A Madman Dreams of Turing Machines by Janna Levin (PDF)

Description

Kurt Gödel’s Incompleteness Theorems sent shivers through Vienna’s intellectual circles and directly challenged Ludwig Wittgenstein’s dominant philosophy. Alan Turing’s mathematical genius helped him break the Nazi Enigma Code during WWII. Though they never met, their lives strangely mirrored one another—both were brilliant, and both met with tragic ends. Here, a mysterious narrator intertwines these parallel lives into a double helix of genius and anguish, wonderfully capturing not only two radiant, fragile minds but also the zeitgeist of the era.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I began writing a short story about Alan Turing last year. Despite a lengthy scribbled outline it remains a stunted opening gambit. After reading Janna Levin’s A Madman Dreams of Turing Machines I really feel far less of a need to finish what I started, because she basically captured what I’d kept confined in my head, off the page. I still might finish it one day, but after reading David Leavitt’s beautiful Turing biography (The Man Who Knew Too Much: Alan Turing and the Invention of the Computer) and this incredible historical fiction of Levin’s I feel like they’ve jointly completed what I wanted to see carried out: a sensitive, detailed, intellectually astute and “literary” portrait of this far too underappreciated genius and his tragic decline.This is the historically-informed story of two 20th century intellectual giants, Alan Turing and Kurt Gödel. Other real life figures make supporting appearances such as Wittgenstein and Otto Neurath. There are also very brief and well-placed metafictional entries and minute allusions that bring the author into the fold in a narrator-as-character manner, as can be seen in the very (non-)beginning of the book:”There is no beginning. I’ve tried to invent one but it was a lie and I don’t want to be a liar. This story will end where it began, in the middle. A triangle or a circle. A closed loop with three points.At one apex is a paranoid lunatic, at another is a lonesome outcast: Kurt Gödel, the greatest logician of many centuries; and Alan Turing, the brilliant code breaker and mathematician. Their genius is a testament to our worth, an antidote to insignificance; and their bounteous flaws are luckless but seemingly natural complements, as though greatness can be doled out only with an equal measure of weakness.”The connection between mental illness and artistic and intellectual greatness is a long established cliché by this point and is probably far too often overstated via confirmation bias. There’s a fantastic documentary called Dangerous Knowledge which focuses on four mathematicians and/or scientists who all grappled with hugely complex and difficult issues like the nature of the deepest structures of reality, infinity, human consciousness, free will v. determinism, etc, and all ended up killing themselves. Turing and Gödel are two of the four. There’s an implication that it was their theories and obsessive intellectual aspirations that drove them to commit suicide, which I think is a rather flawed notion considering the facts and other plausible explanations. However, it does make for compelling narrative to peer into the lives of tortured geniuses consumed by their own big brains or whatever, and is an excellent sounding board for thinking about the pursuit of knowledge and its various costs and benefits. In any case, these are fascinating stories, and Turing’s in particular I find the most captivating and tragic.Alan Turing’s influence is felt hugely in the realm of computer science, cryptology, Artificial Intelligence and mathematical logic more generally. He’s often credited as one of the single most important influences on the development of the modern computer–without Turing we may not be having this exchange of information right now. He also played a hugely instrumental role in cracking the German Naval Enigma Code in WWII with his tireless cryptology work and innovations in the field which allowed for a far more rapid decoding of the German transmissions that were quite literally matters of life or death. After the war he was arrested for admitting to having homosexual relationships to the police after he reported being burgled by a casual fling–arrested and prosecuted by the very same government he’d served and protected. Instead of going to prison he was chemically castrated. The regimen of huge doses of estrogen caused him to gain weight and grow breasts, fall into a chemical depression, and ultimately end his life by eating a cyanide-glazed apple, mimicking one of his favorite films, Snow White. Turing was persecuted to death. The British government has the blood of a genius (who saved them from further Axis-led destruction) on their hands. Only as recently as 2009 has the British government issued an official apology for this incident that occurred in 1952 (however the same government has rejected the proposal to posthumously pardon Turing of his “crimes”). It took the Roman Catholic Church 359 years to finally officially apologize for persecuting Galileo for positing that the Earth revolves around the sun, so perhaps this is the sign of a kind of progress, but it still all feels far too little, far too late.Kurt Gödel was a mathematician and logician (the distinction between the two starts to break down at a certain point) who famously constructed his Incompleteness Theorems, which I still have trouble explaining, because I’m a dummy when it comes to mathematics and formal logic (Gödel’s Incompleteness Theorem For Dummies). I am truly ignorant about mathematical matters, but I can appreciate from my perch of acknowledged ignorance the allure of “the sanctity and purity of mathematics, the profound truth so completely immune to human stains.” Gödel was also an absolute loon. He held a deep paranoid fear of being poisoned and as such rarely ate anything and only enough to keep his skeletal frame alive, and had elaborate rituals involving his wife’s cooking. He was also a member of the famed Vienna Circle, a group of intellectuals who met weekly to discuss the tenets of their new unifying idealistic philosophy of Logical Positivism. Gödel, along with Wittgenstein, each in their own ways, aided in dismantling this group with their unorthodox ideas. There are great sections in this book where Gödel’s proposed notions of “Incompleteness” cause a great uproar amongst those seeking complete unifying theories to knit all of reality together. Gödel lived much longer than Turing, but ultimately died by starving himself to death both out of his paranoid notions of being poisoned and for other sad and errant reasons: there’s a passage in the book where Gödel delusionally claims that his refusal to eat is a proof of his free will, something he desperately wanted to believe in, along with the existence of an afterlife.Turing and Gödel never met, but they were certainly aware of each other’s work and so the only way they collide in the book is in mentioning one another’s ideas.Janna Levin is a physicist with a concentration in philosophy (her primary professional focus is cosmology but she had formal focus on philosophy as well, and I think it shows) yet on the stylistic level her writing is fantastic and surely shames huge numbers of authors who’ve workshopped their way through MFAs and maybe even published for years and years, while narrowly focused on literary fiction and nothing else. Janna Levin churns out steadily captivating prose that soars richly and exultantly without succumbing to a plummeted decadence; regularly supplanting ho-hum descriptions with a strikingly vivid lyricism through the conjuring of unusual imago-sensory crossbreeds that dance across the neural pathways with pleasantly assured aplomb.The book is thoroughly researched as the notes provided at the back of the book further prove. It’s intellectually dexterous in its portrayals of these brilliant and flawed figures. The subjects (and the sort of human beings most tightly latched upon them) that are classically conceived of as cold and cerebral and arrogantly cocksure are sensitively imbued with the squirming life and heat of fallibility, frailty, confusion, and the portrayal of the true scientific spirit, where truth is provisional, and self-doubt and self-interrogation are constant companions.While this is a book of heady ideas, it’s also a humanizing ode. The sections on Turing especially tugged the heartstrings. He was an odd but deeply sympathetic person. There are gripping descriptions of London being bombed by the German Luftwaffe, of Alan’s loneliness and tragic loss of his one true love as a schoolboy, and multiple gorgeous sections about the interconnectivity of things that just need to be read to be felt.Both Turing and Gödel chased after the Truth with great fervor accompanied by great doubt. This classic yearning for the Truth of All Truths is maybe something many can easily set aside as not worth wasting time over when there is a more pressing desire for the Pursuit of Happiness on offer. I myself have often done this and will continue to do it. Hitting a wall where I no longer hunger for deep abstract truths about the nature of consciousness or reality or death, etc. But the desire never fully cools either. Also, even if one doesn’t care at all about such cliché or high-minded foolishness, everyone knows what it’s like to yearn strongly for something Ideal, be it Romantic Love or the Perfect Career or the Perfect Artistic Creation and so on. As Olga Neurath says to Gödel about her and her husband finally accepting his Incompleteness Theorem:”Your incompleteness theorem was hard for him to accept. It was hard for all of us, for every mathematician alive. But then Moritz always knew that it did not matter what he believed. What matters is the truth. And somehow you found it hidden where none of us could see. We all came to realize that mathematics is still flawless–no paradoxes, contradictions–just some truths that cannot be proven. Not so bad. We can live with that. He could live with that. […] I myself worried from the start. Kurt, you worried us. It was hard for us for a time, to be sure. If not even arithmetic is complete, then what could we hope for from out philosophies, from our sciences, from the very things that were to be our salvation? The buoys that we clung–perhaps, I would admit now, with too much desperation–were taken away. […] And here we are again with our hopes being crushed. I used to believe that when I was older I would come to some kind of conclusion, some calming resolution, and then the restlessness would end. I would know something definitive and questions would fade. But that will never happen. […] We wanted to construct complete worldviews, complete and consistent theories and philosophies, perfect solutions where everything could find its place. But we cannot. The girls I hear playing in the park when I walk to the institute, our neighbor the old woman who will die soon, our own circle, we all prize a resolution, a gratifying ending, completeness and unity, but we are surrounded by incompleteness.So I think that reading about the pursuit of Truth can still be moving and redemptive and nourishing for those who do not currently or never have really put much value on it. And then the journey becomes more valuable than the destination, as the ol’ cliché reminds us.

⭐As I read it, Janna Levin’s novel is a creative exploration of epistemology, the problem of knowing. It briefly but vividly sketches the lives of two men, Kurt Gödel and Alan Turing, and uses their assumptions about reality and the nature of truth to dramatize that certainty about most aspects of existence, and especially about the larger questions of value and meaning, is unattainable. The novel confronts serious questions: Is our existence meaningful or meaningless? What role, if any, should faith and mysticism play in our lives? How reliable is the knowledge gained by a priori reasoning? By inductive empiricism? What constitutes reliable knowledge and how do we go about obtaining it?The first chapter introduces members of the Vienna Circle who in the early twentieth century approach the problem of knowing with the hyper-scientific standards of Logical Positivism. Disciples of Wittgenstein, they wish to discard all unexamined assumptions and build a world-view that is incontestable. The only claims of truth they consider fully reliable are claims founded on empirical observations and the unassailable logic of mathematics. They meet to “distinguish science from superstition. At stake is Everything. Reality. Meaning. Their lives. . . . They hate mysticism and metaphysics, religion and faith. They loathe them. They want to separate out truth” (8-9). They engage in “ripping down notions like `The Absolute,’ `Spirit,’ and `God’ and watched them vaporize before hitting the ground. Faith, Mysticism – it’s not that these ideas are false. They are meaningless” (59). But Kurt Gödel, a member of the Circle, shatters their illusions of certainty by demonstrating that some truths are beyond mathematics. Previous philosophers had believed this was true, but their ideas were only beliefs. “Gödel didn’t believe that truth would elude us. He proved that it would” with a theorem that met the epistemological standards of the Vienna Circle, his theorem being as tangible as “a rock he had dug up from the ground. He could pass it around the table and it would be as real as the rock.” Ironically, what the Positivists considered to be one of the most powerful means of establishing “truth” – the rational system of mathematics – is proven to be “not a complete one” (10-11) and Logical Positivism finds itself undermined by its own principles.Throughout the novel the problem of knowing is approached in a number of ways and with far more complexity than I can describe here. Gödel, for example, engages in a debate with Olga over the distinction between what is true and what is real, and he accepts the truth and reality of an abstract realm of numbers (84). But he is “completely convinced” of the clairvoyance of a Gypsy medium (62) in apparent violation of his own epistemological standards. And Moritz Schlick, the leader of the Vienna Circle and its link with Wittgenstein, can find no way to prove that his own sensory experience is valid (74), instantiating what philosophers for centuries have called the “problem of the external world.” This problem of sensory reliability, particularly in the form of seeing, is raised and/or symbolized many times. Numerous other epistemological issues appear in the novel, each showing another facet of the problem of determining truth.Over in England in the same time frame, Alan Turing gradually undergoes a conversion from religious faith to empirical skepticism and concludes, “We are biological machines. Nothing more. We have no souls, no spirit. But we are bound to mathematics and mathematics is flawless. This has to be true. Where is God in 1 + 1 = 2? There is no God” (107). Turing uses logic and mathematics to invent a computing machine and successfully break Nazi war codes, clearly not inconsequential feats. But Gödel’s and Turing’s stories illustrate not only that certainty about many religious and philosophical issues is unobtainable, but also that formidable powers of logic are insufficient in themselves as tools for living. Both men’s lives end in a kind of tragic and pitiable madness.The novel raises the question, “Are our lives meaningful or meaningless?” and uses historical data to conclude that no answer can be given with certainty. Religious faith as a means of knowing is implicitly if not explicitly rejected as unreliable. The narrator describes herself as “Craving an amulet, a jewel, a reason, a purpose, a truth” (220), but can find no reason to embrace any explanation of reality as a certainty. All explanations must be seen as corrigible and provisional. Certainty even about the material, historical world is no more accessible than certainty about a putative metaphysical realm. How does one determine where to begin a biography? Where does that person’s story actually begin? Where does it end? Our lives are the result of and the cause of indeterminable numbers of chains of cause and effect; there are no clear lines of demarcation, no points that clearly identify where a story starts or finishes. The book opens with “There is no beginning. I’ve tried to invent one but it was a lie” (3). It closes with, “There is no ending. I tried to invent one but it was a lie” (220). These are not the words of an unreliable narrator. Quite the opposite. These are the words of a narrator completely committed to speaking truthfully and courageously admitting that, despite our craving for certainty, incontestable “truth” is a will-o’-the-wisp that still eludes us. This is a valuable reminder in an age of unprecendented dangers arising from political and religious absolutism.

⭐While I was interested in the subject, unlike other authors, I just found it a bit hard to keep reading it or engrossed. Could be subjective of course, but I’ll probably never re-read this sadly…

⭐An intriguing concept and one which gives a marvellous introduction to these two men who lived their lives largely unrecognised.

⭐Zu Beginn des 20. Jahrhunderts einwickelte David Hilbert sein Programm zur vollständigen Formalisierung der Mathematik, u.a. in der Hoffnung, ihre Widerspruchsfreiheit streng beweisen zu können. Völlig überraschend fand Kurt Gödel 1931 ein unüberwindliches Hindernis, indem er zeigen konnte, das ein formales System, dass wenigsten so reichhaltig ist, dass die Arithmetik darin formuliert werden kann, notwendigerweise unvollständig ist – in dem Sinn, dass es einen richtigen Satz enthält, der weder formal abgeleitet noch widerlegt werden kann. Inspiriert durch Gödels Methode verfasste Alan Turing 1936 seine Arbeit ‘On computable numbers, with an application to the Entscheidungsproblem’, die zeigte, dass es algorithmisch nicht lösbare Probleme gibt. Um den Begriff der algorithmischen Lösbarkeit präzise fassen zu können, entwarf er einfache Maschinen – die später nach ihm benannt wurden –, von denen er bewies, dass sie in gewisser Hinsicht universell sind.Die Ergebnisse beider Mathematiker beschrieben bisher völlig unbekannte Limits im Herzen der Mathematik, beide hatten aber auch zeitlebens ernsthafte psychische Probleme. Janna Levins Buch erzählt zeitlich breit gestreute Episoden aus dem Leben dieser beiden ‘madmen’; die Geschichten umspannen sowohl die Zeiten ihre großen Entdeckungen, als auch die des Todes der beiden Protagonisten, Gödel 1978 und Turing 1954. Die Autorin erzählt sehr eindrücklich, versucht unaufdringlich den Hintergründen der Problem der beiden Genies mit dem ‘normalen’ Leben nachzuspüren; wiewohl ihre Arbeiten erwähnt werden, erfährt der Leser der Leser darüber aber nicht viele mehr, als in der obigen Zusammenfassung angedeutet.Levin greift auch gelegentlich in persönlicher Rede in die Handlung ein, etwa um die Auswahl der Episoden zu ‘rechtfertigen’ – sie beschreibt die Dinge, wie sie sich ihr aufgedrängt haben – bewusst ohne rechten Einstieg und einem Ende ohne Fazit. Dabei ist die Sicht der Autorin interessant, ihr Stil flüssig und kurzweilig – eine wissenschaftliche Biographie hat sie nie beabsichtigt.Trotzdem bleiben die erzählten Geschichten eher zufällig, beiläufig. Wer mehr über die Interpretation von Gödels und Turings Ergebnissen in allgemein verständlicher Weise erfahren möchte, sein etwa auf Roger Penrose ‘The emporer’s new mind’ (dt. Ausgabe ‘Computerdenken’) verwiesen.

⭐

⭐This is a great book. It focuses not only on the tragic Alan Turing but also on 30s Vienna. Part biography and part fiction this is an erudite and highly challenging novel I can’t recommend enough.

⭐A great story about two geniuses that continued to surprise me

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