122-603: William Thomas Tutte OC FRS FRSC ( / t ʌ t / ; 14 May 1917 – 2 May 2002) was an English and Canadian code breaker and mathematician. During the Second World War , he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher , a major Nazi German cipher system which was used for top-secret communications within the Wehrmacht High Command. The high-level, strategic nature of
244-409: A byte or word , is referred to, it is usually specified by a number from 0 upwards corresponding to its position within the byte or word. However, 0 can refer to either the most or least significant bit depending on the context. Similar to torque and energy in physics; information-theoretic information and data storage size have the same dimensionality of units of measurement , but there
366-453: A lapel pin may be worn, which is a miniature version of the recipient's badge and thus is distinct for each grade. Wear of the insignia is according to guidelines issued by the Chancellery of Honours, which stipulate that the badges be worn before most other national orders, that is, at the end of an individual's medal bar closest to the centre of the chest or at the wearer's neck, with only
488-502: A unit of information , the bit is also known as a shannon , named after Claude E. Shannon . The symbol for the binary digit is either "bit", per the IEC 80000-13 :2008 standard, or the lowercase character "b", per the IEEE 1541-2002 standard. Use of the latter may create confusion with the capital "B" which is the international standard symbol for the byte. The encoding of data by discrete bits
610-545: A 12-wheel rotor cipher machine. The first step, therefore, had to be to diagnose the machine by establishing the logical structure and hence the functioning of the machine. Tutte played a pivotal role in achieving this, and it was not until shortly before the Allied victory in Europe in 1945, that Bletchley Park acquired a Tunny Lorenz cipher machine. Tutte's breakthroughs led eventually to bulk decrypting of Tunny-enciphered messages between
732-482: A Bell Labs memo on 9 January 1947 in which he contracted "binary information digit" to simply "bit". A bit can be stored by a digital device or other physical system that exists in either of two possible distinct states . These may be the two stable states of a flip-flop , two positions of an electrical switch , two distinct voltage or current levels allowed by a circuit , two distinct levels of light intensity , two directions of magnetization or polarization ,
854-606: A Catholic anti-abortion activist, filed suit against the Order of Canada Advisory Council, demanding that the minutes of the meeting relating to Morgentaler be made public. The appointment of Morgentaler prompted former Liberal Member of Parliament (MP) Clifford Lincoln to write that the workings of the Advisory Council were "mysterious", citing what he theorized to be inbuilt partiality and conflict of interest as reasons why Margaret Somerville , whom Lincoln had twice nominated to
976-507: A Companion because he felt that, as a self-proclaimed Father of Confederation , he deserved a knighthood. Smallwood was never knighted and later accepted induction as a Companion. Resignations from the order can take place only through prescribed channels, which include the member submitting to the Secretary General of the Order of Canada a letter notifying the chancellery of his or her desire to terminate their membership, and only with
1098-413: A Member stirred controversy among some of Canada's Christian organizations, as Johanson had taught teenagers methods of safe sex alongside abstinence. Similarly, the acceptance of birth control advocate Elizabeth Bagshaw and gay rights campaigner Brent Hawkes also incited debate. Abortion-rights activist Henry Morgentaler's appointment to the order on 1 July 2008 not only marked the first time
1220-461: A better country." Each of the six to eight hundred nominations submitted each year, by any person or organization, is received by the order's Advisory Council, which, along with the governor general, makes the final choice of new inductees, typically by consensus rather than a vote; a process that, when conceived, was the first of its kind in the world. Appointees are then accepted into the organization at an investiture ceremony typically conducted by
1342-429: A bit was represented by the polarity of magnetization of a certain area of a ferromagnetic film, or by a change in polarity from one direction to the other. The same principle was later used in the magnetic bubble memory developed in the 1980s, and is still found in various magnetic strip items such as metro tickets and some credit cards . In modern semiconductor memory , such as dynamic random-access memory ,
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#17328948688421464-403: A graduate student in mathematics. He published some work begun earlier, one a now famous paper that characterises which graphs have a perfect matching, and another that constructs a non-Hamiltonian graph. Tutte completed a doctorate in mathematics from Cambridge in 1948 under the supervision of Shaun Wylie , who had also worked at Bletchley Park on Tunny. His thesis An Algebraic Theory of Graphs
1586-403: A graduate student, but transferred to mathematics at the end of 1940. As a student, he (along with three of his friends) became one of the first to solve the problem of squaring the square , and the first to solve the problem without a squared subrectangle. Together the four created the pseudonym Blanche Descartes , under which Tutte published occasionally for years. Soon after the outbreak of
1708-492: A key on squared paper, starting a new row after a defined number of characters that was suspected of being the frequency of repetition of the key. If this number was correct, the columns of the matrix would show more repetitions of sequences of characters than chance alone. Tutte knew that the Tunny indicators used 25 letters (excluding J) for 11 of the positions, but only 23 letters for the other. He therefore tried Kasiski's technique on
1830-628: A new division of the order could be established specifically for governors general, their spouses, and members of the royal family, a version of which was adopted in 2013. Bit The bit is the most basic unit of information in computing and digital communication . The name is a portmanteau of binary digit . The bit represents a logical state with one of two possible values . These values are most commonly represented as either " 1 " or " 0 " , but other representations such as true / false , yes / no , on / off , or + / − are also widely used. The relation between these values and
1952-613: A paper entitled How to Draw a Graph in which he proved that any face in a 3-connected graph is enclosed by a peripheral cycle . Using this fact, Tutte developed an alternative proof to show that every Kuratowski graph is non-planar by showing that K 5 and K 3,3 each have three distinct peripheral cycles with a common edge. In addition to using peripheral cycles to prove that the Kuratowski graphs are non-planar, Tutte proved that every simple 3-connected graph can be drawn with all its faces convex, and devised an algorithm which constructs
2074-535: A ribbon bow positioned on the left shoulder. These regulations were altered in 1997, and women may wear their insignia in either the traditional manner or in the same fashion as the men. With the patriation in 1988 of oversight of heraldry from the UK to Canada through the Canadian Heraldic Authority , the constitution of the Order of Canada was amended to include the entitlement of all inductees to petition
2196-453: A similar design to the Sovereign's badge, though without precious stones, and slight differences for each grade. For Companions, the emblem is gilt with a red enamel maple leaf in the central disk; for Officers, it is gilt with a gold maple leaf; and for Members, both the badge itself and the maple leaf are silver. All are topped by a St. Edward's Crown , symbolizing that the order is headed by
2318-520: A single character, the whole key K consisted of two components: K = χ ⊕ ψ {\displaystyle K=\chi \oplus \psi } At Bletchley Park, mark impulses were signified by x and space impulses by • . For example, the letter "H" would be coded as ••x•x . Tutte's derivation of the chi and psi components was made possible by the fact that dots were more likely than not to be followed by dots, and crosses more likely than not to be followed by crosses. This
2440-407: A specified reduction law. The first major advances in matroid theory were made by Tutte in his 1948 Cambridge PhD thesis which formed the basis of an important sequence of papers published over the next two decades. Tutte's work in graph theory and matroid theory has been profoundly influential on the development of both the content and direction of these two fields. In matroid theory, he discovered
2562-404: A time in serial transmission , and by a multiple number of bits in parallel transmission . A bitwise operation optionally processes bits one at a time. Data transfer rates are usually measured in decimal SI multiples of the unit bit per second (bit/s), such as kbit/s. In the earliest non-electronic information processing devices, such as Jacquard's loom or Babbage's Analytical Engine , a bit
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#17328948688422684-417: A time when graph theory was still a primitive subject, Tutte commenced the study of matroids and developed them into a theory by expanding from the work that Hassler Whitney had first developed around the mid-1930s. Even though Tutte's contributions to graph theory have been influential to modern graph theory and many of his theorems have been used to keep making advances in the field, most of his terminology
2806-555: A visit to London , United Kingdom, later in 1970, Michener presented the Queen with her Sovereign's badge for the Order of Canada, which she first wore during a banquet in Yellowknife in July 1970. From the Order of Canada grew a Canadian honours system , thereby reducing the use of British honours (i.e. those administered by the Queen in her UK Privy Council ). Among the civilian awards of
2928-556: Is a Canadian state order and the second-highest honour for merit in the system of orders, decorations, and medals of Canada , after the Order of Merit . To coincide with the centennial of Canadian Confederation , the three-tiered order was established in 1967 as a fellowship recognizing the outstanding merit or distinguished service of Canadians who make a major difference to Canada through lifelong contributions in every field of endeavour, as well as efforts by non-Canadians who have made
3050-534: Is also installed as the Principal Companion for the duration of his or her time in the viceregal post and continues as an extraordinary Companion thereafter. Additionally, any governor general, viceregal consort, former governor general, former viceregal consort, or member of the Canadian royal family may be appointed as an extraordinary Companion, Officer, or Member. Promotions in grade are possible, though this
3172-486: Is in general no meaning to adding, subtracting or otherwise combining the units mathematically, although one may act as a bound on the other. Units of information used in information theory include the shannon (Sh), the natural unit of information (nat) and the hartley (Hart). One shannon is the maximum amount of information needed to specify the state of one bit of storage. These are related by 1 Sh ≈ 0.693 nat ≈ 0.301 Hart. Some authors also define
3294-554: Is more compressed—the same bucket can hold more. For example, it is estimated that the combined technological capacity of the world to store information provides 1,300 exabytes of hardware digits. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 exabytes of information. When optimally compressed, the resulting carrying capacity approaches Shannon information or information entropy . Certain bitwise computer processor instructions (such as bit set ) operate at
3416-459: Is ordinarily not done within five years of the initial appointment, and a maximum of five honorary appointments into any of the three grades may be made by the governor general each year. As of January 2024 , there have been 28 honorary appointments . There were originally, in effect, only two ranks to the Order of Canada: Companion and the Medal of Service . There was, however, also a third award,
3538-460: Is popular is that the necessary computations that are carried out by his algorithms are simple and guarantee a one-to-one correspondence of a graph and its embedding onto the Euclidean plane , which is of importance when parameterising a three-dimensional mesh to the plane in geometric modelling. "Tutte's theorem is the basis for solutions to other computer graphics problems, such as morphing ." Tutte
3660-502: Is suspended a white, enamelled, hexagonal snowflake design, with six equal leaves and diamonds between each. At the centre is a disc bearing a maple leaf in pavé-laid rubies on a white enamel background, surrounded at its edge by a red enamel ring (annulus) bearing the motto of the order. The Chancellor wears the badge of a Companion and is, upon installation as governor general, granted a livery collar for wear at Order of Canada investiture ceremonies. The badges for inductees are of
3782-404: Is the same as modulo 2 subtraction. The reason that this provided a way into Tunny was that although the frequency distribution of characters in the ciphertext could not be distinguished from a random stream, the same was not true for a version of the ciphertext from which the chi element of the key had been removed. This was the case because where the plaintext contained a repeated character and
W. T. Tutte - Misplaced Pages Continue
3904-546: The Association of Universities and Colleges of Canada , and five members of the order who sit on the council for a three-year period. If a nomination involves a non-Canadian citizen, the deputy minister of Foreign Affairs is invited by the Advisory Council to offer evaluation. Decisions of the council and new appointments to and dismissals from the Order of Canada are announced through the Canada Gazette . As of July 2024 ,
4026-467: The Chief Herald of Canada for personal armorial bearings (coats of arms), should they not already possess any. Companions may receive supporters , and all members may have the escutcheon (shield) of their arms encircled with a red ribbon bearing the order's motto in gold, and from which is suspended a rendition of the holder's Order of Canada badge. The Queen, Sovereign of the Order of Canada, approved
4148-539: The Exclusive Or (XOR) function (symbolised by "⊕"), and to extract the two messages and hence obtain the obscuring key. After a fruitless period during which Research Section cryptanalysts tried to work out how the Tunny machine worked, this and some other keys were handed to Tutte, who was asked to "see what you can make of these". At his training course, Tutte had been taught the Kasiski examination technique of writing out
4270-494: The Medal of Courage , meant to recognize acts of gallantry. This latter decoration fell in rank between the other two levels, but was anomalous within the Order of Canada, being a separate award of a different nature rather than a middle grade of the order. Without ever having been awarded, the Medal of Courage was on 1 July 1972 replaced by the autonomous Cross of Valour and, at the same time,
4392-413: The Order of Canada , was described as "one of the greatest intellectual feats of World War II". To decrypt a Tunny message required knowledge not only of the logical functioning of the machine, but also the start positions of each rotor for the particular message. The search was on for a process that would manipulate the ciphertext or key to produce a frequency distribution of characters that departed from
4514-485: The Quebec sovereignty movement , such as Luc-André Godbout, Rina Lasnier and Geneviève Bujold , while Alice Parizeau , another supporter of Quebec sovereignty, was criticized for accepting entry into the order despite her beliefs. Victoria Cross recipient Cecil Meritt cited the fact that he already held Canada's highest decoration as a reason not to be admitted to the Order of Canada. Prince Philip, Duke of Edinburgh ,
4636-670: The Second World War , Tutte's tutor, Patrick Duff, suggested him for war work at the Government Code and Cypher School at Bletchley Park (BP). He was interviewed and sent on a training course in London before going to Bletchley Park, where he joined the Research Section. At first, he worked on the Hagelin cipher that was being used by the Italian Navy. This was a rotor cipher machine that
4758-585: The Tutte Institute for Mathematics and Computing (TIMC), in his honour in 2011. In September 2014, Tutte was celebrated in his hometown of Newmarket, England, with the unveiling of a sculpture, after a local newspaper started a campaign to honour his memory. Bletchley Park in Milton Keynes celebrated Tutte's work with an exhibition Bill Tutte: Mathematician + Codebreaker from May 2017 to 2019, preceded on 14 May 2017 by lectures about his life and work during
4880-658: The Victoria Cross , the Cross of Valour, and the badge of the Order of Merit permitted to be worn before the badges of the Order of Canada. Those in the grades of Companion or Officer may wear their badges on a neck ribbon, while those in the Member group display their insignia suspended by a ribbon from a medal bar on the left chest. Protocol originally followed the British tradition, wherein female appointees wore their Order of Canada emblem on
5002-445: The fount of honour , is at the apex of the Order of Canada as its Sovereign, followed by the governor general, who serves as the fellowship's Chancellor. Thereafter follow three grades, which are, in order of precedence: Companion (French: Compagnon ), Officer (French: Officier ), and Member (French: Membre ), each having accordant post-nominal letters that members are entitled to use. Each incumbent governor general
W. T. Tutte - Misplaced Pages Continue
5124-456: The psi wheels did not move on, the differenced psi character ( Δ ψ {\displaystyle \Delta \psi } ) would be the null character (' / ' at Bletchley Park). When XOR-ed with any character, this character has no effect. Repeated characters in the plaintext were more frequent both because of the characteristics of German (EE, TT, LL and SS are relatively common), and because telegraphists frequently repeated
5246-410: The yottabit (Ybit). When the information capacity of a storage system or a communication channel is presented in bits or bits per second , this often refers to binary digits, which is a computer hardware capacity to store binary data ( 0 or 1 , up or down, current or not, etc.). Information capacity of a storage system is only an upper bound to the quantity of information stored therein. If
5368-449: The 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down a mercury delay line , charges stored on the inside surface of a cathode-ray tube , or opaque spots printed on glass discs by photolithographic techniques. In the 1950s and 1960s, these methods were largely supplanted by magnetic storage devices such as magnetic-core memory , magnetic tapes , drums , and disks , where
5490-408: The Advisory Council feels their actions have brought the order into disrepute. In order for this to be done, the council must agree to take action and then send a letter to the person both telling of the group's decision and requesting a response. Anyone removed from the order is required to return their insignia. As of 2022 , eight people have been removed from the Order of Canada: Alan Eagleson , who
5612-522: The Advisory Council had not been unanimous in its decision, but also proved to be one of the most controversial appointments in the order's history. Opponents of Morgentaler's abortion activism organized protests outside of Rideau Hall on 9 July, while compatriots did the same in front of Government House in St. John's, Newfoundland and Labrador , the official residence of that province's lieutenant governor . One former police detective, Frank Chauvin, along with
5734-622: The Advisory Council operated with partisan bias. Aubin also pointed to the presence on the council of members of the Royal Society of Canada, an organization into which Somerville was received. Peter Savaryn , a member of the Waffen-SS Galician Division , was awarded the Order of Canada in 1987, for which Governor General of Canada Mary Simon expressed "deep regret" in 2023. At a 2006 conference on Commonwealth honours, Christopher McCreery, an expert on Canada's honours, raised
5856-500: The Advisory Council, was turned down for appointment, yet Morgentaler was accepted. Journalist Henry Aubin in the Montreal Gazette opined that the council's rejection of Somerville, her personal opposition to same-sex marriage , and the acceptance of Brent Hawkes, Jane Rule , and Jean Chrétien , all regarded as supporting same-sex unions, as well as the appointment of a controversial figure such as Morgentaler, were all signs that
5978-594: The Bill Tutte Centenary Symposium. In addition to the career benefits of working at the new University of Waterloo , the more rural setting of Waterloo County appealed to Bill and his wife Dorothea. They bought a house in the nearby village of West Montrose, Ontario where they enjoyed hiking, spending time in their garden on the Grand River and allowing others to enjoy the beautiful scenery of their property. They also had an extensive knowledge of all
6100-576: The Canadian honours system , the Order of Canada comes third, after the Cross of Valour and membership in the Order of Merit , which is within the personal gift of Canada's monarch . By the 1980s, Canada's provinces began to develop their own distinct honours and decorations. Canadian historian Margaret MacMillan represented the order at the coronation of King Charles III and Queen Camilla at Westminster Abbey on 6 May 2023. The Canadian monarch, seen as
6222-524: The German High Command (OKW) in Berlin and their army commands throughout occupied Europe and contributed—perhaps decisively—to the defeat of Germany. On 31 August 1941, two versions of the same message were sent using identical keys, which constituted a " depth ". This allowed John Tiltman , Bletchley Park's veteran and remarkably gifted cryptanalyst, to deduce that it was a Vernam cipher which uses
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#17328948688426344-517: The German teleprinter cipher system. The nickname Tunny (tunafish) was used for the first non-Morse link, and it was subsequently used for the Lorenz SZ machines and the traffic that they enciphered. Telegraphy used the 5-bit International Telegraphy Alphabet No. 2 (ITA2). Nothing was known about the mechanism of enciphering other than that messages were preceded by a 12-letter indicator , which implied
6466-507: The Hamiltonicity of polyhedral graphs , by using the construction known as Tutte's fragment . The eventual proof of the four colour theorem made use of his earlier work. The graph polynomial he called the "dichromate" has become famous and influential under the name of the Tutte polynomial and serves as the prototype of combinatorial invariants that are universal for all invariants that satisfy
6588-532: The Order of Canada (post-nominals: CM , in French: Membre de l'ordre du Canada ) have made an exceptional contribution to Canada or Canadians at a local or regional level, group, field or activity. As many as 136 Members may be appointed annually, not including extraordinary Members and those inducted on an honorary basis, and there is no limit on how many Members may be living at one time. As of August 2017 , there were 2,281 living Members. Upon admission into
6710-409: The Order of Canada that would avert the awkwardness around appointing members of the Canadian royal family as full members of the order: He theorized that the Queen, as the order's Sovereign, could simply appoint, on ministerial advice, anyone as an extra member, or the monarch could issue an ordinance allowing for her relations to be made regular members when approved. Similarly, McCreery proposed that
6832-480: The Order of Canada, generally operating without input from ministers of the Crown ; political interference has occurred only once, when in 1978 Paul Desmarais 's investiture was delayed for six months by Prime Minister Pierre Trudeau . However, some of the committee's selections have caused controversy. For instance, the admission in 2001 of sex educator Sue Johanson , host of the long-running Sunday Night Sex Show , as
6954-512: The Order of Canada, members are given various insignia of the organization, all designed by Bruce W. Beatty , who "broke new ground in the design of insignia of Orders within The Queen's realms" and was himself made a member of the order in 1990; Beatty attended every investiture ceremony between 1967 and early 2010. The badge belonging to the Sovereign consists of a jewelled, 18- carat gold crown of rubies , emeralds , and sapphires , from which
7076-431: The Research Section worked out the complete logical structure of the machine, with its set of wheels bearing cams that could either be in a position (raised) that added x to the stream of key characters, or in the alternative position that added in • . Diagnosing the functioning of the Tunny machine in this way was a truly remarkable cryptanalytical achievement which, in the citation for Tutte's induction as an Officer of
7198-440: The Sovereign, and the reverse is plain except for the word CANADA . The ribbon is white and bordered in red stripes, similar to the Canadian national flag . The ribbon bar for each grade has the same ribbon and is differentiated by a maple leaf in the centre, the colour of which matches that on the badge of the related grade (red for Companion, gold for Officer and silver for Member). For civilian wear on less formal occasions,
7320-521: The achievement of outstanding merit or distinguished service by Canadians who made a major difference to Canada through lifelong contributions in every field of endeavour, as well as the efforts made by non-Canadians who have made the world better by their actions. Membership is thus accorded to those who exemplify the order's Latin motto , taken from Hebrews 11:16 of the Christian Bible , desiderantes meliorem patriam , meaning "they desire
7442-409: The ambiguity of relying on the underlying hardware design, the unit octet was defined to explicitly denote a sequence of eight bits. Computers usually manipulate bits in groups of a fixed size, conventionally named " words ". Like the byte, the number of bits in a word also varies with the hardware design, and is typically between 8 and 80 bits, or even more in some specialized computers. In
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#17328948688427564-465: The augmentation of her royal arms for Canada with the order's ribbon in 1987. On the grant to Bishop's College School , Quebec, the Sovereign's insignia of the Order was depicted below the Royal Arms of Canada, the only time the badge has been incorporated into a grant document. The constitution of the Order of Canada states that the insignia remain property of the Crown , and requires any member of
7686-424: The average. This principle is the basis of data compression technology. Using an analogy, the hardware binary digits refer to the amount of storage space available (like the number of buckets available to store things), and the information content the filling, which comes in different levels of granularity (fine or coarse, that is, compressed or uncompressed information). When the granularity is finer—when information
7808-504: The birds in their garden. Dorothea, an avid potter, was also a keen hiker and Bill organised hiking trips. Even near the end of his life Bill still was an avid walker. After his wife died in 1994, he moved back to Newmarket (Suffolk), but then returned to Waterloo in 2000, where he died two years later. He is buried in West Montrose United Cemetery. Order of Canada The Order of Canada (French: Ordre du Canada )
7930-614: The candidates are worthy enough to be accepted into the order, and make recommendations to the governor general, who appoints the new members. The council is chaired by the chief justice of Canada , and includes the clerk of the Privy Council , the deputy minister of Canadian Heritage , the chair of the Canada Council for the Arts , the president of the Royal Society of Canada , the chair of
8052-467: The characteristics of the original plaintext. Because any repeated characters in the plaintext would always generate • , and similarly Δ ψ 1 ⊕ Δ ψ 2 {\displaystyle \Delta \psi _{1}\oplus \Delta \psi _{2}} would generate • whenever the psi wheels did not move on, and about half of the time when they did – some 70% overall. As well as applying differencing to
8174-497: The concern that the three grades of the Order of Canada were insufficient to recognize the nation's very best; one suggestion was to add two more levels to the order, equivalent to knighthoods in British orders. The order of precedence also came under scrutiny, particularly the anomaly that all three grades of the Order of Canada supersede the top levels of each of the other orders (except the Order of Merit), contrary to international practice. In June 2010, McCreery suggested reforms to
8296-402: The differenced values and by November 1942 had produced a way of discovering wheel starting points of the Tunny machine which became known as the "Statistical Method". The essence of this method was to find the initial settings of the chi component of the key by exhaustively trying all positions of its combination with the ciphertext, and looking for evidence of the non-uniformity that reflected
8418-415: The early 21st century, retail personal or server computers have a word size of 32 or 64 bits. The International System of Units defines a series of decimal prefixes for multiples of standardized units which are commonly also used with the bit and the byte. The prefixes kilo (10 ) through yotta (10 ) increment by multiples of one thousand, and the corresponding units are the kilobit (kbit) through
8540-458: The figure-shift and letter-shift characters. To quote the General Report on Tunny: Turingery introduced the principle that the key differenced at one, now called ΔΚ , could yield information unobtainable from ordinary key. This Δ principle was to be the fundamental basis of nearly all statistical methods of wheel-breaking and setting. Tutte exploited this amplification of non-uniformity in
8662-425: The first impulse of the key characters, using a repetition of 25 × 23 = 575. He did not observe a large number of column repetitions with this period, but he did observe the phenomenon on a diagonal. He therefore tried again with 574, which showed up repeats in the columns. Recognising that the prime factors of this number are 2, 7 and 41, he tried again with a period of 41 and "got a rectangle of dots and crosses that
8784-469: The first two. After explaining his findings to Max Newman , Newman was given the job of developing an automated approach to comparing ciphertext and key to look for departures from randomness. The first machine was dubbed Heath Robinson , but the much faster Colossus computer , developed by Tommy Flowers and using algorithms written by Tutte and his colleagues, soon took over for breaking codes. In late 1945, Tutte resumed his studies at Cambridge , now as
8906-446: The full 5-bit characters of the ITA2 code, Tutte applied it to the individual impulses (bits). The current chi wheel cam settings needed to have been established to allow the relevant sequence of characters of the chi wheels to be generated. It was totally impracticable to generate the 22 million characters from all five of the chi wheels, so it was initially limited to 41 × 31 = 1271 from
9028-496: The governor general at Rideau Hall, although the monarch or a provincial viceroy may perform the task, and the ceremony may take place in other locations. Since the 1991 investiture of Ted Rogers , Order of Canada installment ceremonies have been broadcast on various television channels and the Internet; recipients are given a complimentary video recording of their investiture ceremony from Rogers Cable . At certain periods, holders of
9150-408: The governor general's approval can the resignation take effect. On 1 June 2009, the governor general accepted the resignations of astronomer and inventor René Racine , pianist Jacqueline Richard , and Cardinal Jean-Claude Turcotte ; on 11 January 2010, the same was done for Renato Giuseppe Bosisio , an engineering professor, and Father Lucien Larré ; and on 19 April 2010 for Frank Chauvin . It
9272-820: The graph-theoretic situation. Tutte summarised his work in the Selected Papers of W.T. Tutte , 1979, and in Graph Theory as I have known it , 1998. Tutte's work in World War II and subsequently in combinatorics brought him various positions, honours and awards: Tutte served as Librarian for the Royal Astronomical Society of Canada in 1959–1960, and asteroid 14989 Tutte (1997 UB7) was named after him. Because of Tutte's work at Bletchley Park, Canada's Communications Security Establishment named an internal organisation aimed at promoting research into cryptology,
9394-417: The highly sophisticated homotopy theorem and founded the studies of chain groups and regular matroids , about which he proved deep results. In addition, Tutte developed an algorithm for determining whether a given binary matroid is a graphic matroid . The algorithm makes use of the fact that a planar graph is simply a graph whose circuit-matroid, the dual of its bond-matroid , is graphic. Tutte wrote
9516-413: The insignia on eBay ; however, after the bidding reached $ 15,000, eBay removed the item, citing its policy against the sale of government property, including "any die, seal or stamp provided by, belonging to, or used by a government department, diplomatic or military authority appointed by or acting under the authority of Her Majesty." Rideau Hall stated that selling medals was "highly discouraged"; however,
9638-444: The intelligence obtained from Tutte's crucial breakthrough, in the bulk decrypting of Lorenz-enciphered messages specifically, contributed greatly, and perhaps even decisively, to the defeat of Nazi Germany. He also had a number of significant mathematical accomplishments, including foundation work in the fields of graph theory and matroid theory . Tutte's research in the field of graph theory proved to be of remarkable importance. At
9760-409: The level of manipulating bits rather than manipulating data interpreted as an aggregate of bits. In the 1980s, when bitmapped computer displays became popular, some computers provided specialized bit block transfer instructions to set or copy the bits that corresponded to a given rectangular area on the screen. In most computers and programming languages, when a bit within a group of bits, such as
9882-780: The levels of Officer and Member were introduced, with all existing holders of the Medal of Service created as Officers. Lester Pearson's vision of a three-tiered structure to the order was thus fulfilled. Companions of the Order of Canada (post-nominals: CC , in French: Compagnon de l'ordre du Canada ) have demonstrated the highest degree of merit to Canada and humanity, on either the national or international scene. Up to 15 Companions are appointed annually, with an imposed limit of 180 living Companions at any given time, not including those appointed as extraordinary Companions or in an honorary capacity. As of August 2017 , there are 146 living Companions. Since 1994, substantive members are
10004-421: The members of the advisory council are: Few have declined entry into the Order of Canada; as of 1997 , 1.5 per cent of offered appointments to the order had been refused. The identities of those individuals who have declined induction since the 1970s are kept confidential, so the full list is not publicly known. Some, however, have spoken openly about their decisions, including Robert Weaver , who stated that he
10126-631: The only regular citizens who are empowered to administer the Canadian Oath of Citizenship . Officers of the Order of Canada (post-nominals: OC , in French: Officier de l'ordre du Canada ) have demonstrated an outstanding level of talent and service to Canadians, and up to 64 may be appointed each year, not including those inducted as extraordinary Officers or in an honorary capacity, with no limit to how many may be living at one time. As of August 2017 , there were 1,049 living Officers. Members of
10248-546: The order as a result of the Advisory Council moving forward with his pending removal due to his being found guilty of professional misconduct. The Order's Advisory Council considered a request made in 2021 for the expulsion of Julie Payette , the 29th Governor General of Canada, from the order. Payette, an Extraordinary Companion, resigned from the viceregal post over allegations of harassment of personnel at Rideau Hall . The advisory board attempts to remain apolitical and pragmatic in its approach to selecting new members of
10370-979: The order by John Matheson . The snowflake design for the order was suggested by the diplomat John G. H. Halstead . The association was officially launched on 1 July 1967, the 100th anniversary of Canadian Confederation , with Governor General Roland Michener being the first inductee to the order, to the level of Companion, and on 7 July of the same year, 90 more people were appointed, including former Governor General Vincent Massey , former prime minister Louis St. Laurent , novelist Hugh MacLennan , religious leader David Bauer , novelist Gabrielle Roy , historian Donald Creighton , feminist politician and future senator Thérèse Casgrain , pioneering neurosurgeon Wilder Penfield , painter Arthur Lismer , public health leader Brock Chisholm , former political leader M. J. Coldwell , disability advocate Edwin Baker , painter Alex Colville , and ice hockey player Maurice Richard . During
10492-456: The order to return to the chancellery their original emblem should they be upgraded within the order to a higher rank. Thus, while badges may be passed down as family heirlooms, or loaned or donated for display in museums , they cannot be sold. Over the decades, however, a number of Order of Canada insignia have been put up for sale. The first was the Companion's badge of M. J. Coldwell , who
10614-566: The order were presented with other awards, usually commemorative medals. Thus far, two commemoratives have been given automatically to every living member of the Order of Canada: the Queen Elizabeth II Silver Jubilee Medal in 1977 and the Queen Elizabeth II Diamond Jubilee Medal in 2012. The task of the order's advisory council is to evaluate the nominations of potential inductees, decide if
10736-418: The order, while other appointments have been controversial. Appointees are presented with insignia and receive the right to armorial bearings . The process of founding the Order of Canada began in early 1966 and concluded on 17 April 1967, when the organization was instituted by Queen Elizabeth II, on the advice of the Canadian prime minister , Lester B. Pearson , who was assisted with the establishment of
10858-408: The orientation of reversible double stranded DNA , etc. Bits can be implemented in several forms. In most modern computing devices, a bit is usually represented by an electrical voltage or current pulse, or by the electrical state of a flip-flop circuit. For devices using positive logic , a digit value of 1 (or a logical value of true) is represented by a more positive voltage relative to
10980-534: The owner continued efforts to sell the insignia via the internet. Five years later, a miniature insignia presented to Tommy Douglas was put on auction in Ontario as part of a larger collection of Douglas artifacts. Douglas's daughter, Shirley Douglas , purchased the set for $ 20,000. Any of the three levels of the Order of Canada are open to all living Canadian citizens, except all federal and provincial politicians and judges while they hold office. The order recognizes
11102-443: The physical states of the underlying storage or device is a matter of convention, and different assignments may be used even within the same device or program . It may be physically implemented with a two-state device. A contiguous group of binary digits is commonly called a bit string , a bit vector, or a single-dimensional (or multi-dimensional) bit array . A group of eight bits is called one byte , but historically
11224-437: The plane drawing by solving a linear system. The resulting drawing is known as the Tutte embedding . Tutte's algorithm makes use of the barycentric mappings of the peripheral circuits of a simple 3-connected graph. The findings published in this paper have proved to be of much significance because the algorithms that Tutte developed have become popular planar graph drawing methods. One of the reasons for which Tutte's embedding
11346-504: The reigning Canadian monarch, is the order's sovereign; the governor general administers the order on his behalf as Chancellor and Principal Companion. Appointees to the order are recommended by an advisory board and formally inducted by the governor general or the sovereign. As of January 2024 , 8,375 people have been appointed to the Order, including scientists, musicians, politicians, artists, athletes, business people, film stars and benefactors. Some have resigned or have been removed from
11468-517: The representation of 0 . Different logic families require different voltages, and variations are allowed to account for component aging and noise immunity. For example, in transistor–transistor logic (TTL) and compatible circuits, digit values 0 and 1 at the output of a device are represented by no higher than 0.4 V and no lower than 2.6 V, respectively; while TTL inputs are specified to recognize 0.8 V or below as 0 and 2.2 V or above as 1 . Bits are transmitted one at
11590-424: The size of the byte is not strictly defined. Frequently, half, full, double and quadruple words consist of a number of bytes which is a low power of two. A string of four bits is usually a nibble . In information theory , one bit is the information entropy of a random binary variable that is 0 or 1 with equal probability, or the information that is gained when the value of such a variable becomes known. As
11712-552: The thickness of alternating black and white lines. The bit is not defined in the International System of Units (SI). However, the International Electrotechnical Commission issued standard IEC 60027 , which specifies that the symbol for binary digit should be 'bit', and this should be used in all multiples, such as 'kbit', for kilobit. However, the lower-case letter 'b' is widely used as well and
11834-556: The two possible values of one bit of storage are not equally likely, that bit of storage contains less than one bit of information. If the value is completely predictable, then the reading of that value provides no information at all (zero entropic bits, because no resolution of uncertainty occurs and therefore no information is available). If a computer file that uses n bits of storage contains only m < n bits of information, then that information can in principle be encoded in about m bits, at least on
11956-444: The two values of a bit may be represented by two levels of electric charge stored in a capacitor . In certain types of programmable logic arrays and read-only memory , a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. In optical discs , a bit is encoded as the presence or absence of a microscopic pit on a reflective surface. In one-dimensional bar codes , bits are encoded as
12078-497: The uniformity that the enciphering process aimed to achieve. While on secondment to the Research Section in July 1942, Alan Turing worked out that the XOR combination of the values of successive characters in a stream of ciphertext and key emphasised any departures from a uniform distribution. The resultant stream (symbolised by the Greek letter "delta" Δ ) was called the difference because XOR
12200-446: The world better by their actions. Membership is accorded to those who exemplify the order's Latin motto , desiderantes meliorem patriam , meaning "they desire a better country", a phrase taken from Hebrews 11 :16. The three tiers of the order are Companion, Officer and Member. Specific people may be given extraordinary membership and deserving non-Canadians may receive honorary appointment into each grade. King Charles III ,
12322-438: Was a product of a weakness in the German key setting, which they later eliminated. Once Tutte had made this breakthrough, the rest of the Research Section joined in to study the other impulses, and it was established that the five chi wheels all advanced with each new character and that the five psi wheels all moved together under the control of two mu or "motor" wheels. Over the following two months, Tutte and other members of
12444-470: Was also reported that other constituents of the Order of Canada had, in reaction to Henry Morgentaler 's induction into their ranks, indicated that they would return or had returned their emblems in protest, including organizations such as the Missionary Oblates of Mary Immaculate and Madonna House Apostolate doing so on behalf of deceased former members. Members may be removed from the order if
12566-447: Was also used in Morse code (1844) and early digital communications machines such as teletypes and stock ticker machines (1870). Ralph Hartley suggested the use of a logarithmic measure of information in 1928. Claude E. Shannon first used the word "bit" in his seminal 1948 paper " A Mathematical Theory of Communication ". He attributed its origin to John W. Tukey , who had written
12688-503: Was appointed in 1967; his badge was sold at auction in 1981, an act that received criticism from government officials. In 2007, it was revealed that one of the first ever issued insignia of the Order of Canada, a Medal of Service awarded originally to Quebec historian Gustave Lanctot , was put up for sale via e-mail. Originally, the anonymous auctioneer, who had purchased the decoration for $ 45 at an estate sale in Montreal , attempted to sell
12810-460: Was available commercially, so the mechanics of enciphering was known, and decrypting messages only required working out how the machine was set up. In the summer of 1941, Tutte was transferred to work on a project called Fish. Intelligence information had revealed that the Germans called the wireless teleprinter transmission systems "Sägefisch" ('sawfish'). This led the British to use the code Fish for
12932-680: Was born. The family spent some time in Buckinghamshire, County Durham and Yorkshire before returning to Newmarket, where Tutte attended Cheveley Church of England primary school in the nearby village of Cheveley. In 1927, when he was ten, Tutte won a scholarship to the Cambridge and County High School for Boys . He took up his place there in 1928. In 1935 he won a scholarship to study natural sciences at Trinity College, Cambridge , where he specialized in chemistry and graduated with first-class honours in 1938. He continued with physical chemistry as
13054-516: Was considered ground breaking and was about the subject later known as matroid theory. The same year, invited by Harold Scott MacDonald Coxeter , he accepted a position at the University of Toronto . In 1962, he moved to the University of Waterloo in Waterloo , Ontario, where he stayed for the rest of his academic career. He officially retired in 1985, but remained active as an emeritus professor. Tutte
13176-417: Was critical of the "three-tier" nature of the order; Claude Ryan and Morley Callaghan , who both declined the honour in 1967; Mordecai Richler , who twice declined; and Marcel Dubé , Roger Lemelin and Glenn Gould , who all declined in 1970. However, all the above individuals, save for Gould, later did accept appointment into the order. Others have rejected appointment on the basis of being supporters of
13298-474: Was dismissed after being jailed for fraud in 1998; David Ahenakew , who faced calls for his removal due to antisemitic comments he made in 2002; T. Sher Singh , after the Law Society of Upper Canada found him guilty of professional misconduct and revoked his licence to practise law; Steve Fonyo , due to "his multiple criminal convictions, for which there are no outstanding appeals"; Garth Drabinsky , who
13420-485: Was editor in chief of the Journal of Combinatorial Theory until retiring from Waterloo in 1985. He also served on the editorial boards of several other mathematical research journals. Tutte's work in graph theory includes the structure of cycle spaces and cut spaces , the size of maximum matchings and existence of k -factors in graphs, and Hamiltonian and non-Hamiltonian graphs. He disproved Tait's conjecture , on
13542-458: Was found guilty of fraud and forgery in Ontario and has been a fugitive from American law for related crimes; Conrad Black , who was convicted in the United States in 2007 of fraud and obstruction of justice; Ranjit Chandra , whose scientific work was discredited by allegations of fraud; and Johnny Issaluk , following allegations of sexual misconduct. In 2013, Norman Barwin resigned from
13664-413: Was in 1982 offered appointment to the order as an honorary Companion; however, he refused on the grounds that, as the consort of the Queen, he was a Canadian and thus entitled to a substantive appointment. In 1993, the Advisory Council proposed an amendment to the constitution of the Order of Canada, making the monarch's spouse automatically a Companion, but Prince Philip again refused, stating that if he
13786-535: Was instrumental in helping to found the Department of Combinatorics and Optimization at the University of Waterloo. His mathematical career concentrated on combinatorics , especially graph theory , which he is credited as having helped create in its modern form, and matroid theory , to which he made profound contributions; one colleague described him as "the leading mathematician in combinatorics for three decades". He
13908-464: Was mainly responsible for developing the theory of enumeration of planar graphs, which has close links with chromatic and dichromatic polynomials. This work involved some highly innovative techniques of his own invention, requiring considerable manipulative dexterity in handling power series (whose coefficients count appropriate kinds of graphs) and the functions arising as their sums, as well as geometrical dexterity in extracting these power series from
14030-562: Was not in agreement with their conventional usage and thus his terminology is not used by graph theorists today. "Tutte advanced graph theory from a subject with one text ( D. Kőnig 's) toward its present extremely active state." Tutte was born in Newmarket in Suffolk. He was the younger son of William John Tutte (1873–1944), an estate gardener, and Annie ( née Newell; 1881–1956), a housekeeper. Both parents worked at Fitzroy House stables where Tutte
14152-460: Was often stored as the position of a mechanical lever or gear, or the presence or absence of a hole at a specific point of a paper card or tape . The first electrical devices for discrete logic (such as elevator and traffic light control circuits , telephone switches , and Konrad Zuse's computer) represented bits as the states of electrical relays which could be either "open" or "closed". When relays were replaced by vacuum tubes , starting in
14274-503: Was recommended by the IEEE 1541 Standard (2002) . In contrast, the upper case letter 'B' is the standard and customary symbol for byte. Multiple bits may be expressed and represented in several ways. For convenience of representing commonly reoccurring groups of bits in information technology, several units of information have traditionally been used. The most common is the unit byte , coined by Werner Buchholz in June 1956, which historically
14396-434: Was replete with repetitions". It was clear, however, that the first impulse of the key was more complicated than that produced by a single wheel of 41 key impulses. Tutte called this component of the key χ 1 {\displaystyle \chi _{1}} ( chi 1 ). He figured that there was another component, which was XOR-ed with this, that did not always change with each new character, and that this
14518-623: Was the product of a wheel that he called ψ 1 {\displaystyle \psi _{1}} ( psi 1 ). The same applied for each of the five impulses ( χ 1 χ 2 χ 3 χ 4 χ 5 {\displaystyle \chi _{1}\chi _{2}\chi _{3}\chi _{4}\chi _{5}} and ψ 1 ψ 2 ψ 3 ψ 4 ψ 5 {\displaystyle \psi _{1}\psi _{2}\psi _{3}\psi _{4}\psi _{5}} ). So for
14640-512: Was to be appointed, it should be on his merits. Congruent with these arguments, he in 1988 accepted without issue a substantive induction as a Companion of the Order of Australia . In 2013, the constitution of the Order of Canada was amended in a way that permitted the substantive appointment of Royal Family members and Prince Philip accepted induction as the first extraordinary Companion of the Order of Canada on 26 April 2013. Former Premier of Newfoundland Joseph Smallwood declined appointment as
14762-541: Was used in the punched cards invented by Basile Bouchon and Jean-Baptiste Falcon (1732), developed by Joseph Marie Jacquard (1804), and later adopted by Semyon Korsakov , Charles Babbage , Herman Hollerith , and early computer manufacturers like IBM . A variant of that idea was the perforated paper tape . In all those systems, the medium (card or tape) conceptually carried an array of hole positions; each position could be either punched through or not, thus carrying one bit of information. The encoding of text by bits
14884-405: Was used to represent the group of bits used to encode a single character of text (until UTF-8 multibyte encoding took over) in a computer and for this reason it was used as the basic addressable element in many computer architectures . The trend in hardware design converged on the most common implementation of using eight bits per byte, as it is widely used today. However, because of
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