experienced photographers to make mistakes. Some cameras, such as Sinars, have some degree of automation with self-cocking shutters and film-plane metering.
Steep learning curve: In addition to needing the knowledge required to operate a fully manual camera, view camera operators must understand a large number of technical matters that are not an issue to most small format photographers.  They must understand, for example, view camera movements, bellows factors, and reciprocity. A great amount of time and study is needed to master those aspects of large format photography, so learning view camera operation requires a high degree of dedication.
Large size and weight: monorail view cameras are unsuitable for handheld photography and are in most cases difficult to transport. A folding bed field camera like a Linhof Technika with a lens-coupled range finder system even allows action photography.
Shallow depth of field: view cameras require longer focal length lenses than smaller format cameras, especially for the larger sizes, with shallower depth of field.
Small maximum aperture: it is not feasible to make long focal length lenses with the wide maximum apertures available with shorter focal lengths.
High cost: there is limited demand for view cameras, so that there are no economies of scale and they are much more expensive than mass-produced cameras. Some are handmade. Even though the cost of sheet film and processing is much higher than rollfilm, fewer sheets of film are exposed, which partially offsets the cost.
Some of these disadvantages can be viewed as advantages.  For example, slow setup and composure time allow the photographer to better visualize the image before making an exposure. The shallow depth of field can be used to emphasize certain details and deemphasize others (in bokeh style, for example), especially combined with camera movements. The high cost of film and processing encourages careful planning. Because view cameras are rather difficult to set up and focus, the photographer must seek the best camera position, perspective, etc. before exposing.  Beginning 35mm photographers are even sometimes advised to use a tripod specifically because it slows down the picture-taking process.
See also

Cambo
Ebony cameras
Graflex
Large format
Large format lens
Lensbaby
Linhof
Perspective control
Perspective control lens
Press camera
Sinar