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This semantic divergence among North American anglophones, however, remained largely unknown in the Spanish-American colonies. In 1801, the document titled "Letter to American Spaniards"—published in French (1799), in Spanish (1801), and in English (1808)—might have influenced Venezuela's Act of Independence and its 1811 constitution.
The Latter-day Saints' Articles of Faith refer to the American continents as where they are to build Zion.
Common short forms and abbreviations are the "United States", the "U.S.", the "U.S.A.", and "America"; colloquial versions include the "U.S. of A." and "the States". The term "Columbia" (from the Columbus surname) was a popular name for the U.S. and for the entire geographic Americas; its usage is present today in the District of Columbia's name. Moreover, the womanly personification of Columbia appears in some official documents, including editions of the U.S. dollar.
Usage at the United Nations.
Use of the term "American" for U.S. nationals is common at the United Nations, and financial markets in the United States are referred to as "American financial markets".
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American Samoa, an unincorporated territory of the United States, is a recognized territorial name at the United Nations.
Cultural views.
Canada.
Modern Canadians typically refer to people from the United States as "Americans", though they seldom refer to the United States as "America"; in English they use the terms "the United States", "the U.S.", or (informally) "the States" instead. Because of anti-American sentiment or simply national pride, Canadians never apply the term "American" to themselves. Not being an "American" is a part of Canadian identity, with many Canadians resenting being referred to as Americans or mistaken for U.S. citizens. This is often due to others' inability, particularly overseas, to distinguish English-speaking Canadians from Americans, by their accent or other cultural attributes. Some Canadians have protested the use of "American" as a national demonym. People of American origin in Canada are categorized as "Other North American origins" by Statistics Canada for purposes of census counts.
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Spain and Hispanic America.
The use of "American" as a national demonym for U.S. nationals is challenged, primarily by Hispanic Americans. Spanish speakers in Spain and Hispanic America use the term to refer to people and things from the United States (from ), while refers to the continents as a whole (from "América"). The term is also accepted in many parts of Hispanic America to refer to a person or something from the United States; however, this term may be ambiguous in certain parts. Up to and including the 1992 edition, the , published by the Real Academia Española, did not include the United States definition in the entry for ; this was added in the 2001 edition. The Real Academia Española advised against using exclusively for U.S. nationals:
Portugal and Brazil.
Generally, denotes "U.S. citizen" in Portugal. Usage of to exclusively denote people and things of the U.S. is discouraged by the Lisbon Academy of Sciences, because the specific word (also ) clearly denotes a person from the United States. The adjective currently used by the Portuguese press is .
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In Brazil, the term is used to address both that which pertains to the Americas and that which pertains to the U.S.; the particular meaning is deduced from context. Alternatively, the term ("North American") is also used in more informal contexts, while (of the U.S.) is the preferred form in academia. Use of the three terms is common in schools, government, and media. The term is used exclusively for the whole continent, and the U.S. is called ("United States") or ("United States of America"), often abbreviated .
In other contexts.
"American" in the 1994 "Associated Press Stylebook" was defined as, "An acceptable description for a resident of the United States. It also may be applied to any resident or citizen of nations in North or South America." Elsewhere, the "AP Stylebook" indicates that "United States" must "be spelled out when used as a noun. Use U.S. (no space) only as an adjective."
The entry for "America" in "The New York Times Manual of Style and Usage" from 1999 reads:
Media releases from the Pope and Holy See frequently use "America" to refer to the United States, and "American" to denote something or someone from the United States.
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International law.
At least one international law uses "U.S. citizen" in defining a citizen of the United States rather than "American citizen"; for example, the English version of the North American Free Trade Agreement includes:
Many international treaties use the terms "American" and "American citizen":
U.S. commercial regulation.
Products that are labeled, advertised, and marketed in the U.S. as "Made in the USA" must be, as set by the Federal Trade Commission (FTC), "all or virtually all made in the U.S." The FTC, to prevent deception of customers and unfair competition, considers an unqualified claim of "American Made" to expressly claim exclusive manufacture in the U.S: "The FTC Act gives the Commission the power to bring law enforcement actions against false or misleading claims that a product is of U.S. origin."
Alternatives.
There are a number of alternatives to the demonym "American" as a citizen of the United States that do not simultaneously mean any inhabitant of the Americas. One uncommon alternative is "Usonian", which usually describes a certain style of residential architecture designed by Frank Lloyd Wright. Other alternatives have also surfaced, but most have fallen into disuse and obscurity. "Merriam-Webster's Dictionary of English Usage" says:
Nevertheless, no alternative to "American" is common.
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Ada (programming language)
Ada is a structured, statically typed, imperative, and object-oriented high-level programming language, inspired by Pascal and other languages. It has built-in language support for "design by contract" (DbC), extremely strong typing, explicit concurrency, tasks, synchronous message passing, protected objects, and non-determinism. Ada improves code safety and maintainability by using the compiler to find errors in favor of runtime errors. Ada is an international technical standard, jointly defined by the International Organization for Standardization (ISO), and the International Electrotechnical Commission (IEC). , the standard, ISO/IEC 8652:2023, is called Ada 2022 informally.
Ada was originally designed by a team led by French computer scientist Jean Ichbiah of Honeywell under contract to the United States Department of Defense (DoD) from 1977 to 1983 to supersede over 450 programming languages then used by the DoD. Ada was named after Ada Lovelace (1815–1852), who has been credited as the first computer programmer.
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Features.
Ada was originally designed for embedded and real-time systems. The Ada 95 revision, designed by S. Tucker Taft of Intermetrics between 1992 and 1995, improved support for systems, numerical, financial, and object-oriented programming (OOP).
Features of Ada include: strong typing, modular programming mechanisms (packages), run-time checking, parallel processing (tasks, synchronous message passing, protected objects, and nondeterministic select statements), exception handling, and generics. Ada 95 added support for object-oriented programming, including dynamic dispatch.
The syntax of Ada minimizes choices of ways to perform basic operations, and prefers English keywords (such as and ) to symbols (such as and ). Ada uses the basic arithmetical operators , , , and , but avoids using other symbols. Code blocks are delimited by words such as 'declare', 'begin', and 'end', where the 'end' (in most cases) is followed by the keyword of the block that it closes (e.g., ... , ... ). In the case of conditional blocks this avoids a "dangling else" that could pair with the wrong nested 'if'-expression in other languages such as C or Java.
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Ada is designed for developing very large software systems. Ada packages can be compiled separately. Ada package specifications (the package interface) can also be compiled separately without the implementation to check for consistency. This makes it possible to detect problems early during the design phase, before implementation starts.
A large number of compile-time checks are supported to help avoid bugs that would not be detectable until run-time in some other languages or would require explicit checks to be added to the source code. For example, the syntax requires explicitly named closing of blocks to prevent errors due to mismatched end tokens. The adherence to strong typing allows detecting many common software errors (wrong parameters, range violations, invalid references, mismatched types, etc.) either during compile-time, or otherwise during run-time. As concurrency is part of the language specification, the compiler can in some cases detect potential deadlocks. Compilers also commonly check for misspelled identifiers, visibility of packages, redundant declarations, etc. and can provide warnings and useful suggestions on how to fix the error.
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Ada also supports run-time checks to protect against access to unallocated memory, buffer overflow errors, range violations, off-by-one errors, array access errors, and other detectable bugs. These checks can be disabled in the interest of runtime efficiency, but can often be compiled efficiently. It also includes facilities to help program verification. For these reasons, Ada is sometimes used in critical systems, where any anomaly might lead to very serious consequences, e.g., accidental death, injury or severe financial loss. Examples of systems where Ada is used include avionics, air traffic control, railways, banking, military and space technology.
Ada's dynamic memory management is high-level and type-safe. Ada has no generic or untyped pointers; nor does it implicitly declare any pointer type. Instead, all dynamic memory allocation and deallocation must occur via explicitly declared "access types". Each access type has an associated "storage pool" that handles the low-level details of memory management; the programmer can either use the default storage pool or define new ones (this is particularly relevant for Non-Uniform Memory Access). It is even possible to declare several different access types that all designate the same type but use different storage pools. Also, the language provides for "accessibility checks", both at compile time and at run time, that ensures that an "access value" cannot outlive the type of the object it points to.
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Though the semantics of the language allow automatic garbage collection of inaccessible objects, most implementations do not support it by default, as it would cause unpredictable behaviour in real-time systems. Ada supports a limited form of region-based memory management, and in Ada, destroying a storage pool also destroys all the objects in the pool.
A double-dash (), resembling an em dash, denotes comment text. Comments stop at end of line; there is intentionally no way to make a comment span multiple lines, to prevent unclosed comments from accidentally voiding whole sections of source code. Disabling a whole block of code therefore requires the prefixing of each line (or column) individually with . While this clearly denotes disabled code by creating a column of repeated '--' down the page, it also renders the experimental dis/re-enablement of large blocks a more drawn-out process in editors without block commenting support.
The semicolon () is a statement terminator, and the null or no-operation statement is . A single without a statement to terminate is not allowed.
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Unlike most ISO standards, the Ada language definition (known as the "Ada Reference Manual" or "ARM", or sometimes the "Language Reference Manual" or "LRM") is free content. Thus, it is a common reference for Ada programmers, not only programmers implementing Ada compilers. Apart from the reference manual, there is also an extensive rationale document which explains the language design and the use of various language constructs. This document is also widely used by programmers. When the language was revised, a new rationale document was written.
One notable free software tool that is used by many Ada programmers to aid them in writing Ada source code is the GNAT Programming Studio, and GNAT which is part of the GNU Compiler Collection.
"Alire" is a package and toolchain management tool for Ada.
History.
In the 1970s the US Department of Defense (DoD) became concerned by the number of different programming languages being used for its embedded computer system projects, many of which were obsolete or hardware-dependent, and none of which supported safe modular programming. In 1975, a working group, the High Order Language Working Group (HOLWG), was formed with the intent to reduce this number by finding or creating a programming language generally suitable for the department's and the UK Ministry of Defence's requirements. After many iterations beginning with an original straw-man proposal the eventual programming language was named Ada. The total number of high-level programming languages in use for such projects fell from over 450 in 1983 to 37 by 1996.
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HOLWG crafted the Steelman language requirements , a series of documents stating the requirements they felt a programming language should satisfy. Many existing languages were formally reviewed, but the team concluded in 1977 that no existing language met the specifications. The requirements were created by the United States Department of Defense in "The Department of Defense Common High Order Language program" in 1978. The predecessors of this document were called, in order, "Strawman", "Woodenman", "Tinman" and "Ironman". The requirements focused on the needs of embedded computer applications, and emphasised reliability, maintainability, and efficiency. Notably, they included exception handling facilities, run-time checking, and parallel computing.
It was concluded that no existing language met these criteria to a sufficient extent, so a contest was called to create a language that would be closer to fulfilling them. The design that won this contest became the Ada programming language. The resulting language followed the Steelman requirements closely, though not exactly.
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Requests for proposals for a new programming language were issued and four contractors were hired to develop their proposals under the names of Red (Intermetrics led by Benjamin Brosgol), Green (Honeywell, led by Jean Ichbiah), Blue (SofTech, led by John Goodenough) and Yellow (SRI International, led by Jay Spitzen). In April 1978, after public scrutiny, the Red and Green proposals passed to the next phase. In May 1979, the Green proposal, designed by Jean Ichbiah at Honeywell, was chosen and given the name Ada—after Augusta Ada King, Countess of Lovelace, usually known as Ada Lovelace. This proposal was influenced by the language LIS that Ichbiah and his group had developed in the 1970s. The preliminary Ada reference manual was published in ACM SIGPLAN Notices in June 1979. The Military Standard reference manual was approved on December 10, 1980 (Ada Lovelace's birthday), and given the number MIL-STD-1815 in honor of Ada Lovelace's birth year. In 1981, Tony Hoare took advantage of his Turing Award speech to criticize Ada for being overly complex and hence unreliable, but subsequently seemed to recant in the foreword he wrote for an Ada textbook.
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Ada attracted much attention from the programming community as a whole during its early days. Its backers and others predicted that it might become a dominant language for general purpose programming and not only defense-related work. Ichbiah publicly stated that within ten years, only two programming languages would remain: Ada and Lisp. Early Ada compilers struggled to implement the large, complex language, and both compile-time and run-time performance tended to be slow and tools primitive. Compiler vendors expended most of their efforts in passing the massive, language-conformance-testing, government-required Ada Compiler Validation Capability (ACVC) validation suite that was required in another novel feature of the Ada language effort.
The first validated Ada implementation was the NYU Ada/Ed translator, certified on April 11, 1983. NYU Ada/Ed is implemented in the high-level set language SETL. Several commercial companies began offering Ada compilers and associated development tools, including Alsys, TeleSoft, DDC-I, Advanced Computer Techniques, Tartan Laboratories, Irvine Compiler, TLD Systems, and Verdix. Computer manufacturers who had a significant business in the defense, aerospace, or related industries, also offered Ada compilers and tools on their platforms; these included Concurrent Computer Corporation, Cray Research, Inc., Digital Equipment Corporation, Harris Computer Systems, and Siemens Nixdorf Informationssysteme AG.
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In 1991, the US Department of Defense began to require the use of Ada (the "Ada mandate") for all software, though exceptions to this rule were often granted. The Department of Defense Ada mandate was effectively removed in 1997, as the DoD began to embrace commercial off-the-shelf (COTS) technology. Similar requirements existed in other NATO countries: Ada was required for NATO systems involving command and control and other functions, and Ada was the mandated or preferred language for defense-related applications in countries such as Sweden, Germany, and Canada.
By the late 1980s and early 1990s, Ada compilers had improved in performance, but there were still barriers to fully exploiting Ada's abilities, including a tasking model that was different from what most real-time programmers were used to.
Because of Ada's safety-critical support features, it is now used not only for military applications, but also in commercial projects where a software bug can have severe consequences, e.g., avionics and air traffic control, commercial rockets such as the Ariane 4 and 5, satellites and other space systems, railway transport and banking.
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For example, the Primary Flight Control System, the fly-by-wire system software in the Boeing 777, was written in Ada, as were the fly-by-wire systems for the aerodynamically unstable Eurofighter Typhoon, Saab Gripen, Lockheed Martin F-22 Raptor and the DFCS replacement flight control system for the Grumman F-14 Tomcat. The Canadian Automated Air Traffic System was written in 1 million lines of Ada (SLOC count). It featured advanced distributed processing, a distributed Ada database, and object-oriented design. Ada is also used in other air traffic systems, e.g., the UK's next-generation Interim Future Area Control Tools Support () air traffic control system is designed and implemented using SPARK Ada.
It is also used in the French TVM in-cab signalling system on the TGV high-speed rail system, and the metro suburban trains in Paris, London, Hong Kong and New York City.
The Ada 95 revision of the language went beyond the Steelman requirements, targeting general-purpose systems in addition to embedded ones, and adding features supporting object-oriented programming.
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Standardization.
Preliminary Ada can be found in ACM Sigplan Notices Vol 14, No 6, June 1979
Ada was first published in 1980 as an ANSI standard ANSI/MIL-STD 1815. As this very first version held many errors and inconsistencies , the revised edition was published in 1983 as ANSI/MIL-STD 1815A. Without any further changes, it became an ISO standard in 1987. This version of the language is commonly known as Ada 83, from the date of its adoption by ANSI, but is sometimes referred to also as Ada 87, from the date of its adoption by ISO. There is also a French translation; DIN translated it into German as DIN 66268 in 1988.
Ada 95, the joint ISO/IEC/ANSI standard ISO/IEC 8652:1995 was published in February 1995, making it the first ISO standard object-oriented programming language. To help with the standard revision and future acceptance, the US Air Force funded the development of the GNAT Compiler. Presently, the GNAT Compiler is part of the GNU Compiler Collection.
Work has continued on improving and updating the technical content of the Ada language. A Technical Corrigendum to Ada 95 was published in October 2001, and a major Amendment, ISO/IEC 8652:1995/Amd 1:2007 was published on March 9, 2007, commonly known as Ada 2005 because work on the new standard was finished that year.
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At the Ada-Europe 2012 conference in Stockholm, the Ada Resource Association (ARA) and Ada-Europe announced the completion of the design of the latest version of the Ada language and the submission of the reference manual to the ISO/IEC JTC 1/SC 22/WG 9 of the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC) for approval. ISO/IEC 8652:2012(see Ada 2012 RM) was published in December 2012, known as Ada 2012. A technical corrigendum, ISO/IEC 8652:2012/COR 1:2016, was published (see RM 2012 with TC 1).
On May 2, 2023, the Ada community saw the formal approval of publication of the Ada 2022 edition of the programming language standard.
Despite the names Ada 83, 95 etc., legally there is only one Ada standard, the one of the last ISO/IEC standard: with the acceptance of a new standard version, the previous one becomes withdrawn. The other names are just informal ones referencing a certain edition.
Other related standards include ISO/IEC 8651-3:1988 "Information processing systems—Computer graphics—Graphical Kernel System (GKS) language bindings—Part 3: Ada".
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Language constructs.
Ada is an ALGOL-like programming language featuring control structures with reserved words such as "if", "then", "else", "while", "for", and so on. However, Ada also has many data structuring facilities and other abstractions which were not included in the original ALGOL 60, such as type definitions, records, pointers, enumerations. Such constructs were in part inherited from or inspired by Pascal.
"Hello, world!" in Ada.
A common example of a language's syntax is the "Hello, World!" program:
with Ada.Text_IO;
procedure Hello is
begin
Ada.Text_IO.Put_Line ("Hello, world!");
end Hello;
This program can be compiled by using the freely available open source compiler GNAT, by executing
gnatmake hello.adb
Data types.
Ada's type system is not based on a set of predefined primitive types but allows users to declare their own types. This declaration in turn is not based on the internal representation of the type but on describing the goal which should be achieved. This allows the compiler to determine a suitable memory size for the type, and to check for violations of the type definition at compile time and run time (i.e., range violations, buffer overruns, type consistency, etc.). Ada supports numerical types defined by a range, modulo types, aggregate types (records and arrays), and enumeration types. Access types define a reference to an instance of a specified type; untyped pointers are not permitted.
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Special types provided by the language are task types and protected types.
For example, a date might be represented as:
type Day_type is range 1 .. 31;
type Month_type is range 1 .. 12;
type Year_type is range 1800 .. 2100;
type Hours is mod 24;
type Weekday is (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday);
type Date is
record
Day : Day_type;
Month : Month_type;
Year : Year_type;
end record;
Important to note: Day_type, Month_type, Year_type, Hours are incompatible types, meaning that for instance the following expression is illegal:
Today: Day_type := 4;
Current_Month: Month_type := 10;
... Today + Current_Month ... -- illegal
The predefined plus-operator can only add values of the same type, so the expression is illegal.
Types can be refined by declaring subtypes:
subtype Working_Hours is Hours range 0 .. 12; -- at most 12 Hours to work a day
subtype Working_Day is Weekday range Monday .. Friday; -- Days to work
Work_Load: constant array(Working_Day) of Working_Hours -- implicit type declaration
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:= (Friday => 6, Monday => 4, others => 10); -- lookup table for working hours with initialization
Types can have modifiers such as "limited, abstract, private" etc. Private types do not show their inner structure; objects of limited types cannot be copied. Ada 95 adds further features for object-oriented extension of types.
Control structures.
Ada is a structured programming language, meaning that the flow of control is structured into standard statements. All standard constructs and deep-level early exit are supported, so the use of the also supported "go to" commands is seldom needed.
-- while a is not equal to b, loop.
while a /= b loop
Ada.Text_IO.Put_Line ("Waiting");
end loop;
if a > b then
Ada.Text_IO.Put_Line ("Condition met");
else
Ada.Text_IO.Put_Line ("Condition not met");
end if;
for i in 1 .. 10 loop
Ada.Text_IO.Put ("Iteration: ");
Ada.Text_IO.Put (i);
Ada.Text_IO.Put_Line;
end loop;
loop
a := a + 1;
exit when a = 10;
end loop;
case i is
when 0 => Ada.Text_IO.Put ("zero");
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when 1 => Ada.Text_IO.Put ("one");
when 2 => Ada.Text_IO.Put ("two");
-- case statements have to cover all possible cases:
when others => Ada.Text_IO.Put ("none of the above");
end case;
for aWeekday in Weekday'Range loop -- loop over an enumeration
Put_Line ( Weekday'Image(aWeekday) ); -- output string representation of an enumeration
if aWeekday in Working_Day then -- check of a subtype of an enumeration
Put_Line ( " to work for " &
Working_Hours'Image (Work_Load(aWeekday)) ); -- access into a lookup table
end if;
end loop;
Packages, procedures and functions.
Among the parts of an Ada program are packages, procedures and functions.
Functions differ from procedures in that they must return a value. Function calls cannot be used "as a statement", and their result must be assigned to a variable. However, since Ada 2012, functions are not required to be pure and may mutate their suitably declared parameters or the global state.
Example:
Package specification (example.ads)
package Example is
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type Number is range 1 .. 11;
procedure Print_and_Increment (j: in out Number);
end Example;
Package body (example.adb)
with Ada.Text_IO;
package body Example is
i : Number := Number'First;
procedure Print_and_Increment (j: in out Number) is
function Next (k: in Number) return Number is
begin
return k + 1;
end Next;
begin
Ada.Text_IO.Put_Line ( "The total is: " & Number'Image(j) );
j := Next (j);
end Print_and_Increment;
-- package initialization executed when the package is elaborated
begin
while i < Number'Last loop
Print_and_Increment (i);
end loop;
end Example;
This program can be compiled, e.g., by using the freely available open-source compiler GNAT, by executing
gnatmake -z example.adb
Packages, procedures and functions can nest to any depth, and each can also be the logical outermost block.
Each package, procedure or function can have its own declarations of constants, types, variables, and other procedures, functions and packages, which can be declared in any order.
Pragmas.
A pragma is a compiler directive that conveys information to the compiler to allow specific manipulating of compiled output. Certain pragmas are built into the language, while others are implementation-specific.
Examples of common usage of compiler pragmas would be to disable certain features, such as run-time type checking or array subscript boundary checking, or to instruct the compiler to insert object code instead of a function call (as C/C++ does with inline functions).
References.
Rationale.
These documents have been published in various forms, including print.
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Alfonso Cuarón
Alfonso Cuarón Orozco ( ; ; born 28 November 1961) is a Mexican filmmaker. His accolades include four Academy Awards, three Golden Globe Awards and seven BAFTA Awards.
Cuarón made his feature film debut with the romantic comedy "Sólo con tu pareja" (1991), and directed the film adaptations "A Little Princess" (1995), and "Great Expectations" (1998). His breakthrough came with the coming-of-age film "Y tu mamá también" (2001) which earned him a nomination for the Academy Award for Best Original Screenplay. He gained greater prominence for directing the fantasy film "Harry Potter and the Prisoner of Azkaban" (2004), the dystopian drama "Children of Men" (2006), the science fiction drama "Gravity" (2013), and the semi-autobiographical drama "Roma" (2018). The latter two won him Academy Awards for Best Director. He also won Best Film Editing for "Gravity" and Best Cinematography for "Roma".
Early life and education.
Cuarón was born in Mexico City, the son of Alfredo Cuarón, a doctor specializing in nuclear medicine, and Cristina Orozco, a pharmaceutical biochemist. He has a sister Christina, and two brothers; Carlos, also a filmmaker, and Alfredo, a conservation biologist. Cuarón studied philosophy at the National Autonomous University of Mexico and filmmaking at the Centro Universitario de Estudios Cinematográficos, a school within the same university. There he met the director Carlos Marcovich and cinematographer Emmanuel Lubezki, and they made what would be his first short film, "Vengeance Is Mine".
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Career.
1990–1999: Rise to prominence.
Cuarón began working on television in Mexico, first as a technician and then as a director. His television work led to assignments as an assistant director for several film productions including "La Gran Fiesta" (1985), "" (1987) and "Romero" (1989). In 1991 he landed his first big-screen directorial assignment, "Sólo con tu pareja", a sex comedy about a womanizing businessman (played by Daniel Giménez Cacho) who, after having sex with an attractive nurse, is fooled into believing he's contracted AIDS. In addition to writing, producing and directing, Cuarón co-edited the film with Luis Patlán. The film, which also starred cabaret singer Astrid Hadad and model/actress Claudia Ramírez (with whom Cuarón was linked between 1989 and 1993) was a big hit in Mexico. After this success, director Sydney Pollack hired Cuarón to direct an episode of "Fallen Angels", a series of neo-noir stories produced for the Showtime premium cable network in 1993; other directors who worked on the series included Steven Soderbergh, Jonathan Kaplan, Peter Bogdanovich, and Tom Hanks. The episode was entitled, "Murder, Obliquely" (1993) starring Laura Dern, Alan Rickman, and Diane Lane.
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In 1995, Cuarón released his first feature film produced in the United States, "A Little Princess", an adaptation of Frances Hodgson Burnett's classic 1905 novel of the same name. The film received critical acclaim with Janet Maslin of "The New York Times" declaring, "[the film] is a bright, beautiful and enchantingly childlike vision", one that "draw[s] its audience into the wittily heightened reality of a fairy tale" and "takes enough liberties to re-invent rather than embalm Miss Burnett's assiduously beloved story". The film went on to receive two Academy Award nominations for Best Cinematography and Best Production Design. Cuarón's next feature was also a literary adaptation, a modernized version of Charles Dickens's "Great Expectations" starring Ethan Hawke, Gwyneth Paltrow, and Robert De Niro. The film received mixed reviews to negative reviews. Russell Smith of "The Austin Chronicle" did however praise the film writing, ". What's truly intriguing about this film, though, is the stylishness with which Cuaron (A Little Princess) reinvents Dickens' hoary, often-remade tale. This "Great Expectations" has a seductive, enchanting feel that has nothing to do with sweet, gauzy sentiments or calculatedly “magical” Hollywood imagery".
2000–2009: Career breakthrough and success.
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In 2001, Cuarón found himself returning to Mexico with a Spanish-speaking cast to film "Y tu mamá también", starring Gael García Bernal, Diego Luna and Maribel Verdú. It was a provocative and controversial road comedy about two sexually obsessed teenagers who take an extended road trip with an attractive married woman who is much older than they. The film's open portrayal of sexuality and frequent rude humor, as well as the politically and socially relevant asides, made the film an international hit and a major success with critics. The film was distributed through IFC in America allowing the film to collect $13.8 million in the United States, unparalleled at the time for Latin American films. Critic Roger Ebert of "The Chicago Sun-Times" wrote, "It is clear Cuaron is a gifted director, and here he does his best work to date." Cuarón shared an Academy Award nomination for Best Original Screenplay with co-writer and brother Carlos Cuarón.
In 2004, Cuarón directed the third film in the successful "Harry Potter" series, "Harry Potter and the Prisoner of Azkaban". Cuarón faced criticism at the time from some "Harry Potter" fans for his approach to the film, notably its tendency to take more creative liberties with the source material than its predecessors. However, author J. K. Rowling, who had seen and loved Cuarón's film "Y tu mamá también", said that it was her personal favorite from the series so far. Critically, the film was also better received than the first two installments, with some critics remarking its new tone and for being the first "Harry Potter" film to truly capture the essence of the novels. It has been subsequently rated by audience polls and critics as the best of the movie franchise series. The film earned two Academy Award nominations for Best Visual Effects and Best Original Score for John Williams.
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In 2006, Cuarón's feature "Children of Men", an adaptation of the P. D. James novel starring Clive Owen, Julianne Moore, and Michael Caine, received wide critical acclaim including three Academy Award nominations. Cuarón himself received two nominations for his work on the film, in Best Film Editing (with Alex Rodríguez) and Best Adapted Screenplay (with several collaborators).
He created the production and distribution company Esperanto Filmoj ("Esperanto Films", named because of his support for the international language Esperanto), which has credits in the films "Duck Season", "Pan's Labyrinth", and "Gravity". Cuarón also directed the controversial public service announcement "I Am Autism" (2009) for Autism Speaks that was criticized by disability rights groups for its negative portrayal of autism.
2010–present: Awards recognition.
In 2010, Cuarón began to develop the film "Gravity", a drama set in space. He was joined by producer David Heyman, with whom Cuarón worked on "Harry Potter and the Prisoner of Azkaban". Starring Sandra Bullock and George Clooney, the film opened the 70th Venice International Film Festival in August. The film was then released in America in October 2013. The film became a financial success, earning 723.2 million at the box office against a budget of 130 million. The film also received many awards nominations. For the film, he received the Golden Globe Award in the category of Best Director. The film received ten Academy Award nominations, including Best Picture and Best Director. Cuarón won for Best Directing, becoming the first Latin American to win the award, while he and Mark Sanger received the award for Best Film Editing.
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In 2013, Cuarón created "Believe", a science fiction/fantasy/adventure series that was broadcast as part of the 2013–14 United States network television schedule on NBC as a mid-season entry. The series was created by Cuarón for Bad Robot and Warner Bros. Television. In 2014, "Time" placed him in its list of "100 Most Influential People in the World" – Pioneers.
In May 2015, Cuarón was announced as the president of the jury for the 72nd Venice International Film Festival.
Production began in fall 2016 for Cuarón's eighth film, "Roma", a tale of a housekeeper for a middle class Mexican family in 1970s Mexico City, based on the life of his family's longtime maid, Liboria Rodríguez. The project was produced by Cuarón, Gabriela Rodríguez and Nicolás Celis and starred Yalitza Aparicio and Marina de Tavira both of whom received Oscar nominations. The film debuted at the 75th Venice International Film Festival, where it won the Golden Lion, and was distributed to select Mexican and American theaters before its online release on Netflix. "Roma" was highly acclaimed upon release; among its accolades are two Golden Globes (Golden Globe Award for Best Foreign Language Film and Best Director for Cuarón) and three Academy Awards (Best Director, Best Foreign Language Film, and Best Cinematography for Cuarón) out of a leading ten nominations.
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In 2019, Cuaron signed an overall TV deal at Apple. His first series for Apple was the psychological thriller "Disclaimer", starring Cate Blanchett, Kevin Kline, Louis Partridge and Sasha Baron Cohen; it is based on the eponymous novel by Renée Knight, with Cuaron writing and directing every episode.
Style.
Cuaron's style is a mix of several mainstream Hollywood conventions while breaking from that dominant influence by taking an unorthodox approach that uses voiceover narration and by unconventionally lengthy shots. These longer cuts, narration, and often, moving cameras are more typical of documentary film.
In his first feature film the average shot length is around six seconds, and ten years later for "Y Tu Mama Tambien" the average increased to 19.6 seconds. "The Prisoner of Azkaban" had an average of seconds, while the subsequent "Children of Men" had an extraordinary average of 16 seconds between cuts. A typical Hollywood movie cuts every two seconds. Cuarón's career shows mainstream Hollywood influences, which has spilled over to less mainstream films made outside of Hollywood. "Children of Men" was influenced by disaster and science fiction movie conventions. "The Prisoner of Azkaban" was a continuation of Cuarón's take on the coming-of-age genre after "Y, Tu Mama Tambien". That film is in the form of an American road movie, along with teen movie elements. Voice-over narration adds a documentary feel. The narration, interjected by a non-diagetic voice not belonging to any character, highlights the socioeconomic state of not only the main characters, but also minor characters who otherwise seem irrelevant to the overall narrative.
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Themes.
As mentioned above, the voice-over narration in "Y Tu Mama Tambien" contains political messages. In the aforementioned film Cuarón tackles Mexican identity and sovereignty. With the backdrop of the 1990s and the advent of NAFTA and neoliberalism in Mexico, Cuarón critiques Mexico for the path they are heading towards a globalized economy and world. Cuarón also addresses Mexican history such as colonialism and the long unfulfilled promises of the Mexican Revolution of 1910. Using the same film as an example the narrator states that a new political party is in power, but hints that no real change will come about. This is also supported with one of the main characters, Julio, sharing a last name with the Mexican Revolutionary Emiliano Zapata, yet the name does not push Julio into action or in other words he lacks the initiative and interest in the country. These same themes of identity and history, particularly of Mexico, were first addressed in his first feature film "Solo con tu pareja". In both films Cuarón uses allegory that ties into a national identity and/or history. On top of these themes he also tackles class, but that can be considered a subcategory of economics or politics in which he already grapples with.
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Personal life.
Cuarón's first marriage was to Mariana Elizondo with whom he has a son, Jonás Cuarón, born in 1981. Jonás is also a film director, known for "Year of the Nail" and "Desierto". Alfonso's second marriage, from 2001 to 2008, was to Italian actress and freelance journalist Annalisa Bugliani, with whom he has two children.
He has publicly shown his fascination for the Esperanto language and his support for the Esperanto movement. He called his production company Esperanto Filmoj. In October 2023, Cuarón signed an open letter from artists to US President Joe Biden calling for a ceasefire of Israeli bombardment in Gaza.
Cuarón is a vegetarian and has been living in London since 2000.
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Arianism
Arianism (, ) is a Christological doctrine which rejects the traditional notion of the Trinity and considers Jesus to be a creation of God, and therefore distinct from God. It is named after its major proponent, Arius (). It is considered heretical by most modern mainstream branches of Christianity. It is held by a minority of modern denominations, although some of these denominations hold related doctrines such as Socinianism, and some shy away from use of the term Arian due to the term's historically negative connotations. Modern mainstream denominations sometimes connected to the teaching include Jehovah's Witnesses, some individual churches within the Churches of Christ (including the movement's founder Barton W. Stone), as well as some Hebrew Roots Christians and Messianic Jews (although many Messianic Jews also follow Nicene Christianity).
It is first attributed to Arius (), a Christian presbyter who preached and studied in Alexandria, Egypt, although it developed out of various pre-existing strands of Christianity which differed from later Nicene Christianity in their view of Christology. Arian theology holds that Jesus Christ is the Son of God, who was begotten by God the Father with the difference that the Son of God did not always exist but was begotten/made before time by God the Father; therefore, Jesus was not coeternal with God the Father, but nonetheless Jesus began to exist outside time.
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Arius' trinitarian theology, later given an extreme form by Aetius and his disciple Eunomius and called anomoean ('dissimilar'), asserts a total dissimilarity between the Son and the Father. Arianism holds that the Son is distinct from the Father and therefore subordinate to him. The term "Arian" is derived from the name Arius; it was not what the followers of Arius' teachings called themselves, but rather a term used by outsiders. The nature of Arius's and his supporters' teachings were opposed to the theological doctrines held by Homoousian Christians regarding the nature of the Trinity and the nature of Christ. Homoousianism and Arianism were contending interpretations of Jesus's divinity, both based upon the trinitarian theological orthodoxy of the time.
Homoousianism was formally affirmed by the first two ecumenical councils; since then, Arianism has been condemned as "the heresy or sect of Arius". Trinitarian (Homoousian) doctrines were vigorously upheld by Patriarch Athanasius of Alexandria, who insisted that Jesus (God the Son) was "same in being" or "same in essence" with God the Father. Arius dissented: "If the Father begat the Son, then he who was begotten had a beginning in existence, and from this it follows there was a time when the Son was not." The ecumenical First Council of Nicaea of 325 declared Arianism to be a heresy. According to Everett Ferguson, "The great majority of Christians had no clear views about the nature of the Trinity and they did not understand what was at stake in the issues that surrounded it."
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Arianism is also used to refer to other nontrinitarian theological systems of the 4th century, which regarded Jesus Christ—the Son of God, the Logos—as either a begotten creature of a similar or different substance to that of the Father, but not identical (as Homoiousian and Anomoeanism) or as neither uncreated nor created in the sense other beings are created (as in semi-Arianism).
Origin.
Some early Christians whose beliefs would have fallen under 'orthodoxy' in the third and fourth centuries denied the eternal generation of the Son; they viewed the Son as having been begotten in time. These include Tertullian and Justin Martyr. Tertullian is considered a pre-Arian. Among the other church fathers, Origen was accused of Arianism for using terms like "second God", and Patriarch Dionysius of Alexandria was denounced at Rome for saying that Son is a work and creature of God (i.e., a created being). However, the subordinationism of Origen is not identical to Arianism, and it has been generally viewed as closer to the Nicene-Constantinopolitan view of the Trinity.
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Controversy over Arianism arose in the late 3rd century and persisted throughout most of the 4th century. It involved most church members—from simple believers, priests, and monks to bishops, emperors, and members of Rome's imperial family. Two Roman emperors, Constantius II and Valens, became Arians or semi-Arians, as did prominent Gothic, Vandal, and Lombard warlords both before and after the fall of the Western Roman Empire. The antipopes Felix II and Ursinus were Arian, and Pope Liberius was forced to sign the Arian Creed of Sirmium of 357—though the letter says he willingly agreed with Arianism. Such a deep controversy within the early Church during this period could not have materialized without significant historical influences providing a basis for the Arian doctrines.
Arius had been a pupil of Lucian of Antioch at Lucian's private academy in Antioch and inherited from him a modified form of the teachings of Paul of Samosata. Arius taught that God the Father and the Son of God did not always exist together eternally.
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Beliefs.
Little of Arius's own work survives except in quotations selected for polemical purposes by his opponents, and there is no certainty about what theological and philosophical traditions formed his thought. The influence from the One of Neoplatonism was widespread throughout the Eastern Roman Empire, and this influenced Arius.
Arius's basic premise is that only God is independent of existing. Since the Son is dependent, he must, therefore, be called a creature. Arians put forward a question for their belief: "Has God birthed Jesus willingly or unwillingly?" This question was used to argue that Jesus is dependent for his existence since Jesus exists only because God wants him to be.
Arianism taught that the "Logos" was a divine being created by God the Father before the world's creation, serving as the medium for creation, and that the Son of God is subordinate to the Father. The concept of the "Logos" refers to an inner attribute of God associated with wisdom. Jesus is identified as the "Logos" due to a supposed resemblance to this inner aspect of God’s nature.
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A verse from Proverbs was used, according to Arianism, the creation of the Son by God, "The Lord created me at the beginning of his work." Therefore, they posited, the Son was rather the very first and the most perfect of God's creatures, and he was called "God" only by the Father's permission and power. The term "Son" is ambiguous, as Arians use adoptionist theology to support the belief that Jesus was created "ex nihilo" by the Father.
Arians do not believe in the traditional doctrine of the Trinity. The letter of the Arian bishop Auxentius of Durostorum regarding the Arian missionary Ulfilas (–383) gives an overview of Arian beliefs. Ulfilas, ordained by Arian bishop Eusebius of Nicomedia, became a missionary to the Goths and believed that God the Father, the "unbegotten" Almighty, is the only true God. According to Auxentius, Ulfilas believed the Son of God, Jesus, the "only-begotten god", was begotten before time began. The Holy Spirit, he wrote, is the illuminating and sanctifying power of God. Using 1 Corinthians 8:5–6 as a proof text:
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The creed of Ulfilas, which concludes the letter mentioned above, distinguishes God the Father ("unbegotten"), who is the only true God, from the Son of God ("only-begotten") and the Holy Spirit, the illuminating and sanctifying power, which is neither God the Father nor the God the Son:
A letter from Arius to the Arian Eusebius of Nicomedia (died 341) states the core beliefs of the Arians:
Principally, the dispute between Trinitarianism and Arianism was about two questions:
For Constantine, these were minor theological points that stood in the way of uniting the Empire, but for the theologians, it was of huge importance; for them, it was a matter of salvation.
For the theologians of the 19th century, it was already obvious that, in fact, Arius and Alexander/Athanasius did not have much to quarrel about; the difference between their views was very small, and the end of the fight was by no means clear during their quarrel, both Arius and Athanasius suffering a great deal for their own views. Arius was the father of Homoiousianism, and Alexander was the father of Homoousianism, which Athanasius championed. For those theologians, it was clear that Arius, Alexander, and Athanasius were far from a true doctrine of the Trinity, which developed later, historically speaking.
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Guido M. Berndt and Roland Steinacher state clearly that the beliefs of Arius were acceptable ("not especially unusual") to a huge number of orthodox clergy; this is the reason why such a major conflict was able to develop inside the Church since Arius's theology received widespread sympathy (or at least was not considered to be overly controversial) and could not be dismissed outright as individual heresy.
Homoian Arianism.
Arianism had several different variants, including Eunomianism and Homoian Arianism. Homoian Arianism is associated with Acacius and Eudoxius. Homoian Arianism avoided the use of the word "ousia" to describe the relation of Father to Son, and described these as "like" each other. Hanson lists twelve creeds that reflect the Homoian faith:
Struggles with orthodoxy.
First Council of Nicaea.
In 321, Arius was denounced by a synod at Alexandria for teaching a heterodox view of the relationship of Jesus to God the Father. Because Arius and his followers had great influence in the schools of Alexandria—counterparts to modern universities or seminaries—their theological views spread, especially in the eastern Mediterranean.
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By 325, the controversy had become significant enough that the Emperor Constantine called an assembly of bishops, the First Council of Nicaea, which condemned Arius's doctrine and formulated the original Nicene Creed of 325. The Nicene Creed's central term, used to describe the relationship between the Father and the Son, is Homoousios (), or Consubstantiality, meaning "of the same substance" or "of one being". The Athanasian Creed is less often used but is a more overtly anti-Arian statement on the Trinity.
The focus of the Council of Nicaea was the nature of the Son of God and his precise relationship to God the Father. (See Paul of Samosata and the Synods of Antioch.) Arius taught that Jesus Christ was divine or holy and was sent to Earth for the salvation of mankind, but that Jesus Christ was not equal to God the Father (infinite, primordial origin) in rank, and that God the Father and the Son of God were not equal to the Holy Spirit. Under Arianism, Christ was instead not consubstantial with God the Father since both the Father and the Son under Arius were made of "like" essence or being (see homoiousia) but not of the same essence or being (see homoousia).
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In the Arian view, God the Father is a deity and is divine; the Son of God is not a deity, but is still divine. God the Father sent Jesus to earth for salvation of mankind. Ousia is essence or being, in Eastern Christianity, and is the aspect of God that is completely incomprehensible to mankind and human perception. It is all that subsists by itself and which has not its being in another, God the Father and God the Son and God the Holy Spirit all being uncreated.
According to the teaching of Arius, the preexistent Logos and thus the incarnate Jesus Christ was a begotten being; only the Son was directly begotten by God the Father, before ages, but was of a distinct, though similar, essence or substance from the Creator. His opponents argued that this would make Jesus less than God and that this was heretical. Much of the distinction between the differing factions was over the phrasing that Christ expressed in the New Testament to express submission to God the Father. The theological term for this submission is kenosis. This ecumenical council declared that Jesus Christ was true God, co-eternal and consubstantial (i.e., of the same substance) with God the Father.
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Constantine is believed to have exiled those who refused to accept the Nicaean Creed—Arius himself, the deacon Euzoios, and the Libyan bishops Theonas of Marmarica and Secundus of Ptolemais, along with the bishops who signed the creed but refused to join in condemnation of Arius, Eusebius of Nicomedia and Theognis of Nicaea. The emperor also ordered all copies of the "Thalia", the book in which Arius had expressed his teachings, to be burned. However, there is no evidence that his son and ultimate successor, Constantius II, a Semi-Arian Christian, was exiled.
Although he was committed to maintaining what the Great Church had defined at Nicaea, Constantine was also bent on pacifying the situation and eventually became more lenient toward those condemned and exiled at the council. First, he allowed Eusebius of Nicomedia, who was a protégé of his sister, and Theognis to return once they had signed an ambiguous statement of faith. The two, and other friends of Arius, worked for Arius's rehabilitation.
At the First Synod of Tyre in AD 335, they brought accusations against Athanasius, now bishop of Alexandria, the primary opponent of Arius. After this, Constantine had Athanasius banished since he considered him an impediment to reconciliation. In the same year, the Synod of Jerusalem under Constantine's direction readmitted Arius to communion in 336. Arius died on the way to this event in Constantinople. Some scholars suggest that Arius may have been poisoned by his opponents. Eusebius and Theognis remained in the Emperor's favor; when Constantine -who had been a catechumen much of his adult life- accepted baptism on his deathbed, it was from Eusebius of Nicomedia.
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Condemnation by the Council of Nicaea.
Emperor Constantine the Great summoned the First Council of Nicaea, which defined the dogmatic fundaments of Christianity; these definitions served to rebut the questions posed by Arians. Since Arius was not a bishop, he was not allowed to sit on the council, and it was Eusebius of Nicomedia who spoke for him and the position he represented. All the bishops who were there were in agreement with the major theological points of the proto-orthodoxy, since at that time all other forms of Christianity "had by this time already been displaced, suppressed, reformed, or destroyed".
Although the proto-orthodox won the previous disputes, due to the more precise defining of orthodoxy, they were vanquished with their own weapons, ultimately being declared heretics, not because they would have fought against ideas regarded as theologically correct, but because their positions lacked the precision and refinement needed by the fusion of several contradictory theses accepted at the same time by later orthodox theologians.
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Of the roughly 300 bishops in attendance at the Council of Nicaea, two bishops did not sign the Nicene Creed that condemned Arianism. Constantine the Great also ordered a penalty of death for those who refused to surrender the Arian writings:
Ten years after the Council of Nicaea, Constantine the Great, who was himself later baptized by the Arian bishop Eusebius of Nicomedia in 337 AD, convened another gathering of church leaders at the regional First Synod of Tyre in 335, attended by 310 bishops, to address various charges mounted against Athanasius by his detractors, such as "murder, illegal taxation, sorcery, and treason", following his refusal to readmit Arius into fellowship. Athanasius was exiled to Trier (in modern Germany) following his conviction at Tyre of conspiracy, and Arius was, effectively, exonerated.
Athanasius eventually returned to Alexandria in 346, after the deaths of both Arius and Constantine. Though Arianism had spread, Athanasius and other Nicene Christian church leaders crusaded against Arian theology, and Arius was anathemised and condemned as a heretic once more at the ecumenical First Council of Constantinople of 381, attended by 150 bishops. The Roman Emperors Constantius II (337–361) and Valens (364–378) were Arians or Semi-Arians, as was the first King of Italy, Odoacer (433?–493), and the Lombards were also Arians or Semi-Arians until the 7th century. The ruling elite of Visigothic Spain was Arian until 589. Many Goths adopted Arian beliefs upon their conversion to Christianity. The Vandals actively spread Arianism in North Africa.
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Aftermath of Nicaea.
The First Council of Nicaea did not end the controversy, as many bishops of the Eastern provinces disputed the "homoousios", the central term of the Nicene Creed, as it had been used by Paul of Samosata, who had advocated a monarchianist Christology. Both the man and his teaching, including the term "homoousios", had been condemned by the Synods of Antioch in 269.
Hence, after Constantine's death in 337, open dispute resumed again. Constantine's son Constantius II, who had become emperor of the eastern part of the Roman Empire, actually encouraged the Arians and set out to reverse the Nicene Creed. His advisor in these affairs was Eusebius of Nicomedia, who had already at the Council of Nicaea been the head of the Arian party, and was made the bishop of Constantinople.
Constantius used his power to exile bishops adhering to the Nicene Creed, especially St Athanasius of Alexandria, who fled to Rome. In 355 Constantius became the sole Roman emperor and extended his pro-Arian policy toward the western provinces, frequently using force to push through his creed, even exiling Pope Liberius and installing Antipope Felix II.
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The Third Council of Sirmium in 357 was the high point of Arianism. The Seventh Arian Confession (Second Sirmium Confession) held that both "homoousios" (of one substance) and "homoiousios" (of similar substance) were unbiblical and that the Father is greater than the Son. This confession was later known as the Blasphemy of Sirmium.
But since many persons are disturbed by questions concerning what is called in Latin "substantia", but in Greek "ousia", that is, to make it understood more exactly, as to 'coessential,' or what is called, 'like-in-essence,' there ought to be no mention of any of these at all, nor exposition of them in the Church, for this reason and for this consideration, that in divine Scripture nothing is written about them, and that they are above men's knowledge and above men's understanding;
As debates raged in an attempt to come up with a new formula, three camps evolved among the opponents of the Nicene Creed. The first group mainly opposed the Nicene terminology and preferred the term "homoiousios" (alike in substance) to the Nicene "homoousios", while they rejected Arius and his teaching and accepted the equality and co-eternality of the persons of the Trinity. Because of this centrist position, and despite their rejection of Arius, they were called "Semi-Arians" by their opponents.
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The second group also avoided invoking the name of Arius, but in large part followed Arius's teachings and, in another attempted compromise wording, described the Son as being like ("homoios") the Father. A third group explicitly called upon Arius and described the Son as unlike ("anhomoios") the Father. Constantius wavered in his support between the first and the second party, while harshly persecuting the third.
Epiphanius of Salamis labeled the party of Basil of Ancyra in 358 "Semi-Arianism". This is considered unfair by Kelly who states that some members of the group were virtually orthodox from the start but disliked the adjective "homoousios" while others had moved in that direction after the out-and-out Arians had come into the open.
The debates among these groups resulted in numerous synods, among them the Council of Serdica in 343, the Fourth Council of Sirmium in 358 and the double Council of Rimini and Seleucia in 359, and no fewer than fourteen further creed formulas between 340 and 360. This lead the pagan observer Ammianus Marcellinus to comment sarcastically: "The highways were covered with galloping bishops." None of these attempts was acceptable to the defenders of Nicene orthodoxy. Writing about the latter councils, Saint Jerome remarked that the world "awoke with a groan to find itself Arian."
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After Constantius's death in 361, his successor Julian, a devotee of Rome's pagan gods, declared that he would no longer attempt to favor one church faction over another, and allowed all exiled bishops to return. This increased dissension among Nicene Christians. The emperor Valens, however, revived Constantius's policy and supported the "Homoian" party, exiling bishops and often using force. During this persecution many bishops were exiled to the other ends of the Roman Empire, e.g., Saint Hilary of Poitiers to the eastern provinces. These contacts and their common plight led to a rapprochement between the western supporters of the Nicene Creed and the "homoousios" and the eastern Semi-Arians.
Council of Constantinople.
It was not until the co-reigns of Gratian and Theodosius that Arianism was effectively wiped out among the ruling class and elite of the Eastern Empire. Valens died in the Battle of Adrianople in 378 and was succeeded by Theodosius I, who adhered to the Nicene Creed. This allowed for settling the dispute. Theodosius's wife St Flacilla was instrumental in his campaign to end Arianism.
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Two days after Theodosius arrived in Constantinople, 24 November 380, he expelled the Arian bishop, Demophilus of Constantinople, and surrendered the churches of that city to Gregory of Nazianzus, the Homoiousian leader of the rather small Nicene community there, an act which provoked rioting. Theodosius had just been baptized, by bishop Acholius of Thessalonica, during a severe illness, as was common in the early Christian world. In February he and Gratian had published an edict that all their subjects should profess the faith of the bishops of Rome and Alexandria (i.e., the Nicene faith), or be handed over for punishment for not doing so.
Although much of the church hierarchy in the East had opposed the Nicene Creed in the decades leading up to Theodosius's accession, he managed to achieve unity on the basis of the Nicene Creed. In 381, at the Second Ecumenical Council in Constantinople, a group of mainly Eastern bishops assembled and accepted the Nicene Creed of 381, which was supplemented in regard to the Holy Spirit, as well as some other changes: see Comparison of Nicene Creeds of 325 and 381. This is generally considered the end of the dispute about the Trinity and the end of Arianism among the Roman, non-Germanic peoples.
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Among medieval Germanic tribes.
During the time of Arianism's flowering in Constantinople, the Gothic convert and Arian bishop Ulfilas (later the subject of the letter of Auxentius cited above) was sent as a missionary to the Gothic tribes across the Danube, a mission favored for political reasons by the Emperor Constantius II. The Homoians in the Danubian provinces played a major role in the conversion of the Goths to Arianism.
Ulfilas's translation of the Bible into Gothic language and his initial success in converting the Goths to Arianism was strengthened by later events. The conversion of Goths led to a widespread diffusion of Arianism among other Germanic tribes as well, the Vandals, Langobards, Svevi, and Burgundians. When the Germanic peoples entered the provinces of the Western Roman Empire and began founding their own kingdoms there, most of them were Arian Christians.
The conflict in the 4th century had seen Arian and Nicene factions struggling for control of Western Europe. In contrast, among the Arian German kingdoms established in the collapsing Western Empire in the 5th century, there existed entirely separate Arian and Nicene Churches with parallel hierarchies, each serving different sets of believers. The Germanic elites were Arians, and the Romance-majority population was Nicene.
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The Arian Germanic tribes were generally tolerant towards Nicene Christians and other religious minorities, including the Jews.
The apparent resurgence of Arianism after Nicaea was more an anti-Nicene reaction exploited by Arian sympathizers than a pro-Arian development. By the end of the 4th century it had surrendered its remaining ground to Trinitarianism. In Western Europe, Arianism, which had been taught by Ulfilas, the Arian missionary to the Germanic tribes, was dominant among the Goths, Langobards and Vandals. By the 8th century, it had ceased to be the tribes' mainstream belief as the tribal rulers gradually came to adopt Nicene orthodoxy. This trend began in 496 with Clovis I of the Franks, then Reccared I of the Visigoths in 587 and Aripert I of the Lombards in 653.
The Franks and the Anglo-Saxons were unlike the other Germanic peoples in that they entered the Western Roman Empire as Pagans and were converted to Chalcedonian Christianity, led by their kings, Clovis I of the Franks, and Æthelberht of Kent and others in Britain. See also Christianity in Gaul and Christianisation of Anglo-Saxon England.
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The remaining tribes – the Vandals and the Ostrogoths – did not convert as a people nor did they maintain territorial cohesion. Having been militarily defeated by the armies of Emperor Justinian I, the remnants were dispersed to the fringes of the empire and became lost to history. The Vandalic War of 533–534 dispersed the defeated Vandals. Following their final defeat at the Battle of Mons Lactarius in 553, the Ostrogoths went back north and re-settled in south Austria.
From the 5th to the 7th century.
Much of south-eastern Europe and central Europe, including many of the Goths and Vandals respectively, had embraced Arianism (the Visigoths converted to Arian Christianity in 376 through their bishop Wulfila), which led to Arianism being a religious factor in various wars in the Roman Empire.
In the west, organized Arianism survived in North Africa, in Hispania, and parts of Italy until it was suppressed in the 6th and 7th centuries. Visigothic Spain converted to Nicene Christianity through their king Reccared I at the Third Council of Toledo in 589. Grimoald, King of the Lombards (662–671), and his young son and successor Garibald (671), were the last Arian kings in Europe.
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From the 16th to the 19th century.
Following the Protestant Reformation from 1517, it did not take long for Arian and other nontrinitarian views to resurface. The first recorded English antitrinitarian was John Assheton, who was forced to recant before Thomas Cranmer in 1548. At the Anabaptist Council of Venice 1550, the early Italian instigators of the Radical Reformation committed to the views of Michael Servetus,-who was burned alive by the orders of John Calvin in 1553- were promulgated by Giorgio Biandrata and others into Poland and Transylvania.
The anti trinitarian wing of the Polish Reformation separated from the Calvinist "ecclesia maior" to form the "ecclesia minor" or Polish Brethren. These were commonly referred to as "Arians" due to their rejection of the Trinity, though in fact the Socinians, as they were later known, went further than Arius to the position of Photinus. The epithet "Arian" was also applied to the early Unitarians such as John Biddle; though in denial of the pre-existence of Christ they were again largely Socinians, not Arians.
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In 1683, when Anthony Ashley Cooper, 1st Earl of Shaftesbury, lay dying in Amsterdam—driven into exile by his outspoken opposition to King Charles II—he spoke to the minister Robert Ferguson, and professed himself an Arian.
In the 18th century the "dominant trend" in Britain, particularly in Latitudinarianism, was toward Arianism, with which Samuel Clarke, Benjamin Hoadly, William Whiston and Isaac Newton are associated. To quote the "Encyclopædia Britannica" article on Arianism: "In modern times some Unitarians are virtually Arians in that they are unwilling either to reduce Christ to a mere human being or to attribute to him a divine nature identical with that of the Father."
Today.
The teachings of the first two ecumenical councils that entirely reject Arianism include: the Catholic Church, the Eastern Orthodox Church, the Oriental Orthodox Churches, the Assyrian Church of the East; almost all historic Protestant churches including Lutheran, Reformed, Presbyterian, Continental Reformed, Congregationalist, Anglican, Methodist, Baptist, and Free Evangelical; all entirely reject the teachings associated with Arianism.
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Modern groups that currently appear to embrace some of the principles of Arianism include Unitarians and Jehovah's Witnesses. Although the origins of their beliefs are not necessarily attributed to the teachings of Arius, many of the core beliefs of Unitarians and Jehovah's Witnesses are very similar to them.
Jehovah's Witnesses.
Jehovah's Witnesses are often referred to as "modern-day Arians", usually by their opponents, although Jehovah's Witnesses themselves have denied these claims. Significant similarities in doctrine include the identification of the Father as the only true God and of Jesus Christ as the first creation of God and the intermediate agent in the creation of all other things. They also deny the personhood of the Holy Spirit, which some Arians historically affirmed. Jehovah's Witnesses exclusively worship and pray to God the Father, or Jehovah, only through Jesus (the Son) as a mediator.
Iglesia ni Cristo.
Iglesia ni Cristo's Christology has parallels with Arianism in that it affirms that the Father is the only true God, but it denies the preexistence of Christ. Thus, Iglesia ni Cristo is Socinian rather than Arian in its Christology.
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Other Socinian groups.
Other Biblical Unitarians such as the Christadelphians and Church of God General Conference are also typically Socinian rather than Arian in their Christology.
The Church of Jesus Christ of Latter-day Saints.
The Church of Jesus Christ of Latter-day Saints (LDS Church) teaches a nontrinitarian theology concerning the nature of the Godhead. Similarities between LDS doctrines and Arianism were alleged as early as 1846. There are a number of key differences between Arianism and Latter-day Saint theology. Whereas Arianism is a unitarian Christian form of classical theism, Latter-day Saint theology is a non-trinitarian (but not unitarian) form of Christianity outside of classical theism. Arianism also teaches that God is eternal, was never a man, and could not incarnate as a man; in contrast, the LDS Church teaches that "God Himself is an exalted man, perfected, enthroned, and supreme."
Whereas Arianism denies that humans can become gods, the LDS Church affirms that humans can become gods through exaltation. Whereas Arianism teaches that the Son was created, the LDS Church also teaches that the Son was procreated as a literal spirit child of the Heavenly Father and the Heavenly Mother and denies any form of creation "ex nihilo"; the creation of Christ "ex nihilo" is, in contrast, a fundamental premise of Arianism.
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The LDS church, in contrast to the Arian teaching that God is incorporeal, also teaches that God has a tangible body: "The Father has a body of flesh and bones as tangible as man's; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us." Arianism traditionally taught that God is incomprehensible even to the Son. In contrast, the LDS Church rejects the doctrine that God is incomprehensible. Though Arianism teaches that Christ is ontologically inferior and subordinate to the Father, the LDS Church teaches that Christ is equal in power and glory with the Father.
The LDS Church teaches that the Father, Son, and Holy Spirit are three separate beings united in purpose: "the Father, the Son and the Holy Spirit (or Holy Ghost)[...] are three physically separate beings, but fully one in love, purpose and will", as illustrated in Jesus' Farewell Prayer, his baptism at the hands of John the Baptist, his transfiguration, and the martyrdom of Stephen. Thus, the church's first Article of Faith states: "We believe in God, the Eternal Father, and in His Son, Jesus Christ, and in the Holy Ghost."
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Latter-day Saints believe that the three are collectively "one eternal God" but reject the Nicene definition of the Trinity, that the three are consubstantial. In some respects, Latter-day Saint theology is more similar to social trinitarianism than to Arianism.
Spiritism.
According to the reincarnationist religion of Spiritism started by French educator Allan Kardec in the 19th century, Jesus is the highest-order of spirit that has ever incarnated on Earth and is distinct from God, by whom he was created. Jesus is not considered God or part of God as in Nicene Christianity, but is nonetheless the ultimate model of human love, intelligence, and forgiveness, often cited as the governor of Earth.
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Antoninus Pius
Titus Aelius Hadrianus Antoninus Pius (; ; 19 September 86 – 7 March 161) was Roman emperor from AD 138 to 161. He was the fourth of the Five Good Emperors from the Nerva–Antonine dynasty.
Born into a senatorial family, Antoninus held various offices during the reign of Emperor Hadrian. He married Hadrian's niece Faustina, and Hadrian adopted him as his son and successor shortly before his death. Antoninus acquired the cognomen Pius after his accession to the throne, either because he compelled the Senate to deify his adoptive father, or because he had saved senators sentenced to death by Hadrian in his later years. His reign is notable for the peaceful state of the Empire, with no major revolts or military incursions during this time. A successful military campaign in southern Scotland early in his reign resulted in the construction of the Antonine Wall.
Antoninus was an effective administrator, leaving his successors a large surplus in the treasury, expanding free access to drinking water throughout the Empire, encouraging legal conformity, and facilitating the enfranchisement of freed slaves. He died of illness in AD 161 and was succeeded by his adopted sons Marcus Aurelius and Lucius Verus as co-emperors.
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Early life.
Childhood and family.
Antoninus Pius was born Titus Aurelius Fulvus Boionius Antoninus in 86, near Lanuvium (modern-day Lanuvio) in Italy to Titus Aurelius Fulvus, consul in 89, and wife Arria Fadilla. The Aurelii Fulvi were an Aurelian family settled in Nemausus (modern Nîmes). Titus Aurelius Fulvus was the son of a senator of the same name, who, as legate of Legio III Gallica, had supported Vespasian in his bid to the Imperial office and been rewarded with a suffect consulship, plus an ordinary one under Domitian in 85. The Aurelii Fulvi were therefore a relatively new senatorial family from Gallia Narbonensis whose rise to prominence was supported by the Flavians. The link between Antoninus' family and their home province explains the increasing importance of the post of proconsul of Gallia Narbonensis during the late second century.
Antoninus' father had no other children and died shortly after his 89 ordinary consulship. Antoninus was raised by his maternal grandfather Gnaeus Arrius Antoninus, reputed by contemporaries to be a man of integrity and culture and a friend of Pliny the Younger. The Arrii Antonini were an older senatorial family from Italy, very influential during Nerva's reign. Arria Fadilla, Antoninus' mother, married afterwards Publius Julius Lupus, suffect consul in 98; from that marriage came two daughters, Arria Lupula and Julia Fadilla.
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Marriage and children.
Some time between 110 and 115, Antoninus married Annia Galeria Faustina the Elder. They are believed to have enjoyed a happy marriage. Faustina was the daughter of consul Marcus Annius Verus (II) and Rupilia Faustina (often thought to be a step-sister to the Empress Vibia Sabina or more likely a granddaughter of the emperor Vitellius.) Faustina was a beautiful woman, and despite rumours about her character, it is clear that Antoninus cared for her deeply.
Faustina bore Antoninus four children, two sons and two daughters. They were:
When Faustina died in 141, Antoninus was greatly distressed. In honour of her memory, he asked the Senate to deify her as a goddess, and authorised the construction of a temple to be built in the Roman Forum in her name, with priestesses serving in her temple. He had various coins with her portrait struck in her honor. These coins were scripted "DIVA FAUSTINA" and were elaborately decorated. He further founded a charity, calling it "Puellae Faustinianae" or "Girls of Faustina", which assisted destitute girls of good family. Finally, Antoninus created a new "alimenta", a Roman welfare programme, as part of "Cura Annonae".
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The emperor never remarried. Instead, he lived with Galeria Lysistrate, Faustina's freedwoman. Concubinage was a form of female companionship sometimes chosen by powerful men in Ancient Rome, especially widowers like Vespasian, and Marcus Aurelius. Their union could not produce any legitimate offspring who could threaten any heirs, such as those of Antoninus. Also, as one could not have a wife and an official concubine (or two concubines) at the same time, Antoninus avoided being pressed into a marriage with a noblewoman from another family. (Later, Marcus Aurelius would also reject the advances of his former fiancée Ceionia Fabia, Lucius Verus's sister, on the grounds of protecting his children from a stepmother, and took a concubine instead.)
Favour with Hadrian.
Having filled the offices of quaestor and praetor with more than usual success, he obtained the consulship in 120 having as his colleague Lucius Catilius Severus. He was next appointed by the Emperor Hadrian as one of the four proconsuls to administer Italia, his district including Etruria, where he had estates. He then greatly increased his reputation by his conduct as proconsul of Asia, probably during 134–135.
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He acquired much favor with Hadrian, who adopted him as his son and successor on 25 February 138, after the death of his first adopted son Lucius Aelius, on the condition that Antoninus would in turn adopt Marcus Annius Verus, the son of his wife's brother, and Lucius, son of Lucius Aelius, who afterwards became the emperors Marcus Aurelius and Lucius Verus. He also adopted (briefly) the name Imperator Titus Aelius Caesar Antoninus, in preparation for his rule. There seems to have been some opposition to Antoninus' appointment on the part of other potential claimants, among them his former consular colleague Lucius Catilius Severus, then prefect of the city. Nevertheless, Antoninus assumed power without opposition.
Emperor.
On his accession, Antoninus' name and style became "Imperator Caesar Titus Aelius Hadrianus Antoninus Augustus Pontifex Maximus". One of his first acts as emperor was to persuade the Senate to grant divine honours to Hadrian, which they had at first refused; his efforts to persuade the Senate to grant these honours is the most likely reason given for his title of "Pius" (dutiful in affection; compare "pietas"). Two other reasons for this title are that he would support his aged father-in-law with his hand at Senate meetings and that he had saved those men that Hadrian, during his period of ill health, had condemned to death.
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Immediately after Hadrian's death, Antoninus approached Marcus and requested that his marriage arrangements be amended: Marcus' betrothal to Ceionia Fabia would be annulled, and he would be betrothed to Faustina, Antoninus' daughter instead. Faustina's betrothal to Ceionia's brother Lucius Commodus, Marcus' future co-emperor, would also have to be annulled. Marcus consented to Antoninus' proposal.
Antoninus built temples, theaters, and mausoleums, promoted the arts and sciences, and bestowed honours and financial rewards upon the teachers of rhetoric and philosophy. Antoninus made few initial changes when he became emperor, leaving the arrangements instituted by Hadrian as undisturbed as possible. Epigraphical and prosopographical research has revealed that Antoninus' imperial ruling team centered around a group of closely knit senatorial families, most of them members of the priestly congregation for the cult of Hadrian, the "sodales Hadrianales". According to the German historian H.G. Pflaum, prosopographical research of Antoninus' ruling team allows us to grasp the deeply conservative character of the ruling senatorial caste.
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He owned palatial villas near Lanuvium and Villa Magna (Latium) and his ancestral estate at Lorium (Etruria).
Lack of warfare.
There are no records of his involvement in military acts during his tenure, with J. J. Wilkes noting that he likely never saw or commanded a Roman army and was never within five hundred miles of a legion throughout his twenty-three-year reign.
His reign was the most peaceful in the entire history of the Principate, even though there were several military disturbances in the Empire in his time. Such disturbances happened in Mauretania, where a senator was named as governor of Mauretania Tingitana in place of the usual equestrian procurator and cavalry reinforcements from Pannonia were brought in, towns such as Sala and Tipasa being fortified. Similar disturbances took place in Judea, and amongst the Brigantes in Britannia; however, these were considered less serious than prior (and later) revolts among both. It was however in Britain that Antoninus decided to follow a new, more aggressive path, with the appointment of a new governor in 139, Quintus Lollius Urbicus, a native of Numidia and previously governor of Germania Inferior as well as a new man.
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Under instructions from the emperor, Lollius undertook an invasion of southern Scotland, winning some significant victories and constructing the Antonine Wall from the Firth of Forth to the Firth of Clyde. However, the wall was soon gradually decommissioned during the mid-150s and eventually abandoned late during the reign (early 160s) for reasons that are still unclear. Antonine's Wall is mentioned in just one literary source, Antoninus' biography in the "Historia Augusta". Pausanias makes a brief and confused mention of a war in Britain. In one inscription honouring Antoninus, erected by Legio II Augusta, which participated in the building of the Wall, a relief showing four naked prisoners, one of them beheaded, seems to stand for some actual warfare.
Although Antonine's Wall was, in principle, much shorter (37 miles in length as opposed to 73) and, at first sight, more defensible than Hadrian's Wall, the additional area that it enclosed within the Empire was barren, with land use for grazing already in decay. This meant that supply lines to the wall were strained enough such that the costs of maintaining the additional territory outweighed the benefits of doing so. Also, in the absence of urban development and the ensuing Romanization process, the rear of the wall could not be lastingly pacified.
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It has been speculated that the invasion of Lowland Scotland and the building of the wall had to do mostly with internal politics, that is, offering Antoninus an opportunity to gain some modicum of necessary military prestige at the start of his reign. An Imperial salutation followed the campaign in Britannia—that is, Antoninus formally took for the second (and last) time the title of Imperator in 142. The fact that around the same time coins were struck announcing a victory in Britain points to Antoninus' need to publicise his achievements. The orator Fronto was later to say that, although Antoninus bestowed the direction of the British campaign to others, he should be regarded as the helmsman who directed the voyage, whose glory, therefore, belonged to him.
That this quest for some military achievement responded to an actual need is proved by the fact that, although generally peaceful, Antoninus' reign was not free from attempts at usurpation: "Historia Augusta" mentions two, made by the senators Cornelius Priscianus ("for disturbing the peace of Spain"; Priscianus had also been Lollius Urbicus' successor as governor of Britain) and Atilius Rufius Titianus (possibly a troublemaker already exiled under Hadrian). Both attempts are confirmed by the Fasti Ostienses and by the erasing of Priscianus' name from an inscription. In both cases, Antoninus was not in formal charge of the ensuing repression: Priscianus committed suicide and Titianus was found guilty by the Senate, with Antoninus abstaining from sequestering their families' properties.
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There were also some troubles in Dacia Inferior, which required the granting of additional powers to the procurator governor and the dispatch of additional soldiers to the province. On the northern Black Sea coast, the Greek city of Olbia was held against the Scythians. Also during his reign the governor of Upper Germany, probably Gaius Popillius Carus Pedo, built new fortifications in the Agri Decumates, advancing the Limes Germanicus fifteen miles forward in his province and neighboring Raetia. In the East, Roman suzerainty over Armenia was retained by the choice in AD 140 of Arsacid scion Sohaemus as client king.
Nevertheless, Antoninus was virtually unique among emperors in that he dealt with these crises without leaving Italy once during his reign, but instead dealt with provincial matters of war and peace through their governors or through imperial letters to the cities such as Ephesus (of which some were publicly displayed). His contemporaries and later generations highly praised this style of government.
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Antoninus was the last Roman Emperor recognised by the Indian Kingdoms, especially the Kushan Empire. Raoul McLaughlin quotes Aurelius Victor as saying, "The Indians, the Bactrians, and the Hyrcanians all sent ambassadors to Antoninus. They had all heard about the spirit of justice held by this great emperor, justice that was heightened by his handsome and grave countenance, and his slim and vigorous figure." Due to the outbreak of the Antonine epidemic and wars against northern Germanic tribes, the reign of Marcus Aurelius was forced to alter the focus of foreign policies, and matters relating to the Far East were increasingly abandoned in favour of those directly concerning the Empire's survival.
Economy and administration.
Antoninus was regarded as a skilled administrator and builder. Despite an extensive building directive—the free access of the people of Rome to drinking water was expanded with the construction of aqueducts, not only in Rome but throughout the Empire, as well as bridges and roads—the emperor still managed to leave behind a sizable public treasury of around 2.7 billion sesterces. Rome would not witness another Emperor leaving his successor with a surplus for a long time, but the treasury was depleted almost immediately after Antoninus's reign due to the Antonine Plague brought back by soldiers after the Parthian victory.
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The Emperor also famously suspended the collection of taxes from multiple cities affected by natural disasters, such as when fires struck Rome and Narbona, and earthquakes affected Rhodes and the Province of Asia. He offered hefty financial grants for rebuilding and recovery of various Greek cities after two serious earthquakes: the first, , which mainly affected Rhodes and other islands; the second, in 152, which hit Cyzicus (where the huge and newly built Temple to Hadrian was destroyed), Ephesus, and Smyrna. Antoninus' financial help earned him praise from Greek writers such as Aelius Aristides and Pausanias. These cities received the usual honorific accolades from Antoninus, such as when he commanded that all governors of Asia should enter the province when taking office through Ephesus. Ephesus was especially favoured by Antoninus, who confirmed and upheld its distinction of having two temples for the imperial cult (neocorate), therefore having first place in the list of imperial honor titles, surpassing both Smyrna and Pergamon.
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In his dealings with Greek-speaking cities, Antoninus followed the policy adopted by Hadrian of ingratiating himself with local elites, especially with local intellectuals: philosophers, teachers of literature, rhetoricians, and physicians were explicitly exempted from any duties involving private spending for civic purposes, a privilege granted by Hadrian that Antoninus confirmed by means of an edict preserved in the Digest (27.1.6.8). Antoninus also created a chair for the teaching of rhetoric in Athens.
Antoninus was known as an avid observer of rites of religion and formal celebrations, both Roman and foreign. He is known for having increasingly formalized the official cult offered to the Great Mother, which from his reign onwards included a bull sacrifice, a taurobolium, formerly only a private ritual, now being also performed for the sake of the Emperor's welfare. Antoninus also offered patronage to the worship of Mithras, to whom he erected a temple in Ostia. In 148, he presided over the celebrations of the 900th anniversary of the founding of Rome.
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Legal reforms.
Antoninus tried to portray himself as a magistrate of the "res publica", no matter how extended and ill-defined his competencies were. He is credited with splitting the imperial treasury, the fiscus. This splitting had to do with the division of imperial properties into two parts. Firstly, the fiscus itself, or "patrimonium", meaning the properties of the "Crown", the hereditary properties of each succeeding person that sat on the throne, transmitted to his successors in office, regardless of their previous membership in the imperial family. Secondly, the "res privata", the "private" properties tied to the personal maintenance of the emperor and his family, something like a Privy Purse. An anecdote in the "Historia Augusta" biography, where Antoninus replies to Faustina (who complained about his stinginess) that "we have gained an empire [and] lost even what we had before," possibly relates to Antoninus' actual concerns at the creation of the "res privata". While still a private citizen, Antoninus had increased his personal fortune significantly using various legacies, the consequence of his caring scrupulously for his relatives. Also, Antoninus left behind him a reputation for stinginess and was probably determined not to leave his personal property to be "swallowed up by the demands of the imperial throne".
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The "res privata" lands could be sold and/or given away, while the "patrimonium" properties were regarded as public. It was a way of pretending that the Imperial function—and most properties attached to it—was a public one, formally subject to the authority of the Senate and the Roman people. That the distinction played no part in subsequent political history—that the "personal" power of the princeps absorbed his role as office-holder—proves that the autocratic logic of the imperial order had already subsumed the old republican institutions.
Of the public transactions of this period, there is only the scantiest of information. However, to judge by what is extant, those twenty-two years were not remarkably eventful compared to those before and after the reign. However, Antoninus did take a great interest in the revision and practice of the law throughout the empire. One of his chief concerns was to having local communities conform their legal procedures to existing Roman norms: in a case concerning the repression of banditry by local police officers ("irenarchs", Greek for "peacekeepers") in Asia Minor, Antoninus ordered that these officers should not treat suspects as already condemned, and also keep a detailed copy of their interrogations, to be used in the possibility of an appeal to the Roman governor. Also, although Antoninus was not an innovator, he would not always follow the absolute letter of the law. Rather, he was driven by concerns over humanity and equality and introduced into Roman law many important new principles based upon this notion.
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In this, the emperor was assisted by five chief lawyers: Lucius Fulvius Aburnius Valens, an author of legal treatises; Lucius Ulpius Marcellus, a prolific writer; and three others. Of these three, the most prominent was Lucius Volusius Maecianus, a former military officer turned by Antoninus into a civil procurator, and who, given his subsequent career (discovered on the basis of epigraphical and prosopographic research), was the emperor's most important legal adviser. Maecianus would eventually be chosen to occupy various prefectures (see below) as well as to conduct the legal studies of Marcus Aurelius. He also authored an extensive work on "Fidei commissa" (Testamentary Trusts). As a hallmark of the increased connection between jurists and the imperial government, Antoninus' reign also saw the appearance of the "Institutes" of Gaius, an elementary legal textbook for beginners.
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One highlight during his reign occurred in 148, with the 900th anniversary of the foundation of Rome being celebrated by hosting magnificent games in the city. It lasted many days, and a host of exotic animals were killed, including elephants, giraffes, tigers, rhinoceroses, crocodiles and hippopotamuses. While this increased Antoninus's popularity, the frugal emperor had to debase the Roman currency. He decreased the silver purity of the denarius from 89% to 83.5, the actual silver weight dropping from 2.88 grams to 2.68 grams.
Antoninus is a likely candidate for the Antoninus named multiple times in the Talmud as a friend of Rabbi Judah Ha-Nasi. In the Talmudic tractate "Avodah Zarah" 10a–b, Rabbi Judah—exceptionally wealthy and highly revered in Rome—shared a close friendship with a man named Antoninus (possibly Antoninus Pius), who frequently sought his counsel on spiritual (in this context, Jewish), philosophical, and governance matters.
Diplomatic mission to China.
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Furthermore, a piece of Republican-era Roman glassware has been found at a Western Han tomb in Guangzhou along the South China Sea, dated to the early 1st century BC. Roman golden medallions made during the reign of Antoninus Pius and perhaps even Marcus Aurelius have been found at Óc Eo in southern Vietnam, then part of the Kingdom of Funan near the Chinese province of Jiaozhi. This may have been the port city of Kattigara, described by Ptolemy () as being visited by a Greek sailor named Alexander and lying beyond the Golden Chersonese (i.e., Malay Peninsula). Roman coins from the reigns of Tiberius to Aurelian have been discovered in Xi'an, China (site of the Han capital Chang'an), although the significantly greater amount of Roman coins unearthed in India suggest the Roman maritime trade for purchasing Chinese silk was centered there, not in China or even the overland Silk Road running through ancient Iran.
Death and legacy.
In 156, Antoninus Pius turned 70. He found it difficult to keep himself upright without stays. He started nibbling on dry bread to give him the strength to stay awake through his morning receptions.
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Marcus Aurelius had already been created consul with Antoninus in 140, receiving the title of Caesar, i.e., heir apparent. As Antoninus aged, Marcus took on more administrative duties. Marcus's administrative duties increased again after the death, in 156 or 157, of one of Antoninus' most trusted advisers, Marcus Gavius Maximus.
For twenty years, Gavius Maximus had been praetorian prefect, an office that was as much secretarial as military. Gavius Maximus had been awarded with the consular insignia and the honours due a senator. He had a reputation as a most strict disciplinarian ("vir severissimus", according to "Historia Augusta") and some fellow equestrian procurators held lasting grudges against him. A procurator named Gaius Censorius Niger died while Gavius Maximus was alive. In his will, Censorius Niger vilified Maximus, creating serious embarrassment for one of the heirs, the orator Fronto.
Gavius Maximus' death initiated a change in the ruling team. It has been speculated that it was the legal adviser Lucius Volusius Maecianus who assumed the role of grey eminence. Maecianus was briefly Praefect of Egypt, and subsequently Praefectus annonae in Rome. If it was Maecianus who rose to prominence, he may have risen precisely in order to prepare the incoming—and unprecedented—joint succession. In 160, Marcus and Lucius were designated joint consuls for the following year. Perhaps Antoninus was already ill; in any case, he died before the year was out, probably on 7 March.
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Two days before his death, the biographer reports, Antoninus was at his ancestral estate at Lorium, in Etruria, about from Rome. He ate Alpine cheese at dinner quite greedily. In the night he vomited; he had a fever the next day. The day after that, he summoned the imperial council, and passed the state and his daughter to Marcus. The emperor gave the keynote to his life in the last word that he uttered: when the tribune of the night-watch came to ask the password, he responded, "aequanimitas" (equanimity). He then turned over, as if going to sleep, and died. His death closed out the longest reign since Augustus (surpassing Tiberius by a couple of months). His record for the second-longest reign would be unbeaten for 168 years, until 329 when it was surpassed by Constantine the Great.
Antoninus Pius' funeral ceremonies were, in the words of the biographer, "elaborate". If his funeral followed the pattern of past funerals, his body would have been incinerated on a pyre at the Campus Martius, while his spirit would rise to the gods' home in the heavens. However, it seems that this was not the case: according to his "Historia Augusta" biography (which seems to reproduce an earlier, detailed report) Antoninus' body (and not his ashes) was buried in Hadrian's mausoleum. After a seven-day interval ("justitium"), Marcus and Lucius nominated their father for deification. In contrast to their behaviour during Antoninus' campaign to deify Hadrian, the senate did not oppose the emperors' wishes. A "flamen", or cultic priest, was appointed to minister the cult of the deified Antoninus, now "Divus Antoninus".
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A column was dedicated to Antoninus on the Campus Martius, and the temple he had built in the Forum in 141 to his deified wife Faustina was rededicated to the deified Faustina and the deified Antoninus. It survives as the church of San Lorenzo in Miranda.
Historiography.
The only intact account of his life handed down to us is that of the "Augustan History", an unreliable and mostly fabricated work. Nevertheless, it still contains information that is considered reasonably sound; for instance, it is the only source that mentions the erection of the Antonine Wall in Britain.
Antoninus in many ways was the ideal of the landed gentleman praised not only by ancient Romans, but also by later scholars of classical history, such as Edward Gibbon or the author of the article on Antoninus Pius in the "Encyclopædia Britannica" Eleventh Edition.
Some historians have a less positive view of his reign. According to the historian J. B. Bury,
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Krzysztof Ulanowski argues that the claims of military inability are exaggerated, considering that although the sources praise Antoninus' love for peace and his efforts "rather to defend, than enlarge the provinces", he could hardly be considered a pacifist, as shown by the conquest of the Lowlands, the building of the Antonine Wall and the expansion of Germania Superior. Ulanowski also praises Antoninus for being successful in deterrence by diplomatic means.
Descendants.
Although only one of his four children survived to adulthood, Antoninus came to be ancestor to four generations of prominent Romans, including the Emperor Commodus. Hans-Georg Pflaum has identified five direct descendants of Antoninus and Faustina who were consuls in the first half of the third century.
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Advanced Encryption Standard
The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.
AES is a variant of the Rijndael block cipher developed by two Belgian cryptographers, Joan Daemen and Vincent Rijmen, who submitted a proposal to NIST during the AES selection process. Rijndael is a family of ciphers with different key and block sizes. For AES, NIST selected three members of the Rijndael family, each with a block size of 128 bits, but three different key lengths: 128, 192 and 256 bits.
AES has been adopted by the U.S. government. It supersedes the Data Encryption Standard (DES), which was published in 1977. The algorithm described by AES is a symmetric-key algorithm, meaning the same key is used for both encrypting and decrypting the data.
In the United States, AES was announced by the NIST as U.S. FIPS PUB 197 (FIPS 197) on November 26, 2001. This announcement followed a five-year standardization process in which fifteen competing designs were presented and evaluated, before the Rijndael cipher was selected as the most suitable.
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AES is included in the ISO/IEC 18033-3 standard. AES became effective as a U.S. federal government standard on May 26, 2002, after approval by U.S. Secretary of Commerce Donald Evans. AES is available in many different encryption packages, and is the first (and only) publicly accessible cipher approved by the U.S. National Security Agency (NSA) for top secret information when used in an NSA approved cryptographic module.
Definitive standards.
The Advanced Encryption Standard (AES) is defined in each of:
Description of the ciphers.
AES is based on a design principle known as a substitution–permutation network, and is efficient in both software and hardware. Unlike its predecessor DES, AES does not use a Feistel network. AES is a variant of Rijndael, with a fixed block size of 128 bits, and a key size of 128, 192, or 256 bits. By contrast, Rijndael "per se" is specified with block and key sizes that may be any multiple of 32 bits, with a minimum of 128 and a maximum of 256 bits. Most AES calculations are done in a particular finite field.
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AES operates on a 4 × 4 column-major order array of 16 bytes termed the "state":
The key size used for an AES cipher specifies the number of transformation rounds that convert the input, called the plaintext, into the final output, called the ciphertext. The number of rounds are as follows:
Each round consists of several processing steps, including one that depends on the encryption key itself. A set of reverse rounds are applied to transform ciphertext back into the original plaintext using the same encryption key.
The step.
In the step, each byte formula_2 in the "state" array is replaced with a formula_3 using an 8-bit substitution box. Before round 0, the "state" array is simply the plaintext/input. This operation provides the non-linearity in the cipher. The S-box used is derived from the multiplicative inverse over , known to have good non-linearity properties. To avoid attacks based on simple algebraic properties, the S-box is constructed by combining the inverse function with an invertible affine transformation. The S-box is also chosen to avoid any fixed points (and so is a derangement), i.e., formula_4, and also any opposite fixed points, i.e., formula_5.
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While performing the decryption, the step (the inverse of ) is used, which requires first taking the inverse of the affine transformation and then finding the multiplicative inverse.
The step.
The step operates on the rows of the state; it cyclically shifts the bytes in each row by a certain offset. For AES, the first row is left unchanged. Each byte of the second row is shifted one to the left. Similarly, the third and fourth rows are shifted by offsets of two and three respectively. In this way, each column of the output state of the step is composed of bytes from each column of the input state. The importance of this step is to avoid the columns being encrypted independently, in which case AES would degenerate into four independent block ciphers.
The step.
In the step, the four bytes of each column of the state are combined using an invertible linear transformation. The function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes. Together with , provides diffusion in the cipher.
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During this operation, each column is transformed using a fixed matrix (matrix left-multiplied by column gives new value of column in the state):
Matrix multiplication is composed of multiplication and addition of the entries. Entries are bytes treated as coefficients of polynomial of order formula_7. Addition is simply XOR. Multiplication is modulo irreducible polynomial formula_8. If processed bit by bit, then, after shifting, a conditional XOR with 1B16 should be performed if the shifted value is larger than FF16 (overflow must be corrected by subtraction of generating polynomial). These are special cases of the usual multiplication in formula_9.
In more general sense, each column is treated as a polynomial over formula_9 and is then multiplied modulo formula_11 with a fixed polynomial formula_12. The coefficients are displayed in their hexadecimal equivalent of the binary representation of bit polynomials from formula_13. The step can also be viewed as a multiplication by the shown particular MDS matrix in the finite field formula_9. This process is described further in the article Rijndael MixColumns.
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The.
In the step, the subkey is combined with the state. For each round, a subkey is derived from the main key using Rijndael's key schedule; each subkey is the same size as the state. The subkey is added by combining of the state with the corresponding byte of the subkey using bitwise XOR.
Optimization of the cipher.
On systems with 32-bit or larger words, it is possible to speed up execution of this cipher by combining the and steps with the step by transforming them into a sequence of table lookups. This requires four 256-entry 32-bit tables (together occupying 4096 bytes). A round can then be performed with 16 table lookup operations and 12 32-bit exclusive-or operations, followed by four 32-bit exclusive-or operations in the step. Alternatively, the table lookup operation can be performed with a single 256-entry 32-bit table (occupying 1024 bytes) followed by circular rotation operations.
Using a byte-oriented approach, it is possible to combine the , , and steps into a single round operation.
Security.
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The National Security Agency (NSA) reviewed all the AES finalists, including Rijndael, and stated that all of them were secure enough for U.S. Government non-classified data. In June 2003, the U.S. Government announced that AES could be used to protect classified information:
The design and strength of all key lengths of the AES algorithm (i.e., 128, 192 and 256) are sufficient to protect classified information up to the SECRET level. TOP SECRET information will require use of either the 192 or 256 key lengths. The implementation of AES in products intended to protect national security systems and/or information must be reviewed and certified by NSA prior to their acquisition and use.
AES has 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys.
Known attacks.
For cryptographers, a cryptographic "break" is anything faster than a brute-force attacki.e., performing one trial decryption for each possible key in sequence . A break can thus include results that are infeasible with current technology. Despite being impractical, theoretical breaks can sometimes provide insight into vulnerability patterns. The largest successful publicly known brute-force attack against a widely implemented block-cipher encryption algorithm was against a 64-bit RC5 key by distributed.net in 2006.
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The key space increases by a factor of 2 for each additional bit of key length, and if every possible value of the key is equiprobable; this translates into a doubling of the average brute-force key search time with every additional bit of key length. This implies that the effort of a brute-force search increases exponentially with key length. Key length in itself does not imply security against attacks, since there are ciphers with very long keys that have been found to be vulnerable.
AES has a fairly simple algebraic framework. In 2002, a theoretical attack, named the "XSL attack", was announced by Nicolas Courtois and Josef Pieprzyk, purporting to show a weakness in the AES algorithm, partially due to the low complexity of its nonlinear components. Since then, other papers have shown that the attack, as originally presented, is unworkable; see XSL attack on block ciphers.
During the AES selection process, developers of competing algorithms wrote of Rijndael's algorithm "we are concerned about [its] use ... in security-critical applications." In October 2000, however, at the end of the AES selection process, Bruce Schneier, a developer of the competing algorithm Twofish, wrote that while he thought successful academic attacks on Rijndael would be developed someday, he "did not believe that anyone will ever discover an attack that will allow someone to read Rijndael traffic."
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By 2006, the best known attacks were on 7 rounds for 128-bit keys, 8 rounds for 192-bit keys, and 9 rounds for 256-bit keys.
Until May 2009, the only successful published attacks against the full AES were side-channel attacks on some specific implementations. In 2009, a new related-key attack was discovered that exploits the simplicity of AES's key schedule and has a complexity of 2119. In December 2009 it was improved to 299.5. This is a follow-up to an attack discovered earlier in 2009 by Alex Biryukov, Dmitry Khovratovich, and Ivica Nikolić, with a complexity of 296 for one out of every 235 keys. However, related-key attacks are not of concern in any properly designed cryptographic protocol, as a properly designed protocol (i.e., implementational software) will take care not to allow related keys, essentially by constraining an attacker's means of selecting keys for relatedness.
Another attack was blogged by Bruce Schneier
on July 30, 2009, and released as a preprint
on August 3, 2009. This new attack, by Alex Biryukov, Orr Dunkelman, Nathan Keller, Dmitry Khovratovich, and Adi Shamir, is against AES-256 that uses only two related keys and 239 time to recover the complete 256-bit key of a 9-round version, or 245 time for a 10-round version with a stronger type of related subkey attack, or 270 time for an 11-round version. 256-bit AES uses 14 rounds, so these attacks are not effective against full AES.
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The practicality of these attacks with stronger related keys has been criticized, for instance, by the paper on chosen-key-relations-in-the-middle attacks on AES-128 authored by Vincent Rijmen in 2010.
In November 2009, the first known-key distinguishing attack against a reduced 8-round version of AES-128 was released as a preprint.
This known-key distinguishing attack is an improvement of the rebound, or the start-from-the-middle attack, against AES-like permutations, which view two consecutive rounds of permutation as the application of a so-called Super-S-box. It works on the 8-round version of AES-128, with a time complexity of 248, and a memory complexity of 232. 128-bit AES uses 10 rounds, so this attack is not effective against full AES-128.
The first key-recovery attacks on full AES were by Andrey Bogdanov, Dmitry Khovratovich, and Christian Rechberger, and were published in 2011. The attack is a biclique attack and is faster than brute force by a factor of about four. It requires 2126.2 operations to recover an AES-128 key. For AES-192 and AES-256, 2190.2 and 2254.6 operations are needed, respectively. This result has been further improved to 2126.0 for AES-128, 2189.9 for AES-192, and 2254.3 for AES-256 by Biaoshuai Tao and Hongjun Wu in a 2015 paper, which are the current best results in key recovery attack against AES.
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This is a very small gain, as a 126-bit key (instead of 128 bits) would still take billions of years to brute force on current and foreseeable hardware. Also, the authors calculate the best attack using their technique on AES with a 128-bit key requires storing 288 bits of data. That works out to about 38 trillion terabytes of data, which was more than all the data stored on all the computers on the planet in 2016. A paper in 2015 later improved the space complexity to 256 bits, which is 9007 terabytes (while still keeping a time complexity of approximately 2126).
According to the Snowden documents, the NSA is doing research on whether a cryptographic attack based on tau statistic may help to break AES.
At present, there is no known practical attack that would allow someone without knowledge of the key to read data encrypted by AES when correctly implemented.
Side-channel attacks.
Side-channel attacks do not attack the cipher as a black box, and thus are not related to cipher security as defined in the classical context, but are important in practice. They attack implementations of the cipher on hardware or software systems that inadvertently leak data. There are several such known attacks on various implementations of AES.
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In April 2005, D. J. Bernstein announced a cache-timing attack that he used to break a custom server that used OpenSSL's AES encryption. The attack required over 200 million chosen plaintexts. The custom server was designed to give out as much timing information as possible (the server reports back the number of machine cycles taken by the encryption operation). However, as Bernstein pointed out, "reducing the precision of the server's timestamps, or eliminating them from the server's responses, does not stop the attack: the client simply uses round-trip timings based on its local clock, and compensates for the increased noise by averaging over a larger number of samples."
In October 2005, Dag Arne Osvik, Adi Shamir and Eran Tromer presented a paper demonstrating several cache-timing attacks against the implementations in AES found in OpenSSL and Linux's codice_1 partition encryption function. One attack was able to obtain an entire AES key after only 800 operations triggering encryptions, in a total of 65 milliseconds. This attack requires the attacker to be able to run programs on the same system or platform that is performing AES.
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In December 2009 an attack on some hardware implementations was published that used differential fault analysis and allows recovery of a key with a complexity of 232.
In November 2010 Endre Bangerter, David Gullasch and Stephan Krenn published a paper which described a practical approach to a "near real time" recovery of secret keys from AES-128 without the need for either cipher text or plaintext. The approach also works on AES-128 implementations that use compression tables, such as OpenSSL. Like some earlier attacks, this one requires the ability to run unprivileged code on the system performing the AES encryption, which may be achieved by malware infection far more easily than commandeering the root account.
In March 2016, C. Ashokkumar, Ravi Prakash Giri and Bernard Menezes presented a side-channel attack on AES implementations that can recover the complete 128-bit AES key in just 6–7 blocks of plaintext/ciphertext, which is a substantial improvement over previous works that require between 100 and a million encryptions. The proposed attack requires standard user privilege and key-retrieval algorithms run under a minute.
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Many modern CPUs have built-in hardware instructions for AES, which protect against timing-related side-channel attacks.
Quantum attacks.
AES-256 is considered to be quantum resistant, as it has similar quantum resistance to AES-128's resistance against traditional, non-quantum, attacks at 128 bits of security. AES-192 and AES-128 are not considered quantum resistant due to their smaller key sizes. AES-192 has a strength of 96 bits against quantum attacks and AES-128 has 64 bits of strength against quantum attacks, making them both insecure.
NIST/CSEC validation.
The Cryptographic Module Validation Program (CMVP) is operated jointly by the United States Government's National Institute of Standards and Technology (NIST) Computer Security Division and the Communications Security Establishment (CSE) of the Government of Canada. The use of cryptographic modules validated to NIST FIPS 140-2 is required by the United States Government for encryption of all data that has a classification of Sensitive but Unclassified (SBU) or above. From NSTISSP #11, National Policy Governing the Acquisition of Information Assurance: "Encryption products for protecting classified information will be certified by NSA, and encryption products intended for protecting sensitive information will be certified in accordance with NIST FIPS 140-2."
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The Government of Canada also recommends the use of FIPS 140 validated cryptographic modules in unclassified applications of its departments.
Although NIST publication 197 ("FIPS 197") is the unique document that covers the AES algorithm, vendors typically approach the CMVP under FIPS 140 and ask to have several algorithms (such as Triple DES or SHA1) validated at the same time. Therefore, it is rare to find cryptographic modules that are uniquely FIPS 197 validated and NIST itself does not generally take the time to list FIPS 197 validated modules separately on its public web site. Instead, FIPS 197 validation is typically just listed as an "FIPS approved: AES" notation (with a specific FIPS 197 certificate number) in the current list of FIPS 140 validated cryptographic modules.
The Cryptographic Algorithm Validation Program (CAVP) allows for independent validation of the correct implementation of the AES algorithm. Successful validation results in being listed on the NIST validations page. This testing is a pre-requisite for the FIPS 140-2 module validation. However, successful CAVP validation in no way implies that the cryptographic module implementing the algorithm is secure. A cryptographic module lacking FIPS 140-2 validation or specific approval by the NSA is not deemed secure by the US Government and cannot be used to protect government data.
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FIPS 140-2 validation is challenging to achieve both technically and fiscally. There is a standardized battery of tests as well as an element of source code review that must be passed over a period of a few weeks. The cost to perform these tests through an approved laboratory can be significant (e.g., well over $30,000 US) and does not include the time it takes to write, test, document and prepare a module for validation. After validation, modules must be re-submitted and re-evaluated if they are changed in any way. This can vary from simple paperwork updates if the security functionality did not change to a more substantial set of re-testing if the security functionality was impacted by the change.
Test vectors.
Test vectors are a set of known ciphers for a given input and key. NIST distributes the reference of AES test vectors as AES Known Answer Test (KAT) Vectors.
Performance.
High speed and low RAM requirements were some of the criteria of the AES selection process. As the chosen algorithm, AES performed well on a wide variety of hardware, from 8-bit smart cards to high-performance computers.
On a Pentium Pro, AES encryption requires 18 clock cycles per byte (cpb), equivalent to a throughput of about 11 MiB/s for a 200 MHz processor.
On Intel Core and AMD Ryzen CPUs supporting AES-NI instruction set extensions, throughput can be multiple GiB/s. On an Intel Westmere CPU, AES encryption using AES-NI takes about 1.3 cpb for AES-128 and 1.8 cpb for AES-256.
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Anisotropy
Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical or mechanical properties when measured along different axes, e.g. absorbance, refractive index, conductivity, and tensile strength.
An example of anisotropy is light coming through a polarizer. Another is wood, which is easier to split along its grain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions).
Fields of interest.
Computer graphics.
In the field of computer graphics, an anisotropic surface changes in appearance as it rotates about its geometric normal, as is the case with velvet.
Anisotropic filtering (AF) is a method of enhancing the image quality of textures on surfaces that are far away and viewed at a shallow angle. Older techniques, such as bilinear and trilinear filtering, do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily.
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Chemistry.
A chemical anisotropic filter, as used to filter particles, is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the proximal regions filter out larger particles and distal regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration.
In fluorescence spectroscopy, the fluorescence anisotropy, calculated from the polarization properties of fluorescence from samples excited with plane-polarized light, is used, e.g., to determine the shape of a macromolecule. Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photon.
In NMR spectroscopy, the orientation of nuclei with respect to the applied magnetic field determines their chemical shift. In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like the pi system of benzene. This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change.
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Real-world imagery.
Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal).
Physics.
Physicists from University of California, Berkeley reported about their detection of the cosmic anisotropy in cosmic microwave background radiation in 1977. Their experiment demonstrated the Doppler shift caused by the movement of the earth with respect to the early Universe matter, the source of the radiation. Cosmic anisotropy has also been seen in the alignment of galaxies' rotation axes and polarization angles of quasars.
Physicists use the term anisotropy to describe direction-dependent properties of materials. Magnetic anisotropy, for example, may occur in a plasma, so that its magnetic field is oriented in a preferred direction. Plasmas may also show "filamentation" (such as that seen in lightning or a plasma globe) that is directional.
An "anisotropic liquid" has the fluidity of a normal liquid, but has an average structural order relative to each other along the molecular axis, unlike water or chloroform, which contain no structural ordering of the molecules. Liquid crystals are examples of anisotropic liquids.
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