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Advanced Encryption Standard | The {{mono | The
right|320px|thumbnail|In the step, each byte of the state is combined with a byte of the round subkey using the XOR operation (⊕).
In the step, the subkey is combined with the state. For each round, a subkey is derived from the main key using Rijndael's key schedule; each subkey is the same size as the state. The subkey is added by combining of the state with the corresponding byte of the subkey using bitwise XOR. |
Advanced Encryption Standard | Optimization of the cipher | Optimization of the cipher
On systems with 32-bit or larger words, it is possible to speed up execution of this cipher by combining the and steps with the step by transforming them into a sequence of table lookups. This requires four 256-entry 32-bit tables (together occupying 4096 bytes). A round can then be performed with 16 table lookup operations and 12 32-bit exclusive-or operations, followed by four 32-bit exclusive-or operations in the step. Alternatively, the table lookup operation can be performed with a single 256-entry 32-bit table (occupying 1024 bytes) followed by circular rotation operations.
Using a byte-oriented approach, it is possible to combine the , , and steps into a single round operation. |
Advanced Encryption Standard | Security | Security
The National Security Agency (NSA) reviewed all the AES finalists, including Rijndael, and stated that all of them were secure enough for U.S. Government non-classified data. In June 2003, the U.S. Government announced that AES could be used to protect classified information:
The design and strength of all key lengths of the AES algorithm (i.e., 128, 192 and 256) are sufficient to protect classified information up to the SECRET level. TOP SECRET information will require use of either the 192 or 256 key lengths. The implementation of AES in products intended to protect national security systems and/or information must be reviewed and certified by NSA prior to their acquisition and use.
AES has 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys. |
Advanced Encryption Standard | Known attacks | Known attacks
For cryptographers, a cryptographic "break" is anything faster than a brute-force attacki.e., performing one trial decryption for each possible key in sequence . A break can thus include results that are infeasible with current technology. Despite being impractical, theoretical breaks can sometimes provide insight into vulnerability patterns. The largest successful publicly known brute-force attack against a widely implemented block-cipher encryption algorithm was against a 64-bit RC5 key by distributed.net in 2006.
The key space increases by a factor of 2 for each additional bit of key length, and if every possible value of the key is equiprobable; this translates into a doubling of the average brute-force key search time with every additional bit of key length. This implies that the effort of a brute-force search increases exponentially with key length. Key length in itself does not imply security against attacks, since there are ciphers with very long keys that have been found to be vulnerable.
AES has a fairly simple algebraic framework. In 2002, a theoretical attack, named the "XSL attack", was announced by Nicolas Courtois and Josef Pieprzyk, purporting to show a weakness in the AES algorithm, partially due to the low complexity of its nonlinear components. Since then, other papers have shown that the attack, as originally presented, is unworkable; see XSL attack on block ciphers.
During the AES selection process, developers of competing algorithms wrote of Rijndael's algorithm "we are concerned about [its] use ... in security-critical applications." In October 2000, however, at the end of the AES selection process, Bruce Schneier, a developer of the competing algorithm Twofish, wrote that while he thought successful academic attacks on Rijndael would be developed someday, he "did not believe that anyone will ever discover an attack that will allow someone to read Rijndael traffic."Bruce Schneier, AES Announced , October 15, 2000
By 2006, the best known attacks were on 7 rounds for 128-bit keys, 8 rounds for 192-bit keys, and 9 rounds for 256-bit keys.John Kelsey, Stefan Lucks, Bruce Schneier, Mike Stay, David Wagner, and Doug Whiting, Improved Cryptanalysis of Rijndael, Fast Software Encryption, 2000 pp213–230
Until May 2009, the only successful published attacks against the full AES were side-channel attacks on some specific implementations. In 2009, a new related-key attack was discovered that exploits the simplicity of AES's key schedule and has a complexity of 2119. In December 2009 it was improved to 299.5. This is a follow-up to an attack discovered earlier in 2009 by Alex Biryukov, Dmitry Khovratovich, and Ivica Nikolić, with a complexity of 296 for one out of every 235 keys. However, related-key attacks are not of concern in any properly designed cryptographic protocol, as a properly designed protocol (i.e., implementational software) will take care not to allow related keys, essentially by constraining an attacker's means of selecting keys for relatedness.
Another attack was blogged by Bruce Schneier
on July 30, 2009, and released as a preprint
on August 3, 2009. This new attack, by Alex Biryukov, Orr Dunkelman, Nathan Keller, Dmitry Khovratovich, and Adi Shamir, is against AES-256 that uses only two related keys and 239 time to recover the complete 256-bit key of a 9-round version, or 245 time for a 10-round version with a stronger type of related subkey attack, or 270 time for an 11-round version. 256-bit AES uses 14 rounds, so these attacks are not effective against full AES.
The practicality of these attacks with stronger related keys has been criticized, for instance, by the paper on chosen-key-relations-in-the-middle attacks on AES-128 authored by Vincent Rijmen in 2010.
In November 2009, the first known-key distinguishing attack against a reduced 8-round version of AES-128 was released as a preprint.
This known-key distinguishing attack is an improvement of the rebound, or the start-from-the-middle attack, against AES-like permutations, which view two consecutive rounds of permutation as the application of a so-called Super-S-box. It works on the 8-round version of AES-128, with a time complexity of 248, and a memory complexity of 232. 128-bit AES uses 10 rounds, so this attack is not effective against full AES-128.
The first key-recovery attacks on full AES were by Andrey Bogdanov, Dmitry Khovratovich, and Christian Rechberger, and were published in 2011. The attack is a biclique attack and is faster than brute force by a factor of about four. It requires 2126.2 operations to recover an AES-128 key. For AES-192 and AES-256, 2190.2 and 2254.6 operations are needed, respectively. This result has been further improved to 2126.0 for AES-128, 2189.9 for AES-192, and 2254.3 for AES-256 by Biaoshuai Tao and Hongjun Wu in a 2015 paper, which are the current best results in key recovery attack against AES.
This is a very small gain, as a 126-bit key (instead of 128 bits) would still take billions of years to brute force on current and foreseeable hardware. Also, the authors calculate the best attack using their technique on AES with a 128-bit key requires storing 288 bits of data. That works out to about 38 trillion terabytes of data, which was more than all the data stored on all the computers on the planet in 2016. A paper in 2015 later improved the space complexity to 256 bits, which is 9007 terabytes (while still keeping a time complexity of approximately 2126).
According to the Snowden documents, the NSA is doing research on whether a cryptographic attack based on tau statistic may help to break AES.
At present, there is no known practical attack that would allow someone without knowledge of the key to read data encrypted by AES when correctly implemented. |
Advanced Encryption Standard | Side-channel attacks | Side-channel attacks
Side-channel attacks do not attack the cipher as a black box, and thus are not related to cipher security as defined in the classical context, but are important in practice. They attack implementations of the cipher on hardware or software systems that inadvertently leak data. There are several such known attacks on various implementations of AES.
In April 2005, D. J. Bernstein announced a cache-timing attack that he used to break a custom server that used OpenSSL's AES encryption. The attack required over 200 million chosen plaintexts. The custom server was designed to give out as much timing information as possible (the server reports back the number of machine cycles taken by the encryption operation). However, as Bernstein pointed out, "reducing the precision of the server's timestamps, or eliminating them from the server's responses, does not stop the attack: the client simply uses round-trip timings based on its local clock, and compensates for the increased noise by averaging over a larger number of samples."
In October 2005, Dag Arne Osvik, Adi Shamir and Eran Tromer presented a paper demonstrating several cache-timing attacks against the implementations in AES found in OpenSSL and Linux's dm-crypt partition encryption function. One attack was able to obtain an entire AES key after only 800 operations triggering encryptions, in a total of 65 milliseconds. This attack requires the attacker to be able to run programs on the same system or platform that is performing AES.
In December 2009 an attack on some hardware implementations was published that used differential fault analysis and allows recovery of a key with a complexity of 232.
In November 2010 Endre Bangerter, David Gullasch and Stephan Krenn published a paper which described a practical approach to a "near real time" recovery of secret keys from AES-128 without the need for either cipher text or plaintext. The approach also works on AES-128 implementations that use compression tables, such as OpenSSL. Like some earlier attacks, this one requires the ability to run unprivileged code on the system performing the AES encryption, which may be achieved by malware infection far more easily than commandeering the root account.
In March 2016, C. Ashokkumar, Ravi Prakash Giri and Bernard Menezes presented a side-channel attack on AES implementations that can recover the complete 128-bit AES key in just 6–7 blocks of plaintext/ciphertext, which is a substantial improvement over previous works that require between 100 and a million encryptions. The proposed attack requires standard user privilege and key-retrieval algorithms run under a minute.
Many modern CPUs have built-in hardware instructions for AES, which protect against timing-related side-channel attacks. |
Advanced Encryption Standard | Quantum attacks | Quantum attacks
AES-256 is considered to be quantum resistant, as it has similar quantum resistance to AES-128's resistance against traditional, non-quantum, attacks at 128 bits of security. AES-192 and AES-128 are not considered quantum resistant due to their smaller key sizes. AES-192 has a strength of 96 bits against quantum attacks and AES-128 has 64 bits of strength against quantum attacks, making them both insecure. |
Advanced Encryption Standard | NIST/CSEC validation | NIST/CSEC validation
The Cryptographic Module Validation Program (CMVP) is operated jointly by the United States Government's National Institute of Standards and Technology (NIST) Computer Security Division and the Communications Security Establishment (CSE) of the Government of Canada. The use of cryptographic modules validated to NIST FIPS 140-2 is required by the United States Government for encryption of all data that has a classification of Sensitive but Unclassified (SBU) or above. From NSTISSP #11, National Policy Governing the Acquisition of Information Assurance: "Encryption products for protecting classified information will be certified by NSA, and encryption products intended for protecting sensitive information will be certified in accordance with NIST FIPS 140-2."
The Government of Canada also recommends the use of FIPS 140 validated cryptographic modules in unclassified applications of its departments.
Although NIST publication 197 ("FIPS 197") is the unique document that covers the AES algorithm, vendors typically approach the CMVP under FIPS 140 and ask to have several algorithms (such as Triple DES or SHA1) validated at the same time. Therefore, it is rare to find cryptographic modules that are uniquely FIPS 197 validated and NIST itself does not generally take the time to list FIPS 197 validated modules separately on its public web site. Instead, FIPS 197 validation is typically just listed as an "FIPS approved: AES" notation (with a specific FIPS 197 certificate number) in the current list of FIPS 140 validated cryptographic modules.
The Cryptographic Algorithm Validation Program (CAVP) allows for independent validation of the correct implementation of the AES algorithm. Successful validation results in being listed on the NIST validations page. This testing is a pre-requisite for the FIPS 140-2 module validation. However, successful CAVP validation in no way implies that the cryptographic module implementing the algorithm is secure. A cryptographic module lacking FIPS 140-2 validation or specific approval by the NSA is not deemed secure by the US Government and cannot be used to protect government data.
FIPS 140-2 validation is challenging to achieve both technically and fiscally. There is a standardized battery of tests as well as an element of source code review that must be passed over a period of a few weeks. The cost to perform these tests through an approved laboratory can be significant (e.g., well over $30,000 US) and does not include the time it takes to write, test, document and prepare a module for validation. After validation, modules must be re-submitted and re-evaluated if they are changed in any way. This can vary from simple paperwork updates if the security functionality did not change to a more substantial set of re-testing if the security functionality was impacted by the change. |
Advanced Encryption Standard | Test vectors | Test vectors
Test vectors are a set of known ciphers for a given input and key. NIST distributes the reference of AES test vectors as AES Known Answer Test (KAT) Vectors.The AES Known Answer Test (KAT) Vectors are available in Zip format within the NIST site here |
Advanced Encryption Standard | Performance | Performance
High speed and low RAM requirements were some of the criteria of the AES selection process. As the chosen algorithm, AES performed well on a wide variety of hardware, from 8-bit smart cards to high-performance computers.
On a Pentium Pro, AES encryption requires 18 clock cycles per byte (cpb), equivalent to a throughput of about 11 MiB/s for a 200 MHz processor.
On Intel Core and AMD Ryzen CPUs supporting AES-NI instruction set extensions, throughput can be multiple GiB/s. On an Intel Westmere CPU, AES encryption using AES-NI takes about 1.3 cpb for AES-128 and 1.8 cpb for AES-256. |
Advanced Encryption Standard | Implementations | Implementations |
Advanced Encryption Standard | See also | See also
AES modes of operation
Disk encryption
Whirlpool – hash function created by Vincent Rijmen and Paulo S. L. M. Barreto
List of free and open-source software packages |
Advanced Encryption Standard | Notes | Notes |
Advanced Encryption Standard | References | References
alternate link (companion web site contains online lectures on AES) |
Advanced Encryption Standard | External links | External links
AES algorithm archive information – (old, unmaintained)
Animation of Rijndael – AES deeply explained and animated using Flash (by Enrique Zabala / University ORT / Montevideo / Uruguay). This animation (in English, Spanish, and German) is also part of CrypTool 1 (menu Indiv. Procedures → Visualization of Algorithms → AES).
HTML5 Animation of Rijndael – Same Animation as above made in HTML5.
Category:Advanced Encryption Standard
Category:Cryptography
Category:Belgian inventions |
Advanced Encryption Standard | Table of Content | Short description, Definitive standards, Description of the ciphers, High-level description of the algorithm, The {{mono, The {{mono, The {{mono, The {{mono, Optimization of the cipher, Security, Known attacks, Side-channel attacks, Quantum attacks, NIST/CSEC validation, Test vectors, Performance, Implementations, See also, Notes, References, External links |
April 26 | pp-pc1 | |
April 26 | Events | Events |
April 26 | Pre-1600 | Pre-1600
1336 – Francesco Petrarca (Petrarch) ascends Mont Ventoux.
1478 – The Pazzi family attack on Lorenzo de' Medici in order to displace the ruling Medici family kills his brother Giuliano during High Mass in Florence Cathedral.
1564 – Playwright William Shakespeare is baptized in Stratford-upon-Avon, Warwickshire, England (date of birth is unknown). |
April 26 | 1601–1900 | 1601–1900
1607 – The Virginia Company colonists make landfall at Cape Henry.
1721 – A massive earthquake devastates the Iranian city of Tabriz.
1777 – Sybil Ludington, aged 16, allegedly rode to alert American colonial forces to the approach of British regular forces
1794 – Battle of Beaumont during the Flanders Campaign of the War of the First Coalition.
1802 – Napoleon Bonaparte signs a general amnesty to allow all but about one thousand of the most notorious émigrés of the French Revolution to return to France.
1803 – Thousands of meteor fragments fall from the skies of L'Aigle, France; the event convinces European scientists that meteors exist.
1805 – First Barbary War: United States Marines captured Derne under the command of First Lieutenant Presley O'Bannon.
1865 – Union cavalry troopers corner and shoot dead John Wilkes Booth, assassin of President Abraham Lincoln, in Virginia.
1900 – Fires destroy Canadian cities Ottawa and Hull, reducing them to ashes in 12 hours. Twelve thousand people are left without a home.| |
April 26 | 1901–present | 1901–present
1903 – Atlético Madrid Association football club is founded.
1915 – World War I: Italy secretly signs the Treaty of London pledging to join the Allied Powers.
1916 – Easter Rising: Battle of Mount Street Bridge.
1920 – Ice hockey makes its Olympic debut at the Antwerp Games with center Frank Fredrickson scoring seven goals in Canada's 12–1 drubbing of Sweden in the gold medal match."Winners in first Olympic ice hockey tournament" Victoria Daily Times, April 28, 1920 (p. 10). Retrieved 2020-07-27.
1923 – The Duke of York weds Lady Elizabeth Bowes-Lyon at Westminster Abbey.
1925 – Paul von Hindenburg defeats Wilhelm Marx in the second round of the German presidential election to become the first directly elected head of state of the Weimar Republic.
1933 – The Gestapo, the official secret police force of Nazi Germany, is established by Hermann Göring.
1937 – Spanish Civil War: Guernica, Spain, is bombed by the German Condor Legion and the Italian Aviazione Legionaria.
1942 – Benxihu Colliery accident in Manchukuo leaves 1,549 Chinese miners dead.
1943 – The Easter Riots break out in Uppsala, Sweden.
1944 – Georgios Papandreou becomes head of the Greek government-in-exile based in Egypt.
1944 – Heinrich Kreipe is captured by Allied commandos in occupied Crete.
1945 – World War II: Battle of Bautzen: Last successful German tank-offensive of the war and last noteworthy victory of the Wehrmacht.
1945 – World War II: Filipino troops of the 66th Infantry Regiment, Philippine Commonwealth Army, USAFIP-NL and the American troops of the 33rd and 37th Infantry Division, United States Army liberate Baguio as they fight against the Japanese forces under General Tomoyuki Yamashita.
1954 – The Geneva Conference, an effort to restore peace in Indochina and Korea, begins.
1954 – The first clinical trials of Jonas Salk's polio vaccine begin in Fairfax County, Virginia.
1956 – , the world's first successful container ship, leaves Port Newark, New Jersey, for Houston, Texas.
1958 – Final run of the Baltimore and Ohio Railroad's Royal Blue from Washington, D.C., to New York City after 68 years, the first U.S. passenger train to use electric locomotives.
1960 – Forced out by the April Revolution, President of South Korea Syngman Rhee resigns after 12 years of dictatorial rule.
1962 – NASA's Ranger 4 spacecraft crashes into the Moon.
1962 – The British space programme launches its first satellite, the Ariel 1.
1963 – In Libya, amendments to the constitution transform Libya (United Kingdom of Libya) into one national unity (Kingdom of Libya) and allows for female participation in elections.
1964 – Tanganyika and Zanzibar merge to form the United Republic of Tanzania.
1966 – The magnitude 5.1 Tashkent earthquake affects the largest city in Soviet Central Asia with a maximum MSK intensity of VII (Very strong). Tashkent is mostly destroyed and 15–200 are killed.
1966 – A new government is formed in the Republic of the Congo, led by Ambroise Noumazalaye.
1970 – The Convention Establishing the World Intellectual Property Organization enters into force.
1981 – Dr. Michael R. Harrison of the University of California, San Francisco Medical Center performs the world's first human open fetal surgery.
1986 – The Chernobyl disaster occurs in the Ukrainian Soviet Socialist Republic.
1989 – The deadliest known tornado strikes Central Bangladesh, killing upwards of 1,300, injuring 12,000, and leaving as many as 80,000 homeless.
1989 – People's Daily publishes the April 26 Editorial which inflames the nascent Tiananmen Square protests.
1991 – Fifty-five tornadoes break out in the central United States. Before the outbreak's end, Andover, Kansas, would record the year's only F5 tornado.
1993 – The Space Shuttle Columbia is launched on mission STS-55 to conduct experiments aboard the Spacelab module.
1994 – China Airlines Flight 140 crashes at Nagoya Airport in Japan, killing 264 of the 271 people on board.
1994 – South Africa begins its first multiracial election, which is won by Nelson Mandela's African National Congress.
2002 – Robert Steinhäuser kills 16 at Gutenberg-Gymnasium in Erfurt, Germany before committing suicide.
2005 – Cedar Revolution: Under international pressure, Syria withdraws the last of its 14,000 troop military garrison in Lebanon, ending its 29-year military domination of that country (Syrian occupation of Lebanon).
2015 – Nursultan Nazarbayev is re-elected President of Kazakhstan with 97.7% of the vote, one of the biggest vote shares in Kazakhstan's history.
2025 – A car ramming attack at a Lapu-Lapu Day festival kills 11 people and injures at least 30 in Vancouver, Canada. |
April 26 | Births | Births |
April 26 | Pre-1600 | Pre-1600
121 – Marcus Aurelius, Roman emperor (d. 180)
757 – Hisham I of Córdoba (d. 796)
764 – Al-Hadi, Abbasid caliph (d. 786)
1284 – Alice de Toeni, Countess of Warwick (d. 1324)
1319 – John II of France (d. 1364)
1538 – Gian Paolo Lomazzo, Italian painter and academic (d. 1600)
1575 – Marie de' Medici, queen of Henry IV of France (d. 1642) |
April 26 | 1601–1900 | 1601–1900
1647 – William Ashhurst, English banker, Sheriff of London, Lord Mayor of London and politician (d. 1720)
1648 – Peter II of Portugal (d. 1706)
1697 – Adam Falckenhagen, German lute player and composer (d. 1754)
1710 – Thomas Reid, Scottish philosopher and academic (d. 1796)
1718 – Esek Hopkins, American commander (d. 1802)
1774 – Christian Leopold von Buch, German geologist and paleontologist (d. 1853)
1782 – Maria Amalia of Naples and Sicily, Queen of France (d. 1866)
1785 – John James Audubon, French-American ornithologist and painter (d. 1851)
1787 – Ludwig Uhland, German poet, philologist, and historian (d. 1862)
1798 – Eugène Delacroix, French painter and lithographer (d. 1863)
1801 – Ambrose Dudley Mann, American politician and diplomat, 1st United States Assistant Secretary of State (d. 1889)
1804 – Charles Goodyear, American banker, lawyer, and politician (d. 1876)
1822 – Frederick Law Olmsted, American journalist and designer, co-designed Central Park (d. 1903)
1834 – Charles Farrar Browne, American author (d. 1867)
1856 – Joseph Ward, Australian-New Zealand businessman and politician, 17th Prime Minister of New Zealand (d. 1930)
1862 – Edmund C. Tarbell, American painter and educator (d. 1938)
1865 – Akseli Gallen-Kallela, Finnish artist (d. 1931)
1876 – Ernst Felle, German rower (d. 1959)
1877 – James Dooley, Irish-Australian politician, 21st Premier of New South Wales (d. 1950)
1878 – Rafael Guízar y Valencia, Mexican bishop and saint (d. 1938)
1879 – Eric Campbell, British actor (d. 1917)
1879 – Owen Willans Richardson, English physicist and academic, Nobel Prize laureate (d. 1959)
1886 – Ma Rainey, American singer-songwriter (d. 1939)
1886 – Ğabdulla Tuqay, Russian poet and publicist (d. 1913)
1889 – Anita Loos, American author, playwright, and screenwriter (d. 1981)
1889 – Ludwig Wittgenstein, Austrian-English philosopher and academic (d. 1951)
1894 – Rudolf Hess, German politician and Deputy Führer in Nazi regime until 1941 (d. 1987)
1896 – Ruut Tarmo, Estonian actor and director (d. 1967)
1896 – Ernst Udet, leading German fighter pilot in World War I and Chief of Procurement and Supply in the Luftwaffe (d. 1941)
1897 – Eddie Eagan, American boxer and bobsledder (d. 1967)
1897 – Douglas Sirk, German-American director and screenwriter (d. 1987)
1898 – Vicente Aleixandre, Spanish poet and author, Nobel Prize laureate (d. 1984)
1898 – John Grierson, Scottish director and producer (d. 1972)
1899 – Oscar Rabin, Latvian-English saxophonist and bandleader (d. 1958)
1900 – Eva Aschoff, German bookbinder and calligrapher (d. 1969)
1900 – Charles Francis Richter, American seismologist and physicist (d. 1985)
1900 – Hack Wilson, American baseball player (d. 1948) |
April 26 | 1901–present | 1901–present
1904 – Paul-Émile Léger, Canadian cardinal (d. 1991)
1904 – Xenophon Zolotas, Greek economist and politician, 177th Prime Minister of Greece (d. 2004)
1905 – Jean Vigo, French director and screenwriter (d. 1934)
1907 – Ilias Tsirimokos, Greek politician, Prime Minister of Greece (d. 1968)
1909 – Marianne Hoppe, German actress (d. 2002)
1910 – Tomoyuki Tanaka, Japanese screenwriter and producer (d. 1997)
1911 – Paul Verner, German soldier and politician (d. 1986)
1912 – A. E. van Vogt, Canadian-American author (d. 2000)
1914 – Bernard Malamud, American novelist and short story writer (d. 1986)
1914 – James Rouse, American real estate developer (d. 1996)
1916 – Eyvind Earle, American artist, author, and illustrator (d. 2000)
1916 – Ken Wallis, English commander, engineer, and pilot (d. 2013)
1916 – Morris West, Australian author and playwright (d. 1999)
1917 – Sal Maglie, American baseball player and coach (d. 1992)
1917 – I. M. Pei, Chinese-American architect, designed the National Gallery of Art and Bank of China Tower (d. 2019)
1917 – Virgil Trucks, American baseball player and coach (d. 2013)
1918 – Fanny Blankers-Koen, Dutch sprinter and long jumper (d. 2004)
1921 – Jimmy Giuffre, American clarinet player, saxophonist, and composer (d. 2008)
1922 – J. C. Holt, English historian and academic (d. 2014)
1922 – Jeanne Sauvé, Canadian journalist and politician, Governor General of Canada (d. 1993)
1922 – Margaret Scott, South African-Australian ballerina and choreographer (d. 2019)
1924 – Browning Ross, American runner and soldier (d. 1998)
1925 – Vladimir Boltyansky, Russian mathematician, educator and author (d. 2019)
1925 – Gerard Cafesjian, American businessman and philanthropist (d. 2013)
1925 – Michele Ferrero, Italian entrepreneur (d. 2015)
1925 – Frank Hahn, British economist (d. 2013)
1926 – Michael Mathias Prechtl, German soldier and illustrator (d. 2003)
1927 – Jack Douglas, English actor (d. 2008)
1927 – Anne McLaren, British scientist (d. 2007)
1927 – Harry Gallatin, American basketball player and coach (d. 2015)
1927 – Granny Hamner, American baseball player (d. 1993)
1929 – Richard Mitchell, American author and educator (d. 2002)
1930 – Roger Moens, Belgian runner and sportscaster
1931 – Paul Almond, Canadian director, producer, and screenwriter (d. 2015)
1931 – Bernie Brillstein, American talent agent and producer (d. 2008)
1931 – John Cain Jr., Australian politician, 41st Premier of Victoria (d. 2019)
1932 – Israr Ahmed, Indian-Pakistani theologian, philosopher, and scholar (d. 2010)
1932 – Shirley Cawley, English long jumper
1932 – Frank D'Rone, American singer and guitarist (d. 2013)
1932 – Francis Lai, French accordion player and composer (d. 2018)
1932 – Michael Smith, English-Canadian biochemist and geneticist, Nobel Prize laureate (d. 2000)
1933 – Carol Burnett, American actress, singer, and producer
1933 – Al McCoy, American sports announcer (d. 2024)
1933 – Filiberto Ojeda Ríos, Puerto Rican-American general (d. 2005)
1933 – Arno Allan Penzias, German-American physicist and academic, Nobel Prize laureate (d. 2024)
1937 – Jean-Pierre Beltoise, French racing driver and motorcycle racer (d. 2015)
1938 – Duane Eddy, American singer-songwriter, guitarist, and actor (d. 2024)
1938 – Maurice Williams, American doo-wop/R&B singer-songwriter
1940 – Giorgio Moroder, Italian singer-songwriter and producer
1940 – Cliff Watson, English rugby league player (d. 2018)
1940 – Tan Cheng Bock, Singaporean doctor and politician
1941 – Claudine Auger, French model and actress (d. 2019)
1942 – Svyatoslav Belza, Russian journalist, author, and critic (d. 2014)
1942 – Sharon Carstairs, Canadian lawyer and politician, Leader of the Government in the Senate
1942 – Michael Kergin, Canadian diplomat, Canadian Ambassador to the United States
1942 – Bobby Rydell, American singer and actor (d. 2022)
1942 – Jadwiga Staniszkis, Polish sociologist, political scientist, and academic (d. 2024)
1943 – Gary Wright, American singer-songwriter, keyboard player, and producer (d. 2023)
1943 – Peter Zumthor, Swiss architect and academic, designed the Therme Vals
1944 – Richard Bradshaw, English conductor (d. 2007)
1945 – Richard Armitage, American diplomat and government official (d. 2025)
1945 – Howard Davies, English director and producer (d. 2016)
1945 – Dick Johnson, Australian racing driver
1945 – Sylvain Simard, Canadian academic and politician
1946 – Ralph Coates, English international footballer (d. 2010)
1946 – Marilyn Nelson, American poet and author
1946 – Alberto Quintano, Chilean footballer
1949 – Carlos Bianchi, Argentinian footballer and manager
1949 – Jerry Blackwell, American wrestler (d. 1995)
1950 – Junko Ohashi, Japanese singer (d. 2023)
1951 – John Battle, English politician
1954 – Tatyana Fomina, Estonian chess player
1954 – Alan Hinkes, English mountaineer and explorer
1955 – Kurt Bodewig, German politician
1956 – Koo Stark, American actress and photographer
1958 – John Crichton-Stuart, 7th Marquess of Bute, Scottish racing driver (d. 2021)
1958 – Giancarlo Esposito, American actor, director, and producer
1958 – Georgios Kostikos, Greek footballer, coach, and manager
1959 – John Corabi, American singer-songwriter and guitarist
1959 – Pedro Pierluisi, Puerto Rican politician
1960 – H. G. Carrillo, American writer and academic (d. 2020)
1960 – Steve Lombardozzi, American baseball player and coach
1960 – Roger Taylor, English drummer
1961 – Joan Chen, Chinese-American actress, director, producer, and screenwriter
1961 – Chris Mars, American artist
1962 – Colin Anderson, English footballer
1962 – Debra Wilson, American actress and comedian
1963 – Jet Li, Chinese-Singaporean martial artist, actor, and producer
1963 – Colin Scotts, Australian-American football player
1963 – Cornelia Ullrich, German hurdler
1963 – Bill Wennington, Canadian basketball player
1965 – Susannah Harker, English actress
1965 – Kevin James, American actor and comedian
1967 – Glenn Thomas Jacobs, American professional wrestler, actor, businessman and politician
1967 – Marianne Jean-Baptiste, English actress and singer-songwriter
1967 – Toomas Tõniste, Estonian sailor and politician
1970 – Dean Austin, English footballer and manager
1970 – Melania Trump, Slovene-American model; 47th First Lady of the United States
1970 – Kristen R. Ghodsee, American ethnographer and academic
1970 – Tionne "T-Boz" Watkins, American singer-songwriter, dancer, and actress
1971 – Naoki Tanaka, Japanese comedian and actor
1971 – Jay DeMarcus, American bass player, songwriter, and producer
1972 – Jason Bargwanna, Australian racing driver
1972 – Kiko, Spanish footballer
1972 – Natrone Means, American football player and coach
1972 – Avi Nimni, Israeli footballer and manager
1973 – Geoff Blum, American baseball player and sportscaster
1973 – Jules Naudet, French-American director and producer
1973 – Chris Perry, English footballer
1973 – Óscar, Spanish footballer and coach
1975 – Joey Jordison, American musician and songwriter (d. 2021)
1975 – Rahul Verma, Indian social worker and activist
1976 – Václav Varaďa, Czech ice hockey player
1977 – Samantha Cristoforetti, Italian astronaut
1977 – Kosuke Fukudome, Japanese baseball player
1977 – Roxana Saberi, American journalist and author
1977 – Tom Welling, American actor
1978 – Stana Katic, Canadian actress
1978 – Peter Madsen, Danish footballer
1980 – Jordana Brewster, Panamanian-American actress
1980 – Marlon King, English footballer
1980 – Anna Mucha, Polish actress and journalist
1980 – Channing Tatum, American actor and producer
1981 – Caro Emerald, Dutch pop and jazz singer
1981 – Ms. Dynamite, English rapper and producer
1981 – Sandra Schmitt, German skier (d. 2000)
1982 – Novlene Williams-Mills, Jamaican sprinter
1983 – José María López, Argentinian racing driver
1983 – Jessica Lynch, American soldier
1985 – John Isner, American tennis player
1986 – Lior Refaelov, Israeli footballer
1986 – Yuliya Zaripova, Russian runner
1987 – Jorge Andújar Moreno, Spanish footballer
1989 – Melvin Ingram, American football player
1989 – Kang Daesung, South Korean singer
1990 – Jonathan dos Santos, Mexican footballer
1990 – Mitch Rein, Australian rugby league player
1990 – Nevin Spence, Northern Irish rugby player (d. 2012)
1990 – Joey Wendle, American baseball player
1991 – Peter Handscomb, Australian cricketer
1991 – Isaac Liu, New Zealand rugby league player
1992 – Aaron Judge, American baseball player
1992 – Delon Wright, American basketball player
1994 – Daniil Kvyat, Russian racing driver
1994 – Odysseas Vlachodimos, Greek international footballer
1996 – Jordan Pefok, American footballer
1997 – Max Hechtman, American filmmaker, video editor and videographer
1997 – Kirill Kaprizov, Russian ice hockey player
1997 – Amber Midthunder, American actress
1997 – Calvin Verdonk, Indonesian footballer
2001 – Thiago Almada, Argentine footballer
2005 – Alex Sarr, French basketball player |
April 26 | Deaths | Deaths |
April 26 | Pre-1600 | Pre-1600
499 – Emperor Xiaowen of Northern Wei (b. 467)
645 – Richarius, Frankish monk and saint (b. 560)
680 – Mu'awiya I, Umayyad caliph (b. 602)
757 – Pope Stephen II (b. 715)
893 – Chen Jingxuan, general of the Tang Dynasty
962 – Adalbero I, bishop of Metz
1192 – Emperor Go-Shirakawa of Japan (b. 1127)
1366 – Simon Islip, Archbishop of Canterbury
1392 – Chŏng Mong-ju, Korean civil minister, diplomat and scholar (b. 1338)
1444 – Robert Campin, Flemish painter (b. 1378)
1478 – Giuliano de' Medici, Italian ruler (b. 1453)
1489 – Ashikaga Yoshihisa, Japanese shōgun (b. 1465)
1558 – Jean Fernel, French physician (b. 1497) |
April 26 | 1601–1900 | 1601–1900
1686 – Magnus Gabriel De la Gardie, Swedish statesman and military man (b. 1622)
1716 – John Somers, 1st Baron Somers, English jurist and politician, Lord High Chancellor of Great Britain (b. 1651)
1784 – Nano Nagle, Irish nun and educator, founded the Presentation Sisters (b. 1718)
1789 – Petr Ivanovich Panin, Russian general (b. 1721)
1809 – Bernhard Schott, German music publisher (b. 1748)
1865 – John Wilkes Booth, American actor, assassin of Abraham Lincoln (b. 1838)
1881 – Ludwig Freiherr von und zu der Tann-Rathsamhausen, German general (b. 1815)
1895 – Eric Stenbock, Estonian-English author and poet (b. 1860) |
April 26 | 1901–present | 1901–present
1910 – Bjørnstjerne Bjørnson, Norwegian-French author, poet, and playwright, Nobel Prize laureate (b. 1832)
1915 – John Bunny, American actor (b. 1863)
1915 – Ida Hunt Udall, American diarist (b. 1858)
1916 – Mário de Sá-Carneiro, Portuguese poet and writer (b. 1890)
1920 – Srinivasa Ramanujan, Indian mathematician and theorist (b. 1887)
1932 – William Lockwood, English cricketer (b. 1868)
1934 – Arturs Alberings, Latvian politician, former Prime Minister of Latvia (b. 1876)
1934 – Konstantin Vaginov, Russian poet and novelist (b. 1899)
1940 – Carl Bosch, German chemist and engineer, Nobel Prize laureate (b. 1874)
1944 – Violette Morris, French footballer, shot putter, and discus thrower (b. 1893)
1945 – Sigmund Rascher, German physician (b. 1909)
1945 – Pavlo Skoropadskyi, German-Ukrainian general and politician, Hetman of Ukraine (b. 1871)
1946 – James Larkin White, American miner, explorer, and park ranger (b. 1882)
1950 – George Murray Hulbert, American lawyer, judge, and politician (b. 1881)
1951 – Arnold Sommerfeld, German physicist and academic (b. 1868)
1956 – Edward Arnold, American actor (b. 1890)
1957 – Gichin Funakoshi, Japanese martial artist, founded Shotokan (b. 1868)
1964 – E. J. Pratt, Canadian poet and author (b. 1882)
1968 – John Heartfield, German illustrator and photographer (b. 1891)
1969 – Morihei Ueshiba, Japanese martial artist, founded aikido (b. 1883)
1970 – Erik Bergman, Swedish minister and author (b. 1886)
1970 – Gypsy Rose Lee, American actress, striptease dancer, and writer (b. 1911)
1973 – Irene Ryan, American actress and philanthropist (b. 1902)
1976 – Sidney Franklin, American bullfighter (b. 1903)
1976 – Sid James, South African-English actor (b. 1913)
1976 – Armstrong Sperry, American author and illustrator (b. 1897)
1980 – Cicely Courtneidge, Australian-born British actress, comedian and singer (b. 1893)
1981 – Jim Davis, American actor (b. 1909)
1984 – Count Basie, American pianist, composer, and bandleader (b. 1904)
1986 – Broderick Crawford, American actor (b. 1911)
1986 – Bessie Love, American actress (b. 1898)
1986 – Dechko Uzunov, Bulgarian painter (b. 1899)
1987 – Shankar, Indian composer and conductor (b. 1922)
1987 – John Silkin, English lawyer and politician, Shadow Leader of the House of Commons (b. 1923)
1989 – Lucille Ball, American model, actress, comedian, and producer (b. 1911)
1991 – Leo Arnaud, French-American composer and conductor (b. 1904)
1991 – Carmine Coppola, American composer and conductor (b. 1910)
1991 – A. B. Guthrie, Jr., American novelist and historian, (b. 1901)
1991 – Richard Hatfield, Canadian lawyer and politician, 26th Premier of New Brunswick (b. 1931)
1994 – Masutatsu Ōyama, Japanese martial artist, founded Kyokushin kaikan (b. 1923)
1996 – Stirling Silliphant, American screenwriter and producer (b. 1918)
1999 – Adrian Borland, English singer-songwriter, guitarist, and producer (b. 1957)
1999 – Jill Dando, English journalist and television personality (b. 1961)
2003 – Rosemary Brown, Jamaican-Canadian academic and politician (b. 1930)
2003 – Yun Hyon-seok, South Korean poet and author (b. 1984)
2003 – Edward Max Nicholson, Irish environmentalist, co-founded the World Wide Fund for Nature (b. 1904)
2004 – Hubert Selby, Jr., American author, poet, and screenwriter (b. 1928)
2005 – Mason Adams, American actor (b. 1919)
2005 – Elisabeth Domitien, Prime Minister of the Central African Republic (b. 1925)
2005 – Maria Schell, Austrian-Swiss actress (b. 1926)
2005 – Augusto Roa Bastos, Paraguayan journalist, author, and academic (b. 1917)
2007 – Jack Valenti, American businessman, created the MPAA film rating system (b. 1921)
2008 – Árpád Orbán, Hungarian footballer (b. 1938)
2009 – Hans Holzer, Austrian-American paranormal investigator and author (b. 1920)
2010 – Mariam A. Aleem, Egyptian graphic designer and academic (b. 1930)
2010 – Urs Felber, Swiss engineer and businessman (b. 1942)
2011 – Phoebe Snow, American singer-songwriter and guitarist (b. 1950)
2012 – Terence Spinks, English boxer and trainer (b. 1938)
2013 – Jacqueline Brookes, American actress and educator (b. 1930)
2013 – George Jones, American singer-songwriter and guitarist (b. 1931)
2013 – Earl Silverman, Canadian men's rights advocate (b. 1948)
2014 – Gerald Guralnik, American physicist and academic (b. 1936)
2014 – Paul Robeson, Jr., American historian and author (b. 1927)
2014 – DJ Rashad, American electronic musician, producer and DJ (b. 1979)
2015 – Jayne Meadows, American actress (b. 1919)
2015 – Marcel Pronovost, Canadian ice hockey player and coach (b. 1930)
2016 – Harry Wu, Chinese human rights activist (b. 1937)
2017 – Jonathan Demme, American filmmaker, producer and screenwriter (b. 1944)
2022 – Klaus Schulze, German composer and musician (b. 1947)
2023 – Jerry Apodaca, American politician, 24th Governor of New Mexico (b. 1934)
2023 – Tangaraju Suppiah, Singaporean drug trafficker (b. 1977) |
April 26 | Holidays and observances | Holidays and observances
Chernobyl disaster related observances:
Day of Remembrance of the Chernobyl tragedy (Belarus)
Memorial Day of Radiation Accidents and Catastrophes (Russia)
Christian feast day:
Aldobrandesca (or Alda)
Franca Visalta
Lucidius of Verona
Our Lady of Good Counsel
Pope Anacletus and Marcellinus
Rafael Arnáiz Barón
Riquier
Paschasius Radbertus
Peter of Rates (or of Braga)
Robert Hunt (Episcopal Church (USA))
Stephen of Perm, see also Old Permic Alphabet Day
Trudpert
April 26 (Eastern Orthodox liturgics)
Confederate Memorial Day (Florida, United States)
Union Day (Tanzania)
World Intellectual Property Day |
April 26 | References | References |
April 26 | External links | External links
BBC: On This Day
Historical Events on April 26
Category:Days of April |
April 26 | Table of Content | pp-pc1, Events, Pre-1600, 1601–1900, 1901–present, Births, Pre-1600, 1601–1900, 1901–present, Deaths, Pre-1600, 1601–1900, 1901–present, Holidays and observances, References, External links |
Anisotropy | short description | thumb|upright=1.36|WMAP image of the tiny anisotropies in the cosmic microwave background radiation
Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical or mechanical properties when measured along different axes, e.g. absorbance, refractive index, conductivity, and tensile strength.
An example of anisotropy is light coming through a polarizer. Another is wood, which is easier to split along its grain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions). |
Anisotropy | Fields of interest | Fields of interest |
Anisotropy | Computer graphics | Computer graphics
In the field of computer graphics, an anisotropic surface changes in appearance as it rotates about its geometric normal, as is the case with velvet.
Anisotropic filtering (AF) is a method of enhancing the image quality of textures on surfaces that are far away and viewed at a shallow angle. Older techniques, such as bilinear and trilinear filtering, do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily. |
Anisotropy | Chemistry | Chemistry
A chemical anisotropic filter, as used to filter particles, is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the proximal regions filter out larger particles and distal regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration.
In fluorescence spectroscopy, the fluorescence anisotropy, calculated from the polarization properties of fluorescence from samples excited with plane-polarized light, is used, e.g., to determine the shape of a macromolecule. Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photon.
In NMR spectroscopy, the orientation of nuclei with respect to the applied magnetic field determines their chemical shift. In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like the pi system of benzene. This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change. |
Anisotropy | Real-world imagery | Real-world imagery
Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal). |
Anisotropy | Physics | Physics
thumb|300px|right|A plasma globe displaying the nature of plasmas, in this case, the phenomenon of "filamentation"
Physicists from University of California, Berkeley reported about their detection of the cosmic anisotropy in cosmic microwave background radiation in 1977. Their experiment demonstrated the Doppler shift caused by the movement of the earth with respect to the early Universe matter, the source of the radiation. Cosmic anisotropy has also been seen in the alignment of galaxies' rotation axes and polarization angles of quasars.
Physicists use the term anisotropy to describe direction-dependent properties of materials. Magnetic anisotropy, for example, may occur in a plasma, so that its magnetic field is oriented in a preferred direction. Plasmas may also show "filamentation" (such as that seen in lightning or a plasma globe) that is directional.
An anisotropic liquid has the fluidity of a normal liquid, but has an average structural order relative to each other along the molecular axis, unlike water or chloroform, which contain no structural ordering of the molecules. Liquid crystals are examples of anisotropic liquids.
Some materials conduct heat in a way that is isotropic, that is independent of spatial orientation around the heat source. Heat conduction is more commonly anisotropic, which implies that detailed geometric modeling of typically diverse materials being thermally managed is required. The materials used to transfer and reject heat from the heat source in electronics are often anisotropic.
Many crystals are anisotropic to light ("optical anisotropy"), and exhibit properties such as birefringence. Crystal optics describes light propagation in these media. An "axis of anisotropy" is defined as the axis along which isotropy is broken (or an axis of symmetry, such as normal to crystalline layers). Some materials can have multiple such optical axes. |
Anisotropy | Geophysics and geology | Geophysics and geology
Seismic anisotropy is the variation of seismic wavespeed with direction. Seismic anisotropy is an indicator of long range order in a material, where features smaller than the seismic wavelength (e.g., crystals, cracks, pores, layers, or inclusions) have a dominant alignment. This alignment leads to a directional variation of elasticity wavespeed. Measuring the effects of anisotropy in seismic data can provide important information about processes and mineralogy in the Earth; significant seismic anisotropy has been detected in the Earth's crust, mantle, and inner core.
Geological formations with distinct layers of sedimentary material can exhibit electrical anisotropy; electrical conductivity in one direction (e.g. parallel to a layer), is different from that in another (e.g. perpendicular to a layer). This property is used in the gas and oil exploration industry to identify hydrocarbon-bearing sands in sequences of sand and shale. Sand-bearing hydrocarbon assets have high resistivity (low conductivity), whereas shales have lower resistivity. Formation evaluation instruments measure this conductivity or resistivity, and the results are used to help find oil and gas in wells. The mechanical anisotropy measured for some of the sedimentary rocks like coal and shale can change with corresponding changes in their surface properties like sorption when gases are produced from the coal and shale reservoirs.
The hydraulic conductivity of aquifers is often anisotropic for the same reason. When calculating groundwater flow to drains The corresponding free EnDrain program can be downloaded from: . or to wells, 9 pp. The corresponding free WellDrain program can be downloaded from: the difference between horizontal and vertical permeability must be taken into account; otherwise the results may be subject to error.
Most common rock-forming minerals are anisotropic, including quartz and feldspar. Anisotropy in minerals is most reliably seen in their optical properties. An example of an isotropic mineral is garnet.
Igneous rock like granite also shows the anisotropy due to the orientation of the minerals during the solidification process. |
Anisotropy | Medical acoustics | Medical acoustics
Anisotropy is also a well-known property in medical ultrasound imaging describing a different resulting echogenicity of soft tissues, such as tendons, when the angle of the transducer is changed. Tendon fibers appear hyperechoic (bright) when the transducer is perpendicular to the tendon, but can appear hypoechoic (darker) when the transducer is angled obliquely. This can be a source of interpretation error for inexperienced practitioners. |
Anisotropy | Materials science and engineering | Materials science and engineering
Anisotropy, in materials science, is a material's directional dependence of a physical property. This is a critical consideration for materials selection in engineering applications. A material with physical properties that are symmetric about an axis that is normal to a plane of isotropy is called a transversely isotropic material. Tensor descriptions of material properties can be used to determine the directional dependence of that property. For a monocrystalline material, anisotropy is associated with the crystal symmetry in the sense that more symmetric crystal types have fewer independent coefficients in the tensor description of a given property. When a material is polycrystalline, the directional dependence on properties is often related to the processing techniques it has undergone. A material with randomly oriented grains will be isotropic, whereas materials with texture will be often be anisotropic. Textured materials are often the result of processing techniques like cold rolling, wire drawing, and heat treatment.
Mechanical properties of materials such as Young's modulus, ductility, yield strength, and high-temperature creep rate, are often dependent on the direction of measurement. Fourth-rank tensor properties, like the elastic constants, are anisotropic, even for materials with cubic symmetry. The Young's modulus relates stress and strain when an isotropic material is elastically deformed; to describe elasticity in an anisotropic material, stiffness (or compliance) tensors are used instead.
In metals, anisotropic elasticity behavior is present in all single crystals with three independent coefficients for cubic crystals, for example. For face-centered cubic materials such as nickel and copper, the stiffness is highest along the <111> direction, normal to the close-packed planes, and smallest parallel to <100>. Tungsten is so nearly isotropic at room temperature that it can be considered to have only two stiffness coefficients; aluminium is another metal that is nearly isotropic.
For an isotropic material, where is the shear modulus, is the Young's modulus, and is the material's Poisson's ratio. Therefore, for cubic materials, we can think of anisotropy, , as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent:
The latter expression is known as the Zener ratio, , where refers to elastic constants in Voigt (vector-matrix) notation. For an isotropic material, the ratio is one.
Limitation of the Zener ratio to cubic materials is waived in the Tensorial anisotropy index AT that takes into consideration all the 27 components of the fully anisotropic stiffness tensor. It is composed of two major parts and , the former referring to components existing in cubic tensor and the latter in anisotropic tensor so that This first component includes the modified Zener ratio and additionally accounts for directional differences in the material, which exist in orthotropic material, for instance. The second component of this index covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise.
Fiber-reinforced or layered composite materials exhibit anisotropic mechanical properties, due to orientation of the reinforcement material. In many fiber-reinforced composites like carbon fiber or glass fiber based composites, the weave of the material (e.g. unidirectional or plain weave) can determine the extent of the anisotropy of the bulk material. The tunability of orientation of the fibers allows for application-based designs of composite materials, depending on the direction of stresses applied onto the material.
Amorphous materials such as glass and polymers are typically isotropic. Due to the highly randomized orientation of macromolecules in polymeric materials, polymers are in general described as isotropic. However, mechanically gradient polymers can be engineered to have directionally dependent properties through processing techniques or introduction of anisotropy-inducing elements. Researchers have built composite materials with aligned fibers and voids to generate anisotropic hydrogels, in order to mimic hierarchically ordered biological soft matter. 3D printing, especially Fused Deposition Modeling, can introduce anisotropy into printed parts. This is because FDM is designed to extrude and print layers of thermoplastic materials. This creates materials that are strong when tensile stress is applied in parallel to the layers and weak when the material is perpendicular to the layers. |
Anisotropy | Microfabrication | Microfabrication
Anisotropic etching techniques (such as deep reactive-ion etching) are used in microfabrication processes to create well defined microscopic features with a high aspect ratio. These features are commonly used in MEMS (microelectromechanical systems) and microfluidic devices, where the anisotropy of the features is needed to impart desired optical, electrical, or physical properties to the device. Anisotropic etching can also refer to certain chemical etchants used to etch a certain material preferentially over certain crystallographic planes (e.g., KOH etching of silicon [100] produces pyramid-like structures) |
Anisotropy | Neuroscience | Neuroscience
Diffusion tensor imaging is an MRI technique that involves measuring the fractional anisotropy of the random motion (Brownian motion) of water molecules in the brain. Water molecules located in fiber tracts are more likely to move anisotropically, since they are restricted in their movement (they move more in the dimension parallel to the fiber tract rather than in the two dimensions orthogonal to it), whereas water molecules dispersed in the rest of the brain have less restricted movement and therefore display more isotropy. This difference in fractional anisotropy is exploited to create a map of the fiber tracts in the brains of the individual. |
Anisotropy | Remote sensing and radiative transfer modeling | Remote sensing and radiative transfer modeling
Radiance fields (see Bidirectional reflectance distribution function (BRDF)) from a reflective surface are often not isotropic in nature. This makes calculations of the total energy being reflected from any scene a difficult quantity to calculate. In remote sensing applications, anisotropy functions can be derived for specific scenes, immensely simplifying the calculation of the net reflectance or (thereby) the net irradiance of a scene.
For example, let the BRDF be where 'i' denotes incident direction and 'v' denotes viewing direction (as if from a satellite or other instrument). And let P be the Planar Albedo, which represents the total reflectance from the scene.
It is of interest because, with knowledge of the anisotropy function as defined, a measurement of the BRDF from a single viewing direction (say, ) yields a measure of the total scene reflectance (planar albedo) for that specific incident geometry (say, ). |
Anisotropy | See also | See also
Circular symmetry
|
Anisotropy | References | References |
Anisotropy | External links | External links
"Overview of Anisotropy"
DoITPoMS Teaching and Learning Package: "Introduction to Anisotropy"
"Gauge, and knitted fabric generally, is an anisotropic phenomenon"
Category:Orientation (geometry)
Category:Asymmetry |
Anisotropy | Table of Content | short description, Fields of interest, Computer graphics, Chemistry, Real-world imagery, Physics, Geophysics and geology, Medical acoustics, Materials science and engineering, Microfabrication, Neuroscience, Remote sensing and radiative transfer modeling, See also, References, External links |
Alpha decay | Short description | thumb|240px|right|Visual representation of alpha decay
Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus). The parent nucleus transforms or "decays" into a daughter product, with a mass number that is reduced by four and an atomic number that is reduced by two. An alpha particle is identical to the nucleus of a helium-4 atom, which consists of two protons and two neutrons. It has a charge of and a mass of . For example, uranium-238 decays to form thorium-234.
While alpha particles have a charge , this is not usually shown because a nuclear equation describes a nuclear reaction without considering the electrons – a convention that does not imply that the nuclei necessarily occur in neutral atoms.
Alpha decay typically occurs in the heaviest nuclides. Theoretically, it can occur only in nuclei somewhat heavier than nickel (element 28), where the overall binding energy per nucleon is no longer a maximum and the nuclides are therefore unstable toward spontaneous fission-type processes. In practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitter being the second lightest isotope of antimony, 104Sb.F.G. Kondev et al 2021 Chinese Phys. C 45 030001 Exceptionally, however, beryllium-8 decays to two alpha particles.
Alpha decay is by far the most common form of cluster decay, where the parent atom ejects a defined daughter collection of nucleons, leaving another defined product behind. It is the most common form because of the combined extremely high nuclear binding energy and relatively small mass of the alpha particle. Like other cluster decays, alpha decay is fundamentally a quantum tunneling process. Unlike beta decay, it is governed by the interplay between both the strong nuclear force and the electromagnetic force.
Alpha particles have a typical kinetic energy of 5 MeV (or ≈ 0.13% of their total energy, 110 TJ/kg) and have a speed of about 15,000,000 m/s, or 5% of the speed of light. There is surprisingly small variation around this energy, due to the strong dependence of the half-life of this process on the energy produced. Because of their relatively large mass, the electric charge of and relatively low velocity, alpha particles are very likely to interact with other atoms and lose their energy, and their forward motion can be stopped by a few centimeters of air.
Approximately 99% of the helium produced on Earth is the result of the alpha decay of underground deposits of minerals containing uranium or thorium. The helium is brought to the surface as a by-product of natural gas production. |
Alpha decay | History | History
Alpha particles were first described in the investigations of radioactivity by Ernest Rutherford in 1899, and by 1907 they were identified as He2+ ions.
By 1928, George Gamow had solved the theory of alpha decay via tunneling. The alpha particle is trapped inside the nucleus by an attractive nuclear potential well
and a repulsive electromagnetic potential barrier. Classically, it is forbidden to escape, but according to the (then) newly discovered principles of quantum mechanics, it has a tiny (but non-zero) probability of "tunneling" through the barrier and appearing on the other side to escape the nucleus. Gamow solved a model potential for the nucleus and derived, from first principles, a relationship between the half-life of the decay, and the energy of the emission, which had been previously discovered empirically and was known as the Geiger–Nuttall law. |
Alpha decay | Mechanism | Mechanism
The nuclear force holding an atomic nucleus together is very strong, in general much stronger than the repulsive electromagnetic forces between the protons. However, the nuclear force is also short-range, dropping quickly in strength beyond about 3 femtometers, while the electromagnetic force has an unlimited range. The strength of the attractive nuclear force keeping a nucleus together is thus proportional to the number of the nucleons, but the total disruptive electromagnetic force of proton-proton repulsion trying to break the nucleus apart is roughly proportional to the square of its atomic number. A nucleus with 210 or more nucleons is so large that the strong nuclear force holding it together can just barely counterbalance the electromagnetic repulsion between the protons it contains. Alpha decay occurs in such nuclei as a means of increasing stability by reducing size.
One curiosity is why alpha particles, helium nuclei, should be preferentially emitted as opposed to other particles like a single proton or neutron or other atomic nuclei.These other decay modes, while possible, are extremely rare compared to alpha decay. Part of the reason is the high binding energy of the alpha particle, which means that its mass is less than the sum of the masses of two free protons and two free neutrons. This increases the disintegration energy. Computing the total disintegration energy given by the equation
where is the initial mass of the nucleus, is the mass of the nucleus after particle emission, and is the mass of the emitted (alpha-)particle, one finds that in certain cases it is positive and so alpha particle emission is possible, whereas other decay modes would require energy to be added. For example, performing the calculation for uranium-232 shows that alpha particle emission releases 5.4 MeV of energy, while a single proton emission would require 6.1 MeV. Most of the disintegration energy becomes the kinetic energy of the alpha particle, although to fulfill conservation of momentum, part of the energy goes to the recoil of the nucleus itself (see atomic recoil). However, since the mass numbers of most alpha-emitting radioisotopes exceed 210, far greater than the mass number of the alpha particle (4), the fraction of the energy going to the recoil of the nucleus is generally quite small, less than 2%. Nevertheless, the recoil energy (on the scale of keV) is still much larger than the strength of chemical bonds (on the scale of eV), so the daughter nuclide will break away from the chemical environment the parent was in. The energies and ratios of the alpha particles can be used to identify the radioactive parent via alpha spectrometry.
These disintegration energies, however, are substantially smaller than the repulsive potential barrier created by the interplay between the strong nuclear and the electromagnetic force, which prevents the alpha particle from escaping. The energy needed to bring an alpha particle from infinity to a point near the nucleus just outside the range of the nuclear force's influence is generally in the range of about 25 MeV. An alpha particle within the nucleus can be thought of as being inside a potential barrier whose walls are 25 MeV above the potential at infinity. However, decay alpha particles only have energies of around 4 to 9 MeV above the potential at infinity, far less than the energy needed to overcome the barrier and escape. |
Alpha decay | Quantum tunneling | Quantum tunneling
Quantum mechanics, however, allows the alpha particle to escape via quantum tunneling. The quantum tunneling theory of alpha decay, independently developed by George Gamow and by Ronald Wilfred Gurney and Edward Condon in 1928, was hailed as a very striking confirmation of quantum theory. Essentially, the alpha particle escapes from the nucleus not by acquiring enough energy to pass over the wall confining it, but by tunneling through the wall. Gurney and Condon made the following observation in their paper on it:
It has hitherto been necessary to postulate some special arbitrary 'instability' of the nucleus, but in the following note, it is pointed out that disintegration is a natural consequence of the laws of quantum mechanics without any special hypothesis... Much has been written of the explosive violence with which the α-particle is hurled from its place in the nucleus. But from the process pictured above, one would rather say that the α-particle almost slips away unnoticed.
The theory supposes that the alpha particle can be considered an independent particle within a nucleus, that is in constant motion but held within the nucleus by strong interaction. At each collision with the repulsive potential barrier of the electromagnetic force, there is a small non-zero probability that it will tunnel its way out. An alpha particle with a speed of 1.5×107 m/s within a nuclear diameter of approximately 10−14 m will collide with the barrier more than 1021 times per second. However, if the probability of escape at each collision is very small, the half-life of the radioisotope will be very long, since it is the time required for the total probability of escape to reach 50%. As an extreme example, the half-life of the isotope bismuth-209 is .
The isotopes in beta-decay stable isobars that are also stable with regards to double beta decay with mass number A = 5, A = 8, 143 ≤ A ≤ 155, 160 ≤ A ≤ 162, and A ≥ 165 are theorized to undergo alpha decay. All other mass numbers (isobars) have exactly one theoretically stable nuclide. Those with mass 5 decay to helium-4 and a proton or a neutron, and those with mass 8 decay to two helium-4 nuclei; their half-lives (helium-5, lithium-5, and beryllium-8) are very short, unlike the half-lives for all other such nuclides with A ≤ 209, which are very long. (Such nuclides with A ≤ 209 are primordial nuclides except 146Sm.)
Working out the details of the theory leads to an equation relating the half-life of a radioisotope to the decay energy of its alpha particles, a theoretical derivation of the empirical Geiger–Nuttall law. |
Alpha decay | Uses | Uses
Americium-241, an alpha emitter, is used in smoke detectors. The alpha particles ionize air in an open ion chamber and a small current flows through the ionized air. Smoke particles from the fire that enter the chamber reduce the current, triggering the smoke detector's alarm.
Radium-223 is also an alpha emitter. It is used in the treatment of skeletal metastases (cancers in the bones).
Alpha decay can provide a safe power source for radioisotope thermoelectric generators used for space probes and were used for artificial heart pacemakers. Alpha decay is much more easily shielded against than other forms of radioactive decay.
Static eliminators typically use polonium-210, an alpha emitter, to ionize the air, allowing the "static cling" to dissipate more rapidly. |
Alpha decay | Toxicity | Toxicity
Highly charged and heavy, alpha particles lose their several MeV of energy within a small volume of material, along with a very short mean free path. This increases the chance of double-strand breaks to the DNA in cases of internal contamination, when ingested, inhaled, injected or introduced through the skin. Otherwise, touching an alpha source is typically not harmful, as alpha particles are effectively shielded by a few centimeters of air, a piece of paper, or the thin layer of dead skin cells that make up the epidermis; however, many alpha sources are also accompanied by beta-emitting radio daughters, and both are often accompanied by gamma photon emission.
Relative biological effectiveness (RBE) quantifies the ability of radiation to cause certain biological effects, notably either cancer or cell-death, for equivalent radiation exposure. Alpha radiation has a high linear energy transfer (LET) coefficient, which is about one ionization of a molecule/atom for every angstrom of travel by the alpha particle. The RBE has been set at the value of 20 for alpha radiation by various government regulations. The RBE is set at 10 for neutron irradiation, and at 1 for beta radiation and ionizing photons.
However, the recoil of the parent nucleus (alpha recoil) gives it a significant amount of energy, which also causes ionization damage (see ionizing radiation). This energy is roughly the weight of the alpha () divided by the weight of the parent (typically about 200 Da) times the total energy of the alpha. By some estimates, this might account for most of the internal radiation damage, as the recoil nucleus is part of an atom that is much larger than an alpha particle, and causes a very dense trail of ionization; the atom is typically a heavy metal, which preferentially collect on the chromosomes. In some studies, this has resulted in an RBE approaching 1,000 instead of the value used in governmental regulations.
The largest natural contributor to public radiation dose is radon, a naturally occurring, radioactive gas found in soil and rock. If the gas is inhaled, some of the radon particles may attach to the inner lining of the lung. These particles continue to decay, emitting alpha particles, which can damage cells in the lung tissue.EPA Radiation Information: Radon. October 6, 2006, , Accessed December 6, 2006, The death of Marie Curie at age 66 from aplastic anemia was probably caused by prolonged exposure to high doses of ionizing radiation, but it is not clear if this was due to alpha radiation or X-rays. Curie worked extensively with radium, which decays into radon,Health Physics Society, "Did Marie Curie die of a radiation overexposure?" along with other radioactive materials that emit beta and gamma rays. However, Curie also worked with unshielded X-ray tubes during World War I, and analysis of her skeleton during a reburial showed a relatively low level of radioisotope burden.
The Russian defector Alexander Litvinenko's 2006 murder by radiation poisoning is thought to have been carried out with polonium-210, an alpha emitter. |
Alpha decay | References | References
Alpha emitters by increasing energy (Appendix 1) |
Alpha decay | Notes | Notes |
Alpha decay | External links | External links
Image:Ndslivechart.png The LIVEChart of Nuclides - IAEA with filter on alpha decay
Alpha decay with 3 animated examples showing the recoil of daughter |
Alpha decay | See also | See also
Beta decay
Gamma decay
Category:Helium
Category:Nuclear physics
Category:Radioactivity |
Alpha decay | Table of Content | Short description, History, Mechanism, Quantum tunneling, Uses, Toxicity, References, Notes, External links, See also |
Extreme poverty | Multiple issues | thumb|upright=1.6|Number of people living in extreme poverty from 1820 to 2015.
thumb|upright=1.6|Total population living in extreme poverty, by world region 1990 to 2015.
thumb|upright=1.6|The number of people living on less than $1.90, $3.20, $5.50, and $10 globally from 1981 to 2015.
Extreme poverty is the most severe type of poverty, defined by the United Nations (UN) as "a condition characterized by severe deprivation of basic human needs, including food, safe drinking water, sanitation facilities, health, shelter, education and information. It depends not only on income but also on access to services".United Nations. "Report of the World Summit for Social Development", 6–12 March 1995. (archived from the original on 4 July 2019) Historically, other definitions have been proposed within the United Nations.
In 2018, extreme poverty mainly refers to an income below the international poverty line of $1.90 per day (in 2011 prices, $ in dollars), set by the World Bank. In October 2017, the World Bank updated the international poverty line, a global absolute minimum, to $1.90 a day. This is the equivalent of $1.00 a day in 1996 US prices, hence the widely used expression "living on less than a dollar a day". The vast majority of those in extreme poverty reside in South Asia and Sub-Saharan Africa. As of 2018, it is estimated that the country with the most people living in extreme poverty is Nigeria, at 86 million.Laurence Chandy and Homi Kharas (2014), What Do New Price Data Mean for the Goal of Ending Extreme Poverty?, Brookings Institution, Washington, DC. Article was reviewed in The Financial Times: Shawn Donnan (9 May 2014), World Bank eyes biggest global poverty line increase in decades
In the past, the vast majority of the world population lived in conditions of extreme poverty.
The percentage of the global population living in absolute poverty fell from over 80% in 1800 to around 10% by 2015. According to UN estimates, roughly 734 million people or 10% remained under those conditions. The number had previously been measured as 1.9 billion in 1990, and 1.2 billion in 2008. Despite the significant number of individuals still below the international poverty line, these figures represent significant progress for the international community, as they reflect a decrease of more than one billion people over 15 years.
In public opinion surveys around the globe, people surveyed tend to think that extreme poverty has not decreased.Human Progress, "What 19 in 20 Americans Don't Know About World Poverty," 30 April 2018
The reduction of extreme poverty and hunger was the first Millennium Development Goal (MDG1), as set by the United Nations in 2000. Specifically, the target was to reduce the extreme poverty rate by half by 2015, a goal that was met five years ahead of schedule. In the Sustainable Development Goals, which succeeded the MDGs, the goal is to end extreme poverty in all its forms everywhere. With this declaration the international community, including the UN and the World Bank have adopted the target of ending extreme poverty by 2030. |
Extreme poverty | Definition | Definition |
Extreme poverty | Previous definitions | Previous definitions
In July 1993, Leandro Despouy, the then UN Special Rapporteur on extreme poverty and human rights made use of a definition he adapted from a 1987 report to the French Economic and Social CouncilJoseph Wresinski. "Grande pauvreté et precarité économique et sociale", 10–11 February 1987. by Fr. Joseph Wresinski, founder of the International Movement ATD Fourth World, distinguishing "lack of basic security" (poverty) and "chronic poverty" (extreme poverty), linking the eradication of extreme poverty by allowing people currently experiencing it a real opportunity to exercise all their human rights:
This definition was mentioned previously, in June 1989, in the preliminary report on the realization of economic, social and cultural rights by the UN Special Rapporteur Danilo Türk.Danilo Türk. "Preliminary report on the new international economic order and the promotion of human rights", 28 June 1989. It is still in use today, among others, in the current UN Guiding Principles on Extreme Poverty and Human RightsMagdalena Sepúlveda Carmona "Final draft of the guiding principles on extreme poverty and human rights", 18 July 2012. adopted by the UN Human Rights Council in September 2012.UN Human Rights Council. Resolution 21/11 dated 27 September 2012. |
Extreme poverty | Consumption-based definition | Consumption-based definition
alt=|thumb|Poverty headcount ratio at $1.90 a day (2011 PPP) (% of population). Based on World Bank data ranging from 1998 to 2018.
Extreme poverty is defined by the international community as living below $1.90 a day, as measured in 2011 international prices (equivalent to $2.12 in 2018). This number, also known as the international poverty line, is periodically updated to account for inflation and differences in the cost of living;Sala-i-Martin, Xavier. "The world distribution of income: falling poverty and convergence period". The Quarterly Journal of Economics 121.2 (2006): 351–397 (370). it was originally defined at $1.00 a day in 1996. The updates are made according to new price data to portray the costs of basic food, health services, clothing, and shelter around the world as accurately as possible. The latest revision was made in 2015 when the World Bank increased the line to international-$1.90.
Because many of the world's poorest people do not have a monetary income, the poverty measurement is based on the monetary value of a person's consumption. Otherwise the poverty measurement would be missing the home production of subsistence farmers that consume largely their own production. |
Extreme poverty | Alternative definitions | Alternative definitions
thumb|upright=1.6|Share of population living in multidimensional poverty in 2014
The $1.90/day extreme poverty line remains the most widely used metric as it highlights the reality of those in the most severe conditions."Getting to Zero: USAID Discussion Paper" , 21 November 2013. Although widely used by most international organizations, it has come under scrutiny due to a variety of factors. For example, it does not account for how far below the line people are, referred to as the depth of poverty. For this purpose, the same institutions publish data on the poverty gap.
The international poverty line is designed to stay constant over time, to allow comparisons between different years. It is therefore a measure of absolute poverty and is not measuring relative poverty. It is also not designed to capture how people view their own financial situation (known as the socially subjective poverty line). Moreover, the calculation of the poverty line relies on information about consumer prices to calculate purchasing power parity, which are very hard to measure and are necessarily debatable. As with all other metrics, there may also be missing data from the poorest and most fragile countries.
Several alternative instruments for measuring extreme poverty have been suggested which incorporate other factors such as malnutrition and lack of access to a basic education. The Multidimensional Poverty Index (MPI), based on the Alkire-Foster Method, is published by the Oxford Poverty & Human Development Initiative (OPHI): it measures deprivation in basic needs and can be broken down to reflect both the incidence and the intensity of poverty. For example, under conventional measures, in both Ethiopia and Uzbekistan about 40% of the population is considered extremely poor, but based on the MPI, 90% of Ethiopians but only 2% of Uzbeks are in multidimensional poverty.Dan Morrell."Who Is Poor?", Harvard Magazine. January–February 2011.
The MPI is useful for development officials to determine the most likely causes of poverty within a region, using the M0 measure of the method (which is calculated by multiplying the fraction of people in poverty by the fraction of dimensions they are deprived in).OPHI."Alkire-Foster Method" , 2014. For example, in the Gaza Strip of Palestine, using the M0 measure of the Alkire-Foster method reveals that poverty in the region is primarily caused by a lack of access to electricity, lack of access to drinking water, and widespread overcrowding. In contrast, data from the Chhukha District of Bhutan reveals that income is a much larger contributor to poverty as opposed to other dimensions within the region.Sabina Alkire and James Foster."Counting and Multidimensional Poverty", International Food Policy Research Institute. However, the MPI only presents data from 105 countries, so it cannot be used for global measurements. |
Extreme poverty | Share of the population living in extreme poverty | Share of the population living in extreme poverty
thumb|Share of the population living in extreme poverty in selected parts of the world
+Number of people pushed below the $1.90 ($2011 PPP) poverty line (in millions) +Region1990199520002005201020152017Developed countries4.064.994.75.485.287.917.45Latin America & Caribbean66.6164.7565.7754.0435.322.9523.73Middle East & North Africa14.816.499.959.66.8615.7424.16South Asia557.05550.44564.92533.28425.32230.51173.1East Asia & Pacific977.29766.14632.26347.99212.1242.0829.15Europe & Central Asia11.513234.2822.0411.277.356.37Sub-Saharan Africa280.95352.76388.27393.57412.49417.6432.5Total1,9101,7901,7001,3701,110744.14696.45 |
Extreme poverty | Current trends | Current trends |
Extreme poverty | Getting to zero | Getting to zero
upright=2.0|right|thumb|Various projections for the prospect of ending extreme poverty by 2030. The y-axis represents the percentage of people living in extreme poverty worldwide.
thumb|Extreme poverty projection by the World Bank to 2030
Using the World Bank definition of $1.90/day, , roughly 710 million people remained in extreme poverty (or roughly 1 in 10 people worldwide). Nearly half of them live in India and China, with more than 85% living in just 20 countries. Since the mid-1990s, there has been a steady decline in both the worldwide poverty rate and the total number of extreme poor. In 1990, the percentage of the global population living in extreme poverty was 43%, but in 2011, that percentage had dropped down to 21%. This halving of the extreme poverty rate falls in line with the first Millennium Development Goal (MDG1) proposed by former UN Secretary-General Kofi Annan, who called on the international community at the turn of the century to reduce the percentage of people in extreme poverty by half by 2015.
This reduction in extreme poverty took place most notably in China, Indonesia, India, Pakistan and Vietnam. These five countries accounted for the alleviation of 715 million people out of extreme poverty between 1990 and 2010 – more than the global net total of roughly 700 million. This statistical oddity can be explained by the fact that the number of people living in extreme poverty in Sub-Saharan Africa rose from 290 million to 414 million over the same period.United Nations."The Millennium Development Goals Report", 2013. However, there have been many positive signs for extensive, global poverty reduction as well. Since 1999, the total number of extreme poor has declined by an average of 50 million per year. Moreover, in 2005, for the first time in recorded history, poverty rates began to fall in every region of the world, including Africa.Rajiv Shah."Remarks by Administrator Rajiv Shah at the Brookings Institution: Ending Extreme Poverty" , USAID. 21 November 2013.
As aforementioned, the number of people living in extreme poverty has reduced from 1.9 billion to 766 million over the span of the last decades. If we remain on our current trajectory, many economists predict we could reach global zero by 2030–2035, thus ending extreme poverty. Global zero entails a world in which fewer than 3% of the global population lives in extreme poverty (projected under most optimistic scenarios to be fewer than 200 million people). This zero figure is set at 3% in recognition of the fact that some amount of frictional (temporary) poverty will continue to exist, whether it is caused by political conflict or unexpected economic fluctuations, at least for the foreseeable future.World Bank."Prosperity for All: Ending Extreme Poverty", Spring 2014. However, the Brookings Institution notes that any projection about poverty more than a few years into the future runs the risk of being highly uncertain. This is because changes in consumption and distribution throughout the developing world over the next two decades could result in monumental shifts in global poverty, for better or worse.Laurence Chandy et al. "The Final Countdown: Prospects for Ending Extreme Poverty". . Brookings Institution. April 2013.
Others are more pessimistic about this possibility, predicting a range of 193 million to 660 million people still living in extreme poverty by 2035. Additionally, some believe the rate of poverty reduction will slow down in the developing world, especially in Africa, and as such it will take closer to five decades to reach global zero.Alex Thier. "A Global Effort to End Extreme Poverty". USAID. 22 November 2013. Despite these reservations, several prominent international and national organizations, including the UN, the World Bank and the United States Federal Government (via USAID), have set a target of reaching global zero by the end of 2030.
More recent analyses in 2022 on real wages have questioned whether extreme poverty was a "natural" condition of humanity and decreased with the rise of capitalism.
upright=1.4|thumb|Reduction in global poverty by year in percentage points |
Extreme poverty | Exacerbating factors | Exacerbating factors
There are a variety of factors that may reinforce or instigate the existence of extreme poverty, such as weak institutions, cycles of violence and a low level of growth. Recent World Bank research shows that some countries can get caught in a "fragility trap", in which self-reinforcing factors prevent the poorest nations from emerging from low-level equilibrium in the long run.World Bank. "Stop Conflict, Reduce Fragility and End Poverty: Doing Things Differently in Fragile and Conflict-affected Situations". 2013. Moreover, most of the reduction in extreme poverty over the past twenty years has taken place in countries that have not experienced a civil conflict or have had governing institutions with a strong capacity to actually govern. Thus, to end extreme poverty, it is also important to focus on the interrelated problems of fragility and conflict.
USAID defines fragility as a government's lack of both legitimacy (the perception the government is adequate at doing its job) and effectiveness (how good the government is at maintaining law and order, in an equitable manner). As fragile nations are unable to equitably and effectively perform the functions of a state, these countries are much more prone to violent unrest and mass inequality. Additionally, in countries with high levels of inequality (a common problem in countries with inadequate governing institutions), much higher growth rates are needed to reduce the rate of poverty when compared with other nations. Additionally, if China and India are removed from the equation, up to 70% of the world's poor live in fragile states by some definitions of fragility. Some analysts project that extreme poverty will be increasingly concentrated in fragile, low-income states like Haiti, Yemen and the Central African Republic.Nancy Lindborg. "To End Extreme Poverty, Tackle Fragility". USAID. 13 February 2014. However, some academics, such as Andy Sumner, say that extreme poverty will be increasingly concentrated in middle-income countries, creating a paradox where the world's poor do not actually live in the poorest countries.Andy Sumner. "Where Will the World's Poor Live? An Update on Global Poverty and the New Bottom Billion". Center for Global Development. September 2012.
To help low-income earners, fragile states make the transition towards peace and prosperity, the New Deal for Engagement in Fragile States, endorsed by roughly forty countries and multilateral institutions, was created in 2011. This represents an important step towards redressing the problem of fragility as it was originally articulated by self-identified fragile states who called on the international community to not only "do things differently", but to also "do different things".USAID. "Ending Extreme Poverty in fragile contexts". 28 January 2014.
Civil conflict also remains a prime cause for the perpetuation of poverty throughout the developing world. Armed conflict can have severe effects on economic growth for many reasons such as the destruction of assets, destruction of livelihoods, creation of unwanted mass migration, and diversion of public resources towards war. Significantly, a country that experienced major violence during 1981–2005 had extreme poverty rates 21 percentage points higher than a country with no violence. On average, each civil conflict will cost a country roughly 30 years of GDP growth. Therefore, a renewed commitment from the international community to address the deteriorating situation in highly fragile states is necessary to both prevent the mass loss of life, but to also prevent the vicious cycle of extreme poverty.
Population trends and dynamics (e.g. population growth) can also have a large impact on prospects for poverty reduction. According to the United Nations, "in addition to improving general health and well-being, analysis shows that meeting the reproductive health and contraceptive needs of all women in the developing world more than pays for itself").
In 2013, a prominent finding in a report by the World Bank was that extreme poverty is most prevalent in low-income countries. In these countries, the World Bank found that progress in poverty reduction is the slowest, the poor live under the worst conditions, and the most affected persons are children age 12 and under.Olinto, Pedro, et al. "The State of the Poor: Where Are The Poor, Where Is Extreme Poverty Harder to End, and What Is the Current Profile of the World's Poor?" . Economic Premise 125.2 (2013). |
Extreme poverty | International initiatives | International initiatives |
Extreme poverty | Millennium Summit and Millennium Development Goals | Millennium Summit and Millennium Development Goals
In September 2000, world leaders gathered at the Millennium Summit held in New York, launching the United Nations Millennium Project suggested by then UN Secretary-General Kofi Annan. Prior to the launch of the conference, the office of Secretary-General Annan released a report entitled "We The Peoples: The Role of the United Nations in the 21st Century". In this document, now widely known as the Millennium Report, Kofi Annan called on the international community to reduce the proportion of people in extreme poverty by half by 2015, a target that would affect over 1 billion people. Citing the close correlation between economic growth and the reduction of poverty in poor countries, Annan urged international leaders to indiscriminately target the problem of extreme poverty across every region. In charge of managing the project was Jeffrey Sachs, a noted development economist, who in 2005 released a plan for action called "Investing in Development: A Practical Plan to Achieve the Millennium Development Goals".Jeffrey Sachs. "Investing in Development: A Practical Plan to Achieve the Millennium Development Goals", United Nations. 2005. Thomas Pogge criticized the 2000 Millennium Declaration for being less ambitious than a previous declaration from the World Food Summit due to using 1990 as the benchmark rather than 1996.
Overall, there has been significant progress towards reducing extreme poverty, with the MDG1 target of reducing extreme poverty rates by half being met five years early, representing 700 million people being lifted out of extreme poverty from 1990 to 2010, with 1.2 billion people still remaining under those conditions.United Nations. "Goal 1: Eradicate Extreme Poverty & Hunger", 2014. The notable exception to this trend was in Sub-Saharan Africa, the only region where the number of people living in extreme poverty rose from 290 million in 1990 to 414 million in 2010, comprising more than a third of those living in extreme poverty worldwide. |
Extreme poverty | 2005 World Summit | 2005 World Summit
The 2005 World Summit, held in September which was organized to measure international progress towards fulfilling the Millennium Development Goals (MDGs). Notably, the conference brought together more than 170 Heads of State. While world leaders at the summit were encouraged by the reduction of poverty in some nations, they were concerned by the uneven decline of poverty within and among different regions of the globe. However, at the end of the summit, the conference attendees reaffirmed the UN's commitment to achieve the MDGs by 2015 and urged all supranational, national and non-governmental organizations to follow suit. |
Extreme poverty | Sustainable Development Goals | Sustainable Development Goals
thumb|right|Sustainable Development Goals
As the expiration of the Millennium Development Goals approached in 2015, the UN convened a panel to advise on a Post-2015 Development Agenda, which led to a new set of 17 goals for 2030 titled the Sustainable Development Goals (SDGs). The first goal (SDG 1) is to "End poverty in all its forms everywhere."
The HLP report, entitled A New Global Partnership: Eradicate Poverty and Transform Economies Through Sustainable Development, was published in May 2013. In the report, the HLP wrote that:
Ending extreme poverty is just the beginning, not the end. It is vital, but our vision must be broader: to start countries on the path of sustainable development – building on the foundations established by the 2012 UN Conference on Sustainable Development in Rio de Janeiro, and meeting a challenge that no country, developed or developing, has met so far. We recommend to the Secretary-General that deliberations on a new development agenda must be guided by the vision of eradicating extreme poverty once and for all, in the context of sustainable development.
Therefore, the report determined that a central goal of the Post-Millennium Development agenda is to eradicate extreme poverty by 2030. However, the report also emphasized that the MDGs were not enough on their own, as they did not "focus on the devastating effects of conflict and violence on development ... the importance to development of good governance and institution ... nor the need for inclusive growth..." Consequently, there now exists synergy between the policy position papers put forward by the United States (through USAID), the World Bank and the UN itself in terms of viewing fragility and a lack of good governance as exacerbating extreme poverty. However, in a departure from the views of other organizations, the commission also proposed that the UN focus not only on extreme poverty (a line drawn at $1.25), but also on a higher target, such as $2. The report notes this change could be made to reflect the fact that escaping extreme poverty is only a first step.High Level Panel of Eminent Persons. "A New Global Partnership: Eradicate Poverty and Transform Economies Through Sustainable Development", United Nations. 2013.
In addition to the UN, a host of other supranational and national actors such as the European Union and the African Union have published their own positions or recommendations on what should be incorporated in the Post-2015 agenda. The European Commission's communication, published in A decent Life for all: from vision to collective action, affirmed the UN's commitment to "eradicate extreme poverty in our lifetime and put the world on a sustainable path to ensure a decent life for all by 2030". A unique vision of the report was the commission's environmental focus (in addition to a plethora of other goals such as combating hunger and gender inequality). Specifically, the Commission argued, "long-term poverty reduction ... requires inclusive and sustainable growth. Growth should create decent jobs, take place with resource efficiency and within planetary boundaries, and should support efforts to mitigate climate change." The African Union's report, entitled Common African Position (CAP) on the Post-2015 Development Agenda, likewise encouraged the international community to focus on eradicating the twin problems of poverty and exclusion in our lifetime. Moreover, the CAP pledged that "no person – regardless of ethnicity, gender, geography, disability, race or other status – is denied universal human rights and basic economic opportunities".African Union. "Common African Position (CAP) on the Post-2015 Development Agenda", 2014. |
Extreme poverty | Least developed country conferences | Least developed country conferences
The UN least developed country (LDC) conferences were a series of summits organized by the UN to promote the substantial and even development of the world's least developed countries.United Nations. "Paris Declaration and Programme of Action for the Least Developed Countries for the 1900s" , 1992. |
Extreme poverty | Organizations working to end extreme poverty | Organizations working to end extreme poverty |
Extreme poverty | International organizations | International organizations |
Extreme poverty | World Bank | World Bank
thumb|right| Nations of the World Bank Group (WBG)
thumb|right|World Bank logo
In 2013, the Board of Governors of the World Bank Group (WBG) set two overriding goals for the WBG to commit itself to in the future. First, to end extreme poverty by 2030, an objective that echoes the sentiments of the UN and the Obama administration. Additionally, the WBG set an interim target of reducing extreme poverty to below 9% by 2020. Second, to focus on growth among the bottom 40% of people, as opposed to standard GDP growth. This commitment ensures that the growth of the developing world lifts people out of poverty, rather than exacerbating inequality.
As the World Bank's primary focus is on delivering economic growth to enable equitable prosperity, its developments programs are primarily commercial-based in nature, as opposed to the UN. Since the World Bank recognizes better jobs will result in higher income, and thus less poverty, the WBG seeks to support employment training initiatives, small business development programs and strong labor protection laws. However, since much of the growth in the developing world has been inequitable, the World Bank has also begun teaming with client states to map out trends in inequality and to propose public policy changes that can level the playing field.World Bank. "Poverty Overview", 2014.
Moreover, the World Bank engages in a variety of nutritional, transfer payments and transport-based initiatives. Children who experience under-nutrition from conception to two years of age have a much higher risk of physical and mental disability. Thus, they are often trapped in poverty and are unable to make a full contribution to the social and economic development of their communities as adults. The WBG estimates that as much as 3% of GDP can be lost as a result of under-nutrition among the poorest nations. To combat undernutrition, the WBG has partnered with UNICEF and the WHO to ensure all small children are fully fed. The WBG also offers conditional cash transfers to poor households who meet certain requirements such as maintaining children's healthcare or ensuring school attendance. Finally, the WBG understands investment in public transportation and better roads is key to breaking rural isolation, improving access to healthcare and providing better job opportunities for the World's poor.World Bank. "Poverty Reduction in Practice: How and Where We Work", 19 February 2013. |
Extreme poverty | United Nations | United Nations
thumb|right|United Nations Headquarters, Geneva
thumb|right|United Nations Office for the Coordination of Humanitarian Affairs Logo
The UN Office for the Coordination of Humanitarian Affairs (OCHA) works to synchronize the disparate international, national and non-governmental efforts to contest poverty. OCHA seeks to prevent "confusion" in relief operations and to ensure that the humanitarian response to disaster situations has greater accountability and predictability. To do so, OCHA has begun deploying Humanitarian Coordinators and Country Teams to provide a solid architecture for the international community to work through.
The United Nation's Children's Fund (UNICEF) was created by the UN to provide food, clothing and healthcare to European children facing famine and disease in the immediate aftermath of World War II. After the UN General Assembly extended UNICEF's mandate indefinitely in 1953, it actively worked to help children in extreme poverty in more than 190 countries and territories to overcome the obstacles that poverty, violence, disease and discrimination place in a child's path. Its current focus areas are 1) Child survival & development 2) Basic education & gender equality 3) Children and HIV/AIDS and 4) Child protection.
The UN Refugee Agency (UNHCR) is mandated to lead and coordinate international action to protect refugees worldwide. Its primary purpose is to safeguard the rights of refugees by ensuring anyone can exercise the right to seek asylum in another state, with the option to return home voluntarily, integrate locally or resettle in a third country. The UNHCR operates in over 125 countries, helping approximately 33.9 million persons.
The World Food Programme (WFP) is the largest agency dedicated to fighting hunger worldwide. On average, the WFP brings food assistance to more than 90 million people in 75 countries. The WFP not only strives to prevent hunger in the present, but also in the future by developing stronger communities which will make food even more secure on their own. The WFP has a range of expertise from Food Security Analysis, Nutrition, Food Procurement and Logistics.
The World Health Organization (WHO) is responsible for providing leadership on global health matters, shaping the health research agenda, articulating evidence-based policy decisions and combating diseases that are induced from poverty, such as HIV/AIDS, malaria and tuberculosis. Moreover, the WHO deals with pressing issues ranging from managing water safety, to dealing with maternal and newborn health. |
Extreme poverty | Governmental agencies | Governmental agencies |
Extreme poverty | USAID | USAID
thumb|right|USAID logo
thumb|right|USAID Urban Search and Rescue team Fairfax County performs search and rescue operations in Haiti, 17 January 2010.
The US Agency for International Development (USAID) is the lead US government agency dedicated to ending extreme poverty. Currently the largest bilateral donor in the world, the United States channels the majority of its development assistance through USAID and the US Department of State. In President Obama's 2013 State of the Union address, he declared, "So the United States will join with our allies to eradicate such extreme poverty in the next two decades ... which is within our reach." In response to Obama's call to action, USAID has made ending extreme poverty central to its mission statement.USAID. "Mission Statement" , 2014. Under its New Model of Development, USAID seeks to eradicate extreme poverty through the use of innovation in science and technology, by putting a greater emphasis on evidence based decision-making, and through leveraging the ingenuity of the private sector and global citizens.USAID. "Annual Letter", 2014.
A major initiative of the Obama administration is Power Africa, which aims to bring energy to 20 million people in Sub-Saharan Africa. By reaching out to its international partners, whether commercial or public, the US has leveraged over $14 billion in outside commitments after investing only US$7 billion of its own. To ensure that Power Africa reaches the region's poorest, the initiative engages in a transaction based approach to create systematic change. This includes expanding access to electricity to more than 20,000 additional households which already live without power.USAID. "Power Africa", 2014.
In terms of specific programming, USAID works in a variety of fields from preventing hunger, reducing HIV/AIDS, providing general health assistance and democracy assistance, as well as dealing with gender issues. To deal with food security, which affects roughly 842 million people (who go to bed hungry each night),Food and Agriculture Organization of the United Nations. "The State of Food Insecurity in the World", 2013. USAID coordinates the Feed the Future Initiative (FtF). FtF aims to reduce poverty and under-nutrition each by 20% over five years. Because of the President's Emergency Plan for AIDS Relief (PEPFAR) and a variety of congruent actors, the incidence of AIDS and HIV, which used to ravage Africa, reduced in scope and intensity. Through PEPFAR, the United States has ensured over five million people have received life-saving antiviral drugs, a significant proportion of the eight million people receiving treatment in relatively poor nations.USAID. "End Extreme Poverty" , 2014.
In terms of general health assistance, USAID has worked to reduce maternal mortality by 30%, under-five child mortality by 35%, and has accomplished a host of other goals.USAID. "What We Do: Global Health", 2014. USAID also supports the gamut of democratic initiatives, from promoting human rights and accountable, fair governance, to supporting free and fair elections and the rule of law. In pursuit of these goals, USAID has increased global political participation by training more than 9,800 domestic election observers and providing civic education to more than 6.5 million people.USAID. "What We Do: Democracy, Human Rights, and Governance" , 2014. Since 2012, the Agency has begun integrating critical gender perspectives across all aspects of its programming to ensure all USAID initiatives work to eliminate gender disparities. To do so, USAID seeks to increase the capability of women and girls to realize their rights and determine their own life outcomes. Moreover, USAID supports additional programs to improve women's access to capital and markets, builds theirs skills in agriculture, and supports women's desire to own businesses.USAID. "What We Do: Fostering Women's Leadership", 2014. |
Extreme poverty | Others | Others
Other major government development agencies with annual aid programmes of more than $10 billion include: GIZ (Germany), FCDO (United Kingdom), JICA (Japan), European Union and AFD (France). |
Extreme poverty | Non-Governmental Organizations | Non-Governmental Organizations
A multitude of non-governmental organizations operate in the field of extreme poverty, actively working to alleviate the poorest of the poor of their deprivation. To name but a few notable organizations: Save the Children, the Overseas Development Institute, Concern Worldwide, ONE, Trickle Up and Oxfam have all done a considerable amount of work in extreme poverty.
Save the Children is the leading international organization dedicated to helping the world's indigent children. In 2013, Save the Children reached over 143 million children through their work, including over 52 million children directly. Save the Children also recently released their own report titled "Getting to Zero", in which they argued the international community could feasibly do more than lift the world's poor above $1.25/day.
The Overseas Development Institute (ODI) is a UK based think tank on international development and humanitarian issues. ODI is dedicated to alleviating the suffering of the world's poor by providing high-quality research and practical policy advice to the World's development officials. ODI also recently released a paper entitled, "The Chronic Poverty Report 2014–2015: The road to zero extreme poverty", in which its authors assert that though the international communities' goal of ending extreme poverty by 2030 is laudable, much more targeted resources will be necessary to reach said target. The report states that "To eradicate extreme poverty, massive global investment is required in social assistance, education and pro-poorest economic growth".
Concern Worldwide is an international humanitarian organization whose mission is to end extreme poverty by influencing decision makers at all levels of government (from local to international). Concern has also produced a report on extreme poverty in which they explain their own conception of extreme poverty from a NGO's standpoint. In this paper, named "How Concern Understands Extreme Poverty", the report's creators write that extreme poverty entails more than just living under $1.25/day, it also includes having a small number of assets and being vulnerable to severe negative shocks (whether natural or man made).
ONE, the organization co-founded by Bono, is a non-profit organization funded almost entirely by foundations, individual philanthropists and corporations. ONE's goals include raising public awareness and working with political leaders to fight preventable diseases, increase government accountability and increase investment in nutrition.One International. "About" Finally, Trickle Up is a micro-enterprise development program targeted at those living on under $1.25/day, which provides the indigent with resources to build a sustainable livelihood through both direct financing and considerable training efforts.Trickle Up. "Our Approach"
Oxfam is a non-governmental organization that works prominently in Africa; their mission is to improve local community organizations and it works to reduce impediments to the development of the country. Oxfam helps families suffering from poverty receive food and healthcare to survive. There are many children in Africa experiencing growth stunting, and this is one example of an issue that Oxfam targets and aims to resolve.
Cash transfers appear to be an effective intervention for reducing extreme poverty, while at the same time improving health and education outcomes. |
Extreme poverty | Campaigns | Campaigns
Giving What We Can
Global Poverty Project
Live Below the Line
Make Poverty History |
Extreme poverty | See also | See also
Cost of poverty
Income inequality metrics
Least developed countries
List of countries by percentage of population living in poverty
Millennium Development Goals (2015)
Poverty reduction
Poverty threshold
Sustainable Development Goals (2030) |
Extreme poverty | Notes | Notes |
Extreme poverty | References | References |
Extreme poverty | External links | External links
Eradicate Extreme Poverty and Hunger by 2015 | UN Millennium Development Goal curated by the Center for Latin American and Caribbean Studies at Michigan State University
The Life You Can Save – Acting Now to End World Poverty
Scientific American Magazine (September 2005 Issue) Can Extreme Poverty Be Eliminated?
International Movement ATD Fourth World
Walk In Her Shoes
Category:Measurements and definitions of poverty |
Extreme poverty | Table of Content | Multiple issues, Definition, Previous definitions, Consumption-based definition, Alternative definitions, Share of the population living in extreme poverty, Current trends, Getting to zero, Exacerbating factors, International initiatives, Millennium Summit and Millennium Development Goals, 2005 World Summit, Sustainable Development Goals, Least developed country conferences, Organizations working to end extreme poverty, International organizations, World Bank, United Nations, Governmental agencies, USAID, Others, Non-Governmental Organizations, Campaigns, See also, Notes, References, External links |
Analytical engine | Short description | thumb|Portion of the calculating machine with a printing mechanism of the analytical engine, built by Charles Babbage, as displayed at the Science Museum (London)
The analytical engine was a proposed digital mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage. It was first described in 1837 as the successor to Babbage's difference engine, which was a design for a simpler mechanical calculator.
The analytical engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer that could be described in modern terms as Turing-complete. In other words, the structure of the analytical engine was essentially the same as that which has dominated computer design in the electronic era. The analytical engine is one of the most successful achievements of Charles Babbage.
Babbage was never able to complete construction of any of his machines due to conflicts with his chief engineer and inadequate funding. It was not until 1941 that Konrad Zuse built the first general-purpose computer, Z3, more than a century after Babbage had proposed the pioneering analytical engine in 1837. |
Analytical engine | Design | Design
thumb|Two types of punched cards used to program the machine. Foreground: 'operational cards', for inputting instructions; background: 'variable cards', for inputting data
Babbage's first attempt at a mechanical computing device, the difference engine, was a special-purpose machine designed to tabulate logarithms and trigonometric functions by evaluating finite differences to create approximating polynomials. Construction of this machine was never completed; Babbage had conflicts with his chief engineer, Joseph Clement, and ultimately the British government withdrew its funding for the project.
During this project, Babbage realised that a much more general design, the analytical engine, was possible. The work on the design of the analytical engine started around 1833.
The input, consisting of programs ("formulae") and data, was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter, and a bell. The machine would also be able to punch numbers onto cards to be read in later. It employed ordinary base-10 fixed-point arithmetic.
There was to be a store (that is, a memory) capable of holding 1,000 numbers of 40 decimal digits each (ca. 16.6 kB). An arithmetic unit (the "mill") would be able to perform all four arithmetic operations, plus comparisons and optionally square roots. Initially (1838) it was conceived as a difference engine curved back upon itself, in a generally circular layout, with the long store exiting off to one side. Later drawings (1858) depict a regularised grid layout. Like the central processing unit (CPU) in a modern computer, the mill would rely upon its own internal procedures, roughly equivalent to microcode in modern CPUs, to be stored in the form of pegs inserted into rotating drums called "barrels", to carry out some of the more complex instructions the user's program might specify.
The programming language to be employed by users was akin to modern day assembly languages. Loops and conditional branching were possible, and so the language as conceived would have been Turing-complete as later defined by Alan Turing. Three different types of punch cards were used: one for arithmetical operations, one for numerical constants, and one for load and store operations, transferring numbers from the store to the arithmetical unit or back. There were three separate readers for the three types of cards. Babbage developed some two dozen programs for the analytical engine between 1837 and 1840, and one program later. These programs treat polynomials, iterative formulas, Gaussian elimination, and Bernoulli numbers.
In 1842, the Italian mathematician Luigi Federico Menabrea published a description of the engine in French, based on lectures Babbage gave when he visited Turin in 1840. In 1843, the description was translated into English and extensively annotated by Ada Lovelace, who had become interested in the engine eight years earlier. In recognition of her additions to Menabrea's paper, which included a way to calculate Bernoulli numbers using the machine (widely considered to be the first complete computer program), she has been described by many as the first computer programmer, although others have challenged this view. |
Analytical engine | Construction | Construction
Late in his life, Babbage sought ways to build a simplified version of the machine, and assembled a small part of it before his death in 1871.
In 1878, a committee of the British Association for the Advancement of Science described the analytical engine as "a marvel of mechanical ingenuity", but recommended against constructing it. The committee acknowledged the usefulness and value of the machine, but could not estimate the cost of building it, and were unsure whether the machine would function correctly after being built.
thumb|Henry Babbage's analytical engine mill, built in 1910, in the Science Museum (London)
Intermittently from 1880 to 1910, Babbage's son Henry Prevost Babbage was constructing a part of the mill and the printing apparatus. In 1910, it was able to calculate a (faulty) list of multiples of pi. This constituted only a small part of the whole engine; it was not programmable and had no storage. (Popular images of this section have sometimes been mislabelled, implying that it was the entire mill or even the entire engine.) Henry Babbage's "analytical engine mill" is on display at the Science Museum in London. Henry also proposed building a demonstration version of the full engine, with a smaller storage capacity: "perhaps for a first machine ten (columns) would do, with fifteen wheels in each". Such a version could manipulate 20 numbers of 25 digits each, and what it could be told to do with those numbers could still be impressive. "It is only a question of cards and time", wrote Henry Babbage in 1888, "... and there is no reason why (twenty thousand) cards should not be used if necessary, in an analytical engine for the purposes of the mathematician".
In 1991, the London Science Museum built a complete and working specimen of Babbage's Difference Engine No. 2, a design that incorporated refinements Babbage discovered during the development of the analytical engine. This machine was built using materials and engineering tolerances that would have been available to Babbage, quelling the suggestion that Babbage's designs could not have been produced using the manufacturing technology of his time.
In October 2010, John Graham-Cumming started a "Plan 28" campaign to raise funds by "public subscription" to enable serious historical and academic study of Babbage's plans, with a view to then build and test a fully working virtual design which will then in turn enable construction of the physical analytical engine. As of May 2016, actual construction had not been attempted, since no consistent understanding could yet be obtained from Babbage's original design drawings. In particular it was unclear whether it could handle the indexed variables which were required for Lovelace's Bernoulli program. By 2017, the "Plan 28" effort reported that a searchable database of all catalogued material was available, and an initial review of Babbage's voluminous Scribbling Books had been completed.
Many of Babbage's original drawings have been digitised and are publicly available online. |
Analytical engine | Instruction set | Instruction set
thumb|upright=3|center|Plan diagram of the analytical engine from 1840
Babbage is not known to have written down an explicit set of instructions for the engine in the manner of a modern processor manual. Instead he showed his programs as lists of states during their execution, showing what operator was run at each step with little indication of how the control flow would be guided.
Allan G. Bromley has assumed that the card deck could be read in forwards and backwards directions as a function of conditional branching after testing for conditions, which would make the engine Turing-complete:
...the cards could be ordered to move forward and reverse (and hence to loop)...
The introduction for the first time, in 1845, of user operations for a variety of service functions including, most importantly, an effective system for user control of looping in user programs.
There is no indication how the direction of turning of the operation and variable cards is specified. In the absence of other evidence I have had to adopt the minimal default assumption that both the operation and variable cards can only be turned backward as is necessary to implement the loops used in Babbage's sample programs. There would be no mechanical or microprogramming difficulty in placing the direction of motion under the control of the user.
In their emulator of the engine, Fourmilab say:
The Engine's Card Reader is not constrained to simply process the cards in a chain one after another from start to finish. It can, in addition, directed by the very cards it reads and advised by whether the Mill's run-up lever is activated, either advance the card chain forward, skipping the intervening cards, or backward, causing previously-read cards to be processed once again.
This emulator does provide a written symbolic instruction set, though this has been constructed by its authors rather than based on Babbage's original works. For example, a factorial program would be written as:
N0 6
N1 1
N2 1
×
L1
L0
S1
–
L0
L2
S0
L2
L0
CB?11
where the CB is the conditional branch instruction or "combination card" used to make the control flow jump, in this case backward by 11 cards. |
Analytical engine | Influence | Influence |
Analytical engine | Predicted influence | Predicted influence
Babbage understood that the existence of an automatic computer would kindle interest in the field now known as algorithmic efficiency, writing in his Passages from the Life of a Philosopher, "As soon as an analytical engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise—By what course of calculation can these results be arrived at by the machine in the shortest time?" |
Analytical engine | Computer science | Computer science
From 1872, Henry continued diligently with his father's work and then intermittently in retirement in 1875.
Percy Ludgate wrote about the engine in 1914 and published his own design for an analytical engine in 1909. Available on-line at: Fano.co.UK It was drawn up in detail, but never built, and the drawings have never been found. Ludgate's engine would be much smaller (about than Babbage's, and hypothetically would be capable of multiplying two 20-decimal-digit numbers in about six seconds.
In his work Essays on Automatics (1914) Leonardo Torres Quevedo, inspired by Babbage, designed a theoretical electromechanical calculating machine which was to be controlled by a read-only program. The paper also contains the idea of floating-point arithmetic.Torres Quevedo, Leonardo. Automática: Complemento de la Teoría de las Máquinas, (pdf), pp. 575–583, Revista de Obras Públicas, 19 November 1914.Torres Quevedo. L. (1915). "Essais sur l'Automatique – Sa définition. Etendue théorique de ses applications", Revue Génerale des Sciences Pures et Appliquées, vol. 2, pp. 601–611.Ronald T. Kneusel. Numbers and Computers, Springer, pp. 84–85, 2017. In 1920, to celebrate the 100th anniversary of the invention of the arithmometer, Torres presented in Paris the electromechanical arithmometer, which consisted of an arithmetic unit connected to a (possibly remote) typewriter, on which commands could be typed and the results printed automatically.
Vannevar Bush's paper Instrumental Analysis (1936) included several references to Babbage's work. In the same year he started the Rapid Arithmetical Machine project to investigate the problems of constructing an electronic digital computer.
Despite this groundwork, Babbage's work fell into historical obscurity, and the analytical engine was unknown to builders of electromechanical and electronic computing machines in the 1930s and 1940s when they began their work, resulting in the need to re-invent many of the architectural innovations Babbage had proposed. Howard Aiken, who built the quickly-obsoleted electromechanical calculator, the Harvard Mark I, between 1937 and 1945, praised Babbage's work likely as a way of enhancing his own stature, but knew nothing of the analytical engine's architecture during the construction of the Mark I, and considered his visit to the constructed portion of the analytical engine "the greatest disappointment of my life". The Mark I showed no influence from the analytical engine and lacked the analytical engine's most prescient architectural feature, conditional branching. J. Presper Eckert and John W. Mauchly similarly were not aware of the details of Babbage's analytical engine work prior to the completion of their design for the first electronic general-purpose computer, the ENIAC. |
Analytical engine | Comparison to other early computers | Comparison to other early computers
If the analytical engine had been built, it would have been digital, programmable and Turing-complete. It would, however, have been very slow. Luigi Federico Menabrea reported in Sketch of the Analytical Engine: "Mr. Babbage believes he can, by his engine, form the product of two numbers, each containing twenty figures, in three minutes".
By comparison the Harvard Mark I could perform the same task in just six seconds (though it is debatable that computer is Turing complete; the ENIAC, which is, would also have been faster). A modern CPU could do the same thing in under a billionth of a second.
Name First operational Numeral system Computing mechanism Programming Turing complete Memory Difference engine Not built until the 1990s (design 1820s) Decimal Mechanical Not programmable; initial numerical constants of polynomial differences set physically Physical state of wheels in axes Analytical engine Not built (design 1830s) Decimal Mechanical Program-controlled by punched cards (design; not built, yet) Physical state of wheels in axes Ludgate's analytical engine Not built (design 1909) Decimal Mechanical Program-controlled by punched cards (not built) Physical state of rods Torres' analytical machine 1920 Decimal Electro-mechanical Not programmable; input and output settings specified by patch cables Mechanical relays Zuse Z1 1939 Binary floating point Mechanical Not programmable; cipher input settings specified by patch cables Physical state of rods Bombe 1939 (Polish), March 1940 (British), May 1943 (US) Character computations Electro-mechanical Not programmable; cipher input settings specified by patch cables Physical state of rotors Zuse Z2 1940 Binary fixed point Electro-mechanical (mechanical memory) Program-controlled by punched film stock (no conditional branch) Physical state of rods Zuse Z3 May 1941 Binary floating point Electro-mechanical Program-controlled by punched film stock (but no conditional branch) In theory Mechanical relays Atanasoff–Berry computer 1942 Binary Electronic Not programmable; linear system coefficients input using punched cards Regenerative capacitor memory Colossus Mark 1 December 1943 Binary Electronic Program-controlled by patch cables and switches Thermionic valves (vacuum tubes) and thyratrons Harvard Mark I – IBM ASCC May 1944 Decimal Electro-mechanical Program-controlled by 24-channel punched paper tape (but no conditional branch) Debatable Mechanical relays Colossus Mark 2 1 June 1944 Binary Electronic Program-controlled by patch cables and switches Conjectured Zuse Z4 March 1945 (or 1948) Binary floating point Electro-mechanical Program-controlled by punched film stock In 1950 Mechanical relays ENIAC December 1945 Decimal Electronic Program-controlled by patch cables and switches Vacuum tube triode flip-flops Manchester Baby June 1948 Binary Electronic Binary program entered into memory by keyboard (first electronic stored-program digital computer) Williams cathode ray tube EDSAC May 1949 Binary Electronic Five-bit opcode and variable-length operand (first stored-program computer offering computing services to a wide community). Mercury delay lines |
Analytical engine | In popular culture | In popular culture
The cyberpunk novelists William Gibson and Bruce Sterling co-authored a steampunk novel of alternative history titled The Difference Engine in which Babbage's difference and analytical engines became available to Victorian society. The novel explores the consequences and implications of the early introduction of computational technology.
Moriarty by Modem, a short story by Jack Nimersheim, describes an alternative history where Babbage's analytical engine was indeed completed and had been deemed highly classified by the British government. The characters of Sherlock Holmes and Moriarty had in reality been a set of prototype programs written for the analytical engine. This short story follows Holmes as his program is implemented on modern computers and he is forced to compete against his nemesis yet again in the modern counterparts of Babbage's analytical engine.
A similar setting to The Difference Engine is used by Sydney Padua in the webcomic The Thrilling Adventures of Lovelace and Babbage. It features an alternative history where Ada Lovelace and Babbage have built the analytical engine and use it to fight crime at Queen Victoria's request. The comic is based on thorough research on the biographies of and correspondence between Babbage and Lovelace, which is then twisted for humorous effect.
The Orion's Arm online project features the Machina Babbagenseii, fully sentient Babbage-inspired mechanical computers. Each is the size of a large asteroid, only capable of surviving in microgravity conditions, and processes data at 0.5% the speed of a human brain.
Charles Babbage and Ada Lovelace appear in an episode of Doctor Who, "Spyfall Part 2", where the engine is displayed and referenced. |
Analytical engine | References | References |
Analytical engine | Bibliography | Bibliography
|
Analytical engine | External links | External links
The Babbage Papers, Science Museum archive
The Analytical Engine at Fourmilab, includes historical documents and online simulations
Image of a later Plan of Analytical Engine with grid layout (1858)
First working Babbage "barrel" actually assembled, circa 2005
Special issue, IEEE Annals of the History of Computing, Volume 22, Number 4, October–December 2000
Babbage, Science Museum, London (archived)
Plan 28: Building Charles Babbage's Analytical Engine
Category:Charles Babbage
Category:Computer-related introductions in 1837
Category:English inventions
Category:Mechanical calculators
Category:Mechanical computers
Category:One-of-a-kind computers
Category:Ada Lovelace |
Analytical engine | Table of Content | Short description, Design, Construction, Instruction set, Influence, Predicted influence, Computer science, Comparison to other early computers, In popular culture, References, Bibliography, External links |
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