Literature and mathematics have little to do with each other. One of the few writers of fiction to portray mathematicians is Swift, who satirizes them in Gulliver's Travels as the inhabitants of the floating island of Laputa. Swift describes the Laputans as an inept and foolish people, who are so preoccupied with mathematics and astronomy that they are oblivious to the world around them and incapable of the simplest practical tasks. His main purpose is to ridicule the mathematicians (and mathematical scientists) of his day, especially Newton. But at the same time, he is attacking mathematics itself, a subject that he regards as useless and frivolous intellectual game, and psychologically harmful. In fact, the underlying premise of this satire is that, by focussing the mind on abstractions, mathematics makes people less aware of their surroundings, and consequently undermines their ability to communicate with others, and to carry on the ordinary activities of life.
Swift opens his case against mathematics by describing the Laputan's odd appearance and behavior: "Their Heads were all reclined either to the Right, or the Left; one of their Eyes turned inward, and the other directly up to the Zenith." With the eye turned turned inward they are calculating the positions of the stars and planets, while with the other they are observing the heavens to check their predictions. The Laputans are so absorbed by these mathematical exercises that whenever they talk to each other, an attendant, called a flapper, has to tap the speaker on the mouth with an inflated bladder to remind him that he is speaking. And when Gulliver is brought to the royal palace of Laputa, the king is so involved in a mathematical problem that it is an hour before he notices his visitor's presence. As Gulliver explains, "It seems, the Minds of these People are so taken up with intense Speculations, that they neither can speak, or attend to the Discourses of others, without being rouzed by some external Taction upon the Organs of Speech and Hearing".
The idea behind these comical scenes - the stereotype of the absent-minded mathematician is hardly original to Swift. He may have borrowed some of his material from Plutarch's account of Archimedes during the Roman invasion of Syracuse. "(Archimedes) was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. But while Plutarch describes Archimedes' absent-mindedness as a sign of the great mathematician's powers of concentration, Swift represents the same trait in the Laputans as a mental deficiency, no doubt to make fun of Newton, who was notoriously inattentive. As usual, he exaggerates for satirical effect: the Laputans aren't just absent-minded, they are pathologically withdrawn and unable to communicate with others - in fact, practically autistic. While much of this account is facetious, Swift is implying that mathematics affects the mind like an opiate, turning people's attention inward and dulling their consciousness of the external world.
Besides being socially dysfunctional, the Laputans are incompetent in all practical matters. For instance, when a Laputan tailor tries to fit Gulliver for a new suit of clothes, he uses a rule, a compass and quadrant to take Gulliver's measurements, and ends up making ill-fitting clothes due to a mistake in his calculations. Nor are the Laputans any better at constructing buildings, their houses being "very ill built, the Walls bevil, without one right Angle in any Apartment; and this Defect ariseth from the Contempt they bear for practical Geometry; which they despise as vulgar and mechanick." On one hand, Swift is claiming that mathematics is useless for all practical tasks. For all the Laputan's knowledge of geometry - the pure geometry of Euclid, as opposed to the "practical Geometry," which they hold in contempt, they can't even build two walls at right angles two each other. Swift mocks their reliance on abstract theories, such as the tailor's futile attempt to measure Gulliver with mathematical instruments, the rule, compass and quadrant. For example, he describes how the Laputans draw a diagram resembling a geometrical proof to plot the course of their island across the sky. As a result, the island follows a zigzag course that brings them no closer to their destination. No doubt Swift would have been surprised to learn that mankind would one day use mathematics to guide aircraft across the sky.
In describing the Laptuan's ineptitude, Swift is expressing his contempt for theoretical knowledge, as he does throughout Gulliver's Travels. But while he makes fun of all academic subjects, he reserves his most scathing attack for mathematics: not only does he dismiss it as useless, he claims that it actually make people less capable of reasoning about concrete subjects. As Gulliver remarks about the Laputans, "I have not seen a more clumsy, awkward, and unhandy People, nor so slow and perplexed in their Conceptions upon all other Subjects, except those of Mathematicks and Musick." A fog of abstraction fills their minds, preventing them from thinking clearly about practical problems. Swift's implied argument is that the Laputan's obsession with abstract reasoning causes their other mental faculties, especially those that apply to concrete matters - to atrophy. This mental deficiency, which prevents them from focussing on anything outside their own minds, is the real causes of their incompetence.
In offering this comical account of the Laputan's ineptness, Swift is just warming up his attack against mathematics. He has a more serious charge to bring: that mathematicians are unable to communicate. The Laputans, who can't even hold a conversation without being slapped in the face to remind them to speak and listen, are too absorbed by their own thoughts to pay any attention to the ideas of others. And not only are they unable to communicate with each other, the only contact they have with the world below is by lowering messages to the ground by strings. This is clearly Swift's metaphor for how poorly the mathematicians of his day explained their discoveries to the rest of society. There is some truth to this charge. Newton, for example, went to great lengths to conceal the reasoning that led to his theories of gravitation and motion. Furthermore, he wrote his Principia in the style of classical Greek geometry - a series of theorems and proofs - rather than in his new language of calculus, which would have his ideas far more accessible to his contemporaries. Consequently, the Principia is notoriously opaque. On one hand, Swift is arguing that mathematicians can't communicate because they are indifferent to any human activities other than mathematics, a charge he makes explicit by describing a conversation between Gulliver and the King:
"His Majesty discovered not the least Curiousity to enquire into the Laws, Government, History, Religion or Manners of the Countries where I had been; but confined his Questions to the State of Mathematicks."
But Swift is also making a more far-reaching claim: that abstract reasoning, by its very nature, prevents people from expressing themselves clearly about concrete ideas. For example, the reason the Laputan's houses are so lopsided is that the instructions they give are "too refined for the Intellectuals of their Workmen; which occasions perpetual mistakes." Presumably, when the Laputans try to convey something as concrete as construction plans, the details become lost in a mist of abstractionsOf course, Swift is not the only writer to express hostility toward abstract ideas. George Orwell, an admirer of Swift, expresses a similar mistrust in Politics and the English Language:
"When you think of something abstract you are more inclined to use words from the start, and unless you make a conscious effort to prevent it, the existing dialect will come rushing in and do the job for you, at the expense of blurring or even changing your meaning.
Both Orwell and Swift are claiming that abstract ideas are a source of vagueness and confusion in language. While Swift is attacking abstract ideas in general, it is clear that he views mathematics as the worst offender.
As a consequence of their inability to communicate, Swift proceeds to argue, mathematicians are isolated from the rest of society, an isolation that is symbolized by the separation of Laputa from the Earth below. Swift is implying that mathematicians as a group are intellectually isolated from the mainstream of human society. In describing Laputa as a closed and self-absorbed community, he is portraying the mathematical profession as a cult, separated from the surrounding society, whose members devote their time to arcane rituals and mystical beliefs, which they make no attempt to explain to the uninitiated. They resemble the ancient Pythagoreans, who were forbidden to reveal their mathematical secrets to outsiders. Swift is suggesting that the insularity of mathematicians is due to the very nature of their subject, which he believes is compartmentalized and separated from other branches of knowledge. He views mathematics as existing in a vacuum, receiving no infusions of ideas from other areas of human thought, and that as a result, mathematicians live in an intellectual ghetto. Basically, he regards abstract thinking as a disease of the mind, which mathematicians, in league with philosophers and scientists, are responsible for spreading with their abstract theories.
We get an insight into his misconception of
mathematics and science from his description of the Laputan's extreme anxieties
over the fate of the solar system: "They are under continual Disquietudes, never enjoying
a Minute's Peace of Mind; and their Disturbances proceed from Causes which very
little affect the rest of Mortals. Their Apprehensions arise from several
Changes they dread in the Celestial Bodies. For Instance; that the Earth by the
continual Approaches of the Sun towards it, must in the Course of Time be
absorbed or swallowed up."
The Laputans appear to be on the verge of a collective
nervous breakdown over their fear that the Earth is about to collide with the
Sun. The notion that mathematicians are predisposed to mental instability is
itself a common stereotype. For Swift to exaggerate the irrational fears of the
Laputans, who are supposedly guided entirely by reason and logic, is an obvious
satirical device. But the way he
develops this theme says more about his own failure to understand the
motivations of mathematicians and scientists than it does about mathematicians
themselves.
For what Swift is really making fun of in the passage
quoted above is one of the oldest scientific problems: the motion of the
planets. The passage appears to be loosely based on a genuine mathematical
problem that goes back to Newton and remains unsolved to this day: the
stability of the solar system. Briefly put, the question is whether the orbits
of the planets will remain roughly the same, or whether they will become wildly
chaotic over time, possibly causing the Earth to plunge into the Sun. It is a
problem that has greatly influenced the development of mathematics and physics,
and given rise to the modern theory of chaos. It is also clear that Swift
regards such a question as utterly pointless. But what is most revealing is the
reason he gives for the Laputan's interest in it: namely, their neurotic fear
about the destruction of the world. In
reality, people have studied the motion of the planets since ancient times, and
their primary motive for doing so has been scientific curiosity. For Swift,
such a motive is incomprehensible. As far as he is concerned, all these
centuries of stargazing have been a waste of time, for curiosity is a human
impulse that is foreign to him. As Orwell has pointed out, "(Swift's) implied
aim is a static, incurious civilization - the world of his own day, a little
cleaner, a little saner, with no radical change and no poking into the
unknowable." Since Swift himself has no curiosity about the natural world, he
is unable to imagine why anyone else would want to study it. This inability to
understand what motivates science is behind his hostility to the whole
scientific enterprise. It is the reason why he distorts the motives of
mathematicians and scientists throughout Gulliver's
Travels. By basing the Laputan's
astronomical pursuits on their fear of impending doom, he manages to twist
scientific curiosity into a paranoid delusion. Now, in reading this satire, we can ask whether Swift
has anything worthwhile to say about mathematics and mathematicians, or is it
all just a comedy of the absurd? And second, do any readers today find it
convincing? We can begin with the least convincing argument, namely that
mathematics is useless. It is safe to say
that Swift failed to convince the public that mathematics has no practical
uses, or that abstract concepts are pointless. Most people today are aware, on
some level, that mathematics is the foundation of modern science, and that as a
result, it has made possible the technology that we take for granted today.
They accept that abstract mathematical and scientific theories are essential
for society, even if they don't understand them. To take just one example, the
public recognizes the importance of the theory of relativity, and admires its
creator, Albert Einstein, even though they may not understand its details, or
know the names of the nineteenth century mathematicians - Gauss, Riemann, and
so on - whose work made this theory possible. But if Swift didn't succeed in discrediting
mathematics, he did manage to give life to many negative stereotypes about
mathematicians themselves through his characterization of the Laputans. Many
people today share his basic assumptions about mathematicians, if not his
hostility toward them. They believe, perhaps unconsciously, that mathematicians
are anti-social nerds who are oblivious to what is going on around them, and
that they are uninterested in the practical applications of mathematics. While Swift's satire of the supposed personality
traits of mathematicians borders on the absurd, he makes a more plausible case
against the mathematical profession as a whole when he describes the Laputan's
isolation and their failure to communicate with the outside world. In many
ways, the image of the Laputans lowering messages to the ground by strings is
central to this satire. The obvious
implication is that mathematicians have brought about their isolation by
failing to explain their subject to the rest of mankind. Here, amidst all of the silliness in this satire,
Swift has found a grain of truth. Mathematicians are isolated from society for
the simple reason that the public knows so little about their subject. Most
people today have no idea what mathematicians do, what the purpose of
mathematics is, or what it has contributed to civilization. The public's
ignorance about mathematics is hardly surprising, for mathematicians themselves
have done very little to enlighten others about their work. One can scarcely
think of a leading mathematician - one comparable, let us say, to a Nobel Prize
winner in science - who has written anything intelligible to the layman about
mathematics or its broader significance for society. This lack of communication
is one of the main reasons why so many people accept the kinds of stereotypes
of mathematicians that Swift puts forth in this satire. People often harbor
stereotypes about foreign cultures, whether ethnic, racial or religious, and
for the public today, mathematicians belong to a very foreign culture. By
failing to communicate about their subject, mathematicians have perpetuated the
public's misconceptions about mathematics. It is these misconceptions that
Swift has used so effectively in this satire.
Perhaps most importantly of all, they take it for
granted that mathematicians are unable to communicate about their subject. In
fact, one of Swift's main claims in this satire is that this failure is due
very nature of mathematics. Mathematics - so he would have us believe - is so
insulated and compartmentalized from the rest of culture, that it creates an intrinsic barrier
between mathematicians and the rest of the human race. Whether or not this
claim has any substance is less important than that the public perceives it to
be true. The real significance of Swift's satire is that it points out the wide
cultural gap between mathematicians and the rest of society. If mathematicians
are ever to bridge this gap, they will have to do more to explain why their
subject is important and what it offers to society. By doing so, they can begin
to overcome the perception that they live on a floating island, unable to
communicate with the rest of the human race. Copyright 2003 by Paul Trow