THE AGITATION for the Universal Colour Bill1 continued for three years; and up to the last moment of that period it seemed as though Anarchy were destined to triumph.
A whole army of Polygons, who turned out to fight as private soldiers, was utterly annihilated by a superior force of Isosceles Triangles—the Squares and Pentagons meanwhile remaining neutral.Worse than all, some of the ablest Circles fell a prey to conjugal fury. Infuriated by political animosity, the wives in many a noble household wearied their lords with prayers to give up their opposition to the Colour Bill; and some, finding their entreaties fruitless, fell on and slaughtered their innocent children and husband, perishing themselves in the act of carnage. It is recorded that during that triennial agitation no less than twenty-three Circles2 perished in domestic discord.
Great indeed was the peril. It seemed as though the Priests had no choice between submission and extermination; when suddenly the course of events was completely changed by one of those picturesque incidents which Statesmen ought never to neglect, often to anticipate, and sometimes perhaps to originate, because of the absurdly disproportionate power with which they appeal to the sympathies of the populace.
It happened that an Isosceles of a low type, with a brain little if at all above four degrees—accidentally dabbling in the colours of some Tradesman whose shop he had plundered—painted himself, or caused himself to be painted (for the story varies) with the twelve colours of a Dodecagon.3 Going into the Market Place he accosted in a feigned voice a maiden, the orphan daughter of a noble Polygon, whose affection in former days he had sought in vain; and by a series of deceptions— aided, on the one side, by a string of lucky accidents too long to relate, and, on the other, by an almost inconceivable fatuity and neglect of ordinary precautions on the part of the relations of the bride—he succeeded in consummating the marriage. The unhappy girl committed suicide on discovering the fraud to which she had been subjected.
When the news of this catastrophe spread from State to State the minds of the Women were violently agitated. Sympathy with the miserable victim and anticipations of similar deceptions for themselves, their sisters, and their daughters, made them now regard the Colour Bill in an entirely new aspect. Not a few openly avowed themselves converted to antagonism; the rest needed only a slight stimulus to make a similar avowal. Seizing this favourable opportunity, the Circles hastily convened an extraordinary Assembly of the States; and besides the usual guard of Convicts, they secured the attendance of a large number of reactionary Women.
Amidst an unprecedented concourse, the Chief Circle of those days—by name Pantocyclus— arose to find himself hissed and hooted by a hundred and twenty thousand Isosceles. But he secured silence by declaring that henceforth the Circles would enter on a policy of Concession; yielding to the wishes of the majority, they would accept the Colour Bill. The uproar being at once converted to applause, he invited Chromatistes, the leader of the Sedition, into the centre of the hall, to receive in the name of his followers the submission of the Hierarchy. Then followed a speech, a masterpiece of rhetoric, which occupied nearly a day in the delivery, and to which no summary can do justice.
With a grave appearance of impartiality he declared that as they were now finally committing themselves to Reform or Innovation, it was desirable that they should take one last view of the perimeter of the whole subject, its defects as well as its advantages. Gradually introducing the mention of the dangers to the Tradesmen, the Professional Classes and the Gentlemen, he silenced the rising murmurs of the Isosceles by reminding them that, in spite of all these defects, he was willing to accept the Bill if it was approved by the majority. But it was manifest that all, except the Isosceles, were moved by his words and were either neutral or averse to the Bill.
Turning now to the Workmen he asserted that their interests must not be neglected, and that, if they intended to accept the Colour Bill, they ought at least to do so with full view of the consequences. Many of them, he said, were on the point of being admitted to the class of the Regular Triangles; others anticipated for their children a distinction they could not hope for themselves. That honourable ambition would now have to be sacrificed.With the universal adoption of Colour, all distinctions would cease; Regularity would be confused with Irregularity; development would give place to retrogression; the Workman would in a few generations be degraded to the level of the Military, or even the Convict Class; political power would be in the hands of the greatest number, that is to say the Criminal Classes, who were already more numerous than the Workmen, and would soon out-number all the other Classes put together when the usual Compensative Laws of Nature were violated.
A subdued murmur of assent ran through the ranks of the Artisans, and Chromatistes, in alarm, attempted to step forward and address them. But he found himself encompassed with guards and forced to remain silent while the Chief Circle in a few impassioned words made a final appeal to the Women, exclaiming that, if the Colour Bill passed, no marriage would henceforth be safe, no woman’s honour secure; fraud, deception, hypocrisy would pervade every household; domestic bliss would share the fate of the Constitution and pass to speedy perdition. “Sooner than this,” he cried, “Come death.”
At these words, which were the preconcerted signal for action, the Isosceles Convicts fell on and transfixed the wretched Chromatistes; the Regular Classes, opening their ranks, made way for a band of Women who, under direction of the Circles, moved, back foremost, invisibly and unerringly upon the unconscious soldiers; the Artisans, imitating the example of their betters, also opened their ranks. Meantime bands of Convicts occupied every entrance with an impenetrable phalanx.
The battle, or rather carnage, was of short duration.4 Under the skilful generalship of the Circles almost every Woman’s charge was fatal and very many extracted their sting uninjured, ready for a second slaughter. But no second blow was needed; the rabble of the Isosceles did the rest of the business for themselves. Surprised, leader-less, attacked in front by invisible foes, and finding egress cut off by the Convicts behind them, they at once—after their manner—lost all presence of mind, and raised the cry of “treachery.” This sealed their fate. Every Isosceles now saw and felt a foe in every other. In half an hour not one of that vast multitude was living; and the fragments of seven score thousand of the Criminal Class slain by one another’s angles attested the triumph of Order.
The Circles delayed not to push their victory to the uttermost. The Working Men they spared but decimated. The Militia of the Equilaterals was at once called out; and every Triangle suspected of Irregularity on reasonable grounds, was destroyed by Court Martial, without the formality of exact measurement by the Social Board. The homes of the Military and Artisan classes were inspected in a course of visitations extending through upwards of a year; and during that period every town, village, and hamlet was systematically purged of that excess of the lower orders which had been brought about by the neglect to pay the tribute of Criminals to the Schools and University, and by the violation of the other natural Laws of the Constitution of Flatland. Thus the balance of classes was again restored.
Needless to say that henceforth the use of Colour was abolished, and its possession prohibited. Even the utterance of any word denoting Colour, except by the Circles or by qualified scientific teachers, was punished by a severe penalty. Only at our University in some of the very highest and most esoteric classes—which I myself have never been privileged to attend—it is understood that the sparing use of Colour is still sanctioned for the purpose of illustrating some of the deeper problems of mathematics.5 But of this I can only speak from hearsay.
Elsewhere in Flatland, Colour is now non-existent. The art of making it is known to only one living person, the Chief Circle for the time being; and by him it is handed down on his death-bed to none but his Successor. One manufactory alone produces it; and, lest the secret should be betrayed, the Workmen are annually consumed, and fresh ones introduced. So great is the terror with which even now our Aristocracy looks back to the far-distant days of the agitation for the Universal Colour Bill.
1 Here Abbott is commenting on the proliferation of “universal rights” that began in the Victorian era. This was a time when the English social system was struggling toward greater equality—first for the common man and then for women, be they noble or common. Were it not for the rigidly conservative views of Queen Victoria, that goal might have been attained much sooner.
In 1832 the class of men able to vote in elections to Parliament was widened significantly, and the Reform Bill of 1867 widened it further, but not to women. The 1792 publication of A Vindication of the Rights of Woman by Mary Wollstonecraft (1759–1797) had given birth to what became known later as Woman Suffrage, and later still as the Women’s Rights or Feminist Movement. In the 1870s Parliament received a petition with 3 million signatures (the population of the United Kingdom was then about 28 million) urging that women be allowed to vote, but the prime ministers of the day—Gladstone and Disraeli—dared not oppose Her Majesty, so the issue was shelved. However, in 1869 some women were allowed to vote in municipal (local) elections. In 1897 all of the relevant organizations merged into a single National Union of Woman Suffrage Societies. Emmeline Pankhurst (1858–1928), her daughter Christabel (1880–1958), and the publicity stunts of the “suffragettes” kept the political pot boiling. After World War I, in which women had done large numbers of jobs previously restricted to men (such as manufacturing munitions), opposition evaporated. An act of Parliament extending the vote to women aged thirty or over passed in the House of Commons in 1917 and was ratified in the second chamber, the House of Lords, in 1918. In 1928 the voting age was reduced to twenty-one, the same as for men. (It is now eighteen.) Similar events unfolded in many other countries, notably the United States, beginning with Lucretia Mott (1793–1880) and Elizabeth Cady Stanton (1815–1902), whose advocacy of the antislavery movement led them into a general fight for women’s rights. The first country to give women the vote was New Zealand in 1893, followed by Australia in 1902.
Victorian intellectuals would have spent hours discussing such issues. Abbott was personally acquainted with many politicians and other leading figures of his time, and no doubt he saw Flatland as an opportunity to put some of his own views into print.
2 In nongeometric contexts, Abbott employs non-constructible numbers—that is, numbers such that the polygon with that many sides cannot be constructed using ruler and compasses (and therefore makes no appearance in Euclid).
3 This is a twelve-sided polygon. The first edition of Flatland (and some modern editions, such as the Shambhala one, which appears to have been based on the first edition) has “dodecahedron.” This is a solid with twelve pentagonal faces.
4 The Victorians were no strangers to the use of military force to suppress the rights of subject peoples, and the best-known instance is the Indian Mutiny of 1857. India had in some sense been considered British territory since 1600, when the East India Company was given monopoly trading rights. In 1818 the British Empire in India became the British Empire of India; about half of India was ruled by Indians but was stripped of any serious military power and was split into about 360 politically independent units. In 1857 Indian troops (sepoys) under the East India Company embarked on a widespread rebellion against British rule. This is sometimes called the Sepoy Mutiny, but it went much deeper; in particular, the Hindu religion was being challenged by Christian missionaries, causing considerable resentment. The new Enfield rifle offered a pretext for revolt: Loading it necessitated biting off the ends of cartridges, and the sepoys believed—apparently with some justification—that the grease used as lubrication for the cartridges was made from a mixture of pig and cow fat. This was therefore an insult both to Muslims and to Hindus. In April 1857, se-poys at Meerut refused to use the cartridges and were jailed for lengthy terms, in irons. On May 10 their comrades mutinied, shot their British officers, and marched to Delhi. There they persuaded the former Mughal emperor Bahâdur Shâh II (1775– 1862) to be named leader of the revolt, which spread to Agrâ, Cawnpore, and Lucknow. Fighting went on until peace was officially restored on 8 July 1858. There were atrocities on both sides, but British reprisals far outweighed the actions that caused them. Hundreds of sepoys were shot from cannons, and thousands of civilians were killed after perfunctory trials or no trials at all. Despite Bahâdur Shâh’s age—he was over eighty—and the fact that he had been forced to accept nominal leadership, he and his family were exiled to Burma (now Myanmar). Britain blamed the East India Company for the mess, although British troops had been trampling all over the subcontinent for centuries, and in 1858 the Government of India Act transferred power over India to the government of Queen Victoria. In 1876 she took on the title Empress of India.
5 Today’s mathematicians, faced with the need to visualize complicated multidimensional geometry, often resort to the same remedy as the Flatlanders. Color can be used to distinguish different features of a complicated diagram with many overlapping components, making it easy to focus on any particular one—in effect imagining a “section” of the diagram at the appropriate level in the color dimension by ignoring all other colors. Or, especially in applications to science and commerce, the values of certain variables—“dimensions”—can be color-coded. In representations of the celebrated Mandelbrot set, a fractal introduced by Benoit Mandelbrot and one of the most complex forms ever specified by a simple equation, colors encode how rapidly a moving point escapes from some given region. See Flatter-land chapter 5, “One and a Quarter Dimensions,” and The Beauty of Fractals by Heinz-Otto Peitgen and Peter H. Richter. In Symmetry in Chaos, by Michael J. Field and Martin Golubitsky, color is used to encode the probability that a moving point lies in a given region of a dynamical attractor. The latter two of these books contain a wealth of beautiful color images.