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What do you make of Georges Perec? What do you consider his best work?

What we need to question is bricks, concrete, glass, our table manners, our utensils, our tools, the way we spend our time, our rhythms. To question that which seems to have ceased forever to astonish us. We live, true, we breathe, true; we walk, we go downstairs, we sit at a table in order to eat, we lie down on a bed on order to sleep. How? Where? When? Why? Describe your street. Describe another. Compare.The French writer Georges Perec (1936–1982) was, to my mind, one of the most remarkable, stimulating and thought-provoking writers of the 20th century.Perec was many writers.He was a novelist. He was an essayist. He was a poet.He wrote radio plays for German radio, even though French was his first language and he started out unsure if he even liked Germany and its culture.He pulled off an incredible feats of linguistic virtuosity, including one of the world’s longest palindromes. He composed fiendishly hard crosswords.He spent much of his life haunted by depression, and his writing is a struggle against the void and silence and emptiness: he embraced constraints as a way of containing and incorporating the difficulty of writing anything at all, and yet his writing is full of life and detail and conviviality, and the celebration of friendship and fellowship. He rather half-heartedly attempted suicide, at one point (a friend met him the next morning and found Perec with bandaged wrists, and Perec smiled meekly and said I’ve been a little bit silly); but although he died young, it was because of the cancer caused by his lifelong smoking habit. He spent the last years of his life happily in love and writing some of his best work.Like James Joyce, Perec stared bleak circumstances in the face, and instead of succumbing to them or moaning about them, he cracked jokes and told good stories and built a tower of words that was fit to live in.Perec was born to a French Jewish family. His father was in the French Army and was killed during the German invasion of France. His mother was rounded up by the Nazis and died in the camps. Georges himself was taken in and adopted by his paternal aunt and uncle.He studied history and sociology at the Sorbonne, and began writing articles and reviews. In 1958–59 he did his national service in the French army, serving as a paratrooper. For a while he had a rather bizarre double life, being a soldier by day and then putting on his tweeds and hanging out in Parisian bars with his friends at night, discussing ideas and left-wing politics and being an intellectual. This became the background of his second book, Quel petit vélo à guidon chromé au fond de la cour? (1966), which I’ll get to later. But I’m getting ahead of myself.He came to adulthood in the 1950s, then, and the literary world of 50s and 60s France was high on an intellectual cocktail of left-wing politics and structuralism. Sartre still had his wits about him and de Beauvoir was active, but the real stars were people like Claude Lévi-Strauss, Roland Barthes, Jacques Lacan. These were the people that writers of Perec’s generation grew up thinking of as the adults in the room; Perec’s instinct was to simultaneously absorb their influence and take the piss out of them. He once compared them in a jokey newspaper article to pop stars, praising Lacan’s latest hit “Your unconscious is structured like a language, yeah, yeah, yeah.”Perec made his name with the 1965 novel Les Choses: Une Histoire des Années Soixante, translated as Things: A Story of the Sixties. The title was in part a sly joke about Jean-Paul Sartre’s 1964 autobiography, Les Mots (Words), which had been a major hit of the era.Things won the Prix Renaudot, and made Perec a minor literary celebrity, to the point that Georges Pompidou made a joke about him and his book: the then-Prime Minister of France asked somebody what this Perec fellow did for a living and, on being told that Perec worked as a filing clerk in a medical lab, Pompidou quipped ‘Ah, I had a feeling that he wasn’t too busy with Things.’He married teacher Paulette Petras in 1960. They separated fairly amicably in 1969, but never divorced.From then on, Perec lived on both his salary as an archivist in the Centre national de la recherche scientifique, and from his income as a writer.He never had children. He had a string of mostly unhappy love affairs (he thought he was small, funny-looking and unattractive) and suffered from depression in his 30s, but then in 1976 he met filmmaker Catherine Binet. They fell in love, and were very happy.I love the story of their first date: they were eating dinner in a Paris restaurant and Binet spilled some sauce on her dress. Before she had time to feel mortified about it, Perec grinned, reached down to his dish of skate in black butter, scooped up some butter on his finger and smeared it on his own shirt. Perec’s biographer recorded that ‘she had never known such charm.’He died from lung cancer in 1982.David Bellos’ magisterial biography of Perec is subtitled A Life in Words, and there’s an argument to be made for Perec as the writer who, since James Joyce, has been most fascinated with and preoccupied by the most basic building-blocks of language: words themselves.Perec didn’t discover his true voice, or rather voices, or rather space as a writer, for some time.He was fascinated with ordinariness. Partly out of the mid-20th century French left-wing ‘critique of everyday life’, but also because of his own perception of his marginality as a writer. He was small, Jewish and an orphan, and on more than one occasion as a child he ran away from home—not to go anywhere in particular, just to get away. He was in analysis from an early age and recognised that he was very good at not telling his analyst what his problems were. Perec was both amused and pained that people assumed from his Breton-sounding surname that his family was from Brittany: actually, Perec had been his paternal ancestors changing ‘Peretz’ to make it more French-sounding.Perec shared the common interest in tales of travel and adventure, but he also advocated what he called ‘endotics’, the study of what’s in your immediate environment, the opposite of ‘exotics’: what exactly is on my desk? What do I do every day? What are the things I take for granted, but which form the entire texture of the life around us? Perec’s attitude was a bit like that of the singer in Talking Heads’ ‘Once in a Lifetime’: How did I get here?Things crystallised his early interest in sociology. It’s not so much a novel about individuated characters, as about what those characters want out of life. Hence the title ‘a story of the Sixties’: it’s about the pleasures and frustrations of consumerism. The main characters, Jerôme and Sylvie, work in the then-thriving fields of market research and opinion polling and their main problem is that they never, ever feel like they have enough money. (To be fair, for most of the book they really don’t have much of it.) They want to stand back from consumer society and criticise it like the good middle-class 60s French young people they are, but they also desperately want that new coffee table, enough money for a good meal with friends. Yet they find themselves scrimping coins to afford cigarettes.Jerôme and Sylvie are not shown in terms of being a couple with a dynamic relationship, but are a unit who want the same things as each other. They and their friends are seen as representative; this isn’t a soap opera. Their longing for a better life isn’t depicted as evidence that they are personally shallow or empty and materialistic: this is how a better life is represented to them by the world they live in.As Perec puts it with dry wit:In the past millions fought, and millions still do fight, for their crust of bread. Jerôme and Sylvie did not quite believe you could go into battle for a chesterfield settee.But that, Perec goes on, is nevertheless something that they would have felt like fighting for. Not better employment conditions or healthcare, but a round-the-world holiday or a really cool stereo.The characters are depicted as being representative of their generation, or at least of their immediate circle. This is even clearer in the original French, where the reader becomes aware from page one that the first half of the book is written in the imperfect tense, a tense that doesn’t exist as fully in English as it does in French. Everything the characters do is represented as something that they ‘would’ do, i.e. in terms of their habits: the phrase ils auraient, ‘they would’, is all over the first few pages.Towards the end of the book, when Jerôme and Sylvie’s personal fortunes take a turn for the better, the book switches to the future tense, telling you what will happen to them, and this change in tense contributes to the peculiarly haunting quality of the last few pages.Things doesn’t really have a narrative; it charts the rise and fall of Jerôme and Sylvie’s frustrations and hopes, ending on an ambiguous note which reflects Perec’s own identification of himself and his friends with his characters, but also an ultimate scepticism about whether the things they want are really worth having.Les Choses got Perec’s name into the papers, and as usual with French intellectual life in those days, he was seen as part of a movement; the new ‘sociological novel’.What he chose to do then was, therefore, completely perverse.Quel petit vélo à guidon chromé au fond de la cour? (What wee moped with chrome handlebars at the back of the yard?) was a novella written about an anecdote dating from Perec’s military service, when he and some friends had attempted to run a caper which would save a conscript from being sent to fight in Algeria. (Perec had a lifelong love of criminal caper stories, and wrote several of them.) Instead of being another sober sociological fiction, it was written in a bizarre, erratic, slangy version of French derived in part from Perec’s love of the work of Raymond Queneau, the great poet, novelist, editor and polymath, who was rapidly becoming one of his main heroes and a close friend. Quel petit vélo was greeted mostly with bafflement: Perec had entirely failed to do what he was supposed to do, namely, repeat himself.Perec’s second novel proper, Un homme qui dort (A Man Asleep), came out of his experience of depression.Written in the second person, the novel describes the experiences of a young man who decides to let life go by and do nothing with it.He doesn’t simply lie down and die. He goes about his daily routine, making his morning coffee, washing his clothes in his bedsit, going to university and at least pretending to study, coming home, eating the same dinner (steak frites) in the same cheap bistro every night. It’s a haunting portrayal of deep loneliness.However, there was an invisible factor about the book which nobody recognised at the time. Perec wrote it by taking and discreetly adapting sentences from previous writers, until they all had the same ‘voice’. This picture of a solitary man is in fact built from the words of numerous other writers: it wouldn’t have been possible to tell the story if it hadn’t been told many times before.Un homme qui dort looks like a very personal piece of writing, and it was, but it was personal in the way that Perec’s mature writing was personal: by brilliantly playing with the words on the page in ways that other writers don’t, and achieving something which looked completely ‘natural’.Perec’s next novel, La Disparition (1969), translated into English as A Void, is his most notorious in that it’s a lipogram, a text written without the use of a letter of the alphabet. In this, case the letter was ‘e’, in French as in English the most-used letter.This was not a mere stunt for Perec. He found that arbitrary constraints freed his imagination. Writing Things had been laborious for him, but once he started to use constraints in his writing he became more prolific. The most significant plot element in La Disparition is that, whenever a character is obliged by the story to use a word with an ‘e’ in it, they disappear.People disappearing had been a theme in his life. His father went to fight in WW2 and never returned. His mother had been taken away by the Nazis and never came back. The official letter reporting her death had been headed Acte de disparition.Constraints gave Perec a kind of arbitrary power over his own work: it set a boundary to what was doable and not doable that didn’t have to be justified. (Why write a novel with no ‘e’ in it? Why not?) I think that writing with constraints helped Perec to focus. Without them, the temptation to cram everything in, to try to write everything that was on his mind, was too great.La Disparition was greeted by French reviewers with wary admiration and, again, some bafflement, but Perec was most pleased by one reviewer, who completely failed to notice that the novel was missing the letter ‘e’. Although the review wasn’t very complimentary and the reviewer had entirely missed the point, Perec took this to be justification that he’d pulled off the lipogram so skilfully that someone wouldn’t even notice that he’d done it.In 1967, Perec had become a member of Oulipo, the Ouvroir de littérature potentielle, the gathering of writers and mathematicians who liked to experiment with new ways of writing. Italo Calvino was also a member. Oulipo had been co-founded by Queneau and François Le Lionnais, and Perec was one of its younger and most enthusiastic members. Perec had limited talent for mathematics but he was interested in it—he was, by all accounts, very good indeed at his day job, which was basically analogue data storage and processing—and he would become the member of Oulipo who was most determined to fulfil Queneau’s injunction that it was all very well playing around with experimental methods of writing, but the real goal should be to create truly memorable literature using those methods.Queneau himself had composed Cent mille milliards de poèmes (1961), a short book containing ten sonnets printed on cards, with each line printed on a separate strip, like those kids’ books where you can combine different animal pictures to make new animals. In Queneau’s case you could combine different lines to make new poems, as each line made just as much sense before or after each previous or successive line of every other poem in the sequence, and they all had the same rhyme scheme.The result was that you could create [math]10^{14}[/math] poems, or 100,000,000,000,000, hence the title: One hundred thousand billion poems.Queneau calculated that if you were to try to read every single poem that it was possible to generate, and were prepared to spend 24 hours a day doing it, it would take you 190,258,751 years to finish it.In the late 1960s, Perec started planning what would become his masterpiece, a novel that the great computer scientist Donald Knuth has called ‘perhaps the greatest 20th century novel’: La vie mode d’emploi (1978), translated as Life A User’s Manual.Notice the French habit of declaring the genre of a book on the front cover. In this case, it’s not Roman, ‘novel’, but Romans, ‘novels’.La vie combined all of Perec’s interests into the one book:An interest in the everyday: the novel is a description of what’s going on in each room of a Parisian apartment block at the same moment in time;Stories and tales, in that each apartment comes trailing ample amounts of backstory to fill you in on who’s who and what they’re doing;A fascination with the artistic process, in the form of the wealthy Bartlebooth, who has filled in his later years carrying out an elaborate project to learn to paint watercolours from a skilled artist, then travel round the world painting 500 of them, have them made into jigsaw puzzles by a skilled craftsman, then assemble the puzzles, and then remove the paintings and bleach the colours out of them so that the whole project cancels itself out and it’s as if it never happened;Arbitrary constraint, in the form of 42 lists that determined what objects and things had to be in each room of the block, as well as lists that dictated when Perec didn’t have to follow his own rules, and a special chessboard move that dictated in what order the rooms had to be visited;A love of literary reference: one chapter is basically a condensed version of the entire story of A Man Asleep, or rather a slight variant of it;A fascination with consumer culture and things, in that the contents of the apartment block are lovingly detailed, and if someone’s had e.g. a birthday party, you will know what they had to eat and drink.Most of the writing process of La vie consisted of Perec’s creation of his own plan, and the resulting planning process itself; he did the actual drafting very quickly indeed, so quickly that his girlfriend Binet, after reading the first draft, said Georges, it’s great, but you can’t send this out—it’s full of terrible French. (The French can be quite firm about what constitutes ‘good’ French and ‘bad’ French.) Perec grumbled but redrafted it in accordance with standards of elegance and idiomatic correctness. The result is a big fat novel, but one that reads with great ease and speed, and conveys a very satisfying impression of coherence on more than one level—because it is coherent on more than one level, but you can’t discern what they all are.And as in all Perec’s best work, life itself is seen to elude and exceed the most fantastically detailed plan. Bartlebooth’s exercise in futility is itself doomed. There’s more stuff going on than we can take in.Life A User’s Manual is an experimental novel that reads like a classic one. Its structure is unusual, but transparent: every chapter is a moment in a room, frozen in time. It’s comic and tragic, bursting with stories and not forcing them to make some kind of overall point. (Some of the situations are bizarre: in one apartment where a dinner party is being hosted, the guests are waiting patiently at the dinner table while the host and hostess are screwing energetically in the bath, being watched by their cat.)Out of the immobility of the instant that the book takes place in, lives and stories and family sagas go off in all directions. Life A User’s Manual has nothing weird or difficult or self-consciously confrontational about it.The closest it gets to looking like an avant-garde novel is at its centre, where we find a list of pithy, one-line descriptions of each chapter in the book. On closer inspection, we find that each of these lines has exactly the same number of characters and spaces, and that the last letter of the first line is ‘e’, which is also the second last letter of the second line, and the third last letter of the third line, and so on, until it’s the first letter in the line.Then the pattern recurs but with the letter ‘g’, and then all over again with the letter ‘o’. The word ego is thus built into this long list.In the original, the letters are ‘a’. ‘m’, and ‘e’, which spell the word âme, ‘soul’.Writing this long list—the soul of the book, if you like—would have been hard enough in itself; translating it was an act of sorcery by David Bellos.Perec wrote a lot of other things too.Species of Spaces was a short book about the different kinds of spaces in which we live, going from the area immediately around the writing desk to the world and the universe beyond. Perec was always fascinated by those inscriptions kids write into their books, when they give their address and go on to add their country, then ‘The Earth, The Solar System, The Milky Way, ‘The Universe’.Je me souviens, ‘I Remember’, is a long list of apparently banal memories which Perec composed. Not ones which were personal and private to him, but which were his and also could have been anyone else’s. For example, I could write such a list and include things like ‘I remember the Cadbury’s Icebreaker’ or ‘I remember the Dun Laoghaire-Holyhead car ferry St Columba’ and somebody else might go Oh yeah, I remember that too.Experimental demonstration of the tomatotopic organisation in the Soprano (Cantatrix sopranica L.) was the only work that Perec wrote in English. It was a spoof scientific paper about the effects on a soprano of throwing tomatoes at her, which he composed in a deliberate parody of the grindingly bad English of French scientific researchers, complete with numerous citations to fictitious previous research on related subjects and snuck it into the archive of the lab where he worked to see if anyone would notice. It’s now published as part of his works.Les Revenentes was his reaction from writing La Disparition. It’s a short story in which ‘e’ is the only vowel. Perec pulls this off by numerous examples of creative misspelling, and it’s based on a family story about the loss of some jewels, which winds up in a very funny and (for Perec) unusually explicit account of a wild pansexual orgy.W or the Memory of Childhood is his bleakest and most disturbing book. It’s a mixture of a story about a disappeared boy and an account of a society, W, which is apparently based on Olympian ideals but which turns out to be a nightmarish dystopia in which starving athletes are forced to compete for food; the story turns especially gut-wrenching in its description of how the society treats women. It’s basically an allegory for the concentration camps which his own mother died in. Perec had read and was affected by David Rousset’s 1946 book about the camps, L'Univers concentrationnaire.Petit traité invitant à la découverte de l'art subtil du go, co-written with Pierre Lusson and Jacques Roubaud, was an introduction to the ancient Chinese game of Go, which became an obsession for Perec and his friends in the 1960s.The Art of Asking Your Boss for a Raise came out of Perec’s interest in data storage and computing. It began with a found object: Perec was asked by French computing researcher Jacques Perriaud to write something based on an actual flowchart which specified how an employee of a given establishment could ask their boss for a raise. Perec tweaked it a bit, and then wrote out the narrative of a nameless second-person character who laboriously goes through every possible loop in the flowchart in an increasingly darkly comic effort to get to his boss and ask him for a raise (in some versions of the loop, you do get as far as his office but you can’t ask him for a raise because he’s died from eating expired eggs).And then there are numerous articles, stories, crosswords, games, lipograms, palindromes and other things, many of which have been translated into English.On what would have been Georges Perec’s 80th birthday, he got a Google Doodle, although it wasn’t visible to much of the English-speaking world.In the end, except for readers who are as generally fascinated as I am with Perec’s techniques, I suspect that most of his works will come to be regarded as planets orbiting the brilliant star that is Life A User’s Manual, a book that everyone ought to read, in which Perec’s interest in people and in stories was given full scope precisely because it was kept in such control by considerations of structure.One of my favourite of his shorter works isn’t even a proper piece of writing so much as a transcript of something he said, at a meeting of the editorial committee of a journal he and his friends wanted to launch.The committee was endlessly deliberating over finer points of editorial policy when Perec spoke up, drawing from of all things his military service. He had trained as a paratrooper, and his unit, the 18th Parachute Regiment, was not the only paratroop unit to have served with some infamy in the Algerian War of Independence. Perec himself had been excused from going to Algeria because his father had died in the war, and like all French people of his generation with a conscience, he’d been firmly opposed to France holding on to Algeria.Nevertheless, he drew on his experience of parachuting to explain, with characteristic fullness of detail, what he thought they needed to do. (I’ve omitted a lot, including some of Perec’s more specific remarks about the connotations of what it meant for him to be a paratrooper at the time that he was one):When you look at the eyes of the ones facing you, you realise that everyone has something in common, deep down, beyond their fear, beyond the fact that you know that they’re fascists, you know that these guys are absolute bastards, that these guys are the dregs, you feel there’s something in common, but you can’t manage to define exactly what it is. Perhaps it’s simply the fact that they’re all in the same situation that you are, and that they’re all going to have to jump out of the plane door when the moment comes. […] You may be obliged to feel trust at all costs, and that it isn’t possible to refuse something. It isn’t possible to say no. It isn’t possible to take refuge, for example, in nihilism, or even intellectualism, no longer possible, even, to intellectualise. You’re facing into the void, and you have suddenly to throw yourself out. Suddenly you have to refuse your fear. Suddenly, have to refuse to give up.And then? Then, you have to launch yourself.[…]You had absolutely to launch yourself. It wasn’t possible to do otherwise. It was necessary to jump, necessary to throw yourself out, in order to be convinced that it might perhaps have a meaning, might perhaps have repercussions you didn’t even know about yourself. On the absolutely individual level, for me it had absolutely unarguable overtones. The fact that prior to 1958 I couldn’t manage to accept myself, and that now, I am constantly managing it. That I couldn’t manage to define myself, and now I’m fully capable of doing so. […] The reason why we are all here, more or less, is that we’re all participants in a review, and that the review has been searching for itself, searching for the last two years. That’s my personal impression, and mine alone.I think it has to launch itself, has to accept to jump.That’s all.

What is the best world atlas?

27 Best World Atlases For Map Lovers In 2020Owning a least one good world atlas is a must for any cartophile or map lover. But why stop at one? Below we’ve profiled 27 brilliant world atlases all map lovers would be happy to own.To make your life a little easier we’ve broken them down into 5 categories:Essential – Everyone should own at least one of these.Child & Student – Perfect for kids.Historical – For those that love history.Food & Drink – For those that love food and/or drink.Other – The world’s most interesting alternative atlases.We’ve tried to include as much information about each Atlas as possible including reviews (from Amazon), list price (Amazon almost always sells for less), publisher, edition and publication year (so you know how up-to-date it is).We hope you find one or two new Atlases you’ve never considered before or better yet never heard of altogether.Essential World Atlases1. National Geographic Atlas of the WorldDescription: If you’ve got the budget for it you can’t go wrong with National Geographic’s 10th edition of its Atlas of the World. Published to mark the 100th anniversary of National Geographic it includes:Illustrated mapsInformational graphics about changing global themes such as:climate changepopulation and urbanizationhealth and longevityhuman migrationcommunications technologyworld economyLargest and most comprehensive collection of political maps ever published by National GeographicSpecial sections for the Oceans, Space, and Flags and FactsIndex, with more than 150,000 place namesReview: 4.7/5Publisher: National GeographicPublication date: September 30, 2014Edition: 10thList Price: $195.00Buy: Click To Buy On Amazon2. Oxford Atlas of the WorldDescription: The only world atlas updated annually, guaranteeing that users will find the most current geographic information, Oxford’s Atlas of the World is the most authoritative atlas on the market.Full of crisp, clear cartography of urban areas and virtually uninhabited landscapes around the globe, the Atlas is filled with maps of cities and regions at carefully selected scales that give a striking view of the Earth’s surface.It opens with a fascinating look at world statistics and 18 pages of stunning satellite images, all sourced from NASA’s latest Earth Observation Satellite, Landsat 8.The extraordinarily extensive front matter continues with a “Gazetteer of Nations” that has been comprehensively checked and updated to include recent economic and political changes, and a 48-page “Introduction to World Geography,” beautifully illustrated with tables and graphs on numerous topics of geographic significance, such as the geology and atmosphere of Earth, food and water supply, biodiversity, energy, global conflict, human health, and standards of living.The hundreds of city and world maps that form the body of the Atlas have been thoroughly updated for this 23rd edition.Providing the finest global coverage available, the Atlas of the World is not only the best-selling volume of its size and price, but also the benchmark by which all other atlases are measured.Review: 4.3/5Publisher: Oxford University PressPublication date: October 1, 2016Edition: 23rdList Price: $89.95Buy: Click To Buy On Amazon3. Oxford New Concise World AtlasDescription: With hundreds of dramatic, full-color, large-format maps produced by Europe’s finest team of cartographers, the fifth edition of the New Concise World Atlas solidifies Oxford’s position as the only publisher of regularly updated atlases at every desirable size and price.Containing over 100 pages of the most up-to-date topographic and political maps, the New Concise World Atlas also features a new front section of satellite imagery to replace the old “Earth in Space” section, as well as new detailed maps of the ocean seafloors. In addition to this new front section, there are 16 extra pages of world maps for this new edition covering areas such as Kazakhstan, Central Asia, Egypt, Morocco, Algeria, Tunisia, Peru, and Brazil.Recent changes to the world’s geography are thoroughly captured in this edition; fully updated tables and world statistics provide data on climate, population, area, and physical dimensions. Finally, an index with over 58,000 items make searching for lesser-known locales quick and easy.Truly international in scope, created with meticulous care, and reflecting the very latest political developments and census information, Oxford’s New Concise World Atlas, Fifth Edition achieves the highest standard among international map resources. This engaging and affordable resource is second to none in the superb quality of its maps, the breadth of its coverage, and its easy-to-use convenience.Review: 4.3/5Publisher: Oxford University PressPublication date: November 1, 2015Edition: 5thList Price: $39.95Buy: Click To Buy On Amazon4. The Times Comprehensive Atlas of the WorldDescription: Now in its fourteenth edition, the Times Comprehensive Atlas of the World continues to be the benchmark of cartographic excellence. The world atlas is relied on and trusted by governments, media companies and international organizations around the world including the United Nations and the European Commission.New features:Double page map of the Arctic OceanNew maps of sub-ice features in the Arctic Ocean and the AntarcticPhysical maps of all the continentsMajor updates include:5000 place name changes, most notably in Japan, Brazil, South Korea, Taiwan and Spain.A beautifully illustrated section on current issues, including climate change, economy and energy, and a new section on the power of maps.Updated national parks and conserved areas including the Kavango Zambezi Transfrontier Conservation Area (KAZA TFCA), the largest conservation zone in the world.Realignment of the international boundary between Burkina Faso and Niger resulting from the International Court of Justice decision.Addition of Brussel as alternative local name form for Bruxelles (Brussels) as city is officially bilingual. Now shown as Brussel/Bruxelles.New administrative structures in Burkina Faso, Côte d’Ivoire, Kenya and Madagascar, and the addition of the new Indian state of Telangana.Addition of over 50 major waterfalls around the world.Review: 4.2/5Publisher: Times BooksPublication date: September 25, 2014Edition: 14th Revised editionList Price: $200.00Buy: Click To Buy On Amazon5. National Geographic Concise Atlas of the WorldDescription: With more than 470 maps and graphics, this atlas delivers award-winning cartography with superbly designed and amazingly informative maps and graphics providing accurate coverage of the whole world.Including introductory sections for each continent and the flags and country facts at the end of each continental section, this atlas features stunning satellite images that portray unique physical geography and highlights the sprawling extent of major cities.Review: 3.8/5Publisher: National GeographicPublication date: August 30, 2016Edition: 4thList Price: $29.95Buy: Click To Buy On AmazonChild & Student Atlases6. National Geographic Kids Beginner’s World AtlasDescription: Jam-packed with the latest data, bright, bold images, large maps, a brand-new design, and lively information about the world’s land, people, and animals, the third edition Beginner’s World Atlas will be the most up-to-date world reference for kids ages 5–8.True to National Geographic’s reputation and legacy, they’ve created this atlas with the same care and attention to detail as our renowned adult atlases. “No one does maps or atlases with as much panache and knowledge as National Geographic,” said the Washington Post.With completely up-to-date facts-at-a-glance, a glossary, pronunciation guide, and comprehensive index, this completely revised atlas takes young readers on a high-energy tour of the world and will be a must-have in every home and school.Vibrant color, fresh design, amazing photography, and new icons will help kids quickly identify information related to land, plants, animals, languages and culture, and all aspects of the physical and political world. Parents and teachers will appreciate the front matter with information for children about maps and how to use the atlas.Review: 4.6/5Ages: 5 – 8 yearsPublisher: National Geographic Children’s BooksPublication date: August 9, 2011Edition: 3rdList Price: $18.95Buy: Click To Buy On Amazon7. National Geographic Kids World AtlasDescription: National Geographic’s classic atlas for kids is now fully revised and updated, with a reduced trim that makes it easy to carry and easy to browse. Complete with geo-themed games, crosswords, picture puzzles and more, this is the atlas for today’s young explorers, as well as the perfect homework reference source.National Geographic is committed to being the number one provider of the best atlases for young people of all ages. This new edition of the award-winning world atlas for kids includes the latest data, newest maps and graphs, a fresh and compelling design, and lively essays about the world and its wonders.Review: 4.8/5Ages: 8 – 12 yearsPublisher: National Geographic Children’s BooksPublication date: July 9, 2013Edition: 4thList Price: $14.99Buy: Click To Buy On Amazon8. National Geographic Student World AtlasDescription: The new fourth edition of National Geographic’s award-winning Student Atlas of the World is more fascinating and fact-filled than ever, and has gone interactive with new digital extras, including scannable pages that link to photo galleries and quizzes.Dynamic, user-friendly content includes photos, facts, charts, graphics, and full-color political, physical, and thematic maps on important topics. From the cartographic experts at National Geographic comes the latest edition of its award-winning student atlas, with everything kids want and need to know about our changing world!Review: 4.3/5Ages: 12 and upPublisher: National Geographic Children’s BooksPublication date: July 8, 2014Edition: 4thList Price: $12.99Buy: Click To Buy On Amazon9. Wiley/National Geographic College Atlas of the WorldDescription: In an exclusive partnership with National Geographic, Wiley offers a powerful resource that is affordable, compact, and authoritative. It puts our world in your students’ grasp, presenting 25 global themes, from tectonics, the biosphere, and energy sources to population, health, literacy, and more, along with such timely topics as environmental stress and flash points for conflict and terror.Review: 4.5/5Publisher: WileyPublication date: July 20, 2010Edition: 2ndList Price: $11.68Buy: Click To Buy On Amazon10. MapsDescription: This book of maps is a visual feast for readers of all ages, with lavishly drawn illustrations from the incomparable Mizielinskis.It features not only borders, cities, rivers, and peaks, but also places of historical and cultural interest, eminent personalities, iconic animals and plants, cultural events, and many more fascinating facts associated with every region of our planet.Review: 4.6/5Grade Level: Kindergarten – 12Publisher: Big Picture PressPublication date: October 8, 2013Edition: TraList Price: $35.00Buy: Click To Buy On AmazonHistorical World Atlases11. Atlas of World HistoryDescription: Oxford’s Atlas of World History is the result of years of intensive work by a specialist team of scholars, editors, and cartographers. It presents the story of humanity in its physical setting, from the emergence of the earliest hominoids to the present day.Truly international in scope, the atlas incorporates the latest research into Asian, African, and Central and South American history, as well as the traditional core of North American and European events.The Atlas includes sections on the Ancient World, Medieval World, Early Modern World, Age of Revolutions, and the Twentieth Century and Beyond. Each section opens with an introduction that highlights the main socioeconomic, cultural and religious themes of the period, followed by spreads of maps, text, illustrations and captions that discuss specific regions and eras.Spreads depict everything from hunting in Africa in 10,000 BC to the kingdoms of Southeast Asia in the earliest years of the millennium, the decline of the Byzantine Empire, the growth of the Atlantic economies in the 18th century, and standards of living since 1945.The Atlas features some 450 vivid full-color maps illustrating the major themes and events of world history, 100 photographs, 60 diagrams and hundreds of thousands of words of explanatory text.Unique for such an atlas, the entire work is thoroughly cross-referenced, allowing the reader to move backwards and forwards in time or across the world from region to region, following themes or lines of inquiry across pages.The new edition brings the Atlas into the 21st Century and up to the present day. New and updated maps and illustrations cover a wide range of evolving subjects such as population changes, international trading, urbanization, political and economic developments, literacy rates, the concentration of world languages, and many more important and always timely subjects.Coverage of Africa, South Asia, Eastern Europe, and every other part of the world is revisited and updated, making this the most up-to-date atlas of world history available, in addition to being the most complete.A comprehensive index of more than 8,000 entries includes numerous alternative name forms used over the centuries. The Atlas of World History closes with a bibliography that provides a booklist for suggested further reading.Equally well-suited for a general audience and students of history or international relations, the Atlas of World History continues Oxford’s presence as the premier publisher of world atlases.Review: 4.0/5Publisher: Oxford University PressPublication date: October 15, 2010Edition: 2ndList Price: $49.95Buy: Click To Buy On Amazon12. Atlas of the Civil WarDescription: In this one-of-a-kind atlas, scores of archival maps and dozens of newly created maps trace the battles, political turmoil, and great themes of America’s most violent and pivotal clash of arms.From the Antebellum South to Fort Sumter, the assassination of Abraham Lincoln, and the fitful peace of Reconstruction, National Geographic’s Atlas of the Civil War displays eye-opening maps—and a gripping, self-contained story—on every spread.Eighty-five rare period maps, many seen here for the first time, offer the cartographic history of a land at war with itself: from 19th-century campaign maps surveying whole regions and strategies to vintage battlefield charts used by Union and Confederate generals alike, along with commercial maps produced for a news-hungry public, and comprehensive Theater of War maps.In 35 innovative views created especially for this book, the key moments of major battles are pinpointed by National Geographic’s award-winning cartographers using satellite data to render the terrain with astonishing detail.In addition, more than 320 documentary photographs, battlefield sketches, paintings, and artifacts bear eyewitness testimony to the war, history’s first to be widely captured on film.Review: 4.7/5Publisher: National Geographic;Publication date: October 20, 2009Edition: FirstList Price: $40.00Buy: Click To Buy On Amazon13. On the Map: A Mind-Expanding Exploration of the Way the World LooksDescription: Imagine a world without maps. How would we travel? Could we own land? What would men and women argue about in cars? Scientists have even suggested that mapping—not language—is what elevated our prehistoric ancestors from ape-dom.Follow the history of maps from the early explorers’ maps and the awe-inspiring medieval Mappa Mundi to Google Maps and the satellite renderings on our smartphones, Garfield explores the unique way that maps relate and realign our history—and reflect the best and worst of what makes us human.Featuring a foreword by Dava Sobel and packed with fascinating tales of cartographic intrigue, outsize personalities, and amusing “pocket maps” on an array of subjects from how to fold a map to the strangest maps on the Internet, On the Map is a rich historical tapestry infused with Garfield’s signature narrative flair.Map-obsessives and everyone who loved Just My Type will be lining up to join Garfield on his audacious journey through time and around the globe.Review: 4.0/5Publisher: GothamPublication date: November 5, 2013Edition: NAList Price: $17.00Buy: Click To Buy On Amazon14. Atlas of Cursed PlacesDescription: This alluring read includes 40 locations that are rife with disaster, chaos, paranormal activity, and death.The locations gathered here include the dangerous Strait of Messina, home of the mythical sea monsters Scylla and Charybdis; the coal town of Jharia, where the ground burns constantly with fire; Kasanka National Park in Zambia, where 8 million migrating bats darken the skies; the Nevada Triangle in the Sierra Nevada mountains, where hundreds of aircraft have disappeared; and Aokigahara Forest near Mount Fuji in Japan, the world’s second most popular suicide location following the Golden Gate Bridge.Review: 3.6/5Publisher: Black Dog & LeventhalPublication date: October 6, 2015Edition: FirstList Price: $24.99Buy: Click To Buy On Amazon15. Atlas of Lost CitiesDescription: Like humans, cities are mortal. They are born, they thrive, and they eventually die.In Atlas of Lost Cities, Aude de Tocqueville tells the compelling narrative of the rise and fall of such notable places as Pompeii, Teotihuacán, and Angkor. She also details the less well known places, including Centralia, an abandoned Pennsylvania town consumed by unquenchable underground fire; Nova Citas de Kilamba in Angola, where housing, schools, and stores were built for 500,000 people who never came; and Epecuen, a tourist town in Argentina that was swallowed up by water.Beautiful, original artwork shows the location of the lost cities and depicts how they looked when they thrived.Review: 3.4/5Publisher: Black Dog & LeventhalPublication date: April 5, 2016Edition: FirstList Price: $24.99Buy: Click To Buy On Amazon16. The Map BookDescription: From the earliest of times, maps have fired our imaginations and helped us make sense of our world, from the global to the very local. Head of Map Collections at the British Library, Peter Barber has here compiled an historic and lavish atlas, charting the progress of civilization as our knowledge of the world expanded.Simply organized as a progression through time, The Map Book collects some 175 maps that span four millennia – from the famed prehistoric Bedolina (Italy) incision in rock from around 1500 B.C. to the most modern, digitally enhanced rendering.Many of the maps are beautiful works of art in their own right. From Europe to the Americas, Africa to Asia, north to south, there are maps of oceans and continents charted by heroic adventurers sailing into the unknown, as accounts spread of new discoveries, shadowy continents begin to appear n the margins of the world, often labeled ‘unknown lands.’Other maps had a more practical use: some demarcated national boundaries or individual plots of land; military plans depicted enemy positions; propaganda treatises showed one country or faction at an advantage over others.So much history resides in each map–cultural, mythological, navigational–expressing the unlimited extent of human imagination. This is captured in the accompanying texts–mini essays by leading map historians–that are as vivid and insightful as the maps themselves.They make The Map Book as much a volume to be read as to be visually admired.Review: 4.1/5Publisher: Walker BooksPublication date: November 15, 2005Edition: 1stList Price: $50.00Buy: Click To Buy On Amazon17. New Historical Atlas of the WorldDescription: The Historical Atlas of the World presents important periods and turning points in 5,000 years of world history in over 100 pages of thematic maps.Atlas Features: 2015 copyright updated to include recent world events, Presents major periods of world history through more than 100 bold, colorful maps, Thematic maps include literacy, languages, religions, and more.Review: 4.4/5Publisher: Rand McNallyPublication date: July 31, 2015Edition: 6thList Price: $12.00Buy: Click To Buy On AmazonFood & Drink World Atlases18. World Atlas of WineDescription: The seventh edition will confirm the status of The World Atlas of Wine as the most essential and authoritative wine reference work. Reflecting the changing nature of the wine scene, the Atlas details developments in climate, technique and fashion as well as new regulations made over the last six years.A new Australian map highlights the importance of cool-climate regions as global warming takes effect, for example,while dynamic regions such as coastal Croatia, South Africa’s Swartland and Ningxia in China are covered for the first time. The world’s increasing appetite for wine is matched by a growing thirst for knowledge,which this book will amply satisfy.Review: 4.8/5Publisher: Mitchell BeazleyPublication date: October 8, 2013Edition: 7thList Price: $60.00Buy: Click To Buy On Amazon19. World Atlas of WhiskyDescription: Award-winning author and whisky expert Dave Broom explores over 200 distilleries and examines over 400 expressions. Detailed descriptions of the Scottish distilleries can be found here, while Ireland, Japan, the USA, Canada and the rest of the world are given exhaustive coverage.There are tasting notes on single malts from Aberfeldy to Tormore, Yoichi (and coverage of the best of the blends). Six specially created ‘Flavour Camp Charts’ group whiskies by style, allow readers to identify new whiskies from around the world to try.This extrensively updated and extended edition features new material on burgeoning areas, including detailed coverage of many recently opened US craft distilleries, new distilleries in Germany, Austria and Switzerland, and discussion of the growing whisky scene in Latin America.With over 200 beautiful colour photographs and 21 colour maps locating distilleries and whisky-related sites, this is a stylish celebration of the heritage, romance, craftsmanship and versatility of whisky.Review: 4.8/5Publisher: Mitchell BeazleyPublication date: October 14, 2014Edition: 2nd revisedList Price: $39.99Buy: Click To Buy On Amazon20. World Atlas of BeerDescription: Take a brew-lover’s trip around the world in this definitive, revised, and expanded guide.Join renowned experts Tim Webb and Stephen Beaumont on the ultimate beer journey, covering more than 35 countries from Austria to New Zealand. This richly illustrated, comprehensive guide kicks off in Europe, travels through the Americas, and ends in Asia.Along the way, you’ll learn about everything from the wheat beers of Bavaria, Belgium’s Trappist ales, and Finnish sahti to British bitters, barrel-aged Californian beers, Vietnamese bìa hoi, and more, with full tasting notes for over 500 must-try brews.Webb and Beaumont also offer a fascinating history of beer and an in-depth look at the science and art of beermaking.This newly revised and expanded edition of The World Atlas of Beer features ten additional countries—including Poland, Switzerland, Spain, Ireland, Iceland, and China—as well as up-to-the-moment beer industry information and trends. With this ultimate companion in hand, you can explore the best beers in the whole world.Review: 4.9/5Publisher: Sterling EpicurePublication date: October 18, 2016Edition: NAList Price: $30.00Buy: Click To Buy On Amazon21. The World Atlas of CoffeeDescription: Taking the reader on a global tour of coffee-growing countries, The World Atlas of Coffee presents the bean in full-color photographs and concise, informative text. It shows the origins of coffee — where it is grown, the people who grow it; and the cultures in which coffee is a way of life — and the world of consumption — processing, grades, the consumer and the modern culture of coffee.Plants of the genus Coffea are cultivated in more than 70 countries but primarily in equatorial Latin America, Southeast Asia and Africa. For some countries, including Central African Republic, Colombia, Ethiopia, and Honduras, coffee is the number one export and critical to the economy.Organized by continent and then further by country or region, The World Atlas of Coffee presents the brew in color spreads packed with information. They include:The history of coffee generally and regionallyThe role of colonialism (for example, in Burundi under colonial rule of Belgium, coffee production was best described as coercive. Every peasant farmer had to cultivate at least 50 coffee trees near their home.)Map of growing regions and detail mapsCharts explaining differences in growing regions within a countryInset boxes (For example, what is the Potato Defect? Is Cuban coffee legal in the United States?)The politics of coffee and the fair trade, organic and shade grown phenomenaBeautiful color photographs taken in the field.Americans consume 400 million cups of coffee per day, equivalent to 146 billion cups of coffee per year, making the United States the leading consumer of coffee in the world. The World Atlas of Coffee is an excellent choice for these coffee lovers.Review: 4.8/5Publisher: Firefly BooksPublication date: October 23, 2014Edition: NAList Price: $35.00Buy: Click To Buy On Amazon22. Atlas of FoodDescription: The Atlas of Food provides an up-to-date and visually appealing way of understanding the important issues relating to global food and agriculture. In mapping out broad areas of investigation—contamination of food and water, overnutrition, micronutrient deficiency, processing, farming, and trade—it offers a concise overview of today’s food and farming concerns.Buttressed by engaging prose and vivid graphics, Erik Millstone and Tim Lang convincingly argue that human progress depends on resolving global inequality and creating a more sustainable food production system.Review: 4.7/5Publisher: University of California PressPublication date: March 1, 2013Edition: UpdatedList Price: $24.95Buy: Click To Buy On AmazonOther World Atlases23. Atlas of Improbable PlacesDescription: It is perhaps the eighth wonder of our world that despite modern mapping and satellite photography our planet continues to surprise us.Hidden lairs beneath layers of rock, forgotten cities rising out of deserted lands and even mankind’s own feats of engineering eccentricity lie in the most unusual of destinations.Travis Elborough goes in search of the obscure and bizarre, the beautiful and estranged. Taking in the defiant relics of ancient cities such as Ani, a once thriving metropolis lost to conquered lands, and the church tower of San Juan Parangaricuto, that miraculously stands as the sole survivor of a town sunk by lava.Through the labyrinths of Berlin and Beijing – underground realms dug for refuge, espionage and even, as Canada’s Moose Jaw, used as the playground for gangsters trading liquor and money over cards.Never forgetting the freaks and wonders of nature’s own unusual masterpieces: the magical underground river shaped like a dragon’s mouth in the Philippines and the floating world of Palmerston.With beautiful maps and stunning photography illustrating each destination, Atlas of Improbable Places is a fascinating voyage to the world’s most incredible destinations.As the Island of Dolls and the hauntingly titled Door to Hell – an inextinguishable fire pit – attest, mystery is never far away. The truths and myths behind their creation are as varied as the destinations themselves.Standing as symbols of worship, testaments to kingships or even the strange and wonderful traditions of old and new, these curious places are not just extraordinary sights but reflections on man’s own relationship with the world around us.Review: 4.1/5Publisher: Aurum PressPublication date: October 15, 2016Edition: First EditionList Price: $29.99Buy: Click To Buy On Amazon24. Atlas of Remote IslandsDescription: There are still places on earth that are unknown. Visually stunning and uniquely designed, this wondrous book captures fifty islands that are far away in every sense-from the mainland, from people, from airports, and from holiday brochures.Author Judith Schalansky used historic events and scientific reports as a springboard for each island, providing information on its distance from the mainland, whether its inhabited, its features, and the stories that have shaped its lore.With stunning full-color maps and an air of mysterious adventure, Atlas of Remote Island is perfect for the traveler or romantic in all of us.Review: 4.1/5Publisher: Penguin BooksPublication date: October 5, 2010Edition: First EditionList Price: $30.00Buy: Click To Buy On Amazon25. Atlas of CitiesDescription: More than half the world’s population lives in cities, and that proportion is expected to rise to three-quarters by 2050.Urbanization is a global phenomenon, but the way cities are developing, the experience of city life, and the prospects for the future of cities vary widely from region to region. The Atlas of Cities presents a unique taxonomy of cities that looks at different aspects of their physical, economic, social, and political structures; their interactions with each other and with their hinterlands; the challenges and opportunities they present; and where cities might be going in the future.Each chapter explores a particular type of city–from the foundational cities of Greece and Rome and the networked cities of the Hanseatic League, through the nineteenth-century modernization of Paris and the industrialization of Manchester, to the green and “smart” cities of today.Expert contributors explore how the development of these cities reflects one or more of the common themes of urban development: the mobilizing function (transport, communication, and infrastructure); the generative function (innovation and technology); the decision-making capacity (governance, economics, and institutions); and the transformative capacity (society, lifestyle, and culture).Using stunning info-graphics, maps, charts, tables, and photographs, the Atlas of Cities is a comprehensive overview of the patterns of production, consumption, generation, and decay of the twenty-first century’s defining form.Presents a one-of-a-kind taxonomy of cities that looks at their origins, development, and future prospectsFeatures core case studies of particular types of cities, from the foundational cities of Greece and Rome to the “smart” cities of todayExplores common themes of urban development, from transport and communication to lifestyle and cultureIncludes stunning info-graphics, maps, charts, tables, and photosReview: 4.4/5Publisher: Princeton University PressPublication date: August 24, 2014Edition: NAList Price: $49.50Buy: Click To Buy On Amazon26. Map: Exploring the WorldDescription: Map: Exploring the World brings together more than 300 fascinating maps from the birth of cartography to cutting-edge digital maps of the twenty-fist century.The book’s unique arrangement, with the maps organized in complimentary or contrasting pairs, reveals how the history of our attempts to make flat representations of the world has been full of beauty, ingenuity and innovation.Selected by an international panel of curators, academics and collectors, the maps reflect the many reasons people make maps, such as to find their way, to assert ownership, to record human activity, to establish control, to encourage settlement, to plan military campaigns or to show political power.The selection includes the greatest names in cartography, such as James Cook, Gerard Mercator, Matthew Fontaine Maury and Phyllis Pearsall, as well as maps from indigenous cultures around the world, rarely seen maps from lesser’known cartographers, and maps of outstanding beauty and surprising individuality from the current generation of map makers.Review: 5/5Publisher: Phaidon PressPublication date: September 28, 2015Edition: 1stList Price: $59.95Buy: Click To Buy On Amazon27. Transit Maps of the WorldDescription: Transit Maps of the World is the first and only comprehensive collection of historical and current maps of every rapid-transit system on earth. In glorious, colorful graphics, Mark Ovenden traces the cartographic history of mass transit—including rare and historic maps, diagrams, and photographs, some available for the first time since their original publication.Now expanded with thirty-six more pages, 250 city maps revised from previous editions, and listings given from almost a thousand systems in total, this is the graphic designer’s new bible, the transport enthusiast’s dream collection, and a coffee-table essential for everyone who’s ever traveled in a city.Review: 4.6/5Publisher: Penguin BooksPublication date: November 3, 2015Edition: Expanded and updatedList Price: $35.00Buy: Click To Buy On AmazonWe hope you enjoyed the list. However, if you think we’ve missed any great atlases, please let us know in the comments section below.Know anyone else who loves a good Atlas? Then please share this post with thThink This Map Was Brilliant? Get Our Most Brilliant Maps Free Each WeekNational Geographic Kids Beginner's World Atlas$18.95(406)World Atlas$16.94(375)The Atlas of Food: With a New Introduction$29.95(10)Map: Exploring the World$45.63$59.95(78)Ads by AmazonFiled Under: World Map

Didn't the Polish crack the Enigma code a few years before Alan Turing?

YES.Polish cryptanalysts broke Enigma ciphers in the 1930s - long before the British codebreakers at Bletchley Park did during the war. This achievement was one of the relatively obscure facts surrounding WW2.Now, I can simply stop here because apparently the question only asks for a yes/no response. However, that will be too boring and disappointing to those readers who are curious about exactly how Polish codebreakers unraveled some of the most formidable ciphers in the history of cryptography. Having read about the Polish code-breaking effort, I am thoroughly fascinated by a true story about extraordinary human ingenuity, determination, patriotism, and treachery that was every bit as praiseworthy and compelling as the endeavour of British codebreakers at Bletchley Park during WW2. It is a story that warrants an in-depth account.Thus, this answer is dedicated to recounting the achievements of Polish codebreakers (and to honouring a promise made to a Quora friend of mine!).Since every story has an underlying context, the same is true of the this story. Thus, for the sake of full understanding, I will recount not only the codebreaking endeavour of the Poles but also the historical context and the crucial characters involved in this story.Let the story begin!!!The Development of Polish Cryptanalytic ExpertiseThe year 1918 witnessed momentous developments in Europe. It marked the end of the Great War and the beginning of a period of political turmoil that would dramatically transform Europe.The situation was particularly dire for Poland. The Bolshevik revolution was sweeping across Russia, precipitating the country into a civil war between the Communist and Imperial factions. Unfortunately for Poland, Lenin’s determination to annex Poland and turn it into a Communist satellite state led to the Polish-Soviet War in 1920.The intrusion of Soviet forces into Poland and the spectre of a Communist domination prompted capitalist European countries to form a military coalition to support Poland in the struggle against Soviet aggression.Despite this multinational military support, the Poles knew that they could not rely completely on foreign intervention to repel the Soviet invaders. They had to do some of the fighting by themselves. Because their resources were limited and their military was relatively small, they had to employ those assets intelligently. How could they do that? - by deploying their forces at the right place at the right time. The only way to accomplish that was to determine in advance Soviet military intentions => Polish military intelligence was born.The first capability that it developed was radio intelligence. The widespread use of radios by the Soviets to maintain communication between the front lines and their distant HQs filled the air with radio signals that represented coded messages.One aspect of radio intelligence was traffic analysis which involved analyzing directions from where messages emanated. This provided information about calls signs and some hints about unit dispositions and movements. This allowed the Poles to deduce with some degree of accuracy what the Soviets might do. But as you can guess, intelligence revealed by traffic analysis was wholly inadequate in many situations where full knowledge of enemy intention was crucial for Polish commanders.Thus, the decryption of Russian enciphered messages became the top priority for Polish intelligence. Three Polish officers would play a critical role in this effort: Jan Kowalewski, Maksymilian Ciezki, and Antoni Palluth.Jan KowalewskiKowalewski was highly instrumental in the establishment of Polish intelligence. He not only turned Poland into a world-leader in cryptanalysis but also implemented an innovative approach to codebreaking. Being an engineer, Kowalewski was convinced that code-breaking was amenable to mathematical analysis. So he recruited mathematicians for his team. This was arguably an unprecedented step in cryptography because prior to this, code-breakers were predominantly linguists.Kowalewski’s innovative approach to cryptanalysis quickly proved its worth. Soviet ciphers were broken quickly. This revealed almost everything: orders of battle, dispositions of units, and even details of a new cipher system the Soviets were going to use.The power of mathematical analysis in codebreaking was vindicated on 12th August 1920. On that day Polish radio intelligence intercepted a message several pages long and was encrypted using a new cipher system. Kowalewski’s team rose to the challenge by unravelling the new cipher in just one hour. Although they could not decipher the message completely, what they uncovered was more than enough to alert the Polish army to an impending Soviet offensive directed at Warsaw on 14th August 1920.Armed with this actionable intelligence, the Polish high command quickly ordered the jamming of Russian radio communication between front line forces bound for Warsaw and HQ in Moscow. This served to delay the Soviet offensive, giving the Poles a few more days time to prepare defenses. When the Soviets arrived, they faced determined and skillful Polish opposition. The battle ended in a decisive Polish victory that were referred to as Miracle on the Vistula.A Soviet telegram signed by Stalin and deciphered by Jan Kowalewski’s team during the Russo-Polish war.The Polish government appreciated the role military intelligence had played in the Polish-Soviet War, and in particular Kowalewski’s pioneering mathematics-assisted approach to code-breaking. The need for a dedicated code-breaking organization was heightened in light of the awareness that for centuries Poland - being surrounded by Germany in the West and Russia in the East - had been subjected to many acts of aggression by both military powers. Knowing that they could not compete with either nations in military strength, the Poles determined to compensate for that weakness with world-class code-breaking prowess that would enable them to employ their assets intelligently against the Germans and Russians in a future conflict. This situation gave impetus to the establishment of the Biuro Szyfrów - Cipher Bureau.The codebreakers at the Cipher Bureau regularly intercepted and broke foreign coded radio messages. The Poles were particularly interested in German ciphers. They knew that the Germans - having lost the Great War - would seek to avenge the humiliation of that defeat by planning for another war.Initially, the Poles were successful in breaking German cipher. In the German section of the Cipher Bureau, the Poles had employed standard techniques in a book written by Marcel Givierge - a French army general and cryptographic expert. He directed French military cryptanalytic effort in the Great War. He left his mark by devising cryptographic techniques during the war and publishing them for everyone to read.Drawing on the book, the Poles had been able to break German coded messages, including the doppelwürfelverfahren (double dice) cipher system - which presented the greatest challenge for the Poles. The double dice system worked by shuffling the letters of a message twice, each time using a predetermined scheme (analogous to a huge anagram). Although the double dice system was sufficiently described in Givierge’s reference book, breaking double dice ciphers was not trivial and required considerable efforts. But it was at least within the bound of human effort and the Poles had notable success in breaking double dice.However, this period of success would come to a halt in 1928 when the Poles encountered a complete new cipher that defeated all standard codebreaking techniques.Let’s conclude this section with a brief introduction of 2 of the aforementioned figures in Polish intelligence.Maksymilian Ciezki was a career army officer who served in Kowalewski’s team during the war and went on to work for the Cipher Bureau. He discharged his duties well enough to earn a high mark from Kowalewski on his appraisal form. Ciezki would go on to become chief of the German section in the Cipher Bureau and oversee the cryptanalysis of Enigma ciphers in the 1930s.Antoni Palluth had a passion and a remarkable aptitude for radios. He had served in radio intelligence during the war, engaging in radio interception and traffic analysis. After the war, he joined his friends to found AVA Radio Company - a small company specializing in making all kinds of radio equipment for the Polish military. But he was no regular entrepreneur. He was on the payroll of Polish intelligence service and pursued all kinds of clandestine activities under his guise as a factory manager, the foremost of which was codebreaking. In fact, he occupied a position in the German section in the Cipher Bureau overseen by Maksymilian Ciezki. His company would later create the technologies designed to break Enigma.The mysterious German cipherIn reality, the Poles encountered the new cipher in Feb 1926 when they intercepted messages sent by the German Navy. The new cipher used to encode them was evident just by looking at the messages. The streams of coded letters showed no discernible patterns similar to any known patterns. In fact, the letters appeared completely random and in nearly equal frequency. The Poles had no doubt that they had come upon a new form of cipher. What’s more? Judging by the apparent randomness and equal frequency of the letters, it was most likely that the messages were generated by a machine.This was an unpleasant but unsurprising realization for the Poles. They knew from the reference work of Givierge that mechanical ciphers would replace manual ciphers. But at the same time, their inability to break the new cipher did not concern them because the German navy was of little interest to them. The threat to Poland’s national security came primarily from the German Army whose ciphers the Poles had been able to break.That would change in 1928 when the German army followed suit and employed the new cipher. This frustrated all Polish attempts at uncovering German military secrets. The Poles became anxious about the future of their country as they appreciated the consequences of their failure to read German military communications.Polish Intelligence had heard that the enciphering machine was called Enigma. But they had never seen one. This machine was invented by German engineer Arthur Scherbius to provide commercial businesses with a tool to protect confidential information. It was an ingenious contraption that had a very simple mechanism. I described meticulously how the machine worked in this answer.How exactly did the Enigma machine work? How did the plugboard and the rotors change the letters?Now, Enigma machines were available on the market. The Cipher Bureau acquired a few Enigmas, disassembled them to study their enciphering mechanism. However, this knowledge did not help them break coded messages of the German military. The reason could be inferred from the marketing material of the Enigma’s Company which stated that the company could tailor the rotors to the specification of individual customers. Thus, it was safe to assume that the German Army had requested the company to make custom rotors that were different from those in the commercial version as well some other modifications to make the military variant more difficult to break.The challenge confronting the Poles appeared to be insurmountable. But there was hope. Kowalewski had just returned from Japan (on a mission to help the Japanese improve their own cryptographic system). Since Enigma was a mechanical cipher, he reasoned that a mathematical mind would be better suited to break it. So he requested that mathematicians be recruited for the Cipher Bureau.Fortunately for Kowalewski, he would get precisely the mathematical talent that would break the Enigma.The Polish MathematiciansThe 1920s witnessed the flourishing of Polish mathematics with the establishment of world-class mathematics departments at some universities.One such university was Adam Mickiewicz University in Poznań. It was here that three brilliant Polish mathematicians would be recruited for the Cipher Bureau. They were Marian Rejewski, Henryk Zygalski, Jerzy_Rozycki.Of these three, Marian Rejewski was the most talented would play a critical role in breaking the Enigma.Marian Rejewski was born into a middle class family. In his youth, he was a studious and high-achieving student at a German-speaking school. He displayed an inclination and remarkable aptitude for mathematics. His father - the owner of a going concern - hoped that Marian would follow in his footsteps. But Marian’s uncle - a gifted mathematician - persuaded him that a mathematics degree would assure him of a prosperous career in the insurance industry.So Marian decided to study mathematics in university. He attended Poznan University - an institution that boasted a first-rate mathematics department. It was here that he met and befriended Jerzy Różycki and Henryk Zygalski.One day in 1928, at the end of a lecture, professor Zdzisław Krygowski - a noted mathematician - requested Rejewski, Rozycki, and Zygalski to stay in the classroom to discuss something important with them.Professor Krygowski told them:There is a fascinating project I think all three of you might enjoy - as you seem to be more interested in crosswords and puzzles. I also trusted we are all loyal to the Polish cause.There is a man I would like you to meet. He is from the Polish Government. His Department is seeking to recruit talented mathematicians who they trust and who are fluent in German as soon as possible. I have been asked to recommend my most talented and trusted students for a study of the utmost importance to the Polish cause. I don’t know any more than that… interested?Jerzy responded impulsively: “Of course”. His two friends were a bit dubious, but Jerzy’s response inclined them to nod in agreement.These three students were about to be initiated into the obscure world of cryptography. One day, the three students came to a small room dimly lit room. A sense of anxiety gripped as a man greeted and spoke to them.The following conversation unfolded between them.Man: So here I have Marian Rejewski, Henryk Zygalski, and Jerzy Rozycki. I trusted you are each loyal to Poland?They nodded in response. The man continued: “What is your view on recent events in Germany?”Henryk responded quickly: “It is a matter of concern to me. I believe it is only a matter of time before Poland is invaded by Germany. It is inevitable that they will seek to re-incorporate us into their empire.”Man: “Do you not think that Germany’s expansionist ambition has been extinguished?”Henryk: “No. I believe that the current economic situation in Germany can only serve to intensify resentment against the Allies. If the current situation is not resolved, a further war, in my view, is inevitable. And if that happens, I am certain that the security of Poland will be jeopardy.”Man: “And would you welcome a return to German domination?”Henryk: “Of course of. Poland must remain free”.Man: “I see. And is Mr. Zygalski’s view shared by you all?”Marian and Jerzy nodded.The man then identified himself: “Good. Allow me to introduce myself. I am Major Maksymilian Ciezki of the Cipher Bureau. I am in charge of the German section. Our function is to intercept coded messages from Germany and decode them. Our bureau operates in the utmost secrecy. I am not in uniform because I am here today in connection with a matter that required discretion.I apologized for my questions. Can I be clear then that each of you supports a free Poland? Think carefully before you answer. If you choose to continue, you may place your lives in danger.”His words sent chill down the spines of the three men. But being patriots, the three men agreed to commit themselves to the task.Maksymilian: “Excellent. My department have decided to take a fresh approach to our work. We are seeking talented and motivated mathematicians. We want to train them in codebreaking. This is a completely new concept. You three have been recommended to me as outstanding students. We are concerned about certain messages that we have intercepted but been unable to decode. My office decided that mathematics students fluent in Germany may be able to overcome this challenge.There is a limited amount of information I can give you at this stage. What I can tell you is that in 1926, the German Navy began using a type of code we could not recognise. The German land forces started using the code in 1928. Our experts have concentrated on breaking this code but to date have not been able to make any progress.We are convinced that the coded messages are being generated by a mechanical device. We are certain that Germany is rearming. Poland will inevitably be one of their first targets. Our national security is threatenedThe government and I are formally inviting you to participate in our training programme, which will commence as soon as possible. This would involve attending a course for two evenings a week in cryptology.It is imperative that you maintain utmost secrecy both concerning the existence of the course and your participation in it. In addition, you will be required to keep up-to-date with your ongoing university studies. The professor has insisted upon that.There must be nothing that could draw attention to any of you. In addition, you will be required to sign documentation confirming your agreement to maintain confidential state secrets. You must understand that signature of these forms imposes serious obligations upon you and that any breach would result in repercussions of the most severe nature.”Maksymilian’s serious tone struck a measure of apprehension in Rejewski, Różycki, Zygalski. But at the same time, the challenge piqued the curiosity of the three students.After signing all documents necessary to obtain security clearance, they began their training in cryptology in earnest. In the end, only a few students, including Marian, Jerzy and Henryk, managed to complete the courses and their mathematics program. Marian was the best among them who graduated with distinction. Maksymilian invited them to work for the Cipher Bureau. However, there were no well-paying jobs for cryptologists. Plus, Marian had intended to pursue a career as an actuary. So he decided to go to Göttingen to receive further education. But before he departed, Antoni Palluth had one last secret to share with him and other graduates of the cryptology course.In a small room, Antoni showed the men a machine that looked like a typewriter.Pay attention, gentlemen. This is an electromechanical rotor cypher machine. It was invented and patented in 1919 by a Dutchman named Hugo Koch. In 1923, a Berlin engineer named Arthur Scherbius established a company to produce the machines. Scherbius had envisaged that the machine — which he called Enigma — would be of interest to companies who required secret correspondence to preserve confidential trade information. It was for this purpose that the machine was advertised and sold.However, we believe that this machine, or at least a modified version of it, is being used by the German forces to transmit messages. It is a device that has confounded the best minds in the world.As you will remember from the earlier lectures here, previous types of cyphers have generally been solved through searching for repeat patterns. That method is ineffective with the Enigma.That is why we selected mathematicians to train in codebreaking. This machine has added a whole new dimension to the craft of cryptology. We are convinced there is a mathematical solution to the problem.Marian surely was excited by the Enigma. After studying in Gottingen for one year, he became bored and decided to go to Poland to work on the Enigma cipher.But there was a problem that even Marian’s mathematical brilliance and determination could not overcome. As noted before, the German military was employing a specially modified version of the Enigma that was markedly more complex than the commercial Enigma that Antoni had revealed to the Polish cryptologists. Without knowing the internal wiring of the military model of the machine, it was practically impossible for the Poles to decode Enigma ciphers.In a stroke of incredible luck and irony, the Poles would get help from a citizen of their country’s future enemy.A German TraitorOn November 2nd 1931, agents of the French secret service held a meeting in Paris. The meeting revolved around an offer of top secret information by a German agent.Captain Gustave Bertrand fired prodding questions at his operative Rodolphe Lemoine to test his confidence.I understand that this man is of impeccable reputation. H.T.S, a civil servant of rankin the German Secret Service. Married with two children. A man who fought for German in the Great War. What is more, his brother is highly ranked in the German Army. Surely this man is better qualified to be a double agent than a traitor? What possible motivation can he have? I cannot see how we can justify funding this project.Lemoine delivered a calm and convincing response:But you have not had the opportunity to meet him in person. I have. He is desperate for money. What could be simpler? I assure you, gentlemen, I have spoken to Herr S. at length regarding his motivation for contacting us and I have no doubt that having himself been betrayed by his native country, he is more than willing to become a mercenary for our cause. He has a price and if we will pay it, we will have his unfailing loyalty.Reassured by Lemoine’s response, captain Lemoine granted his approval. The other agents also expressed their agreement.Captain Bertrand firmly stated:The funding of this project will stretch our budget to the limit. I want to be certain it is worthwhile. I will accompany you to the meeting scheduled for next week. I want to assess this gentleman in person. This operation will be given the highest level security clearance.Who was H.T.S exactly?Hans-Thilo SchmidtBorn in 1888 in Berlin, Hans was the second son of an eminent professor and his wife who was descended from the Prussian aristocracy. Schmidt enlisted in the German Army and fought in the Great War. After the war, the Treaty Of Versaille limited the German Army to a maximum of 100,000 men and prohibited it from having offensive weapons.The small size of the Reichswehr increased the selectivity of its officer corps. Only the best candidates qualified for the small number of posts available. Because Hans Thilo Schmidth wasn’t deemed good enough to be retained, he was dismissed - much to Hans’s humiliation. He then tried to make a living as an owner of a soap business. But the post-war hyperinflation destroyed his business, precipitating his family into poverty.The humiliation caused by this reversal of fortune was exacerbated by his resentment towards his elder brother - Rudolph Schmidth. Like Hans, Rudolph had fought during the Great War. Unlike Hans, he was retained by the Army. Not only that, he rose through the ranks and reached the pinnacle of success through the appointment as Chief of Staff of the Signal Corps. In this capacity, he oversaw all aspects of secret communications, including cipher systems. In fact, it was Rudolph who sanctioned the Army’s use of Enigma cipher.Following the collapse of his soap business, Hans-Thilo was forced to ask his brother for help, and Rudolph offered him a job at the Chiffrierstelle in Berlin. The Chiffrierstelle was no ordinary organization. It was the cipher department of the High Command of the Wehrmacht - responsible for administrating Germany’s secret communications. It was Enigma’s command center, a top-secret facility dealing with highly sensitive information.The job required Hans to relocate to Berlin and leave behind his family in Bavaria because of the high cost of living in Berlin. So Hans Thilo Schmidt ended up living alone in expensive Berlin, impecunious and envious of his perfect brother and resentful toward a nation which had rejected him. He resolved to avenge this humiliation. He decided that the best way to fulfil this aim was to sell classified Enigma information to Germany’s enemies. This would not only allow him to earn a lot of money but also undermine Germany’s national security.This set the stage for a top secret exchange with French Secret Service.On 8th November 1931, Schmidt arrived at the Grand Hotel in Verviers, Belgium to meet French secret service agents. Inside a room, Captain Bertrand carefully studied Hans and his documents. After convincing himself of the authenticity of the documents, Bertrand began talking to Schmidt.“You have the money here?” - asked Schmidt.When Captain Bertrand presented a suitcase containing cash before Schmidt, he exhaled in relief.Schmidt revealed his repressed thoughts: “I fought in the Great War, for Germany of course. I was injured. After the war, there was no work for the injured soldiers. I had to apply for dole money. I risked my life for my country then I was left to starve on the street with my family. I had to beg and borrow money for food.”Captain Bertrand: But then you found work.Schmidt replied bitterly: “Yes, work, and I was paid a pittance. Not enough to feed my family. There is rocketing inflation in Germany. It was insulting. The High Command, like my brother, live like aristocracy. They never went near the front line. They didn’t risk lives.Smidth carried on, in a flat one: “Germany betrayed me. Now I will betray Germany.”Bertrand’s doubt about Schmidt’s reliability vanished. It was clear to him that the German had succumbed to greed and that as long as the French secret service could supply money, Schmidt would provide them with a direct link to Enigma.The result of that meeting was a set of photographs of two top secret documents1/ gebrauchsanweisung für die chiffriermachine enigma (instructions for using the enigma encryption machine)2/ Schlüsselanleitung für die Chiffriermaschine Enigma (key instructions for the Enigma cipher machine)These documents were essentially instructions for using the Enigma machine. Although they did not describe the internal wirings of the machine, they contained the information from which those wirings could be deduced.Thanks to Schmidt’s treachery, it was now possible for the French to create an accurate replica of the German military Enigma machine.However, despite this valuable information, the French were unable to make any progress on breaking Enigma. The reason was they did not have the code book containing key settings for the Enigma. This was a problem made possible by a fundamental principle of cryptography: The strength of a cipher system consists not in keeping secret the enciphering mechanism but in keeping secret the keys.Indeed, this explained the Germans’ overconfidence in the Enigma. They knew that as long as they could keep the keys from falling into enemy hands, they would prevent them from reading Enigma-enciphered messages.So the French did not take advantage of the information supplied by Schmidt. They did not even bother making an Enigma replica because it would still be useless without the keys.Also, the French had become complacent. Germany at that time had not yet emerged as a military threat so they had no interest in breaking Enigma ciphers. The same could be said of the British who had not regarded Germany as a threat.However, there was one nation that could not afford to be complacent: Poland. The Poles at the Cipher Bureau were desperate for any information related to Enigma they could get. As luck would have it, France and Poland had signed an agreement for military cooperation which obliged both nations to help each other in all matters of national security. So the French offered Schmidt’s information to the Poles who eagerly accepted it. The Poles constructed an Enigma replica and proceeded to find a way to break Enigma ciphers in earnest.Polish Codebreakers Tackled EnigmaStarting in November 1932, Marian Rejewski set about breaking Enigma ciphers. Captain Maksymilian supplied Marian with the following materials:A commercial Enigma.A copy of the operating instructions originally provided by Hans Thilo Schmidt.In addition, Marian had at his disposal hundreds of coded messages intercepted by Polish signal intelligence. He spent hours examining these messages and identified one thing they all had in common: a group of six letters that appeared at the top of every message as illustrated below:(Each piece of info in the 1st line was interpreted as follows:1/ 1230 = 12h30 = the time at which this message was produced.2/ 3tle = this message consisted of 3 parts of of which this was the 1st part (1tl)3/ 180 = this message contained 180 characters.4/ WZA RSL = the characteristic 6-letter group)What did those six letters represent? Marian deduced correctly that they were the message keys that were repeated twice. A message key was referred to as an indicator. They were generated based on the key setting defined in an Enigma key book. All German army units were periodically issued (once a month) with key books that contained lines of key setting for a particular day in a month. A key was composed of the following elements:The arrangement of the three rotating rotors.The plugboard for swapping keyboard inputs.The ringstellung - ring position.The ringstellung warrant some elaboration. Enigma rotors came in 2 versions: those with a ring of numbers (1-> 26) and those with a ring of letters (A-Z). A ringstellung = a specific letter/number for each rotor forming a sequence visible through the rotor windows.Rotors with alphabetic letter-ringsRotors with number ringsLeft: a key book showing key settings for rotors with number rings. Right: a key book showing key settings for rotors with letter rings.Now, although the Germans could have used the same key to encipher all messages, they were discouraged from doing so because using the same key to encrypt numerous messages would increase the risk of the key being uncovered by the enemy. Instead, Enigma operators were advised to choose a unique indicator for each message, then encipher this key using the daily key.So for instance, if on a given day the ringstellung for the key of that day was YHZ (from the key book), then an operator was not supposed to use YHZ as the key for any message he produced. Instead, he was supposed to do the following steps:Choose a unique key for every message, let’s say WAK.Encode WAK using the predefined ringstellung YHZ which would yield, say OLQ (from the lampboard).Write OLQ at the top of the message.Adjust the rotor to WAK and then began enciphering the main message.But that wasn’t enough. A message transmitted via radio could be corrupted by various causes. So the Germans decided to encrypt an indicator twice as a way to verify that the key was not distorted during transmission. So WAK would be encrypted twice using YHZ to become, say AHWTFS. This 6-letter group would be placed at the top of a message. Enigma operators who received this message would first set the rotors to YHZ (the predefined ringstellung), then type in AHWTFS. If he got WAKWAK, then they knew that the key for that message was WAK. They would adjust the rotors to WAK and proceed to decipher the message. Note how the decoding process was the mirror image of the encoding process. This was made possible by the reflector - the leftmost fixed wheel in the illustration below.Unbeknownst to the Germans, by encrypting the message keys twice, they unwittingly gave Marian a way to break Enigma ciphers.Here is howMarian was convinced that there existed a relationship between those 6-letter groups and the ringstellung on a given day, and that with sufficient tenacity and wit he would find a way to determine key for that day. So he directed his attention towards those 6-letter groups. He would gather as many of them from the messages intercepted on that day. One example was shown below:An illustration of the 6-letter repeated encrypted indicator that Marian would examine on a typical dayMarian scrutinized those letters for hours, trying to find a pattern. Eventually he had a crucial realization.Since the 6 letters represented the indicator repeated twice, there was a positional relationship between the letters. Specifically:The 1st and 4th letters = cipher letters of the plaintext indicator’s 1st letter.The 2nd and 5th letters = cipher letters of the plaintext indicator’s 2nd letter.The 3rd and 6th letters = cipher letters of the plaintext indicator’s 3rd letter.This insight led him to form tables relating the above pairs of letters. For example, one table may look like this.He studied those tables of relationships. Eventually he discovered an interesting pattern: disjointed circular chains of letters. One such chain was: (ek)e (1st row) -> k (2nd row) -> k (1st row) -> e (2nd row) = (ek)Repeating this process for other letters will yield the following circular chains.(atuvmsidwpxy)(bfjgol)(crzh)(ek)(qn)Marian referred to these disjointed chains as the characteristic set of a given day. Take note of this important fact.Marian’s next insight was that each of the cipher letters and consequently the chains of letters were the results of permutations. This followed immediately from the mechanism of the Enigma which consisted in:Transposition (the rotor replaced an input letter with another letter through an electrical pathway).Swapping (the plugboard swapped the input letter with another one).The implication? The encipherment could be modelled by mathematical equations - especially permutation equations. What’s more? The solution to those equations would reveal the ringstellung which would lead to complete decipherment!Marian found himself with a mathematical puzzle - precisely the kind of challenges that he loved and for which he was well equipped to tackle. At Poznan university, he had studied Group Theory under professor Krygowski. One subject of this branch of mathematics was combinatorics. It was a course he thoroughly enjoyed and he would now apply the knowledge to this puzzle.Each cipher letter was generated by a permutation process which always turned a letter into a different one. There were 6 cipher letters so there were 6 corresponding permutations. Let’s label them A,B,C,D,E,F.For example, permutation A could be (letters in the 1st row were turned into the corresponding ones in the 2nd row)This permutation be written in terms of characteristic sets.A = (admqzb)(c)(enpvjhrt)(fiwoy)(glksxu)Although Marian did not know the individual permutation, he did know the results of the pairwise products of the permutations A,B,C,D,E,F.Specifically,AD = characteristic sets of the (1st, 4th) pair.BE = characteristic sets of the (2nd, 5th) pair.CF = characteristic sets of the (3rd, 6th) pair.Marian came up with and demonstrated a number of theories about permutations. I will present only the most relevant theory.Given a permutation composed of an even number of disjoint circular chains, then this permutation can be expressed as a product of two permutations of the same degree, where each permutation also consists of disjoint cycles.Let’s look at a concrete example. Suppose that Marian found the following characteristic sets from the many intercepted messages:AD = (lwpmv) (tzeqn) (arh) (kiu) (sfj) (gxy) (b) (c) (o) (d) (number of disjoint cycles = 10 so degree = 10)BE= (ohfrlt) (qsyizj) (amceu) (ndxpv) (kb) (gw) (number of disjoint cycles = 6 so degree = 6)CF= (cqelbosptnfkj) (uhzaydxvrgwim) (number of disjoint cycles = 2 so degree = 2)It was possible to determine individual permutations A,B,C,D,E,F using Marian’s Theorem. For the sake of simplicity, let’s demonstrate this with a simpler example:AD = (adf)(bef)(c)(g) (degree = 4)One possible solutions is[math]A = (ah)(de)(fb)(cg)[/math] and [math]D = (hd)(ef)(ba)(cg)[/math](A and D each had degree = 4)(a->h (in A), h-> d (in B) => a->d (in AB). d->e (in A), e->f (in B) => d->f (in AB). This completes the cycle: (adf)Another solution is:[math]A = (ae)(db)(fh)(cg)[/math] and [math]D = (ed)(bf)(ha)(cg)[/math]Cool huh?Marian applied the above procedure to figure out all possible solutions for A,B,C,D,E,F. You can imagine that at the beginning, he had to manually calculate everything - a tedious process until he invented a machine that automated this process.The next two crucial insights Marian had that came of painstaking scrutiny of the characteristics sets and from trying various rotor settings were:the cycle structure of the characteristic sets depended entirely on the rotor setting AND not the plugboard.The characteristic sets AD, BE, CF produced by a specific rotor setting were nearly unique.(The cycle structure = the sequence of chain lengths where a chain length = number of characters in a cycle. So this characteristic set (ohfrlt) (qsyizj) (amceu) (ndxpv) (kb) (gw) has the following cycle structure (6)(6)(5)(5)(2)(2))As regards the 1st discovery, this makes sense because the plugboard only swapped letters so it could not have any effect on the number of links. This was a very consequential discovery because the permutation by the plugboard has the largest value when 10 swapping cables were used (the standard number used during the war): 150,738,274,937,250: > 150 trillions.By contrast, the permutation associated with the rotor setting was only 6 x 26 x 26 x 26 = 105,456 (6 = 3! = number of ways of arranging the 3 rotors and 26 = number of letters (or numbers) on each of the 3 rotors)The implication? Marian only had to examine the characteristic sets produced by each of the 105,456 rotor settings. Although that was still a fairly large number, it was at least manageable and certainly within the bound of manual labor!!! With this crucial insight, the seemingly insurmountable challenge now became solvable.The second insight was very telling because it implied that from the characteristic sets we could identify the rotor settings. It followed that if Marian could create a catalogue that mapped a rotor setting to a cycle structure, then he would be able to uncover part of the key setting for the Enigma.So Marian and his colleagues set about cataloguing the characteristic sets produced by each of the 105,456 rotor settings. This endeavor took about 1 year to complete: laborious but certainly worth the time and effort.The biggest challenge was finally solved. But there were still other parts of the daily key that Marian need to figure out.One was the internal wiring of the rotor. Thanks to Hans Thilo Schmidt, Marian was able to deduce the wirings of all three rotors from the documents the German traitor had given away. Marian fully recognized the enormous value of Hans’s documents through his remarkAsche’s documents were welcomed like manna from heaven, and all doors were immediately opened.(Asche was the codename of Hans Thilo Schmidt. Due to the need for absolute secrecy, Hans’s identity was never disclosed to anyone).The next piece of the puzzle was the static wheel that stood between the plugboard and the rightmost rotor:This drum also had 26 pins for 26 letters each of which was connected to a letter on the keyboard. Now, 26 letters so the number of possible permutations was 26! = 403,291,461,126,605,635,584,000,000 (27 digits) - a huuuuge number. Which permutation did the Germans choose for the drum?Incredibly, Marian found the permutation through a combination of reasonable guess + luck. First, Marian tried the permutation used for the commercial Enigma. It did not work. He tried other permutations but to no avail.Then he thought:The wiring of the keyboard to the entry fixed drum. Initially I assumed that the wiring on the machine matched that of the commercial Enigma. I was wrong. Once I realized my mistake I spent considerable time trying to deduct the order of the letters on the fixed drum. Then I recalled my time at the German-speaking school. My German teachers were always ordered and logical. So I thought to myself - if I possessed a German mind, how would I set out the order of the letters? I guessed the order of letters was alphabetical(i.e: a is connected to a, b is connected to b, … z is connected to z)IT WORKED!!! Much to the surprise of Marian.So the only unsolved piece that remained was the plugboard. Surprisingly, determining the swapping pairs was very easy. After determining the rotor settings for a certain day, Marian would set the rotors accordingly and typed in the ciphertext without any swapping cable. The resulting plaintext message would obviously be gibberish composed of misspelt words caused by the letters not being swapped.Being fluent in Germans could, Marian could see which letters needed to be swapped to correct the words. For example: the phrase “akkact ak dawn” was “attack at dawn” meaning that letters k and t needed to be swapped. So a cable connecting k and t needed to be plugged in. Eventually, Marian would be able to figure out all the swapping and the plaintext message would be revealed.And that - ladies and gentlemen - was how Marian Rejewski broke Enigma. Although several members of the Polish Cipher Bureau (and ironically: Hans Thilo Schmidt) deserved credit for this success, Marian was the genius who deserved the greatest credit. It was only through his ingenuity and mathematical talent that the supposedly unbreakable Enigma was broken. With the catalogue mapping rotor settings to cycle structure completed, the Cipher Bureau began uncovering large numbers of German military messages on any given day. When a German miltiary delegation led by Hermann Göring visited the Tomb of the Unknown Soldiers next to the building of the Cipher Bureau, Marian looked down at them, delighted in the knowledge that he could read their most secret communications.I will conclude this section with one very interesting fact. In several meetings with Major Gwido Langer - the Cipher Bureau’s chief, Hans Thilo Schmidt gave him not only operating instructions for the Enigma but also the key books. This exchanged lasted almost 7 years. But Langer never gave the key books to Marian Rejewski and his colleagues. This begs the question: why didn’t he share the keys with the codebreakers? It would have saved them a lot of effort and time.The answer was: the astute Langer had foreseen that one day Schmidt might no longer be able to help for whatever reasons. If that happened, the Poles could count on no one but themselves. Without the keys, Marian Rejewski would be compelled to exercise his ingenuity to deal with new cryptographic challenges in the future. In other words, Langer wanted Marian and his colleagues to be challenged so that they would become self-sufficient. Marian Rejewski had overcome that challenge brilliantly: he broke Enigma ciphers without the daily keys held by Langer.Mechanical Decryption of the EnigmaAlthough Marian’s cataloguing method worked, it was too time-consuming and tedious. Since time was of the essence, Marian recognized the need for a faster method to find the rotor setting. This motivation led to the next breakthrough in the cryptanalysis of the Enigma.Marian designed an electromechanical contraption now referred to as the Bomba. The design was realized by Antoni Palluth - owner of the AVA radio company and a member of the Cipher Bureau.Each Bomba constituted an Enigma with a specific rotor arrangement. Since There were six arrangements of the rotors (3! = 6), the Poles built 6 Bombas. The machine operated on the principle formulated by Marian: exploited the doubly-enciphered indicator. According to Marian, it worked in the following manner:using group theory of permutations from mathematics, we were able to build up a catalogue of all possible keys. This machine will search the key code message for patterns then stop automatically as soon as the pattern is found in the stored catalogue. Once we have the key codes, the Enigma can then be primed to read the message.The bomba significantly reduced the amount of time taken to find the rotor setting to 2 hours. It was an ingenious and arguably unprecedented advance in codebreaking: the mechanization of decryption in response to the mechanization of encryption.In consideration of his accomplishment and service, Marian Rejewski was awarded the Silver Cross of Merit in 1936 and the Gold Cross of Merit in 1938.The Poles Hit Dead EndIn December 1938, the Germans made significant changes to the Enigma that made the cipher vastly more difficult to break for the Poles.One change was made on the increase in the number of swapping cables from 6 to 10. This greatly raised the number of ways a message could be enciphered (from 100,391,791,500 (6 cables) to 150,738,274,937,250 (10 cables))Another change was the instruction for Enigma operators to use a new ringstellung for every message. Prior to this, the German operators were either lazy or inexperienced and kept using the same and easy-to-guess ringstellung for many messages (Such as AAA, XYZ, or BER (Berlin) or even the first 3 letters of their girlfriend’s name LOL). These stupid mistakes was of great aid to the Poles because it allowed them to sometimes deduce correctly what the message keys were without having to find the characteristic sets. This advantage went out of the window starting in December 1938 and thereafter.The other change, far more damaging to the Poles, was the introduction of 2 new rotors, increasing the number of available rotors from 3 to 5. This meant that the number of possible rotor arrangements was 5x4x3 = 60 - a 10-fold increase. This posed two challenges to the Poles:They needed to determine the internal wiring of the 2 new motors.They would need 60 bombas for the 60 possible arrangements of the 5 rotors. The cost for all of those machines far exceeded the available budget of the Cipher Bureau at the time.Remarkably, the Poles managed to solve the first problem. Back in September 1939, despite the Wehrmacht High Command’s order to use a new ringstellung for every new message, the Sicherheitsdienst - one of the Third Reich’s numerous security agencies - continued to use the same ringstellung for every new message well after the 2 new rotors were introduced in December 1938. It was a fatal and stupid mistake that enabled Marian to deduce the wiring for the 2 new rotors.Despite this success, the other problems - building 60 bombas - remained unresolved. The Poles simply could not afford all 60 machines.The consequence? Starting since the early 1939, the Cipher Bureau was confronted with an intelligence blackout. Their success rate dropped drastically from 70% in the previous year to a mere 10%. Finally, the Germans had outpaced the Poles.The Polish cryptanalytic success had come to an end - much to the disappointment and apprehension of the Poles.Intelligence Sharing with the French and BritishIn desperation, the Poles decided to ask the French and British for help. They intended to disclose their breakthroughs on the Enigma with their allies in exchange for any material aid that would enable them to continue their work.This set the stage for a secret meeting in a forest near Warsaw on 25th-26th July 1939. Prominent representatives of British and French intelligence services were invited to the meeting. The British delegation consisted of Dilly Knox, Alastair Denniston, Wilfred Dunderdale. The French delegation consisted of Gustave Bertrand, Henri Braquenié.The French and British interacted with prominent members of the Cipher Bureau, including Gwido Langer, Maksymilian Ciężki, Marian Rejewski, Henryk Zygalski, and Jerzy Rozycki.The British and French were excited. They were keen to see what the Poles had to offer.Langer set the meeting in motion.Langer: “So we are all in agreement so far as the sharing of information is concerned. Good. Then, gentlemen, I am delighted to inform you that we at this bureau have enjoyed considerable success in deciphering messages sent by the Germans by virtue of the Enigma machine. We have prepared certain information which we can make available to your departments if we can be assured of your assistance.”Langer paused and observed the reaction of the British and French.Dilly Knox was incredulous: “I don’t believe it! It is impossible to decipher messages sent with the Enigma machine.”Langer gauged the atmosphere and asked: “Am I to gather from your reactions that neither of your departments have had any success in decoding the Enigma?”“That’s correct. We have had our top minds working on this for years without success.” - Knox responded in a tone that smacked of embarrassment.Captain Bertrand: “Yes, my department has not had any success with this code and has considered it unbreakable.”Langer was disappointed:“Very well, gentlemen. It would appear that this meeting, which was specifically convened for the purpose of sharing information, falls short of my expectations. If my understanding is correct, you have no intelligence that can be of use to my department. Which leaves my bureau in the position of simply giving your departments top-secret information in good faith. Forgive me, gentlemen. I have to consider the implications of that.”Langer left the room to confer with his colleagues. He expressed his disappointment openly:We had expected that some intelligence could be provided to ourselves. You must understand — I am concerned about the security risk which extended knowledge of our position could present. We have successfully managed to maintain the extent of our advancement on decoding the Enigma securely within our unit. I do not need to emphasise to anyone present the importance of maintaining the utmost secrecy with this information.This is an unmitigated disaster... The risk to our organisation and to Poland is unquantifiable if it becomes known we can decipher the messages from Germany. Giving them information in return for nothing is an enormous risk with no advantage to ourselves.Jerzy responded:“If only it were that simple. We have no choice. We must share the information with the Allies. We need sixty Bomba machines and sixty of Zygalski’s sheets to enable us to continue to decode the messages rapidly. We do not have the resources to construct the machines required. The danger to Poland increases with each hour that passes. Never has our need to decode the German messages been more urgent. We must secure an undertaking from the Allies that they will supply equipment in return for our knowledge. It is vital we are able to continue our work.”Marian agreed with Jerzy:“The messages must be decoded speedily. It is vital we have more equipment. We are never going to have the funding necessary here for the production of the equipment needed. We cannot maintain our previous levels of codebreaking without either the machines and sheets, which the British can presumably provide. Not now the Germans have introduced the five rotor system.”Henryk added:“Now that Poland has a promise of assistance from Britain in the event of attack and the treaty with France, surely our providing assistance will assist Poland and demonstrate we are operating in good faith?”After soliciting their colleagues’s opinions, Langer telephoned General Waclaw Stachiewicz to obtain his his approval to share their knowledge on Enigma with the Allies.Meanwhile in the meeting room, the British and French were getting anxious.Dillwyn Knox said to himself: “Well, it looks like there isn’t going to be much information sharing. Do you really think they have been able to advance with breaking the code for the Enigma machine?”Alastair Denniston shook his head: “I don’t believe they have. We have the best minds working on this day and night with no progress.”Captain Braquenié: “They whisper it is the unbreakable code in my department.”Captain Bertrand: “I happen to know that they have exceptional mathematicians working on this. I am hoping they just may be able to surprise us, gentlemen.”Captain Braquenié: “Well let’s see, I have to confess my ignorance. I had thought Poland a land of peasants.”Dillwyn Knox added: “Well it will be interesting to see if they are going to trust us. Personally, I don’t think they will have much choice.”You could perceive a sense of snobbery and condescension in the conversation (land of peasants). The French and the British appeared to think that since the British and French could not break Enigma, then the uncultured and unsophisticated Poles could not do it. Little did they know, they were sorely mistaken.Then Langer returned, looking much more relaxed than when he left.“Good news, gentlemen. I have been authorised to let you witness our Bomba in operation. As I explained earlier, our cryptologists have been working day and night to reach this stage of development. In view of Germany’s aggressive behaviour and the recent treaties between our nations, we are delighted to share our information. Given that, at present, you are not able to disclose any advances to ourselves, we are insistent on a condition that you provide assistance in providing equipment to decypher the Enigma. I will explain in more detail as we progress. Gentlemen, please be seated. I think you will be pleasantly surprised by what you are about to witness.”The British and French representatives were incredulous but returned to their places at Langer’s suggestion. Marian began the demonstration by showing an intercepted coded message to everyone in the room.“This is a message which our radio interceptor team traced. It is passed immediately to our section and to our team here.” - said Langer.Marian, Jerzy and Henryk unveiled a machine - it was a Bomba. They proceeded to operate the machine to decipher the sample coded message.The guests watched quietly in suspense, and then started with shocked surprise as the Bomba started making lots of tickling noise.Marian: “It’s quite noisy. The machine is electrically powered and systematically works through the 17,576 possible different positions for the rotors. When it finds the right one it stops. It can take up two hours to work through all the possible permutations. That means, in a maximum of two hours, we will have the daily keys which were being used by the Germans on the day the message was sent. Once we have the daily keys in operation for a particular day, we can decode all the messages sent that day without further requirement of the Bomba. We can use the Enigma machine, which we have here.”.While waiting for the Bomba to find the key, Marian unveiled a replica of the military Enigma that he had designed (without having ever seen an actual machine).Dillwyn Knox was astonished. He asked: “How on earth did you discover all of this?”Marian replied: “I was fortunate to have some assistance. I was given some manuals and codes relating to the Enigma machine. I understand that I have you to thank” - Marian turned to Captain Bertrand (recall that he got the document from Hans Thilo Schmidt)Dillwyn Knox: “Yes. I myself worked extensively on the documentation you (Bertrand) provided, but I came to the conclusion that it was impossible to decipher the Enigma with that information alone. Although I made some progress developing a formula to ascertain the daily setting of the keys, eventually I concluded it was impossible to ascertain the wiring of the rotors.”Marian stood proudly before the Bomba. “I reconstructed the internal wiring of the military Enigma.”“What? You discovered the internal wirings for the drum. How?” - Dillwyn Knox jumped to his feet.(Note: The drum Dilly Knox was referring to was the static drum between the plugboard and the rightmost rotor.)Marian laughed. ‘You won’t like this. Initially, I worked through a number of methods which I considered probable. None of those worked. So I guessed.Knox asked in disbelief: “How could you guess?”Marian crossed his arms, enjoying the attention riveted upon him. ‘It just came to me one day as I worked through all the possible complex combinations. I stopped. I thought “what would my German teacher at school have done?” I remembered the German love of order. Then it was simple. I knew without any shadow of a doubt that I had searched too hard for a solution. The keyboard of the military version displayed the letters in alphabetical order, the letters round the rims of the rotors were ordered in alphabetical order. What could be more simple?”There was a resounding thump as Dillwyn Knox’s fist pounded down on the table. “I can’t believe it. How simple. Why didn’t I think of that?”At this point, the Bomba stopped making noise. It had found the ringstellung for the sample coded message. Jerzy set the rotors to the resulting ringstellung and typed in the coded message which yielded the plaintext message:“Section 4 U Boats head to Gdansk 1400 hours 19th”At this point, the astonishment felt by the British and the French reached its climax. Dilly Knox stood up to give a round of applause. The other attendees followed suit.“Absolutely first rate work!” - said Knox.The British and French were fairly embarrassed for underestimating the Poles. Whatever doubts they had with regards to the success and ability of the Poles vanished following the demonstration. The British who had given up on Enigma now realized that the supposedly unbreakable Enigma could be broken. The Polish achievements revived their hope in the cryptanalytic battle with the German ciphers in the imminent war.In September 1939, Nazi Germany invaded Poland. The Cipher Bureau’s systematic codebreaking effort had come to an end.SummaryThe Poles indeed had broken the Enigma cipher for many years before the British did. It was an achievement that attested to the intelligence, talent and ingenuity of the Polish codebreakers, especially Marian Rejewski who single-handedly came up with the mathematical theory to find the permutations that produced the indicator, who discovered the characteristic sets and the crucial relationship between cycle structures and the rotor setting, and who devised the method to find that rotor setting. This achievement became even more remarkable in light of the fact that British and French were convinced that the Enigma was invincible. Although this success would be highly unlikely without the treachery of Hans Thilo-Schmidt who supplied the materials needed to deduced the wirings of the rotors, and without luck (the guessing of the mapping between the static drum and the keyboard), those facts did not diminish the worth of Marian’s accomplishment.Much respect to the achievements of Polish codebreakers.I hope the readers find this a compelling read. (I am delighted to complete this answer in fulfillment of a longstanding promise to a friend :D)Reference(s)1/ The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography - Simon Singh.2/ X, Y & Z: The Real Story of How Enigma Was Broken - Dermon Turing, Arkady Rzegocki.3/ The Cypher Bureau - Eilidh McGinness

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