Dongzu (Aidan) Lee

ANNOTATED BIBLIOGRAPHY1

Primary Sources

Papers

Turing, Alan. “Turing’s Treatise on Enigma.” (1939 - 1942) US National Archives and Records Administration. https://www.archives.gov/files/press/press-releases/2015/images/turing- enigma-treatise.pdf

This paper had been written by Turing between 1939 and 1942 while working at , but it had been classified for many years after the war by the British government; only in 1996 it became declassified. It is most informative on how Turing structured and manipulated input and algorithm in such ways as to maximize production of “contradictions” - for the purpose of skipping them - in , a computing machine he devised to deduce “rotor settings” from a given Enigma-encrypted message. What is the meaning of contradiction in Bombe? How to understand it best? A sign. An indication. An extra layer of information which neither True nor False solely as the answer(output) could deliver. Because of the way Bombe was set up, it communicated a unique meaning, and that was contradiction’s greatest use in Bombe.

In the world of logic, contradiction often results from an inverted (i.e. up-side-down) self- inference such as in: “This statement is false.” (i.e. If it is true, it must be false, and if it is false, it must be true.) In the physical universe, a bridge may fall down if contradiction is present, because it means we have not fully thought out everything. In the world of Bombe, however, contradiction simply means randomness resulting from factors beyond the input – such as the rotor settings. Why? Simply because Turing programmed Bombe so, to signal certain useful meaning by way of contradictions.

The most informative part of the Treatise is Chapter 6, titled “The steckered Enigma. Bombe and Spider.” It is easy to fear Primary Sources, especially papers, as too challenging, and to resort to Secondary Sources for understanding. But Primary Sources often show us something no Secondary Sources can: chronological development of ideas. Secondary Sources give us only the completed final picture, which is a bit similar to seeing a movie’s ending first, with everything mixed in between. Seeing the thought process as it happens can be valuable. Understanding what came in response to what, and why something was necessary at that time can provide crucial missing pieces. I note just three such points:

1. I learned that Turing too was following Rejewski’s approach at first - in avoiding the Plugboard [i.e. Stecker] problem by divorcing it completely rather than using some of its constraints to his advantage as he did later, especially with help of insights from Welchman:

“From this picture we see that one characteristic which is independent of the Stecker is

1 Within each category, I have tried to list each entry loosely (i.e. not always, especially for categories such as Wikipedia) in the order of importance in making my website. 1

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that there must be a letter which enciphered at either position 2 or position 5 of the crib gives the same result … In order to apply the multiple encipherment condition one naturally wants to be able to perform the multiple encipherments without Stecker in one operation.”

But later he states: “In our original description of the Bombe we thought of it as a method of looking for characteristics of a crib which are independent of Stecker, but in the last section we thought of it more as a machine for making Stecker deductions. This last way of looking at it has obviously great possibilities, and so we will start afresh with this idea.”

2. Rejewski’s Cyclometer left many traces on Bombe: “If one has two of these ‘Letchworth Enigmas’ [i.e. Enigma only with Rotors, without the Plugboard] one can connect the output points of the one to the input points of the other and then the connections through the two Enigmas between the two sets of contacts left over will give the effect of successive encipherments at the positions occupied by the two Enigmas. Naturally this can be extended to the case of longer series of Enigmas, the output of each being connected to the input of the next. Now let us return to our crib and see how we could use these Letchworth Enigmas. For each of our ‘chains’ we could set up a series of Enigmas.”

These were exactly Rejewski’s technical ideas behind Cyclometer – generating cycle of chains, closed loop created by feeding input to output and output to input among multiple Enigmas! Only that they differed in purpose: Cyclometer was for building a catalogue, or a complete world of possible truths, whereas Bombe was for discarding what was impossible from what was assumed to be true (i.e. cribs).

3. Often we fail to notice enormous contributions made by “hardware” makers; we tend to think engineering and manufacturing as relatively easy. In the case of Bombe, “algorithm’ was installed not as software. It was the hardware itself – arrangements of the drums, discs, wires and relays constituted its algorithm! Turing makes it very clear that Mr. Harold Keen, the manufacturer of Bombe, was much more than an engineer who followed Turing’s designs; Keen himself was an innovator. At the time there were neither semiconductors nor vacuum tubes (as least not common), Keen achieved making machines that behaved as if following software instructions – in the span of a few months! I had wrongly thought the idea of automatically moving onto the next rotor position in response to contradiction indication (a crucial feature in automation) was Turing’s. Turing gives the entire credit to Keen:

“It is therefore necessary to have some arrangement by which immediately after the spider stops the point of entry of the current is altered to the point to which the relay which closed was connected, or is left unaltered in the case that 25 relays closed. Mr. Keen has invented some device for doing this, depending entirely on relay wiring. I do not know the details at present, but apparently the effect is that the machine does not stop at all except in cases in which either just one relay closes or 25 relays close.”

Turing, Alan. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the Mathematical Society, 2 Received 28 May, 1936.- Read 12 November, 1936. https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf

I relied on Wikipedia and YouTube to understand this paper, because it was very difficult

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to understand. Nevertheless, it was important because of the way Bombe may fit into Turing’s world of ideas, before and after Bletchley Park. Surely Bombe could not have appeared out of the blue; it must have been related to something that came before. I think Bombe was one specific way to implement Turing’s conceptual framework on computer.

Turing, Alan. “Computing Machinery and Intelligence.” Mind, Volume LIX, Issue 236, October 1950, pp. 433–460. https://academic.oup.com/mind/article/LIX/236/433/986238

This is Turing’s paper on AI, published 10 years after Bombe (in 1950). Turing is no longer asking what computer can or cannot do, or if we can create a computer for universal tasks; he is asking whether we can distinguish between human and computer, offering his famous test - if we can't determine which party is the computer after conversation, the machine can be said to think like a human. “Cribs” might have inspired Turing’s thoughts on AI, since they are precisely the type of work best suited to AI.

Rejewski, Marian. “How Polish Mathematicians Deciphered Enigma.” IEEE Anals on the History of Computing, Vol.3., No.3. (July 1981) http://chc60.fgcu.edu/images/articles/rejewski.pdf

Rejewski wrote this paper many years after his groundbreaking work, based on recollection of how the Poles broke Enigma. Through remarkable insights and ingeniousness, Rejewski was able to observe certain unique characteristics - such as identically shaped sets of cycle-lengths that are present – resulting from the Enigma Protocol and tracked them.

Rejewski, Marian. “Mathematical Solution of the Enigma Cipher.” Cryptologia, vol. 6, no. 1, 1982, pp. 1–18. (Translated by Christopher Kasparek) https://web.archive.org/web/20141030213141/http://cryptocellar.web.cern.ch/cryptocellar/ Enigma/rew80.pdf

In addition to showing Cyclometer, Rejewski shows how Henryk Zygalski invented perforated sheets that showed relative placement characteristic of female per each rotor position. Using razor blades, Poles punched holes for each rotor position that would produce female. They would pile these on top of each other, staggered in manners corresponding to the observed relative positions of the females.

Patents

Scherbius, Arthur. “Enigma Patent.” Cipher Machines and Cryptology. (See below) http://users.telenet.be/d.rijmenants/en/enigmaproc.htm

Scherbius died from an accident in 1929, leaving the possibility on how he might subsequently have improved Enigma into a historical guess.

News

New York Times. “Germany Seeks an Alliance against Us; Asks Mexico and Japan to Join Her; Full Text of Her Proposal Made Public.” March 1, 1917. https://www.mentalfloss.com/article/92771/wwi-centennial-america-outraged- zimmermann-telegram

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Kirby, Rollin. “Exploding In His Hands.” The World. March 3, 1917. https://www.eurasiareview.com/24052017-1917-the-year-of-the-century-analysis

Telegrams

Zimmermann, Arthur. “Zimmermann Telegram.” Intercepted from 2nd from London #5747 https://mediarichlearning.com/media-vault-zimmermann-telegram/

Zimmermann, Arthur. “Zimmermann Telegram.” Deciphered from 2nd from London #5747 https://mediarichlearning.com/media-vault-zimmermann-telegram/

Videos

Breaking The Codes. Documentary film directed by Norman de Lacy Evans. 2:23:00. 2009, London. DigiComTV, 2009. Amazon Prime Video.

A great documentary on Enigma and Bombe, from which I obtained a short footage (0:02:44) and uploaded to my site. Since my entire footage is an interview / personal recollection by Ms. Ronnie Hulick on her actual work with American Bombe, this is Primary Source.

Audios

Rebuilt Bombe Operating Sound Recording. Made by John Harper and the Bombe Rebuild Project Team (Recording made at Bletchley Park in September 2006) Audio file, 0:59sec. http://www.ellsbury.com/bombe-sound.htm

Because this is not the sound of the original Bombe (all were destroyed at the end of WWII) but a rebuilt Bombe, one may argue that this is not a Primary Source. However, since the purpose of rebuilding was faithful reproduction of Bombe, this should be still regarded as a Primary Source. The rebuilt Bombe is not to interpret but to reproduce the original.

The rebuilt Bombe let us hear the sound of rotor switching from one setting to the next setting. It occurs fast; the beauty is that there is no need to test every plug-pairing for each rotor position. If all 27 relays are energized (i.e. contradiction indication), Bombe simply moves (without testing another plug-pairing hypothesis) to the next rotor position, which is the clunking sound you hear.

Photos & Archives

Turing Digital Archiv. http://turingarchive.org/browse.php/K/1/43

Best resource on Turing. Turing had tragically short life (his mother outlived him by more than 20 years) but achieved perhaps more than any figure born last century, and this archive offers a wealth of materials for us to follow his life and his passion. Some parts are

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heavy with mathematics, but there are lighter materials as well: personal correspondences displaying enthusiasm, curiosity, imagination and playfulness, such as how to play the game of Go, or how to invent a totally different typewriter. As a tribute to Turing, I was searching for something that would hint at his character, and this archive had almost everything I was looking for.

Bundesarchiv. https://www.bundesarchiv.de/DE/Navigation/Home/home.html

This German national archive has every German historical photo one can think of, including photos of Enigma in action during WWII.

Crypto Museum. https://www.cryptomuseum.com

Along with Ciphermachines and Cryptology, Crypto Museum shows what amateur enthusiasts can do for history. The site is an initiative of Paul Reuvers and Marc Simons, both self-employed engineers from Eindhoven (Netherlands).

Ciphermachines and Cryptology. http://users.telenet.be/d.rijmenants/index.htm

One of the best simulation sites on Enigma and cryptography. Since 2004, this site has been updated by Dirk Rijmenants. The simulation software has detailed and historically accurate configurations.

National Cryptologic Museum Foundation. https://cryptologicfoundation.org

This is a governmental site, and not as interesting or useful as other sites made by individuals.

Bletchley Park. https://bletchleypark.org.uk

Official Website of Bletchley Park. Has rare photos of Bletchley Park and blueprints of Bombe parts.

National Museum of the Royal Navy. Enigma. https://nmrn.org.uk/explore/curators- highlights/enigma

Wikipedia (Photos). https://www.wikipedia.org

Wikipedia is a great resource for historical photos as well, which would qualify as Primary Sources.

Henryk Zygalski (L), Jerzy Różycki (C) and Marian Rejewski (R). Photo. PAP/PAI https://polandin.com/38779822/polish-cryptanalyst-commemorated-in-the-uk

One of the rare photos in the Internet with all three.

Paper Replica

Pringles Enigma Kit for Download. The Paper Enigma. Franklin Heath Ltd. http://wiki.franklinheath.co.uk/index.php/Enigma/Paper_Enigma

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Understanding Enigma requires good visualization and ability to juggle many things simultaneously in the head. As such, fancy simulation software is not as effective as simple paper sheets with wire drawings glued to a Pringles Can in showing what happens to the circuits. In fact, paper drawings are what Turing endorsed as the best visualization method in his Treatise, and his Treatise is filled with such drawings – as they did not have Pringles back then, which came out in 1967: “The comic strips. For demonstration purposes, it is best to replace the machine by a paper model. (Chapter 1, Turing’s Treatise on Enigma)”

Pringles Enigma was most useful for following as well: when studying how Cyclometer worked, I connected two sets of Pringles Enigma without the Plugboard, and when studying how Bomba worked, I connected three sets without the Plugboard.

With that said, whether Pringles Enigma would qualify as Primary Source is debatable, similar to the case of Rebuilt Bombe considered above but more complicated. The issue is whether any interpretations or descriptions are involved rather than immediate, first-hand accounts of truth. In output results, there is no difference between Pringles Enigma and real Enigma, once the initial settings of the two are synchronized through sharing of the identical key. Even though it looks nothing like a real , and even though it reveals all inner wirings unlike a real Enigma machine, Pringles Enigma should still be regarded as Primary Source, not Secondary, because it still concerns itself with truth, not interpretations or descriptions, of an Enigma machine. The resulting output from Pringles Enigma must be identical to that of the real Enigma machine, and the revealed wiring is not an interpretation of fact, but fact itself. Therefore, Pringles Enigma should be regarded as Primary Source.

Books

Stripp, Alan, and F. H. Hinsley. Codebreakers: The Inside Story of Bletchley Park. London: Thistle Publishing, 2015.

Primary Source books are rare; this is a rare exception and excellent as well. Highly technical and detailed book written by codebreakers who worked at Bletchley Park, edited and organized by Alan Stripp of Hut 6 and of Hut 4. Chapter 11, written by Stripp,“The Enigma machine: Its mechanism and use,” was most helpful.

Jackson, John. Solving Enigma's Secrets: The Official History of Bletchley Park's Hut 6. London: BookTower Publishing, 2014.

This is a photo-copy of the original book, which was written by various staff of Hut 6 in 1945/6. The original copy is to be found in the National Archives, HW43/72. The original book had been classified as “Top Secret” until 1979. The part on Hut 6 was released for publishing only in 2006. Although somewhat disorganized, this has advantage of being written when the memory was freshest to everyone who worked there. Excellent account of Philip Stuart Milner-Barry - British chess player, chess writer, World War II codebreaker and civil servant.

Alexander, Conel Hugh O'Donel. Cryptographic History of Work on German Naval Enigma. The National Archives, Kew, Richmond, Surrey, TW9 4DU. Reference HW 25/1. http://www.ellsbury.com/gne/gne-000.htm

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The original of this document is held in the United Kingdom (see above), but thanks to Mr. Graham Ellsbury, we may have an access through the above website. (So please do not look for this book in Amazon.)

Doenitz, Karl. The Memoirs of Karl Doenitz Ten Year and Twenty Days. Barnsley, S. Yorkshire: Frontline Books, an imprint of Pen & Sword Books Ltd., 2012.

Perspective on Enigma from someone who made a career (coordinating “the Wolfpack”) and a world-war out of its security. Most valuable account from the opposite side. His confession that he could never think Enigma could possibly be broken is an amazing statement reflecting the Germans’ conviction on mathematics, which led to their demise.

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Secondary Sources

Papers

Carter, Frank. “The Turing Bombe.” The Rutherford Journal. http://rutherfordjournal.org/article030108.html

Absolutely the best short explanation on Bombe. So many articles and books fail to explain Bombe – because they try to “describe” it. Bombe cannot be understood by “descriptions.” Bombe is a special-purpose computing machine, and the best way to understand it is by feeding an input and observing what the algorithm does to it, one step at a time. I decided to quote this paper at length on my website because I could not explain better (and to save words).

Carter, Frank. “Appendix 2: “Enigma and the Bombe in Depth.” In : Bletchley Park's Architect of Intelligence, edited and written by Joel Greenberg, pp. 290-351. Barnsley, S. Yorkshire: Frontline Books, an imprint of Pen & Sword Books Ltd., 2014.

The Appendix 2, written by Frank Carter, is a more detailed version of the above paper by the same author. Endorsed by the daughter of Welchman (who was the brain behind the “Diagonal Board”, which made Bombe so much more usable), the whole book is well written. But still the most lucid and important part is Frank Carter’s analysis provided in Appendix 2. I do not make a separate entry for the book in this Bibliography.

Ellsbury, Graham. “The Enigma and the Bombe.” http://www.ellsbury.com/enigmabombe.htm

Reading the three Secondary Source papers completed my rough understanding of Bombe. Along with Frank Carter’s article, this is perhaps best written, most concise, most beautiful explanation on Turing’s Bombe. Most books fall way short of the three papers in clarity. Perhaps it helps that Ellsbury is a computer scientist and Carter, an engineer. I uploaded the paper on my website.

Link, David. “Resurrecting Bomba Kryptologiczna: Archaeology of Algorithmic Artefacts, I.” Cryptologia, vol. 33, no. 2, 2009, pp. 166–182. http://www.alpha60.de/research/bomba_krypt/DavidLink_BombaCryptologiczna_Cryptolog ia2009.pdf

This paper written by David Link was the best paper on Rejewski’s Bomba. There were questions on whether Bomba would actually produce deciphered texts (no unit survived – the design was based on recollections of Rejewski) and the author meticulously shows not just the logic but actual experiment, fully vindicating Rejewski’s work. I provided a link for self-download on my website for those who are interested, as well as using some of its pictures it to illustrate the concept of “offsetting.”

Christensen, Chris. “Polish Mathematicians Finding Patterns in Enigma Messages.” Mathematics Magazine, vol. 80, (2007), pp. 247-273. https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/christensen247.p df

An excellent paper on the Poles’ methodology, especially on Cyclometer, but challenging on the permutation theories which I have not learned yet in school. This paper won an 8

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award from Mathematical Association of America in 2008. I uploaded the paper on my website.

Stanford University Course Handout (#36) on Enigma Machine, Course: CS 106J. Taught by Professors Eric Roberts and Jerry Cain on May 15, 2017. https://web.stanford.edu/class/cs106j/assignments/Assignment-05

This handout succinctly explains the dynamic nature of Enigma scramblers, with beautiful pictures. I found this 5-page handout more helpful than volumes of books in understating the essence. I used some of the pictures from the handout on my website to explain Enigma’s initial setting and rotor(s) that advance with each click, but the best way to understand Enigma’s structure would be to visit the actual site above and study the whole of “Assignment 5: The Enigma Machine.”

Gaj, Kris, and Arkadiusz Orłowski. “Facts and Myths of Enigma: Breaking Stereotypes.” Lecture Notes in Computer Science Advances in Cryptology — EUROCRYPT 2003, pp. 106–122. https://link.springer.com/content/pdf/10.1007%2F3-540-39200-9_7.pdf

This paper helped me understand how the internal wiring of the Enigma worked as well as the Polish methods.

Hamer, David H. “Enigma: Actions involved in the ‘Double Stepping’ of the Middle Rotor.” David Hamer’s Website on Cryptology. http://www.intelligenia.org/downloads/rotors1.pdf

A quirk caused by Enigma’s middle rotor at that time which would make actual permutation for scrambler orientations 26x25x26=16,900 instead of 26x26x26 is explained in this paper by an enthusiast of cryptology. He passed away in 2017.

Monk, Ray. “Turing and Wittgenstein on Logic and Mathematics.” The Eighteenth British Wittgenstein Society Lecture. 2020. https://www.britishwittgensteinsociety.org

Reading this fascinating (if a bit combative) conversation between Wittgenstein and Turing, which took place before Turing came to Bletchley Park, provided me with clues on how Turing came to possess such sweeping intellectual vision. Turing lived at the forefront of ideas. His intellectual community consisted of David Hilbert, Kurt Gödel, Alonzo Church, John von Neumann, Ludwig Wittgenstein – some of the most creative minds of the time. They were asking the “big” questions - the “fundamental” questions - such as asking whether there can be a genuine logical contradiction, different from mere verbal confusion. The conversation may appear trivial, but it provides yet another clue to the breadth and depth of his training. And freedom: every question seemed permitted.

Books

Hodges, Andrew. - The Enigma: The Book that Inspired the Film . London: Princeton University Press, 2014.

This book, written by mathematician Andrew Hodges, is perhaps the best book I could find on the “big picture” – what the compelling issues were and how they were solved. Hodges is very precise and accurate without being dry or nit-picking. He is comprehensive, noticing patterns in Turing’s lives, looking for patterns and connections among big ideas such decidability, Bombe, Automatic Computing Engine, AI. Although this is not a difficult

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book to follow (he is superb at explaining), for deeper understanding, I would still read this only after having read all the technical papers mentioned above (i.e. Frank Carter) and having understood the nuts and bolts first.

Singh, Simon. The Code Book: The Evolution of Secrecy from Mary Queen of Scots to Quantum Cryptography. Knopf Doubleday Publishing Group, First Anchor Books Edition, September 2000.

This was a very entertaining book, very fast and easy to read, and superbly organized. However, I would like to point out 2 points that other readers may perhaps notice as well. In an attempt to make the book readily accessible, I feel that the author has oversimplified Enigma - for instance, he skipped “Ring” setting altogether. If you skip Ring, “Stepping” and “Turnover” are other concepts you have to skip, which is fine as long as you are aware of it. Second, I spotted a minor unrealistic example in the book: In Chapter 4, the example of “characteristic chain” he gives is (3, 9, 7, 7), but characteristic chain can be manifest only in pairs, such as (9, 9, 3, 3, 1, 1); as such, (3, 9, 7, 7) cannot be generated in reality.

Turing, Dermot. X, Y & Z. The Real Story of How Enigma was Broken. Stroud, Gloucestershire: The History Press, 2018.

Dermot Turing is a nephew of Alan Turing. This book’s unique contribution is in illuminating how the collaboration among the French (“X”), the English (“Y”) and the Polish (“Z”) was critical to breaking Enigma, an aspect that had often been neglected. It is a tribute to the Poles and especially the French about whose role very little was known (the French were instrumental in communicating, encouraging and organizing, making the crucial relay from Pyry to Bletchley Park happen. In addition to little-known factual details, the author provides many rare photos of his own (e.g. the humble building in Pyry where relay took place, the Château near Paris where the Poles stayed while in exile, etc.) throughout the book. Although such photos would qualify as Primary Sources, to avoid duplicate entry, I am listing this book only once under Secondary Sources.

Kahn, David. The Codebreakers: The Comprehensive History of Secret Communication from Ancient Times to the Internet. New York: Scribner,1996.

David Kahn is a British authority on cryptology, and this book is a comprehensive history on cryptology. Thorough, meticulous and insightful, but unfortunately it did not have much on Enigma, Rejewski or Turing because this book was originally published in 1967, whereas the British embargo on Enigma secrecy was lifted only in 1976. Nevertheless, I found it a great survey of cryptology.

Kahn, David. Seizing the Enigma: The Race to Break the German U-Boat Codes, 1939–1943. Barnsley, S. Yorkshire: Frontline Books, an imprint of Pen & Sword Books Ltd., 2012

This book adds to Kahn’s previous book on history of cryptology, The Codebreakers, the declassified historical findings on Enigma, Rejewski and Turing. His is masterful at explaining difficult concepts verbally, without even using diagrams. I made many quotes from this book on my site.

Petzold, Charles. Code: The Hidden Language of Computer Hardware and Software. Redmond, Washington: Microsoft Press, 2009.

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This is one of the best books I have read anywhere, on any topic. This book may not explain much about Enigma or Turing, but it helped me countless ways. It helped me understand what is so special about binary digits (0,1), the simplest number system possible, which Turing adopted as the basic building block of information that could be used to make something as big as the universe. Just like the binary digits, this book delivers profound ideas in the simplest possible way.

Sebag-Montefiore, Hugh. Enigma the Battle for the Code. London: The Orion Publishing Group Ltd., 2017.

Technical and helpful with details.

Tuchman, Barbara W. The Zimmermann Telegram. New York: A Random House Trade Paperback Edition, 2014.

This is a master historian’s perspective on shaping of “historical event” seen through the lens of Zimmermann incident. She warns that historic forces do not forgive the wishful, the lazy, the naïve, the unprepared, the clueless in deciding national destinies. Deeply moving and persuasive.

McKay, Sinclair. The Lost World of Bletchley Park: The Illustrated History of the Wartime Codebreaking Centre. London: Aurum Press, 2013.

McKay, Sinclair. The Secret Life of Bletchley Park: The WWII Codebreaking Centre and the Men and Women Who Worked There. London: Aurum Press, 2012.

Healy, Mark, and John Prigent (ed.). Panzerwaffe: The Campaigns in the West 1940, Volume I. London: Ian Allan, 2008.

Encyclopedia

(i) on War

Ray, Michael. “Luftwaffe.” In Encyclopæ dia Britannica. 2020 ed. https://www.britannica.com/topic/Luftwaffe

Limbach, Raymond. “Blitzkrieg.” In Encyclopæ dia Britannica. 2020 ed. https://www.britannica.com/topic/blitzkrieg

Copeland, B.J. “Ultra.” In Encyclopæ dia Britannica. 2020 ed. https://www.britannica.com/topic/Ultra-Allied-intelligence-project

“Wolfpack (naval tactic).” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Wolfpack_(naval_tactic)

“German Submarine U-13 (1935).” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/German_submarine_U-13_(1935)

“Battle of France.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Battle_of_France

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Lewis, Robert. “Bletchley Park.” In Encyclopæ dia Britannica. 2020 ed. https://www.britannica.com/place/Bletchley-Park

“Biuro Szyfrów.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Biuro_Szyfr%C3%B3w

“Bombe.” In Encyclopæ dia Britannica, 2020 ed. https://www.britannica.com/topic/Bombe

(ii) on Logic

“Gödel’s Theorem.” In Encyclopedia of Philosophy. Paul Edwards (Ed.). New York: Macmillan Publishing Co., Inc. & The Free Press. London: Collier MacMillan Publishers. 1972.

I should have read Primary Sources on Gödel, but I felt it was plainly beyond my current ability and I had to be satisfied with reading a summary on his most important work. This is one big loose end on my research, although this Encyclopedia was superb.

“Proof by contradiction.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Proof_by_contradiction

“Reductio ad absurdum.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Reductio_ad_absurdum

“Machine that always halts.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Machine_that_always_halts

“Turing's proof.” https://en.wikipedia.org/wiki/Turing%27s_proof

“Entscheidungsproblem.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Entscheidungsproblem

“Church–Turing thesis.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis

“Undecidable problem.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Undecidable_problem

“Universal Turing machine.” In Wikipedia. 2020 ed. https://en.wikipedia.org/wiki/Universal_Turing_machine

“Turing Machines.” In Stanford Encyclopedia of Philosophy. 2018 ed. https://plato.stanford.edu/entries/turing-machine

Articles

Jackson, Joab. “How Alan Turing set the rules for computing: The Turing Machine gave the world a model for how computers could operate.” Computerworld. June 22, 2012. https://www.computerworld.com/article/2504774/how-alan-turing-set-the-rules-for- computing.html

Two thought-provoking points in particular: (i) Enigma was analogue, whereas Turing’s

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mind was digital; and (ii) inconclusive knowledge can still be most useful (such as in search engines).

"‘By today's definitions, the Enigma was an analog computer. What he [and his team] built was much closer to [the operations] of a digital computer,’ Rensselaer's Hendler explained. ‘Essentially he showed the power of digital computing in attacking this analog problem. This really changed the whole way that the field thought about what computers could do.’ But far from restricting progress of computer science, the knowledge of such inconclusiveness paved the way for building previously unimagined technologies. It allowed engineers to create immensely helpful services such as Internet search engines, despite knowing that the answers such services were to provide would not always be complete.”

Thanks to Turing, we now know as a matter of logic that there cannot be an algorithm that never fails to make a decision. Nevertheless, thanks also to Turing, we know now that algorithms of “complex imperfections” (e.g. Bombe) are far superior to those of “simplistic perfections” (e.g. Enigma). We should get used to uncertainties, inconclusiveness and partial solutions. Perhaps that is what Turing had in mind when he said 70 years ago:

“We can only see a short distance ahead, but we can see plenty there that needs to be done. (Turing, Computing Machinery and Intelligence.)”

I cannot think of more timely wisdom than this timeless one in facing the unknown. Turing still inspires us.

Travis, Ben. “Bletchley Park Code-Breakers: Who Was Gordon Welchman?” Evening Standard, Sept. 7, 2015. https://www.standard.co.uk/stayingin/tvfilm/bletchley-park-code-breakers- who-was-gordon-welchman-a2928831.html

This article helped me learn different British cryptanalysts who assisted Alan Turing in breaking Enigma. The breakthroughs required massive efforts in diverse ways.

Higginbotham, Adam. “There Are Still Thousands of Tons of Unexploded Bombs in Germany, Left over from World War II.” Smithsonian.com. Jan. 1, 2016. https://www.smithsonianmag.com/history/seventy-years-world-war-two-thousands-tons- unexploded-bombs-germany-180957680

This photo shows bombs being dropped indiscriminately over civilians and military alike, even on Germany. Below, the smoke coming from the bombs is visible. Turing saved many lives on both sides of the war by breaking Enigma, which played a critical role in ending war early.

YouTube

“Turing Machines Explained.” Video file, 0:05:24. YouTube. Posted by Mark Jago of Computerphile, August 29, 2014. https://www.youtube.com/watch?v=dNRDvLACg5Q

Assistant Professor Mark Jago of the University of Nottingham is superb and most effective at explaining difficult concepts. I was tremendously helped by these very short videos. Also some of the replies and comments to the video posted were helpful as well.

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Dongzu (Aidan) Lee

“Turing & The Halting Problem.” Video file, 0:06:13. YouTube. Posted by Mark Jago of Computerphile, August 21, 2014. https://www.youtube.com/watch?v=macM_MtS_w4

“Proof that Computers Can't Do Everything (The Halting Problem).” Video file, 0:07:51. YouTube. Posted by udiprod (email: [email protected]), September 27, 2013. https://www.youtube.com/watch?v=92WHN-pAFCs

Maps

[September 1939], German and Soviet Invasion of Poland Map. Map. Poland,1939. Holocaust Encyclopedia. https://encyclopedia.ushmm.org

Quotes

AZ Quotes. https://www.azquotes.com

Perhaps with the exception of the statement by Turing himself, all those that I quoted on the “Legacy” page would best be regarded as Secondary Sources, because they are not directly related to my research topic and I am trying to use them to show my points.

Websites

Cryptography Stack Exchange. Last modified 2020. Accessed March 1, 2020 https://crypto.stackexchange.com/

An open-source, question-and-answer site for software developers, mathematicians and others interested in cryptography. To a coder such as myself, this site was most useful in understanding how Enigma worked, including its quirk on middle-rotor notch such as “double-stepping.” Although not central to my argument, I quoted from this site to give a brief “manual” on Enigma’s inner-working for those interested in knowing technical details and for accuracy’s sake. Enigma was a very complicated machine - with its rotor settings (divided into rotor choices, rotor orders and initial positions), plugboard settings, ring settings, double-stepping and turnover points.

Twitter Account: @StyxSwimmer (Blog). “Swimming the Styx: For When You Need a Decidedly Unwise Place to Swim. Understanding the Enigma. Enigma Example Message.” GIF. Last modified January 19, 2014. Accessed March 1, 2020. http://swimmingthestyx.com/?p=368

The simple GIF on this site shows path-selection per typing occurring inside Enigma. Often, small ingenuities like this can be most helpful.

Dade, Louise. “Enigma Encipherment Stages.” The Electropaedia. Battery and Energy Technologies. Enigma's Secrets How it Worked and How the Code was Broken. JPG. Last modified 2005. Accessed March 1, 2020. https://www.mpoweruk.com/enigma.htm

The JPG on this site neatly shows one path taken inside Enigma.

Casselman, Bill. “The Polish Attack on Enigma II: Zygalski Sheets.” American Mathematical Society (“AMS”). Last modified March 23, 2011. Accessed March 1, 2020. https://ams.org/publicoutreach/feature-column/fc-2013-12

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Concise, but detailed and thorough. I took the photo of Zygalski Sheets from this site.

Vestergaard, Erik. “The German Cipher Machine Enigma.” Last modified March 2017. Accessed May 1, 2020. https://www.matematiksider.dk/enigma_eng.html

A Danish mathematics teacher made a comprehensive website to explain Enigma. I first learned about the paper by Christensen here.

Polish Greatness (Blog). “Enigma connections using three rotors and reflector.” The Enigma Machine Part 3. The Science of Secrets How the Poles Cracked the Enigma Code. JPG. Last modified March 23, 2011. Accessed March 1, 2020. https://polishgreatness.blogspot.com/2011/03

The JPG on this site shows the possible paths that can be formed through combination of parts.

“Alan Turing Biography.” Biography.com, A&E Television Networks. Last modified July 16, 2019. Accessed March 1, 2020. https://biography.com/scientist/alan-turing

“Alan Turing, 23 June 1912 – 7 June 1954.” New Scientist. Last modified March 23, 2011. Accessed March 1, 2020. https://newscientist.com/people/alan-turing

Hodges, Andrew. “Alan Turing: The Enigma.” Last modified 23 July 2014. Accessed March 1, 2020. https://www.turing.org.uk/index.html

Website made and maintained by the Author of Alan Turing - The Enigma.

Salvo, Victor, et al. “Alan Turing.” Legacy Project Chicago. Last modified 2016. Accessed March 1, 2020. https://www.legacyprojectchicago.org/person/alan-turing

Turing’s legacy lives on.

“How Alan Turing Cracked the Enigma Code.” IWM, Imperial War Museums, Last modified 2016. Accessed March 1, 2020. https://www.iwm.org.uk/history/how-alan-turing-cracked- the-enigma-code

Helgason, Guðmundur. “Wolfpacks listed by years.” uboat.net. Last modified 2020. Accessed March 1, 2020. https://uboat.net/ops/wolfpacks

Definitive website on U-boats since 1995, created and maintained with amazing passion by an enthusiast of history and technology.

“U-Boat Attacks of World War II: 6 Months of Secret Terror in the Atlantic.” New England Historical Society. Jan. 13, 2020. https://www.newenglandhistoricalsociety.com/u-boat- attacks-of-world-war-ii-6-months-of-secret-terror-in-the-atlantic

“War of Secrets: Cryptology in WWII.” National Museum of the United States Air Force™, May 1, 2015. https://www.nationalmuseum.af.mil/Visit/Museum-Exhibits/Fact- Sheets/Display/Article/196193/war-of-secrets-cryptology-in-wwii

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Dongzu (Aidan) Lee

“Who Were the Codebreakers?” Bletchley Park. https://bletchleypark.org.uk/our-story/bletchley- park-people/who-were-the-codebreakers

“Victory in Europe Day: How World War II Changed the UK.” Office for National Statistics. https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/articles /victoryineuropedayhowworldwariichangedtheuk/2015-05-08

“WW2 Technology: German U-Boats - Ran Levi.” Curious Minds Podcast, https://www.cmpod.net/all-transcripts/wolf-packs-and-floating-coffins-u-boats-in-wwii-text

The text and photos in this website showed me the dangers of being at war, with all the destruction and bombs. This also explained why Alan Turing shortening the war by two years was so significant; it prevented a lot of casualties.

Datta, Anwittaman. “Enigma Emulator.” Last modified 2016. Accessed May 1, 2020. https://piotte13.github.io/enigma-cipher

A great website from Singapore that emulates the working of Enigma. Free download of the program.

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