| This story appears in the collection Tales of the Night made up of stories by Hoeg that are all set on the evening of March 19, 1929. In this one, a depressed young Danish mathematician takes a train ride through Central Africa with Joseph Korzeniowski (a.k.a. Joseph Conrad, author of "Heart of Darkness").
The character of the mathematician here is obsessed with the certainty of mathematics and proudly uses it to "avoid" the real world:
| (quoted from Journey into a Dark Heart)
Until a year previously and for as long as he could remember, David had been a mathematician. Not the sort who studies the discipline because he believes he has a quicker grasp of it than of any other, or because one must make a career of something, or out of curiosity. No, he became a mathematician out of a deep burning passion for that crystal-clear, purifying algebraic science from which all earthly uncertainty has been distilled.
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| (quoted from Journey into a Dark Heart)
"I am von Lettow. General Paul von Lettow Voerbeck."
Even to David, who prided himself somewhat on his ignorance of that part of the world not featured in mathematics journals, this name as it was uttered seemed to fill the air with all the weight of an equestrian statue suddenly materializing in the room.
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David speaks to General von Lettow and Joseph K. about his goal of eliminating all uncertainty, of a mathematical theory that would explain and predict everything out of a few simply principles. However, as he explains, the work of Kurt Gödel has showed mathematics instead to be built on shaky ground, like the Tower of Pisa:
| (quoted from Journey into a Dark Heart)
"In Vienna," he continued slowly, "I met...someone with a very clear view of things. He is working on a particular theorem, a proposition. When I saw this proposition it seemed to me to shatter my dream. Of course he is not the only one. There have, as I have asid, been various indiciations of what was afoot. But he showed me Venice, he showed me that it is the foundations that are unsound. He has proved, no, he intends to prove -- that when one is dealing with a complex system, and we humans are complex" - here he felt himself reddening under the girl's gaze - "within any complex system there are certain elements that cannot be deduced from its basic characteristics. This may mean that, even had we known every particular of the circumstances surrounding this journey, we would still have been unable to guard against the unpredictable."
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This is not a bad characterization of one implication of Gödel's theorem: that even though you can figure out a lot from a few basic principles, they are never enough to figure out everything. Also, the story is well written and the comfort of the other characters with uncertainty is a nice counterpoint to David's paranoia about it. However, speaking as someone who has read a great deal of mathematical fiction, I cannot help but be put off by the fact that David's character is a stereotype. And, as a mathematician concerned about the impression that fiction makes on people about my profession, I worry that the frequent appearance of characters like this in fiction will give readers the impression that mathematics departments are populated with broken people like David. They are not. I know of nobody who is seriously troubled by the idea that there will always be things we do not know. In fact, most mathematicians I know enjoy the pursuit of knowledge and so this would sound more like an exciting challenge than the terrifying nightmare that David seems to think it is.
Note:
Although David is a fictional character, the story mentions two real mathematicians: Gödel and Galois.
| Contributed by
Vijay Fafat
A short story set in the heart of Africa and one in which Godel’s Incompleteness Theorems play a central role in the life of one of the characters.
David Rehn was a young, precocious mathematician (“he became a mathematician out of a deep, burning passion for that crystal-clear, purifying algebraic science from which all earthly uncertainty has been distilled.”) till he ran into a young boy at the University of Vienna – Kurt Godel. When the young “Herr Warrum” described his ideas which would shake the world of mathematics at its foundations a few years later, David went into a state of shock and retired from mathematics. Subsequently, a long turn of events finds him on a train with some fellow passengers and a terrorist, bounding toward its doom over a bridge far ahead (with a twist in the end). As the passengers muse over their lives and philosophize, the mathematician, facing the supposedly final moments of his life, reminisces how his faith in the certainty of mathematics was shattered by Godel and led him to rethink about the entire edifice of mathematics and even the social sciences which may be teetering under their own collective weight.
There are many passages which are very lyrically written, and the part where David despairs over the problem of incompleteness built into the foundations of mathematics reminded me of the extremely sad letter full of pathos which Wolfgang Bolyai wrote to his son, Johann, imploring him not to pursue a proof of Euclid's fifth postulate, citing his own repeated failures in that journey. If one is not easily convinced that David could walk away from his passion at the "mere" thought that foundations of his subject might be crumbling or may even be entirely inconsistent - since Godel's Theorem says that that sword of Damocles will forever remain hanging over any sufficiently complex mathematics - one should read the heart-wrenching paragraph from that letter (not part of this story but perhaps will give the reader a perspective on David's mindset):
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“You should not investigate the parallels in that way; I know also that path till the end, I also have the measure of this bottomless night: every light, every joy of my life has been extinguished in it. I implore you for God’s sake leave the parallels in peace. You must shy away from it as you would from a dissolute contact. It will bring to an end all your abilities, your health, your peace of mind and your life’s happiness. This bottomless pit will swallow a thousand Newtons, it will never see the light of day and poor mankind will never have something that is pure, not even geometry; it has inflicted a deep and permanent wound in my soul; God forbid that it bites into you so deeply. It robs for one the joy of geometry, for life. I planned to sacrifice myself for truth. I would have been ready to become a martyr if only I could give geometry, purified of this stigma, to mankind. Fearful, enormous work have I done, have by far achieved more than ever achieved before, but I have never found any complete satisfaction. Here, however, the Latin proverb applies: si paulum a summon discessit, vergit ad imum. I have backed out when I found that one cannot reach the bottom of this night from the Earth. Unfortunately, there is no consolation for me and for the entire mankind. Learn from my example.”
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I do, however, feel that some statements in the story do not make logical sense (or perhaps David, in his despondent state, is no longer thinking clearly and consistently). E.g. David bemoans toward the end:
| (quoted from Journey into a Dark Heart)
“This may mean that, even had we known every particular of the circumstances surrounding this journey, we would still have been unable to guard against the unpredictable.”
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I doubt any serious mathematician or a half-serious analytic mind thinks in this fashion, as the unpredictability in the world would be omnipresent even in a mathematical world where Godel's theorems did not exist. The basic concepts of chaos theory ensure that predictability in complex systems in the manner expressed by David is impossible no matter the foundations of mathematics. David should know that the kind of predictability he wants is not precluded by Godel but something far less esoteric.
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