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Grothendieck is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation. Relatively little of his work after 1960 was published by the conventional route of the learned journal, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal. His influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules. Although lauded as "the Einstein of mathematics", his work also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems.
"EGA", "SGA", "FGA".
The bulk of Grothendieck's published work is collected in the monumental, yet incomplete, "Éléments de géométrie algébrique" ("EGA") and "Séminaire de géométrie algébrique" ("SGA"). The collection "Fondements de la Géometrie Algébrique" ("FGA"), which gathers together talks given in the Séminaire Bourbaki, also contains important material.
Grothendieck's work includes the invention of the étale and l-adic cohomology theories, which explain an observation made by André Weil that argued for a connection between the topological characteristics of a variety and its diophantine (number theoretic) properties. For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers. Weil had realized that to prove such a connection, one needed a new cohomology theory, but neither he nor any other expert saw how to accomplish this until such a theory was expressed by Grothendieck.
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This program culminated in the proofs of the Weil conjectures, the last of which was settled by Grothendieck's student Pierre Deligne in the early 1970s after Grothendieck had largely withdrawn from mathematics.
Major mathematical contributions.
In Grothendieck's retrospective "Récoltes et Semailles", he identified twelve of his contributions that he believed qualified as "great ideas". In chronological order, they are:
Here the term "yoga" denotes a kind of "meta-theory" that may be used heuristically; Michel Raynaud writes the other terms "Ariadne's thread" and "philosophy" as effective equivalents.
Grothendieck wrote that, of these themes, the largest in scope was topoi, as they synthesized algebraic geometry, topology, and arithmetic. The theme that had been most extensively developed was schemes, which were the framework "par excellence" for eight of the other themes (all but 1, 5, and 12). Grothendieck wrote that the first and last themes, topological tensor products and regular configurations, were of more modest size than the others. Topological tensor products had played the role of a tool rather than of a source of inspiration for further developments; but he expected that regular configurations could not be exhausted within the lifetime of a mathematician who devoted oneself to it. He believed that the deepest themes were motives, anabelian geometry, and Galois–Teichmüller theory.
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Influence.
Grothendieck is considered by many to be the greatest mathematician of the twentieth century. In an obituary David Mumford and John Tate wrote:
Although mathematics became more and more abstract and general throughout the 20th century, it was Alexander Grothendieck who was the greatest master of this trend. His unique skill was to eliminate all unnecessary hypotheses and burrow into an area so deeply that its inner patterns on the most abstract level revealed themselves–and then, like a magician, show how the solution of old problems fell out in straightforward ways now that their real nature had been revealed.
By the 1970s, Grothendieck's work was seen as influential, not only in algebraic geometry and the allied fields of sheaf theory and homological algebra, but influenced logic, in the field of categorical logic.
According to mathematician Ravi Vakil, "Whole fields of mathematics speak the language that he set up. We live in this big structure that he built. We take it for granted—the architect is gone". In the same article, Colin McLarty said, "Lots of people today live in Grothendieck's house, unaware that it's Grothendieck's house."
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Geometry.
Grothendieck approached algebraic geometry by clarifying the foundations of the field, and by developing mathematical tools intended to prove a number of notable conjectures. Algebraic geometry has traditionally meant the understanding of geometric objects, such as algebraic curves and surfaces, through the study of the algebraic equations for those objects. Properties of algebraic equations are in turn studied using the techniques of ring theory. In this approach, the properties of a geometric object are related to the properties of an associated ring. The space (e.g., real, complex, or projective) in which the object is defined, is extrinsic to the object, while the ring is intrinsic.
Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces ("spectra") and associated rings the primary objects of study. To that end, he developed the theory of schemes that informally can be thought of as topological spaces on which a commutative ring is associated to every open subset of the space. Schemes have become the basic objects of study for practitioners of modern algebraic geometry. Their use as a foundation allowed geometry to absorb technical advances from other fields.
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His generalization of the classical Riemann–Roch theorem related topological properties of complex algebraic curves to their algebraic structure and now bears his name, being called "the Grothendieck–Hirzebruch–Riemann–Roch theorem". The tools he developed to prove this theorem started the study of algebraic and topological K-theory, which explores the topological properties of objects by associating them with rings. After direct contact with Grothendieck's ideas at the Bonn Arbeitstagung, topological K-theory was founded by Michael Atiyah and Friedrich Hirzebruch.
Cohomology theories.
Grothendieck's construction of new cohomology theories, which use algebraic techniques to study topological objects, has influenced the development of algebraic number theory, algebraic topology, and representation theory. As part of this project, his creation of topos theory, a category-theoretic generalization of point-set topology, has influenced the fields of set theory and mathematical logic.
The Weil conjectures were formulated in the later 1940s as a set of mathematical problems in arithmetic geometry. They describe properties of analytic invariants, called local zeta functions, of the number of points on an algebraic curve or variety of higher dimension. Grothendieck's discovery of the ℓ-adic étale cohomology, the first example of a Weil cohomology theory, opened the way for a proof of the Weil conjectures, ultimately completed in the 1970s by his student Pierre Deligne. Grothendieck's large-scale approach has been called a "visionary program". The ℓ-adic cohomology then became a fundamental tool for number theorists, with applications to the Langlands program.
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Grothendieck's conjectural theory of motives was intended to be the "ℓ-adic" theory but without the choice of "ℓ", a prime number. It did not provide the intended route to the Weil conjectures, but has been behind modern developments in algebraic K-theory, motivic homotopy theory, and motivic integration. This theory, Daniel Quillen's work, and Grothendieck's theory of Chern classes, are considered the background to the theory of algebraic cobordism, another algebraic analogue of topological ideas.
Category theory.
Grothendieck's emphasis on the role of universal properties across varied mathematical structures brought category theory into the mainstream as an organizing principle for mathematics in general. Among its uses, category theory creates a common language for describing similar structures and techniques seen in many different mathematical systems. His notion of abelian category is now the basic object of study in homological algebra. The emergence of a separate mathematical discipline of category theory has been attributed to Grothendieck's influence, although unintentional.
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In popular culture.
"Colonel Lágrimas" ("Colonel Tears" in English), a novel by Puerto Rican–Costa Rican writer Carlos Fonseca is about Grothendieck.
The Benjamín Labatut book "When We Cease to Understand the World" dedicates one chapter to the work and life of Grothendieck, introducing his story by reference to the Japanese mathematician Shinichi Mochizuki. The book is a lightly fictionalized account of the world of scientific inquiry and was a finalist for the National Book Award.
In Cormac McCarthy's "The Passenger" and its sequel "Stella Maris", a main character is a student of Grothendieck's.
The Istituto Grothendieck has been created in his honor.
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Alcoholics Anonymous
Alcoholics Anonymous (AA) is a global, peer-led mutual-aid fellowship focused on an abstinence-based recovery model from alcoholism through its spiritually inclined twelve-step program. AA's Twelve Traditions, besides emphasizing anonymity, stress lack of hierarchy, staying non-promotional, and non-professional, while also unaffiliated, non-denominational, apolitical and free to all. AA estimated it is active in 180 countries with an estimated membership of nearly two million—73% in the United States and Canada.
AA traces its origins to a 1935 meeting between Bill Wilson (commonly referred to as Bill W.) and Dr. Bob Smith (Dr. Bob), two individuals seeking to address their shared struggles with alcoholism. Their collaboration, influenced by the Christian revivalist Oxford Group, evolved into a mutual support group that eventually became AA. In 1939, the fellowship published "Alcoholics Anonymous: The Story of How More than One Hundred Men Have Recovered from Alcoholism""," colloquially known as the "Big Book". This publication introduced the twelve-step program and provided the basis for the organization's name. Later editions of the book expanded its subtitle to reflect the inclusion of "Thousands of Men and Women".
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The Twelve Steps outline a suggested program of ongoing drug rehabilitation and self-improvement. A key component involves seeking alignment or divining with a personally defined concept of "God as we understood Him". The steps begin with an acknowledgment of powerlessness over alcohol and the unmanageability of life due to alcoholism. Subsequent steps emphasize rigorous honesty, including the completion of a "searching and fearless moral inventory," acknowledgment of "character defects," sharing the inventory with a trusted person, making amends to individuals harmed, and engaging in regular prayer or meditation to seek "conscious contact with God" and guidance in following divine will. The final step, the 12th, focuses on maintaining the principles of recovery, sharing the message with other alcoholics, and participating in "12th Step work," such as peer sponsorship, organizing meetings, and outreach to institutions like hospitals and prisons.
AA meetings differ in format, with variations including personal storytelling, readings from the Big Book, and open discussions. While certain meetings may cater to specific demographic groups, attendance is generally open to anyone with a desire to stop drinking alcohol. The organization is self-supporting through member donations and literature sales. Its operations follow an "inverted pyramid" structure, allowing local groups significant autonomy. AA does not accept external funding or contributions.
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Empirical evidence supports AA's efficacy. A 2020 Cochrane review found that manualized AA and Twelve-Step Facilitation (TSF) therapy demonstrated higher rates of continuous abstinence compared to alternative treatments, such as cognitive-behavioral therapy, with added healthcare cost savings over time.
Criticism of AA has addressed various aspects of its program and operations. Concerns have been raised about its overall success rate, the perceived religious nature of its approach, and allegations of cult-like elements. Additional critiques include reports of "thirteenth-stepping," where senior members engage romantically with newer members, and legal challenges related to safety and the religious content of court-mandated participation in AA programs.
History.
Hazard's search for treatment, spiritual conversion, & involvement with the Oxford Group.
Rowland Hazard’s journey from Carl Jung’s psychiatric treatment to spiritual conversion through the Oxford Group played a pivotal role in shaping the foundations of Alcoholics Anonymous, influencing its principles of recovery. In 1926, Hazard went to Zurich, Switzerland, to seek treatment for alcoholism with psychiatrist Carl Jung. When Hazard ended treatment with Jung after about a year, and came back to the US, he soon resumed drinking, and returned to Jung in Zurich for further treatment. Jung told Hazard that his case was nearly hopeless (as with other alcoholics) and that his only hope might be a "spiritual conversion" with a "religious group".
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Back in America, Hazard went to the Oxford Group, whose teachings were eventually the source of such AA concepts as "meetings" and "sharing" (public confession), making "restitution", "rigorous honesty" and "surrendering one's will and life to God's care". He became converted to a lifetime of sobriety while on a train ride from New York to Detroit after reading "For Sinners Only," by Oxford Group member AJ Russell. Hazard underwent a spiritual conversion" with the help of the Group and began to experience the liberation from drink that he was seeking. Members of the group introduced Hazard to Ebby Thacher, whom Hazard brought to the Calvary Rescue Mission, directed by Oxford Group leader Sam Shoemaker.
Bill Wilson & his spiritual awakening.
In keeping with the Oxford Group teaching that a new convert must win other converts to preserve his own conversion experience, Thacher contacted his old friend Bill Wilson, whom he knew had a drinking problem. Thacher approached Wilson, saying that he had "got religion", was sober, and that Wilson could do the same if he set aside objections and instead formed a personal idea of God, "another power" or "higher power".Feeling a "kinship of common suffering", Wilson attended his first group gathering, although he was drunk. Within days, Wilson admitted himself to the Charles B. Towns Hospital after drinking four beers on the way—the last alcohol he ever drank. Under the care of Dr. William Duncan Silkworth, an early benefactor of AA, Wilson's detox included the deliriant belladonna. At the hospital, a despairing Wilson experienced a bright flash of light, which he felt to be God revealing himself.
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Founding of AA.
Wilson's early efforts and influence of the Oxford Group.
Following his hospital discharge, Wilson joined the Oxford Group and tried to recruit other alcoholics to the group. These early efforts to help others kept him sober, but were ineffective in getting anyone else to join the group. Dr. Silkworth suggested that Wilson place less stress on religion (as required by The Oxford Group) and more on the science of treating alcoholism. Bill W. would later write: "The early AA got its ideas of self-examination, acknowledgment of character defects, restitution for harm done, and working with others straight from the Oxford Group and directly from Sam Shoemaker, their former leader in America, and from nowhere else". According to Mercadante, however, the AA concept of "powerlessness over alcohol" departs significantly from Oxford Group belief. According to AA, alcoholism cannot be cured, whereas the Oxford Group stressed the possibility of complete victory over sin.
Beginnings of AA.
In 1935, AA began in Akron, Ohio, as the outcome of a meeting between Wilson—who became known as "Bill W." in AA circles—and Dr. Robert Smith, an Akron surgeon, who would become Wilson's first recruitment success. On a business trip by Bill W. to Akron, he was introduced to the surgeon, who despite connections with the Oxford Group, was unable to stay sober. Bill W. explained that alcoholism affects the mind, emotions, and body, a concept he had learned from Dr. Silkworth at Towns Hospital in New York, where he had been a patient multiple times. Convinced by these insights, Dr. Bob took his last alcoholic drink on 10 June 1935 and never drank again, soon achieving sobriety. This date is regarded by AA as its inception.
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Bill W. and Dr. Bob started working with alcoholics at Akron's City Hospital. One patient, who soon achieved sobriety, joined them and together, the three men formed the foundation of what would later become known as Alcoholics Anonymous.
In late 1935, a new group of alcoholics began forming in New York, followed by another in Cleveland in 1939. Over the course of four years, these three initial groups helped around 100 people achieve sobriety. In early 1939, the fellowship published its foundational text, "Alcoholics Anonymous", which outlined AA's philosophy; introduced the Twelve Steps; and included the case histories of 30 individuals who had achieved recovery. The Twelve Steps were influenced by the Oxford Group's six steps and various readings, including William James's "The Varieties of Religious Experience". This publication marked a significant milestone in AA's development.
The first meeting outside the Oxford Group was held at Dr. Bob's house with 80 members in attendance. Dr. Bob began the meeting in his dining room by identifying himself as an alcoholic, and placing his foot on the dining room table, read the Sermon on the Mount from the Gospel of Matthew.
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The first female member, Florence Rankin, joined AA in March 1937, and the first non-Protestant member, a Roman Catholic, joined in 1939. The first Black AA group commenced in 1945 in Washington, D.C., founded by Jim S., an African-American physician from Virginia.
The Alcoholic Foundation.
In 1938, Dr. Bob and Bill created The Alcoholic Foundation in New York, bringing in friends of John D. Rockefeller Jr. as board members. Although they sought to raise significant funds, Rockefeller advised that large contributions might jeopardize the Fellowship. The foundation opened a small office in New York, funded primarily by AA members, to handle inquiries and distribute the Alcoholics Anonymous book. The next year, Rockefeller organized a dinner to promote AA, which further increased the number of inquiries. The office became effective. Each request received a personal reply and a pamphlet, enhancing interest in the book. Consequently, many new AA groups were established, and by the end of 1940, membership had grown to 2,000.
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Media coverage leads to expansion.
In 1939, media coverage, particularly from "The Cleveland Plain Dealer", generated a surge of interest and requests for help. The Cleveland group, although small, successfully assisted many alcoholics, quickly growing from 20 to around 500 members. A subsequent article in "Liberty" magazine resulted in a flood of requests for assistance, further expanding AA's reach. In 1941, "The Saturday Evening Post" published an article about AA, sparking a surge in inquires, and AA membership tripled over the next year. AA-related interviews on American radio and favorable articles in US magazines led to increased book sales and membership.
As the growing fellowship faced disputes over structure, purpose, authority, and publicity, Bill W. began promoting the Twelve Traditions. He first introduced his ideas on these in an April 1946 article for "The Grapevine", titled "Twelve Suggested Points for AA Tradition", aiming to preserve the organization's unity and purpose as AA expanded. He described the input he received as a "welter of exciting and fearsome experience" which greatly influenced the development of the Traditions. From December 1947 to November 1948, "The Grapevine" published the Traditions individually, and in 1950, the First International Convention in Cleveland officially adopted them.
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Creation of the General Service Conference (GSC).
In 1951, AA's headquarters in New York expanded its activities, including public relations, support for new groups, services to hospitals and prisons, and cooperation with agencies in the field of alcoholism. It also published standard AA literature and oversaw translations, while the "AA Grapevine" gained substantial circulation. Despite these essential services, they were managed by a disconnected board of trustees, primarily linked to Bill and Dr. Bob.
Recognizing the need for accountability, delegates from across the US and Canada were convened, leading to the first meeting of the AA General Service Conference in 1951. This successful gathering established direct oversight of AA's trusteeship by the fellowship itself, ensuring the organization's future governance. At the 1955 conference in St. Louis, Missouri, Bill W. relinquished stewardship of AA to the General Service Conference, as AA had grown to millions of members internationally.
International expansion.
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The World Service Meeting (WSM), established in 1969, is a biennial international forum at which AA delegates from around the world exchange ideas and experiences about carrying the message of recovery. Held in various cities around the world, the WSM focuses on sharing strategies to help alcoholics in different countries and languages.
Today, AA is present in approximately 180 nations worldwide. By 2018, AA had 2,087,840 members and 120,300 AA groups worldwide. There are AA meetings in Beijing, China.
In July 2024, AA launched its first UK-wide advertising campaign with a unique approach—no logos, phone numbers, or links—focusing on subtle messaging like "You Are Not Alone" and "Alcohol Isn't the Answer". The campaign, created by The Raised Eyebrow Society, aims to attract people struggling with alcohol without violating AA's principles of anonymity and non-promotion.
AA will celebrate its 100th anniversary meeting in Indianapolis, Indiana, in 2035. The international convention is anticipated to attract tens of thousands of attendees to the Indiana Convention Center and Lucas Oil Stadium.
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AA literature.
Alcoholics Anonymous publishes several books, reports, pamphlets, and other media, including a periodical known as the "AA Grapevine". Two books are used primarily: "Alcoholics Anonymous" (the "Big Book") and, expounding on the big book in regard to its subject, "Twelve Steps and Twelve Traditions." As with all AA literature, the texts are freely available on AA.org.
The Big Book.
In 1939, Bill W. and other members wrote the book initially titled "Alcoholics Anonymous: The Story of How More than One Hundred Men Have Recovered from Alcoholism", from which AA drew its name, informally known as the "Big Book". The second edition of the Big Book was released in 1955, the third in 1976, and the fourth in 2001. The first part of the book, which details the program, has remained largely intact since the 1939 edition, with minor statistical updates and edits. The second part contains personal stories that are updated with every edition to reflect current AA membership, resulting in earlier stories being removed—these were published separately in 2003 in the book "Experience, Strength, and Hope".
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The Big Book suggests a twelve-step program in which members admit that they are powerless over alcohol and need help from a "higher power". It offers guidance and strength through prayer and meditation from God or a higher power of their own understanding; take a moral inventory with care to include resentments; list and become ready to remove character defects; list and make amends to those harmed; continue to take a moral inventory, pray, meditate, and try to help other alcoholics recover. The second half of the book, "Personal Stories" (subject to additions, removal, and retitling in subsequent editions), is made of AA members' redemptive autobiographical sketches.
Illness and allergy terminology.
AA's Big Book calls alcoholism "an illness which only a spiritual experience will conquer". Ernest Kurtz says this is "The closest the book Alcoholics Anonymous comes to a definition of alcoholism". Somewhat divergently in his introduction to The Big Book, non-member and early benefactor William Silkworth said those unable to moderate their drinking suffer from an allergy. In presenting the doctor's postulate, AA said "The doctor's theory that we have an allergy to alcohol interests us. As laymen, our opinion as to its soundness may, of course, mean little. But as ex-problem drinkers, we can say that his explanation makes good sense. It explains many things for which we cannot otherwise account". AA later acknowledged that "alcoholism is not a true allergy, the experts now inform us".
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"Twelve Steps and Twelve Traditions".
The "Twelve Steps and Twelve Traditions" is a book published in 1953 that serves as a key text for AA. Written by AA co-founder Bill W., it provides detailed explanations of the Twelve Steps and the Twelve Traditions. The book is commonly used in AA meetings and individual study, offering a framework for understanding the organization's approach to recovery and community. The story of Eddie Rickenbacker "and his courageous company" appears in the book. It pertains to when his plane crashed in the Pacific and is used in the closing remarks of Tradition One: "Our common welfare should come first; personal recovery depends upon AA unity".
"Grapevine".
"The Grapevine", established in June 1944 by six AA members in New York, became AA's national journal by 1945 and later its international journal. Supported by Bill W., the magazine featured first-person stories, AA news, and discussions on key topics like women in AA and veterans returning from war.
Initially intended as a resource for alcoholics worldwide, the Grapevine evolved into a unifying publication for the AA community, chronicling the Fellowship's growth, including the creation of the General Service Structure and publication of later editions of the Big Book. The Twelve Traditions were introduced to AA by Bill W. in April 1946 through an article titled "Twelve Suggested Points for AA Tradition". The AA Preamble, inspired by the foreword of the book "Alcoholics Anonymous", was written by one of the Grapevine's early editors Tom. Y. and first appeared in the June 1947 issue. In 1986, it was reaffirmed as AA's international journal by the General Service Conference.
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The AA program.
Twelve steps.
AA's program extends beyond abstaining from alcohol. Its goal is to effect enough change in the alcoholic's thinking "to bring about recovery from alcoholism" through "an entire psychic change," or spiritual awakening. A spiritual awakening is meant to be achieved by taking the Twelve Steps, and sobriety is furthered by volunteering for AA and regular AA meeting attendance or contact with AA members.
Taking AA's 12 steps are a "suggested", but not required, "program of recovery"—also called a "spiritual solution". They start with members admitting to being "powerless over alcohol" (which the Big Book calls an "Illness" or "malady", but never a "disease’’), and out of control—for which on going divining and following the will an unspecified 'higher power' ("God, as we understood Him") could restore them to "sanity". In the steps members acknowledge and make amends and seek to correct personal character defects aided by their higher power for guidance. Those "having achieved a spiritual awakening as a result of these steps" are suggested to carry AA's message to other alcoholics. This is often done through meetings of AA groups as well as with members taking on sponsees, although the Big Book makes no mention of the latter term. While taking care to avoid becoming affiliated, some AA members perform outreach to hospitals, treatment centers and correctional facilities.
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Sponsorship.
Members are encouraged to find an experienced fellow alcoholic, called a sponsor, to help them understand and follow the AA program. The sponsor should preferably have experienced all twelve of the steps, be the same sex as the sponsored person, and refrain from imposing personal views on the sponsored person. Following the helper therapy principle, sponsors in AA may benefit from their relationship with their charges, as "helping behaviors" correlate with increased abstinence and lower probabilities of binge drinking.
Twelve Traditions.
The Twelve Traditions provide essential guidelines—not rules—that help AA groups navigate their relationships both internally and with the outside world. These traditions ensure that membership is open to anyone seeking to stop drinking, with no dues or fees required. These Traditions foster an altruistic, unaffiliated, non-coercive, and non-hierarchical organization, limiting AA's mission to helping alcoholics at a non-professional level while avoiding publicity. To prioritize recovery, the traditions discourage hierarchies, dogma, public controversies, property acquisition, and outside contributions. Members are advised against using AA for personal gain or public prestige, and anonymity is emphasized, particularly in media, with no prescribed consequences for breaches.
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Meetings.
Overview.
AA meetings serve as a space where individuals discuss recovery from alcoholism, with flexibility in how meetings are conducted. While AA offers pamphlets suggesting formats, groups have the autonomy to organize their meetings according to their preferences, as long as their decisions do not impact other groups or AA as a whole. Despite cultural differences influencing certain rituals, many elements of AA meetings remain consistent worldwide.
Types.
AA meetings encompass a variety of formats, each designed to serve different needs. Open meetings are accessible to anyone, including non-alcoholics who can attend as observers. In contrast, closed meetings are reserved for individuals who identify as having a desire to stop drinking, a declaration that cannot be questioned by other members. Speaker meetings feature one or more members who share their personal stories of recovery, fostering connection and understanding among participants.
Big Book meetings focus on reading and discussing passages from AA's foundational text, while sharing meetings provide an open platform for members to speak freely and share their experiences, with or without a predetermined topic. AA meetings are gatherings where recovery from alcoholism is discussed. One perspective sees them as "quasi-ritualized therapeutic sessions run by and for, alcoholics".
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In recent years, online meetings have become popular, allowing members to connect virtually through platforms like Zoom and What's App. Offline or in-person meetings, often referred to as "brick and mortar" meetings, take place in physical locations, and some groups even host hybrid meetings, enabling participants to attend either in person or virtually.
Inclusivity & language accessibility.
Inclusivity is a core principle of AA meetings, which welcome all alcoholics, though some are tailored to specific demographics such as gender, age, profession, or cultural background. Since the mid-1970s, several 'agnostic' or 'no-prayer' AA groups have begun across the US, Canada, and other parts of the world, which hold meetings that adhere to a tradition allowing alcoholics to freely express their doubts or disbelief that spirituality will help their recovery, and these meetings forgo the use of opening or closing prayers.
Meetings in the United States are held in a variety of languages including Armenian, English, Farsi, Finnish, French, Japanese, Korean, Russian, and Spanish.
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Donations and contributions.
At some point during the meeting a basket is passed around for voluntary contributions. AA's 7th tradition requires that groups be "self-supporting, declining outside contributions".
Serenity prayer.
The Serenity Prayer is commonly used in AA meetings as a tool for reflection and guidance. It was called the AA prayer in the 1940s. Often recited at meetings, it emphasizes the concepts of acceptance, courage, and wisdom, which align with the principles of the AA program. The prayer encourages individuals to accept things they cannot change, to find the courage to make changes where possible, and to seek the wisdom to distinguish between the two.
Sobriety anniversaries and coins.
Sobriety coins, also known as sobriety chips, are tokens given to members of AA to signify the duration of their sobriety. While the chip system is common, it is not universally adopted across all AA groups. The tradition began with Sister Ignatia in Akron, Ohio who distributed medallions to newly released patients as reminders to avoid drinking. The actual sobriety chip as known today is believed to have originated in 1942 in Indianapolis, gaining popularity as various AA groups adopted the practice. Typically, different colored chips represent milestones of sobriety within the first year, with tokens awarded for 24 hours, 30 days, 60 days, 90 days, and beyond, culminating in a bronze chip for one year of sobriety.
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AA members celebrate Founders Day on the weekend closest to 10 June, marking the anniversary of the organization with thousands of attendees engaging in tours of historical sites, sharing recovery stories, and participating in related activities in Akron, Ohio.
Organization and finances.
Structure and governance.
AA describes itself as "not organized in the formal or political sense" and has been referred to as a "benign anarchy," borrowing a phrase from anarchy theorist Peter Kropotkin. The Twelve Traditions guide the functioning of individual AA groups, while the Twelve Concepts for World Service outline how the organization operates on a global scale. Each AA group is self-governing, with AA World Services acting only in an advisory capacity. This "inverted pyramid" style of governance has been key to the organization's resilience and adaptability. In Ireland, Shane Butler noted that AA's lack of top-level leadership might make it seem unsustainable, but its structure has proven extremely robust since its establishment there in 1946.
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AA's 21-member Board of Trustees includes seven "nonalcoholic friends of the fellowship," though the organization is primarily served and run by alcoholics. Members who accept service positions, termed "trusted servants," hold these roles for limited terms, typically ranging from three months to two years, depending on the position and group vote. This approach ensures regular rotation and participation from a broad spectrum of members, maintaining AA's commitment to shared responsibility and leadership.
Financial structure.
AA is entirely self-supporting, relying on voluntary contributions from its members to cover expenses. Contributions to the General Service Office (GSO) are limited to $5,000 per member per year. In addition to these contributions, more than 50% of AA's income comes from the sale of AA literature, such as books and pamphlets. This practice aligns with AA's Seventh Tradition, which emphasizes financial independence by not accepting donations from outside individuals or organizations. The Central Office is also fully self-supporting through the sale of literature and member contributions.
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Employment and service roles.
The Eighth Tradition permits AA to employ "special workers" for roles that require specific expertise or full-time responsibilities, such as administrative tasks. However, these paid roles do not involve working directly with alcoholics in need of help, a function known as the "Twelfth Step". Calls from alcoholics seeking assistance are always passed on to sober AA members who have volunteered to handle them, ensuring the program remains grounded in its peer-to-peer support model.
Organizational operations.
The AA Central Office coordinates activities such as printing literature, responding to public inquiries, and organizing conferences. It operates independently but ensures alignment with the core principles of the organization. Other International General Service Offices—such as those in Australia, Costa Rica, and Russia—function independently of AA World Services in New York, reflecting AA's decentralized and autonomous structure.
Hospitals & institutions.
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In the United States and Canada, AA meetings are held in hundreds of correctional facilities. The AA General Service Office has published a workbook with detailed recommendations for methods of approaching correctional-facility officials with the intent of developing an in-prison AA program. In addition, AA publishes a variety of pamphlets specifically for the incarcerated alcoholic. Additionally, the AA General Service Office provides a pamphlet with guidelines for members working with incarcerated alcoholics.
Demographics.
2014 membership survey.
AA's New York General Service Office survey of over 6,000 members in Canada and the United States concluded that, in North America, AA members who responded to the survey were 62% male and 38% female. The survey found that 89% of AA members were white. Average member sobriety is slightly under 10 years with 36% sober more than ten years, 13% sober from five to ten years, 24% sober from one to five years, and 27% sober less than one year. Before coming to AA, 63% of members received some type of treatment or counseling, such as medical, psychological, or spiritual. After coming to AA, 59% received outside treatment or counseling. Of those members, 84% said that outside help played an important part in their recovery.
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The same survey showed that AA received 32% of its membership from other members, another 32% from treatment facilities, 30% were self-motivated to attend AA, 12% of its membership from court-ordered attendance, and only 1% of AA members decided to join based on information obtained from the Internet. People taking the survey were allowed to select multiple answers for what motivated them to join AA.
Diversity.
A 2024 study found that Black, Hispanic, and younger adults are less likely to attend AA meetings compared to white and older adults, with these disparities remaining consistent over time.
Effectiveness.
Measuring.
Several metrics are used to evaluate the success of AA including abstinence, reduced drinking intensity, reduced alcohol-related consequences, addiction severity, and healthcare costs. Because of the anonymous and voluntary nature of AA meetings, it has been difficult to perform random trials with them. However, environmental and quasi-experiment studies suggest that AA can help alcoholics make positive changes. Until recently, ethical and operational issues had prevented robust randomized controlled trials from being conducted comparing 12-step programs directly to other approaches.
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Reviews and studies.
Long-term recovery effectiveness.
There have been numerous studies on the effectiveness of AA. A 2006 study by Rudolf H. Moos and Bernice S. Moos saw a 67% success rate 16 years later for the 24.9% of alcoholics who ended up, on their own, undergoing a lot of AA treatment. However, this may be influenced by self-selection bias. Project MATCH, a 1990s multi-site study, found AA to be more effective than no treatment. Other studies link increased AA attendance with higher spirituality and reduced alcohol consumption.
A 2020 Cochrane review concluded that AA is more effective than other treatments, such as MET and CBT, in terms of abstinence rates. It also noted similar success in reducing drinking and alcohol-related problems, though this conclusion was based on moderate-certainty evidence. The review found that AA participation via AA twelve step facilitation (AA/TSF) had sustained remission rates 20-60% above other well-established treatments. Additionally, 4 of the 5 economic studies in the review found that AA/TSF lowered healthcare costs considerably. Nick Heather, an addiction researcher, critiqued the review, arguing it may have a sample bias and that it failed to measure outcomes like quality of life or alcohol dependence, which are important for evaluating recovery.<ref name="pmidhttps://pubmed.ncbi.nlm.nih.gov/16856072/"></ref> The authors responded, stating their review showed AA is at least as effective as other treatments and more cost-effective. The authors also noted the lack of quality-of-life measures was due to the limitations of the reviewed studies.
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Comparative effectiveness and cost effectiveness.
A 2020 systematic review indicated that manualized AA and Twelve-Step Facilitation (TSF) therapy yields more healthcare cost savings and leads to higher continuous abstinence rates. A longitudinal study suggests that LifeRing and SMART Recovery fared worse than AA across several outcomes, however, the effects are insignificant when controlling for the baseline alcohol goal of total abstinence. More recent studies employing randomized and blinded trials have shown 12-step programs provide similar benefit compared to motivational enhancement therapy (MET) and cognitive behavioral therapy (CBT), and were more effective in producing continuous abstinence and remission compared to these approaches.
Patterns of engagement and disengagement.
The 2001–2002 National Epidemiological Survey on Alcoholism and Related Conditions (NESARC) found that 3.4% of respondents had attended a 12-step meeting. Of those, 988 had ceased attending, 348 continued attending, and 105 were newcomers. These figures help to understand engagement and disengagement patterns within AA.
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Mechanisms of recovery.
Although AA claims that spirituality is the primary mechanism for achieving change and recovery, there is growing evidence that suggests this is only true for a minority of AA attendees with a high addiction severity. Instead, AA's beneficial effects are carried predominantly by social, cognitive and affective mechanisms. However, atheist and agnostic people are less likely to initiate and sustain AA attendance in comparison to spiritual and religious people.
Criticism.
The effectiveness of AA, compared to other methods and treatments, has been challenged over the years. Lance Dodes, in "The Sober Truth", claims only five to eight percent of the people who go to one or more AA meetings achieve sobriety. Dodes opposes the idea that a social network is needed to overcome substance abuse. Dodes' assertion that AA is ineffective has been criticized. Some other experts claim that the book's conclusion that "[12-step] approaches are almost completely ineffective and even harmful in treating substance use disorders" is wrong. In a 2015 article for "The Atlantic", Gabrielle Glaser criticized the dominance of AA in the treatment of addiction in the United States, citing Dodes's figures and a 2006 Cochrane report, to claim AA had a low success rate. In the past, others have criticized 12-step programs as pseudoscientific Her figures and assertions, however were criticized by other experts.
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Philosophical and sociological dimensions.
AA shares the view that acceptance of one's inherent limitations is critical to finding one's proper place among other humans and God. Such ideas are described as "Counter-Enlightenment" because they are contrary to the Enlightenment's ideal that humans have the capacity to make their lives and societies a heaven on Earth using their own power and reason.
After evaluating AA's literature and observing AA meetings for sixteen months, sociologists David R. Rudy and Arthur L. Greil found that for an AA member to remain sober, a high level of commitment is necessary. This commitment is facilitated by a change in the member's worldview. They argue that to help members stay sober, AA must provide an all-encompassing worldview while creating and sustaining an atmosphere of transcendence in the organization. To be all-encompassing, AA's ideology emphasizes tolerance rather than a narrow religious worldview that may make the organization unpalatable to potential members and thereby limit its effectiveness. AA's emphasis on the spiritual nature of its program, however, is necessary to institutionalize a feeling of transcendence. A tension results from the risk that the necessity of transcendence, if taken too literally, would compromise AA's efforts to maintain a broad appeal. As this tension is an integral part of AA, Rudy and Greil argue that AA is best described as a "quasi-religious organization".
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Criticism and controversy.
Zoombombing.
Zoombombing emerged as a significant challenge for AA meetings during the COVID-19 pandemic, when many groups moved online. Disruptive individuals often infiltrated these virtual meetings, harassing participants and sharing inappropriate content. Some AA members experienced racial hatred. This intrusion undermined the safe, supportive environment essential for recovery, raising concerns about privacy and security. In response, AA groups and Zoom implemented stricter access controls and guidelines to protect participants and maintain a welcoming atmosphere for those seeking help.
Disease model.
Though AA usually avoids the term "disease", 1973 conference-approved literature said "we had the disease of alcoholism", while "Living Sober", published in 1975, contains several references to alcoholism as a disease, including a chapter urging the reader to "Remember that alcoholism is an incurable, progressive, fatal disease". Regardless of official positions, since AA's inception, most members have believed alcoholism to be a disease. Its association with AA, as well as a good deal of its broader acceptance, stems from many members propagating it.
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Bill Wilson explained in 1960 why AA had refrained from using the term "disease":
13th-step and sexual advances.
"Thirteenth-stepping" is a term used to describe a predatory behavior in AA where some individuals exploit vulnerable members for sexual relationships. This can involve unwanted advances and harassment, often targeting newer members who may be more susceptible due to their recovery status.
In 2003, a study in the "Journal of Addiction Nursing" sampled 55 women in AA and found that 35% of these women had experienced a "pass" and 29% had felt seduced at least once in AA settings. This has also happened with new male members who received guidance from older female AA members pursuing sexual company. The authors suggest that both men and women must be prepared for this behavior or find male or female-only groups.
Response.
As of 2010, women-only meetings are a very prevalent part of AA culture, and AA has become more welcoming for women. AA's pamphlet on sponsorship suggests that men be sponsored by men and women be sponsored by women. AA also has a safety flier which states that "Unwanted sexual advances and predatory behaviors are in conflict with carrying the AA message of recovery".
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Criticism of culture.
Stanton Peele argued that some AA groups apply the disease model to all problem drinkers, whether or not they are "full-blown" alcoholics. Along with Nancy Shute, Peele has advocated that besides AA, other options should be readily available to those problem drinkers who can manage their drinking with the right treatment. The Big Book says "moderate drinkers" and "a certain type of hard drinker" can stop or moderate their drinking. The Big Book suggests no program for these drinkers, but instead seeks to help drinkers without "power of choice in drink".
In 1983, a review stated that the AA program's focus on admission of having a problem increases deviant stigma and strips members of their previous cultural identity, replacing it with the deviant identity. A 1985 study based on observations of AA meetings warned of detrimental iatrogenic effects of the twelve-step philosophy and concluded that AA uses many methods that are also used by cults. A later review disagreed, stating that AA's program bore little resemblance to religious cult practices. In 2014, George Eman Vaillant published a paper making the case that Alcoholics Anonymous is not a cult.
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Spirituality.
Some have criticized 12-step programs as "a cult that relies on God as the mechanism of action" and as "overly theistic and outdated". Others have cited the necessity of a "higher power" (an "HP") in formal AA as creating dependence on outside factors rather than internal efficacy. Gabrielle Glaser criticized 12-step programs for being "faith-based", but 12-step programs allow for a very wide diversity of spiritual beliefs, and there are a growing number of secular 12-step meetings.
Secular meetings in Toronto controversy.
Reception to secular 12 step meetings from within AA has been mixed. In 2011, secular meetings in Toronto, where the 12 steps were altered to remove references to God and prayer, were delisted from the Toronto AA online and print directories, effectively removing them from the network of meetings. They appealed this decision, but were rejected, leading to a complaint to the Human Rights Tribunal of Ontario. The Toronto co-ordinating body, the Greater Toronto Area Intergroup of Alcoholics Anonymous, argued both that as a special interest group they have the right to restrict its membership, and that a belief in God is a requirement for groups in Toronto. Mediation between the two groups resulted in the delisted groups being listed again, however the secular groups would be required to not alter the 12 steps.
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Lawsuits and court rulings.
Privileged communication.
In the Fifth Step, AA members typically reveal their own past misconduct to their sponsors. US courts have not extended the status of privileged communication, such as physician-patient privilege or clergy–penitent privilege, to communications between an AA member and their sponsor.
Court rulings on mandatory attendance.
United States courts have ruled that inmates, parolees, and probationers cannot be ordered to attend AA. Though AA itself was not deemed a religion, it was ruled that it contained "enough" religious components (variously described in "Griffin v. Coughlin" below as, inter alia, "religion", "religious activity", "religious exercise") to make coerced attendance at AA meetings a violation of the Establishment Clause of the First Amendment of the constitution. In 2007, the Ninth Circuit of the US Court of Appeals stated that a parolee who was ordered to attend AA had standing to sue his parole office.
Family lawsuit.
The family of Karla Mendez, who was murdered in 2011 by a man she met at an AA meeting, filed a civil lawsuit in 2012 against AA asserting AA had a "reckless disregard for, and deliberate indifference...to the safety and security of victims attending AA meetings who are repeatedly preyed upon at those meetings by financial, violent, and sexual predators...". The lawsuit against AA was dismissed in 2016.
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Big Book manuscript case.
In May 2017, Alcoholics Anonymous World Services Inc. filed a lawsuit in the Supreme Court of the State of New York seeking the return of the original manuscript of the Big Book from its then-owner. AAWS claimed that the manuscript had been given to them as a gift in 1979. This action was criticized by many members of Alcoholics Anonymous since they didn't want their parent organization engaged in lawsuits. Alcoholics Anonymous World Services Inc. asked the court to voluntarily discontinue the action in November 2017.
Notable people who have attended AA.
While AA emphasizes personal anonymity, many notable individuals have publicly acknowledged their participation in the program for various lengths of time.
Roger Ebert stated he was a member of AA according to a 2009 blog entry he wrote. Eminem has posted pictures of AA Sobriety coins. Anthony Hopkins has credited AA with saving him and marked 48 years of sobriety in 2023. Others who have spoken publicly about their AA attendance include James K. Baxter, Art Carney, Bonnie Raitt, Mychal Judge, Moby, Hank Azaria, Matthew Perry, Jim Irsay, Demi Lovato, Elton John, Tom Waits, Capers Williamson, among others. Some have received pushback, including Brad Pitt recently and criticism from some people in AA regarding its anonymity guidelines.
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Alpha compositing
In computer graphics, alpha compositing or alpha blending is the process of combining one image with a background to create the appearance of partial or full transparency. It is often useful to render picture elements (pixels) in separate passes or layers and then combine the resulting 2D images into a single, final image called the composite. Compositing is used extensively in film when combining computer-rendered image elements with live footage. Alpha blending is also used in 2D computer graphics to put rasterized foreground elements over a background.
In order to combine the picture elements of the images correctly, it is necessary to keep an associated "matte" for each element in addition to its color. This matte layer contains the coverage information—the shape of the geometry being drawn—making it possible to distinguish between parts of the image where something was drawn and parts that are empty.
Although the most basic operation of combining two images is to put one over the other, there are many operations, or blend modes, that are used.
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History.
The concept of an alpha channel was introduced by Alvy Ray Smith and Ed Catmull in the late 1970s at the New York Institute of Technology Computer Graphics Lab. Bruce A. Wallace derived the same straight over operator based on a physical reflectance/transmittance model in 1981. A 1984 paper by Thomas Porter and Tom Duff introduced premultiplied alpha using a geometrical approach.
The use of the term "alpha" is explained by Smith as follows: "We called it that because of the classic linear interpolation formula formula_1 that uses the Greek letter formula_2 (alpha) to control the amount of interpolation between, in this case, two images A and B". That is, when compositing image A atop image B, the value of formula_2 in the formula is taken directly from A's alpha channel.
Description.
In a 2D image a color combination is stored for each picture element (pixel), often a combination of red, green and blue (RGB). When alpha compositing is in use, each pixel has an additional numeric value stored in its alpha channel, with a value ranging from 0 to 1. A value of 0 means that the pixel is fully transparent and the color in the pixel beneath will show through. A value of 1 means that the pixel is fully opaque.
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With the existence of an alpha channel, it is possible to express compositing image operations using a "compositing algebra". For example, given two images "A" and "B", the most common compositing operation is to combine the images so that "A" appears in the foreground and "B" appears in the background. This can be expressed as "A" over "B". In addition to over, Porter and Duff defined the compositing operators in, held out by (the phrase refers to holdout matting and is usually abbreviated out), atop, and xor (and the reverse operators rover, rin, rout, and ratop) from a consideration of choices in blending the colors of two pixels when their coverage is, conceptually, overlaid orthogonally:
As an example, the over operator can be accomplished by applying the following formula to each pixel:
Here formula_5, formula_6 and formula_7 stand for the color components of the pixels in the result of the "over", image A, and image B respectively, applied to each color channel (red/green/blue) individually, whereas formula_8, formula_9 and formula_10 are the alpha values of the respective pixels.
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The over operator is, in effect, the normal painting operation (see Painter's algorithm). The in and out operators are the alpha compositing equivalent of clipping. The two use only the alpha channel of the second image and ignore the color components. In addition, plus defines additive blending.
Straight versus premultiplied.
If an alpha channel is used in an image, there are two common representations that are available: straight (unassociated) alpha and premultiplied (associated) alpha.
Comparison.
The most significant advantage of premultiplied alpha is that it allows for correct blending, interpolation, and filtering. Ordinary interpolation without premultiplied alpha leads to RGB information leaking out of fully transparent (A=0) regions, even though this RGB information is ideally invisible. When interpolating or filtering images with abrupt borders between transparent and opaque regions, this can result in borders of colors that were not visible in the original image. Errors also occur in areas of semitransparency because the RGB components are not correctly weighted, giving incorrectly high weighting to the color of the more transparent (lower alpha) pixels.
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Premultiplied alpha may also be used to allow regions of regular alpha blending (e.g. smoke) and regions with additive blending mode (e.g. flame and glitter effects) to be encoded within the same image. This is represented by an RGBA triplet that express emission with no occlusion, such as (0.4, 0.3, 0.2, 0.0).
Another advantage of premultiplied alpha is performance; in certain situations, it can reduce the number of multiplication operations (e.g. if the image is used many times during later compositing). The Porter–Duff operations have a simple form only in premultiplied alpha. Some rendering pipelines expose a "straight alpha" API surface, but converts them into premultiplied alpha for performance.
One disadvantage of premultiplied alpha is that it can reduce the available relative precision in the RGB values when using integer or fixed-point representation for the color components. This may cause a noticeable loss of quality if the color information is later brightened or if the alpha channel is removed. In practice, this is not usually noticeable because during typical composition operations, such as OVER, the influence of the low-precision color information in low-alpha areas on the final output image (after composition) is correspondingly reduced. This loss of precision also makes premultiplied images easier to compress using certain compression schemes, as they do not record the color variations hidden inside transparent regions, and can allocate fewer bits to encode low-alpha areas. The same “limitations” of lower quantisation bit depths such as 8 bit per channel are also present in imagery without alpha, and this argument is problematic as a result.
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Examples.
Assuming that the pixel color is expressed using "straight" (non-premultiplied) RGBA tuples, a pixel value of (0, 0.7, 0, 0.5) implies a pixel that has 70% of the maximum green intensity and 50% opacity. If the color were fully green, its RGBA would be (0, 1, 0, 0.5). However, if this pixel uses premultiplied alpha, all of the RGB values (0, 0.7, 0) are multiplied, or scaled for occlusion, by the alpha value 0.5, which is appended to yield (0, 0.35, 0, 0.5). In this case, the 0.35 value for the G channel actually indicates 70% green emission intensity (with 50% occlusion). A pure green emission would be encoded as (0, 0.5, 0, 0.5). Knowing whether a file uses straight or premultiplied alpha is essential to correctly process or composite it, as a different calculation is required.
Emission with no occlusion cannot be represented in straight alpha. No conversion is available in this case.
Image formats supporting alpha channels.
The most popular image formats that support the alpha channel are PNG and TIFF. GIF supports alpha channels, but is considered to be inefficient when it comes to file size. Support for alpha channels is present in some video codecs, such as Animation and Apple ProRes 4444 of the QuickTime format, or in the Techsmith multi-format codec.
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The file format BMP generally does not support this channel; however, in different formats such as 32-bit (888–8) or 16-bit (444–4) it is possible to save the alpha channel, although not all systems or programs are able to read it: it is exploited mainly in some video games or particular applications; specific programs have also been created for the creation of these BMPs.
Gamma correction.
The RGB values of typical digital images do not directly correspond to the physical light intensities, but are rather compressed by a gamma correction function:
This transformation better utilizes the limited number of bits in the encoded image by choosing formula_14 that better matches the non-linear human perception of luminance.
Accordingly, computer programs that deal with such images must decode the RGB values into a linear space (by undoing the gamma-compression), blend the linear light intensities, and re-apply the gamma compression to the result:
When combined with premultiplied alpha, pre-multiplication is done in linear space, prior to gamma compression. This results in the following formula:
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Note that the alpha channel may or may not undergo gamma-correction, even when the color channels do.
Other transparency methods.
Although used for similar purposes, transparent colors and image masks do not permit the smooth blending of the superimposed image pixels with those of the background (only whole image pixels or whole background pixels allowed).
A similar effect can be achieved with a 1-bit alpha channel, as found in the 16-bit RGBA high color mode of the Truevision TGA image file format and related TARGA and AT-Vista/NU-Vista display adapters' high color graphic mode. This mode devotes 5 bits for every primary RGB color (15-bit RGB) plus a remaining bit as the "alpha channel".
Dithering can be used to simulate partial occlusion where only 1-bit alpha is available.
For some applications, a single alpha channel is not sufficient: a stained-glass window, for instance, requires a separate transparency channel for each RGB channel to model the red, green and blue transparency separately. More alpha channels can be added for accurate spectral color filtration applications.
Some order-independent transparency methods replace the over operator with a commutative approximation.
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Array (data structure)
In computer science, an array is a data structure consisting of a collection of "elements" (values or variables), of same memory size, each identified by at least one "array index" or "key", a collection of which may be a tuple, known as an index tuple. An array is stored such that the position (memory address) of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called a one-dimensional array.
For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: codice_1, codice_2, codice_3, ..., codice_4) so that the element with index "i" has the address 2000 + ("i" × 4).
The memory address of the first element of an array is called first address, foundation address, or base address.
Because the mathematical concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called "matrices". In some cases the term "vector" is used in computing to refer to an array, although tuples rather than vectors are the more mathematically correct equivalent. Tables are often implemented in the form of arrays, especially lookup tables; the word "table" is sometimes used as a synonym of array.
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Arrays are among the oldest and most important data structures, and are used by almost every program. They are also used to implement many other data structures, such as lists and strings. They effectively exploit the addressing logic of computers. In most modern computers and many external storage devices, the memory is a one-dimensional array of words, whose indices are their addresses. Processors, especially vector processors, are often optimized for array operations.
Arrays are useful mostly because the element indices can be computed at run time. Among other things, this feature allows a single iterative statement to process arbitrarily many elements of an array. For that reason, the elements of an array data structure are required to have the same size and should use the same data representation. The set of valid index tuples and the addresses of the elements (and hence the element addressing formula) are usually, but not always, fixed while the array is in use.
The term "array" may also refer to an array data type, a kind of data type provided by most high-level programming languages that consists of a collection of values or variables that can be selected by one or more indices computed at run-time. Array types are often implemented by array structures; however, in some languages they may be implemented by hash tables, linked lists, search trees, or other data structures.
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The term is also used, especially in the description of algorithms, to mean associative array or "abstract array", a theoretical computer science model (an abstract data type or ADT) intended to capture the essential properties of arrays.
History.
The first digital computers used machine-language programming to set up and access array structures for data tables, vector and matrix computations, and for many other purposes. John von Neumann wrote the first array-sorting program (merge sort) in 1945, during the building of the first stored-program computer. Array indexing was originally done by self-modifying code, and later using index registers and indirect addressing. Some mainframes designed in the 1960s, such as the Burroughs B5000 and its successors, used memory segmentation to perform index-bounds checking in hardware.
Assembly languages generally have no special support for arrays, other than what the machine itself provides. The earliest high-level programming languages, including FORTRAN (1957), Lisp (1958), COBOL (1960), and ALGOL 60 (1960), had support for multi-dimensional arrays, and so has C (1972). In C++ (1983), class templates exist for multi-dimensional arrays whose dimension is fixed at runtime as well as for runtime-flexible arrays.
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Applications.
Arrays are used to implement mathematical vectors and matrices, as well as other kinds of rectangular tables. Many databases, small and large, consist of (or include) one-dimensional arrays whose elements are records.
Arrays are used to implement other data structures, such as lists, heaps, hash tables, deques, queues, stacks, strings, and VLists. Array-based implementations of other data structures are frequently simple and space-efficient (implicit data structures), requiring little space overhead, but may have poor space complexity, particularly when modified, compared to tree-based data structures (compare a sorted array to a search tree).
One or more large arrays are sometimes used to emulate in-program dynamic memory allocation, particularly memory pool allocation. Historically, this has sometimes been the only way to allocate "dynamic memory" portably.
Arrays can be used to determine partial or complete control flow in programs, as a compact alternative to (otherwise repetitive) multiple codice_5 statements. They are known in this context as control tables and are used in conjunction with a purpose-built interpreter whose control flow is altered according to values contained in the array. The array may contain subroutine pointers (or relative subroutine numbers that can be acted upon by SWITCH statements) that direct the path of the execution.
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Element identifier and addressing formulas.
When data objects are stored in an array, individual objects are selected by an index that is usually a non-negative scalar integer. Indexes are also called subscripts. An index "maps" the array value to a stored object.
There are three ways in which the elements of an array can be indexed:
Using zero based indexing is the design choice of many influential programming languages, including C, Java and Lisp. This leads to simpler implementation where the subscript refers to an offset from the starting position of an array, so the first element has an offset of zero.
Arrays can have multiple dimensions, thus it is not uncommon to access an array using multiple indices. For example, a two-dimensional array codice_6 with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression codice_7 in the case of a zero-based indexing system. Thus two indices are used for a two-dimensional array, three for a three-dimensional array, and "n" for an "n"-dimensional array.
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The number of indices needed to specify an element is called the dimension, dimensionality, or rank of the array.
In standard arrays, each index is restricted to a certain range of consecutive integers (or consecutive values of some enumerated type), and the address of an element is computed by a "linear" formula on the indices.
One-dimensional arrays.
A one-dimensional array (or single dimension array) is a type of linear array. Accessing its elements involves a single subscript which can either represent a row or column index.
As an example consider the C declaration codice_8 which declares a one-dimensional array of ten integers. Here, the array can store ten elements of type codice_9 . This array has indices starting from zero through nine. For example, the expressions codice_10 and codice_11 are the first and last elements respectively.
For a vector with linear addressing, the element with index "i" is located at the address , where "B" is a fixed "base address" and "c" a fixed constant, sometimes called the "address increment" or "stride".
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If the valid element indices begin at 0, the constant "B" is simply the address of the first element of the array. For this reason, the C programming language specifies that array indices always begin at 0; and many programmers will call that element "zeroth" rather than "first".
However, one can choose the index of the first element by an appropriate choice of the base address "B". For example, if the array has five elements, indexed 1 through 5, and the base address "B" is replaced by , then the indices of those same elements will be 31 to 35. If the numbering does not start at 0, the constant "B" may not be the address of any element.
Multidimensional arrays.
For a multidimensional array, the element with indices "i","j" would have address "B" + "c" · "i" + "d" · "j", where the coefficients "c" and "d" are the "row" and "column address increments", respectively.
More generally, in a "k"-dimensional array, the address of an element with indices "i"1, "i"2, ..., "i""k" is
For example: int a[2][3];
This means that array a has 2 rows and 3 columns, and the array is of integer type. Here we can store 6 elements they will be stored linearly but starting from first row linear then continuing with second row. The above array will be stored as a11, a12, a13, a21, a22, a23.
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This formula requires only "k" multiplications and "k" additions, for any array that can fit in memory. Moreover, if any coefficient is a fixed power of 2, the multiplication can be replaced by bit shifting.
The coefficients "c""k" must be chosen so that every valid index tuple maps to the address of a distinct element.
If the minimum legal value for every index is 0, then "B" is the address of the element whose indices are all zero. As in the one-dimensional case, the element indices may be changed by changing the base address "B". Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing "B" by will cause them to be renumbered from 0 through 9 and 4 through 23, respectively. Taking advantage of this feature, some languages (like FORTRAN 77) specify that array indices begin at 1, as in mathematical tradition while other languages (like Fortran 90, Pascal and Algol) let the user choose the minimum value for each index.
Dope vectors.
The addressing formula is completely defined by the dimension "d", the base address "B", and the increments "c"1, "c"2, ..., "c""k". It is often useful to pack these parameters into a record called the array's descriptor, stride vector, or dope vector. The size of each element, and the minimum and maximum values allowed for each index may also be included in the dope vector. The dope vector is a complete handle for the array, and is a convenient way to pass arrays as arguments to procedures. Many useful array slicing operations (such as selecting a sub-array, swapping indices, or reversing the direction of the indices) can be performed very efficiently by manipulating the dope vector.
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Compact layouts.
Often the coefficients are chosen so that the elements occupy a contiguous area of memory. However, that is not necessary. Even if arrays are always created with contiguous elements, some array slicing operations may create non-contiguous sub-arrays from them.
There are two systematic compact layouts for a two-dimensional array. For example, consider the matrix
In the row-major order layout (adopted by C for statically declared arrays), the elements in each row are stored in consecutive positions and all of the elements of a row have a lower address than any of the elements of a consecutive row:
In column-major order (traditionally used by Fortran), the elements in each column are consecutive in memory and all of the elements of a column have a lower address than any of the elements of a consecutive column:
For arrays with three or more indices, "row major order" puts in consecutive positions any two elements whose index tuples differ only by one in the "last" index. "Column major order" is analogous with respect to the "first" index.
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In systems which use processor cache or virtual memory, scanning an array is much faster if successive elements are stored in consecutive positions in memory, rather than sparsely scattered. This is known as spatial locality, which is a type of locality of reference. Many algorithms that use multidimensional arrays will scan them in a predictable order. A programmer (or a sophisticated compiler) may use this information to choose between row- or column-major layout for each array. For example, when computing the product "A"·"B" of two matrices, it would be best to have "A" stored in row-major order, and "B" in column-major order.
Resizing.
Static arrays have a size that is fixed when they are created and consequently do not allow elements to be inserted or removed. However, by allocating a new array and copying the contents of the old array to it, it is possible to effectively implement a "dynamic" version of an array; see dynamic array. If this operation is done infrequently, insertions at the end of the array require only amortized constant time.
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Some array data structures do not reallocate storage, but do store a count of the number of elements of the array in use, called the count or size. This effectively makes the array a dynamic array with a fixed maximum size or capacity; Pascal strings are examples of this.
Non-linear formulas.
More complicated (non-linear) formulas are occasionally used. For a compact two-dimensional triangular array, for instance, the addressing formula is a polynomial of degree 2.
Efficiency.
Both "store" and "select" take (deterministic worst case) constant time. Arrays take linear (O("n")) space in the number of elements "n" that they hold.
In an array with element size "k" and on a machine with a cache line size of B bytes, iterating through an array of "n" elements requires the minimum of ceiling("nk"/B) cache misses, because its elements occupy contiguous memory locations. This is roughly a factor of B/"k" better than the number of cache misses needed to access "n" elements at random memory locations. As a consequence, sequential iteration over an array is noticeably faster in practice than iteration over many other data structures, a property called locality of reference (this does "not" mean however, that using a perfect hash or trivial hash within the same (local) array, will not be even faster - and achievable in constant time). Libraries provide low-level optimized facilities for copying ranges of memory (such as memcpy) which can be used to move contiguous blocks of array elements significantly faster than can be achieved through individual element access. The speedup of such optimized routines varies by array element size, architecture, and implementation.
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Memory-wise, arrays are compact data structures with no per-element overhead. There may be a per-array overhead (e.g., to store index bounds) but this is language-dependent. It can also happen that elements stored in an array require "less" memory than the same elements stored in individual variables, because several array elements can be stored in a single word; such arrays are often called "packed" arrays. An extreme (but commonly used) case is the bit array, where every bit represents a single element. A single octet can thus hold up to 256 different combinations of up to 8 different conditions, in the most compact form.
Array accesses with statically predictable access patterns are a major source of data parallelism.
Comparison with other data structures.
Dynamic arrays or growable arrays are similar to arrays but add the ability to insert and delete elements; adding and deleting at the end is particularly efficient. However, they reserve linear (Θ("n")) additional storage, whereas arrays do not reserve additional storage.
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Associative arrays provide a mechanism for array-like functionality without huge storage overheads when the index values are sparse. For example, an array that contains values only at indexes 1 and 2 billion may benefit from using such a structure. Specialized associative arrays with integer keys include Patricia tries, Judy arrays, and van Emde Boas trees.
Balanced trees require O(log "n") time for indexed access, but also permit inserting or deleting elements in O(log "n") time, whereas growable arrays require linear (Θ("n")) time to insert or delete elements at an arbitrary position.
Linked lists allow constant time removal and insertion in the middle but take linear time for indexed access. Their memory use is typically worse than arrays, but is still linear.
An Iliffe vector is an alternative to a multidimensional array structure. It uses a one-dimensional array of references to arrays of one dimension less. For two dimensions, in particular, this alternative structure would be a vector of pointers to vectors, one for each row(pointer on c or c++). Thus an element in row "i" and column "j" of an array "A" would be accessed by double indexing ("A"["i"]["j"] in typical notation). This alternative structure allows jagged arrays, where each row may have a different size—or, in general, where the valid range of each index depends on the values of all preceding indices. It also saves one multiplication (by the column address increment) replacing it by a bit shift (to index the vector of row pointers) and one extra memory access (fetching the row address), which may be worthwhile in some architectures.
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Dimension.
The "dimension" of an array is the number of indices needed to select an element. Thus, if the array is seen as a function on a set of possible index combinations, it is the dimension of the space of which its domain is a discrete subset. Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data, a three-dimensional array a block of data, etc.
This should not be confused with the dimension of the set of all matrices with a given domain, that is, the number of elements in the array. For example, an array with 5 rows and 4 columns is two-dimensional, but such matrices form a 20-dimensional space. Similarly, a three-dimensional vector can be represented by a one-dimensional array of size three.
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Advance Australia Fair
"Advance Australia Fair" is the national anthem of Australia. Written by Scottish-born Australian composer Peter Dodds McCormick, the song was first performed as a patriotic song in Australia in 1878. It replaced "God Save the Queen" as the official national anthem by the Whitlam government in 1974, following an indicative opinion survey. The subsequent Fraser government reinstated "God Save the Queen" as the national anthem in January 1976 alongside three other "national songs": "Advance Australia Fair", "Waltzing Matilda" and "Song of Australia". Later in 1977 a plebiscite to choose the "national song" preferred "Advance Australia Fair". This was subsequently proclaimed the national anthem in 1984 by the Hawke government. "God Save the Queen" became the royal anthem (later "God Save the King" on the accession of King Charles III), and is used at public engagements attended by the King or members of the royal family.
The lyrics of the 1984 version of "Advance Australia Fair" were significantly modified from McCormick's original, only retaining a now gender neutral version of the first verse and using a second verse first sung in 1901 at Federation. In January 2021, the official lyrics were changed once again, in recognition of the long habitation of Indigenous Australians.
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History.
Origin.
"Advance Australia Fair" was published in early December 1878 by Scottish-born Australian composer Peter Dodds McCormick (1833–1916) under the pen-name "Amicus" (which means in Latin). It was first sung by Andrew Fairfax, accompanied by a concert band conducted by McCormick, at a function of the Highland Society of New South Wales in Sydney on 30 November 1878 (Saint Andrew's Day). The song gained in popularity and an amended version was sung by a choir of around 10,000 at the inauguration of the Commonwealth of Australia on 1 January 1901. In 1907, the Australian Government awarded McCormick £100 for his composition.
In a letter to R.B. Fuller dated 1 August 1913, McCormick described the circumstances that inspired him to write "Advance Australia Fair" to be sung by a large choir with band accompaniment. McCormick had attended a concert at Sydney's Exhibition Building where various national anthems were played.
The earliest known sound recording of "Advance Australia Fair" appears in "The Landing of the Australian Troops in Egypt" (), a short commercial recording dramatizing the arrival of Australian troops in Egypt en route to Gallipoli.
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Before its adoption as Australia's national anthem, "Advance Australia Fair" had considerable use elsewhere. For example, Australia's national broadcaster, the Australian Broadcasting Commission, used it to announce its radio news bulletins from 1942 to 1952. It was also frequently played at the start or end of official functions. Towards the end of World War II it was one of three songs played in certain picture theatres, along with "God Save the King" and the US national anthem, "The Star-Spangled Banner".
Adoption by the Whitlam government.
Following the collapse of British power and influence after World War II, Australia was forced to abandon its previous conception of itself as a loyal member of a wider global British community. The impetus for the creation of a new identity was described by Donald Horne as "new nationalism" in 1968. A Gallup poll indicated in 1972 that 72% of Australians now supported a new nationally distinct anthem, up from 38% in 1968. The newly elected Whitlam government of 1972 made central the elevation of distinctively Australian symbols. In this vein, Prime Minister Gough Whitlam announced in his 1973 Australia Day address that
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Whitlam also announced that a competition for a new anthem would be held by the Australian Council for the Arts with entrants accepted for both music and lyrics. However, despite around the 2500 entries received for lyrics and 1300 for music, the Council for the Arts could only produce a shortlist of 6 lyrics and no music, reduced from the 12 originally requested. The lyrics selected were "We'll Keep the Faith", "Advance, Australia", "Song of Australia" and three untitled verses. These were widely denounced by artists and the media, with A D Hope calling them "hopeless", James McAuley calling them "hopelessly bad" and "The Australian" describing the choices as "between the unbearable and the unforgivable". One of the judges David Williamson responded to the criticism stating "if you think these are bad, you should have seen the rest of the 2500 or so we rejected".
Many artists commentated on the difficulty of creating a national anthem in the 1970s, with Richard Meale stating that "we had missed the boat" and writer Bob Ellis stating that "You've got to leave out all the gum trees and wallabies, and you can't talk about defending the country against yellow hordes, so there's not much to talk about except an independent stance and belated pride in ourselves. Anything else would embarrass the audience." Ultimately, the government did not include any of the new entries in the final vote, with the poll only including "Advance Australia Fair", "Waltzing Matilda" and "The Song of Australia". This "indicative plebiscite" polled 60,000 people (0.05% of Australians at the time) nationally.
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"Advance Australia Fair" was chosen by 51.4% of respondents and, on 9 April 1974, Whitlam announced in parliament that it was the national anthem, to be used on all occasions except those of a specifically regal nature. The choice came under attack almost immediately, with an editorial noting that "For Australians, the only consolation is that there will be very few occasions when the words are sung," and the Anglican Dean of Sydney commenting "This second-rate secular song is completely inappropriate for use in churches." Officials in four states said that Advance Australia Fair would not be played at official functions and that "God Save the Queen" would not be replaced, with Sir Harry Budd of New South Wales saying that the lyrics "are foolish and banal and their sentiments ridiculous".
During the 1975 election campaign following the dismissal of Whitlam by Sir John Kerr, David Combe proposed that the song be played at the start of the Labor Party's official campaign launch on 24 November 1975 at Festival Hall, Melbourne. Whitlam's speechwriter Graham Freudenberg rejected this idea because, among other reasons, the status of the anthem at that point was still tentative.
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Reversion by the Fraser government.
On 22 January 1976 the Fraser government reinstated "God Save the Queen" as the national anthem for use at royal and vice-regal events, but otherwise provided a choice between "God Save the Queen", "Advance Australia Fair", "Song of Australia" or "Waltzing Matilda" for civilian functions. The choice of four different national anthems was mocked, with "The Age" declaring the new anthem as "God Save Australia's Fair Matilda". His government made plans to conduct a national poll to find a song for use on ceremonial occasions when it was desired to mark a separate Australian identity, whilst maintaining "God Save The Queen" as the national anthem. This was conducted as a plebiscite to choose the National Song, held as an optional additional question in the 1977 referendum on various issues. Despite both Fraser and Whitlam advocating a vote for "Waltzing Matilda", "Advance Australia Fair" was the winner with 43.29% of the vote, defeating the three alternatives, "Waltzing Matilda" (28.28%), "The Song of Australia" (9.65%) and the existing national anthem, "God Save the Queen" (18.78%).
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Re-adoption by the Hawke government.
"Advance Australia Fair", with modified lyrics and reduced to two verses (see development of lyrics), was adopted as the Australian national anthem by the Labor government of Bob Hawke, coming into effect on 19 April 1984. At the same time, "God Save the King/Queen" became known as the royal anthem, and continues to be played alongside the Australian national anthem at public engagements in Australia that are attended by the King or any other members of the Royal Family.
Even though any personal copyright of Peter Dodds McCormick's original lyrics has expired, as he died in 1916, the Commonwealth of Australia claims copyright on the official lyrics and particular arrangements of music. Non-commercial use of the anthem is permitted without case-by-case permission, but the Commonwealth government requires permission for commercial use.
The orchestral arrangement of "Advance Australia Fair" that is now regularly played for Australian victories at international sporting medal ceremonies, and at the openings of major domestic sporting, cultural and community events, is by Tommy Tycho, an immigrant from Hungary. It was commissioned by ABC Music in 1984 and then televised by Channel 10 in 1986 in their Australia Day broadcast, featuring Julie Anthony as the soloist.
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Lyrics.
The lyrics of "Advance Australia Fair", as modified by the National Australia Day Council, were officially adopted in April 1984. The lyrics were updated on 1 January 2021 in an attempt to recognise the legacy of Indigenous Australians, with the word "one" in the second line replacing the previous "young". The lyrics are now as follows:
<poem style="float:left; margin-left: 1em;">I
Australians all let us rejoice,
For we are one and free;
We've golden soil and wealth for toil,
Our home is girt by sea;
Our land abounds in Nature's gifts
Of beauty rich and rare;
In history's page, let every stage
Advance Australia fair!
In joyful strains then let us sing,
Advance Australia fair!</poem>
<poem style="float:left; margin-left: 1em;>II
Beneath our radiant Southern Cross,
We'll toil with hearts and hands;
To make this Commonwealth of ours
Renowned of all the lands;
For those who've come across the seas
We've boundless plains to share;
With courage let us all combine
To advance Australia fair.
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In joyful strains then let us sing
Advance Australia fair!</poem>
Development of lyrics.
Since the original lyrics were written in 1878, there have been several changes, in some cases with the intent of altering the anthem's political focus especially in regard to gender neutrality and Indigenous Australians. Some of these have been minor while others have significantly altered the song. The original song was four verses long. For its 1984 adoption as the national anthem, the song was cut from the four verses to two. The first verse was kept largely as the 1878 original, except for the change in the first line from " let us rejoice" to " let us rejoice". The second, third and fourth verses of the original were dropped, in favour of a modified version of the new third verse which was sung at Federation in 1901.
The lyrics published in the second edition (1879) were as follows:
<poem style="float:left; margin-left: 1em;">I
Australia's sons let us rejoice,
For we are young and free;
We've golden soil and wealth for toil,
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Our home is girt by sea;
Our land abounds in nature's gifts
Of beauty rich and rare;
In history's page, let every stage
Advance Australia fair.
In joyful strains let us sing,
Advance, Australia fair.</poem>
<poem style="float:left; margin-left: 1em;>II
When gallant Cook from Albion sail'd,
To trace wide oceans o'er,
True British courage bore him on,
Til he landed on our shore.
Then here he raised Old England's flag,
The standard of the brave;
"With all her faults we love her still"
"Britannia rules the wave."
In joyful strains then let us sing,
Advance, Australia fair.</poem>
<poem style="float:left; margin-left: 1em;">III
While other nations of the globe
Behold us from afar,
We'll rise to high renown and shine
Like our glorious southern star;
From England soil and Fatherland,
Scotia and Erin fair,
Let all combine with heart and hand
To advance Australia fair.
In joyful strains then let us sing
Advance, Australia fair.</poem>
<poem style="float:left; margin-left: 1em;>IV
Should foreign foe e'er sight our coast,
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Or dare a foot to land,
We'll rouse to arms like sires of yore,
To guard our native strand;
Britannia then shall surely know,
Though oceans roll between,
Her sons in fair Australia's land
Still keep their courage green.
In joyful strains then let us sing
Advance Australia fair.</poem>
The 1901 Federation version of the third verse was originally sung as:
<poem style="float:left; margin-left: 1em;>III
Beneath our radiant Southern Cross,
We'll toil with hearts and hands;
To make our youthful Commonwealth,
Renowned of all the lands;
For loyal sons beyond the seas
We've boundless plains to share;
With courage let us all combine
To advance Australia fair.
In joyful strains then let us sing
Advance Australia fair!</poem>
The lyrics of "Advance Australia Fair", as modified by the National Australia Day Council and officially adopted on 19 April 1984, were as follows:
<poem style="float:left; margin-left: 1em;>I
Australians all let us rejoice,
For we are young and free;
We've golden soil and wealth for toil;
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Our home is girt by sea;
Our land abounds in nature's gifts
Of beauty rich and rare;
In history's page, let every stage
Advance Australia Fair.
In joyful strains then let us sing,
Advance Australia Fair.</poem>
<poem style="float:left; margin-left: 1em;>II
Beneath our radiant Southern Cross
We'll toil with hearts and hands;
To make this Commonwealth of ours
Renowned of all the lands;
For those who've come across the seas
We've boundless plains to share;
With courage let us all combine
To Advance Australia Fair.
In joyful strains then let us sing,
Advance Australia Fair.</poem>
These lyrics were updated on 1 January 2021 to the current version, in which "young" in the second line is replaced with "one" to reflect the pre-colonial presence of Indigenous Australians, who have lived in Australia much longer than Europeans.
Criticism.
General criticism.
In May 1976, after reinstating "God Save the Queen", Fraser advised the Australian Olympic Federation to use "Waltzing Matilda" as the national anthem for the forthcoming Montreal Olympic Games. Fraser responded to criticism of "Waltzing Matilda" compared with "Advance Australia Fair", and countered, "in the second verse... we find these words, 'Britannia rules the waves'."
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The fourth line of the anthem, "our home is girt by sea", has been criticised for using the so-called archaic word "girt". Additionally, the lyrics and melody of the Australian national anthem have been criticised in some quarters as being dull and unendearing to the Australian people. National Party senator Sandy Macdonald said in 2001 that "'Advance Australia Fair' is so boring that the nation risks singing itself to sleep, with boring music and words impossible to understand".
Craig Emerson of the Australian Labor Party has critiqued the anthem, and former MP Peter Slipper has said that Australia should consider another anthem. In 2011, former Victorian Premier Jeff Kennett called for "I Am Australian" to become Australia's national anthem, while former Australian Labor Party leader Kim Beazley defended it, stating: the current "National Anthem is not contradictory to an Australian republic".
Recognition of Indigenous Australians.
The song has been criticised for failing to represent or acknowledge Australia's Indigenous peoples and aspects of the country's colonial past, leading to modification. The lyrics have been accused of celebrating British colonisation and perpetuating the concept of "terra nullius;" the now-changed second line of the anthem ("for we are young and free") was criticised in particular for ignoring the long history of Indigenous Australians. It has also been suggested that the word "fair" celebrates the "civilising" mission of British colonists.
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Since about 2015, public debate about the anthem has increased. Boxer Anthony Mundine stated in 2013, 2017 and 2018 that he would not stand for the anthem, prompting organisers not to play it before his fights. In September 2018 a 9-year-old Brisbane girl was disciplined by her school after refusing to stand for the national anthem; her actions were applauded by some public commenters, and criticised by others. In 2019, several National Rugby League football players decided not to sing the anthem before the first match of the State of Origin series and before the Indigenous All-Stars series with New Zealand; NRL coach and celebrated former player Mal Meninga supported the protesting players and called for a referendum on the subject.
Several alternative versions of "Advance Australia Fair" have been proposed to address the alleged exclusion of Indigenous Australians. Judith Durham of The Seekers and Mutti Mutti musician Kutcha Edwards released their alternative lyrics in 2009, replacing "for we are young and free" with the opening lines "Australians let us stand as one, upon this sacred land". In 2015, Aboriginal Australian soprano Deborah Cheetham declined an invitation to sing the anthem at the 2015 AFL grand final after the AFL turned down her request to replace the words "for we are young and free" with "in peace and harmony". She has advocated for the lyrics being rewritten and endorsed Durham and Edwards' alternative version.
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In 2017 the Recognition in Anthem Project was established and began work on a new version, with lyrics written by poet and former Victorian Supreme Court judge Peter Vickery following consultation with Indigenous communities and others. Vickery's proposed lyrics replaced "we are young and free" with "we are one and free" in the first verse, deleted the second and added two new ones; the second verse acknowledging Indigenous history, immigration and calls for unity and respect, and the third adapting lines from the official second verse. It was debuted at the Desert Song Festival in Alice Springs by an Aboriginal choir. Former prime minister Bob Hawke endorsed Vickery's alternative lyrics in 2018. In 2017, the federal government under then prime minister Malcolm Turnbull granted permission for Vickery's lyrics to be sung at certain occasions as a "patriotic song", but said that before making any official change to the anthem, "The Government would need to be convinced of a sufficient groundswell of support in the wider community".
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In November 2020, NSW Premier Gladys Berejiklian proposed changing one word in the opening couplet, from "we are young and free" to "we are one and free", to acknowledge Australia's Indigenous history. The proposal was supported by the federal Minister for Indigenous Australians, Ken Wyatt, and in December 2020 Prime Minister Scott Morrison announced that he would be advising the governor-general to proclaim the change, to take effect on 1 January 2021. The new wording was highlighted in the No case of the official referendum pamphlet of the Voice to Parliament referendum to support arguments against purported "divisive" constitutional changes.
Dharawal lyrics.
Lyrics for the anthem have been written twice in the Dharug language, an Australian Aboriginal language spoken around Sydney by the Dharawal people.
A first version was first performed in July 2010, at a Rugby League State of Origin match in Sydney, though there was some opposition:
In December 2020, another setting, in Dharug, followed by the anthem in English, was sung before a Rugby Union international between Australia and Argentina:
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Other unofficial variants.
In 2011, about fifty different Christian schools from different denominations came under criticism for singing an unofficial version of the song written by the Sri Lankan immigrant Ruth Ponniah in 1988. The song replaced the official second verse of "Advance Australia Fair" with lyrics that were Christian in nature.
Minister for School Education, Early Childhood and Youth Peter Garrett and chief executive of the National Australia Day Council Warren Pearson admonished the schools for modifying the lyrics of the anthem, and the Australian Parents Council and the Federation of Parents and Citizens' Association of NSW called for a ban on the modified song. Stephen O'Doherty, chief executive of Christian Schools Australia, defended the use of the lyrics in response.
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Automatic number announcement circuit
An automatic number announcement circuit (ANAC) is a component of a central office of a telephone company that provides a service to installation and service technicians to determine the telephone number of a telephone line. The facility has a telephone number that may be called to listen to an automatic announcement that includes the caller's telephone number. The ANAC facility is useful primarily during the installation of landline telephones to quickly identify one of multiple wire pairs in a bundle or at a termination point.
Operation.
By connecting a test telephone set, a technician calls the local telephone number of the automatic number announcement service. This call is connected to equipment at the central office that uses automatic equipment to announce the telephone number of the line calling in. The main purpose of this system is to allow telephone company technicians to identify the telephone line they are connected to.
Automatic number announcement systems are based on automatic number identification. They are intended for use by phone company technicians, the ANAC system bypasses customer features, such as unlisted numbers, caller ID blocking, and outgoing call blocking. Installers of multi-line business services where outgoing calls from all lines display the company's main number on call display can use ANAC to identify a specific line in the system, even if CID displays every line as "line one".
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Most ANAC systems are provider-specific in each wire center, while others are regional or state-/province- or area-code-wide. No official lists of ANAC numbers are published, as telephone companies guard against abuse that would interfere with availability for installers.
Exchange prefixes for testing.
The North American Numbering Plan reserves the exchange ("central office") prefixes "958" and "959" for plant testing purposes. Code 959 with three or four additional digits is dedicated for access to office test lines in local exchange carrier and interoffice carrier central offices. The specifications define several test features for line conditions, such as quiet line and busy line, and test tones transmitted to callers. Telephone numbers are assigned for ring back to test the ringer when installing telephone sets, milliwatt tone (a number simply answers with a continuous test tone) and a loop around (which connects a call to another inbound call to the same or another test number).
ANAC services are typically installed in the "958" range, which is intended for communications between central offices. In some area codes, multiple additional prefixes may be reserved for test purposes. Many area codes reserved 999; 320 was also formerly reserved in Bell Canada territory.
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Other carrier-specific North American test numbers include 555-XXXX numbers (such as 555–0311 on Rogers Communications in Canada) or vertical service codes, such as *99 on Cablevision/Optimum Voice in the United States. MCI Inc. (United States) provides ANI information by dialing 800-444-4444.
Telephone numbers.
Plant testing telephone numbers are carrier-specific, there is no comprehensive list of telephone numbers for ANAC services. In some communities, test numbers change relatively often. In others, a major incumbent carrier might assign a single number which provides test functions on its network across an entire numbering plan area, throughout an entire province or state, or system-wide.
Some telecommunication carriers maintain toll-free numbers for ANAC facilities. Some national toll-free numbers provide automatic number identification by speaking the telephone number of the caller, but these are not intended for use in identifying the customer's own phone number. They are used for the agent in a call center to confirm the telephone a customer is calling from, so that the customer's account information can be displayed as a "screen pop" for the next available customer service representative.
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Amerigo Vespucci
Amerigo Vespucci ( , ; 9 March 1454 – 22 February 1512) was an Italian explorer and navigator from the Republic of Florence for whom "America" is named.
Vespucci participated in at least two voyages of the Age of Discovery between 1497 and 1504, first on behalf of Spain (14991500) and then for Portugal (15011502). In 1503 and 1505, two booklets were published under his name containing colourful descriptions of these explorations and other voyages. Both publications were extremely popular and widely read throughout much of Europe. Historians still dispute the authorship and veracity of these accounts, but they were instrumental in raising awareness of the discoveries and enhancing the reputation of Vespucci as an explorer and navigator.
Vespucci claimed to have understood in 1501 that Brazil was part of a fourth continent unknown to Europeans, which he called the "New World". The claim inspired cartographer Martin Waldseemüller to recognize Vespucci's accomplishments in 1507 by applying the Latinized form "America" to a map showing the New World. Other cartographers followed suit, securing the tradition of marking the name "America" on maps of the newly discovered continents.
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It is unknown whether Vespucci was ever aware of these honours. In 1505, he was made a subject of Castile by royal decree, and he was appointed to the position of "piloto mayor" (master navigator) for Spain's "Casa de Contratación" (House of Trade) in Seville in 1508, a post which he held until his death in 1512.
Biography.
Vespucci was born on 9 March 1454 in Florence, a wealthy Italian city-state and a center of Renaissance art and learning, in the suburb of Peretola.
Family and education.
Amerigo Vespucci was the third son of Nastagio Vespucci, a Florentine notary for the Money-Changers Guild, and Lisa di Giovanni Mini. The family resided in the District of Santa Lucia d'Ognissanti along with other families of the Vespucci clan. Earlier generations of Vespucci had funded a family chapel in the Ognissanti church, and the nearby Hospital of San Giovanni di Dio was founded by Simone di Piero Vespucci in 1380. Vespucci's immediate family was not especially prosperous but they were politically well-connected. Amerigo's grandfather, also named Amerigo Vespucci, served a total of 36 years as the chancellor of the Florentine government, known as the "Signoria"; and Nastagio also served in the "Signoria" and in other guild offices. More importantly, the Vespuccis had good relations with Lorenzo de' Medici, the powerful de facto ruler of Florence.
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Amerigo's two older brothers, Antonio and Girolamo, were sent to the University of Pisa for their education; Antonio followed his father to become a notary, while Girolamo entered the Church and joined the Knights Hospitaller in Rhodes. Amerigo's career path seemed less certain; instead of following his brothers to the university, he remained in Florence and was tutored by his uncle, Giorgio Antonio Vespucci, a Dominican friar in the monastery of San Marco. Fortunately for Amerigo, his uncle was one of the most celebrated humanist scholars in Florence at the time and provided him with a broad education in literature, philosophy, rhetoric, and Latin. He was also introduced to geography and astronomy, subjects that played an essential part in his career. Amerigo's later writings demonstrated a familiarity with the work of the classic Greek cosmographers, Ptolemy and Strabo, and the more recent work of Florentine astronomer Paolo dal Pozzo Toscanelli.
Early career.
In 1478, Guido Antonio Vespucci, Amerigo's other uncle, led a Florentine diplomatic mission to Paris and invited his younger cousin, Amerigo Vespucci, to join him. Amerigo's role is not clear, but it was likely as an attache or private secretary. Along the way they had business in Bologna, Milan, and Lyon. Their objective in Paris was to obtain French support for Florence's war with Naples. Louis XI was noncommittal and the diplomatic mission returned to Florence in 1481 with little to show for their efforts.
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After his return from Paris, Amerigo worked for a time with his father and continued his studies in science. In 1482, when his father died, Amerigo went to work for Lorenzo di Pierfrancesco de' Medici, head of a junior branch of the Medici family. Although Amerigo was twelve years older, they had been schoolmates under the tutelage of Giorgio Antonio Vespucci. Amerigo served first as a household manager and then gradually took on increasing responsibilities, handling various business dealings for the family both at home and abroad. Meanwhile, he continued to show an interest in geography, at one point buying an expensive map made by the master cartographer Gabriel de Vallseca.
Seville.
In 1488, Lorenzo di Pierfrancesco became dissatisfied with his Seville business agent, Tomasso Capponi. He dispatched Vespucci to investigate the situation and provide an assessment of a suggested replacement, Florentine merchant Gianotto Berardi. Vespucci's findings have been lost but Capponi returned to Florence around this time and Berardi took over the Medici business in Seville. In addition to managing Medici's trade in Seville, Berardi had his own business in African slavery and ship chandlery.
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By 1492, Vespucci had settled permanently in Seville. His motivations for leaving Florence are unclear; he continued to transact some business on behalf of his Medici patrons but more and more he became involved with Berardi's other activities, most notably his support of Christopher Columbus's voyages. Berardi invested half a million "maravedis" in Columbus's first voyage, and he won a potentially lucrative contract to provision Columbus's large second fleet. However, profits proved to be elusive. In 1495, Berardi signed a contract with the crown to send 12 resupply ships to Hispaniola but then died unexpectedly in December without completing the terms of the contract.
Vespucci was the executor of Berardi's will, collecting debts and paying outstanding obligations for the firm. Afterwards he was left owing 140,000 "maravedis". He continued to provision ships bound for the West Indies, but his opportunities were diminishing; Columbus's expeditions were not providing the hoped-for profits, and his patron, Lorenzo di Pierfrancesco Medici, was using other Florentine agents for his business in Seville.
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Sometime after he settled in Seville, Vespucci married a Spanish woman, Maria Cerezo. Very little is known about her; Vespucci's will refers to her as the daughter of celebrated military leader Gonzalo Fernández de Córdoba. Historian Fernández-Armesto speculates that she may have been Gonzalo's illegitimate offspring and a connection that would have been very useful to Vespucci. She was an active participant in his business and held power of attorney for Vespucci when he was away.
Voyages and alleged voyages.
The evidence for Vespucci's voyages of exploration consists almost entirely of a handful of letters written by him or attributed to him. Historians have differed sharply on the authorship, accuracy and veracity of these documents. Consequently, opinions also vary widely regarding the number of voyages undertaken, their routes, and Vespucci's roles and accomplishments. Starting in the late 1490s Vespucci participated in two voyages to the New World that are relatively well-documented in the historical record. Two others have been alleged but the evidence is more problematic. Traditionally, Vespucci's voyages are referred to as the "first" through "fourth", even by historians who dismiss one or more of the trips.
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Alleged voyage of 14971498.
A letter, addressed to Florentine official Piero Soderini, dated 1504 and published the following year, purports to be an account by Vespucci of a voyage to the New World, departing from Spain on 10 May 1497, and returning on 15 October 1498. This is perhaps the most controversial of Vespucci's voyages, as this letter is the only known record of its occurrence, and many historians doubt that it took place as described. Some question the authorship and accuracy of the letter and consider it to be a forgery. Others point to the inconsistencies in the narrative of the voyage, particularly the alleged course, starting near Honduras and proceeding northwest for 870 leagues (about )—a course that would have taken them across Mexico to the Pacific Ocean.
Certain earlier historians, including contemporary Bartolomé de las Casas, suspected that Vespucci incorporated observations from a later voyage into a fictitious account of this supposed first one, so as to gain primacy over Columbus and position himself as the first European explorer to encounter the mainland. Others, including scholar Alberto Magnaghi, have suggested that the Soderini letter was not written by Vespucci at all, but rather by an unknown author who had access to the navigator's private letters to Lorenzo de' Medici about his 1499 and 1501 expeditions to the Americas, which make no mention of a 1497 voyage. The Soderini letter is one of two attributed to Vespucci that were edited and widely circulated during his lifetime.
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Voyage of 14991500.
In 1499, Vespucci joined an expedition licensed by Spain and led by Alonso de Ojeda as fleet commander and Juan de la Cosa as chief navigator. Their intention was to explore the coast of a new landmass found by Columbus on his third voyage and in particular investigate a rich source of pearls that Columbus had reported. Vespucci and his backers financed two of the four ships in the small fleet. His role on the voyage is not clear. Writing later about his experience, Vespucci gave the impression that he had a leadership role, but that is unlikely, due to his inexperience. Instead, he may have served as a commercial representative on behalf of the fleet's investors. Years later, Ojeda recalled that "Morigo Vespuche" was one of his pilots on the expedition.
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Voyage of 15011502.
In 1501, Manuel I of Portugal commissioned an expedition to investigate a landmass far to the west in the Atlantic Ocean encountered unexpectedly by a wayward Pedro Álvares Cabral on his voyage around Africa to India. That land would eventually become present-day Brazil. The king wanted to know the extent of this new discovery and determine where it lay in relation to the line established by the Treaty of Tordesillas. Any land that lay to the east of the line could be claimed by Portugal. Vespucci's reputation as an explorer and presumed navigator had already reached Portugal, and he was hired by the king to serve as pilot under the command of Gonçalo Coelho.
Coelho's fleet of three ships left Lisbon in May 1501. Before crossing the Atlantic they resupplied at Cape Verde, where they encountered Cabral on his way home from his voyage to India. This was the same expedition that had found Brazil on its outward-bound journey the previous year. Coelho left Cape Verde in June, and from this point Vespucci's account is the only surviving record of their explorations. On 17 August 1501 the expedition reached Brazil at a latitude of about 6° south. Upon landing it encountered a hostile band of natives who killed and ate one of its crewmen. Sailing south along the coast they found friendlier natives and were able to engage in some minor trading. At 23° S they found a bay which they named Rio de Janeiro because it was 1 January 1502. On 13 February 1502, they left the coast to return home. Vespucci estimated their latitude at 32° S but experts now estimate they were closer to 25° S. Their homeward journey is unclear since Vespucci left a confusing record of astronomical observations and distances travelled.
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Alleged voyage of 15031504.
In 1503, Vespucci may have participated in a second expedition for the Portuguese crown, again exploring the east coast of Brazil. There is evidence that a voyage was led by Coelho at about this time but no independent confirmation that Vespucci took part. The only source for this last voyage is the Soderini letter; but several modern scholars dispute Vespucci's authorship of that letter and it is uncertain whether Vespucci undertook this trip. There are also difficulties with the reported dates and details in the account of this voyage.
Return to Seville.
By early 1505, Vespucci was back in Seville. His reputation as an explorer and navigator continued to grow and his recent service in Portugal did not seem to damage his standing with King Ferdinand. On the contrary, the king was likely interested in learning about the possibility of a western passage to India. In February, he was summoned by the king to consult on matters of navigation. During the next few months he received payments from the crown for his services and in April he was declared by royal proclamation a citizen of Castile and León.
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From 1505 until his death in 1512, Vespucci remained in service to the Spanish crown. He continued his work as a chandler, supplying ships bound for the Indies. He was also hired to captain a ship as part of a fleet bound for the "spice islands" but the planned voyage never took place. In March 1508, he was named chief pilot for the "Casa de Contratación" or House of Commerce which served as a central trading house for Spain's overseas possessions. He was paid an annual salary of 50,000 "maravedis" with an extra 25,000 for expenses. In his new role, Vespucci was responsible for ensuring that ships' pilots were adequately trained and licensed before sailing to the New World. He was also charged with compiling a "model map", the "Padrón Real", based on input from pilots who were obligated to share what they learned after each voyage.
Vespucci wrote his will in April 1511. He left most of his modest estate, including five household slaves, to his wife. His clothes, books, and navigational equipment were left to his nephew Giovanni Vespucci. He requested to be buried in a Franciscan habit in his wife's family tomb. Vespucci died on 22 February 1512.
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Upon his death, Vespucci's wife was awarded an annual pension of 10,000 "maravedis" to be deducted from the salary of the successor chief pilot. His nephew Giovanni was hired into the "Casa de Contratación" where he spent his subsequent years spying on behalf of the Florentine state.
Naming of America.
Vespucci's voyages became widely known in Europe after two accounts attributed to him were published between 1503 and 1505. The Soderini letter (1505) came to the attention of a group of humanist scholars studying geography in Saint-Dié, a small French town in the Duchy of Lorraine. Led by Walter Lud, the academy included Matthias Ringmann and Martin Waldseemüller. In 1506, they obtained a French translation of the Soderini letter as well as a Portuguese maritime map that detailed the coast of lands recently discovered in the western Atlantic. They surmised that this was the "new world" or the "antipodes" hypothesized by classical writers. The Soderini letter gave Vespucci credit for discovery of this new continent and implied that the Portuguese map was based on his explorations.
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In April 1507, Ringmann and Waldseemüller published their "Introduction to Cosmography" with an accompanying world map. The "Introduction" was written in Latin and included a Latin translation of the Soderini letter. In a preface to the "Letter", Ringmann wrote
A thousand copies of the world map were printed with the title "Universal Geography According to the Tradition of Ptolemy and the Contributions of Amerigo Vespucci and Others". It was decorated with prominent portraits of Ptolemy and Vespucci and, for the first time, the name America was applied to a map of the New World.
The "Introduction" and map were a great success and four editions were printed in the first year alone. The map was widely used in universities and was influential among cartographers who admired the craftsmanship that went into its creation. In the following years, other maps were printed that often incorporated the name America. In 1538, Gerardus Mercator used America to name both the North and South continents on his influential map. By this point the tradition of marking the name "America" on maps of the New World was secure.
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In 1513 Waldseemüller published a new map with the New World labelled "Terra Incognita" instead of "America", and the accompanying text names Columbus as discoverer. Many supporters of Columbus felt that Vespucci had stolen an honour that rightfully belonged to Columbus. Most historians now believe that Vespucci was unaware of Waldseemüller's map before his death in 1512 and many assert that he was not even the author of the Soderini letter.
Vespucci letters.
Knowledge of Vespucci's voyages relies almost entirely on a handful of letters written by him or attributed to him. Two of these letters were published during his lifetime and received widespread attention throughout Europe. Several scholars now believe that Vespucci did not write the two published letters in the form in which they circulated during his lifetime. They suggest that they were fabrications based in part on genuine Vespucci letters.
The remaining documents were unpublished manuscripts; handwritten letters uncovered by researchers more than 250 years after Vespucci's death. After years of controversy, the authenticity of the three complete letters was convincingly demonstrated by Alberto Magnaghi in 1924. Most historians now accept them as the work of Vespucci but aspects of the accounts are still disputed.
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Historiography.
Vespucci has been called "the most enigmatic and controversial figure in early American history". The debate has become known among historians as the "Vespucci question". How many voyages did he make? What was his role on the voyages and what did he learn? The evidence relies almost entirely on a handful of letters attributed to him. Many historians have analysed these documents and have arrived at contradictory conclusions.
In 1515, Sebastian Cabot became one of the first to question Vespucci's accomplishments and express doubts about his 1497 voyage. Later, Bartolomé de las Casas argued that Vespucci was a liar and stole the credit that was due Columbus. By 1600, most regarded Vespucci as an impostor and not worthy of his honours and fame. In 1839, Alexander von Humboldt after careful consideration asserted the 1497 voyage was impossible but accepted the two Portuguese-sponsored voyages. Humboldt also called into question the assertion that Vespucci recognized that he had encountered a new continent. According to Humboldt, Vespucci (and Columbus) died in the belief that they had reached the eastern edge of Asia. Vespucci's reputation was perhaps at its lowest in 1856 when Ralph Waldo Emerson called Vespucci a "thief" and "pickle dealer" from Seville who managed to get "half the world baptized with his dishonest name".
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Opinions began to shift somewhat after 1857 when Brazilian historian Francisco Adolfo de Varnhagen wrote that everything in the Soderini letter was true. Other historians followed in support of Vespucci including John Fiske and Henry Harrisse.
In 1924, Alberto Magnaghi published the results of his exhaustive review of Vespucci's writings and relevant cartography. He denied Vespucci's authorship of the 1503 "Mundus Novus" and the 1505 Letter to Soderini, the only two texts published during his lifetime. He suggested that the Soderini letter was not written by Vespucci, but was cobbled together by unscrupulous Florentine publishers who combined several accounts – some from Vespucci, others from elsewhere. Magnaghi determined that the manuscript letters were authentic and based on them he was the first to propose that only the second and third voyages were true, and the first and fourth voyages (only found in the Soderini letter) were fabrications. While Magnaghi has been one of the chief proponents of a two-voyage narrative, Roberto Levellier was an influential Argentinian historian who endorsed the authenticity of all Vespucci's letters and proposed the most extensive itinerary for his four voyages.
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Other modern historians and popular writers have taken varying positions on Vespucci's letters and voyages, espousing two, three, or four voyages and supporting or denying the authenticity of his two printed letters. Most authors believe that the three manuscript letters are authentic while the first voyage as described in the Soderini letter draws the most criticism and disbelief.
A two-voyage thesis was accepted and popularized by Frederick J. Pohl (1944), and rejected by Germán Arciniegas (1955), who posited that all four voyages were truthful. Luciano Formisiano (1992) also rejects the Magnaghi thesis (acknowledging that publishers probably tampered with Vespucci's writings) and declares all four voyages genuine, but differs from Arciniegas in details (particularly the first voyage). Samuel Morison (1974) flatly rejected the first voyage but was noncommittal about the two published letters. Felipe Fernández-Armesto (2007) calls the authenticity question "inconclusive" and hypothesizes that the first voyage was probably another version of the second; the third is unassailable, and the fourth is probably true.
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Legacy.
Vespucci's historical importance may rest more with his letters (whether or not he wrote them all) than his discoveries. Burckhardt cites the naming of America after him as an example of the immense role of the Italian literature of the time in determining historical memory. Within a few years of the publication of his two letters, the European public became aware of the newly discovered continents of the Americas. According to Vespucci:
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