Nature (November 27, 1884), pp. 76--77.

We live in an age of adventure. Men are ready to join in expeditions to the North Pole or to the interior of the African continent, yet we will venture to say that the work before us describes a vast plain as yet untrodden by any Fellow of the Royal Geographical Society, and teeming with a population of which no example has figured in any of our shows. A few years ago a distinguished mathematician published some speculations on the existence of a book-worm ``cabin'd, cribb'd, confin'd'' within the narrow limits of an ordinary sheet of paper, and another writer bewailed ``the dreary infinities of homaloidal space.'' A third remarks, ``there is no logical impossibility in conceiving the existence of intelligent beings, living on and moving along the surface of any solid body, who are able to perceive nothing but what exists on this surface and insensible to all beyond it.'' How delighted Prof. Helmholtz will be to find, if this Flatland writer is worthy of credence, his conjecture is thus verified. `Flatland' is not the real name of this unknown land (the secret is not divulged), but it is so called here to make its character clear to us Spacedenizens. It is a noteworthy fact that one at least of the Flatlanders expresses himself in remarkably correct English, and singularly after the manner of an ordinary Space-human being; and further, though --- we regret to have to record it --- as a martyr in the cause of the truth of a third dimension, he has spent seven long years in the State jail, yet these memoirs have in some mysterious manner found their way into our hands. There is hope then that some one of our readers may yet expatiate in the broad plain, though the penalty will be, we fear, that he must first become as flat as a pancake and then see to it that his configuration (as a triangle, square, or other figure) is regular. This latter is a sine quâ non in Flatland, because, whatever you are, your configuration must be regular, or woe betide you, and you will shuffle off your mortal coil incontinently.

We will not stop to inquire how this and that have come about, but will endeavour to lay before our readers some of the features of this (to us) new world, though we are informed that it has just entered upon its third millennium.1

In Flatland there is no sun nor any light to make shadows, but there is fog. This, which we on this earth consider to be an unmitigated nuisance, is recognized in that other world ``as a blessing scarcely inferior to air itself, and as the Nurse of Arts and Parent of Sciences.'' If there were no fog, all lines would be equally distinct, whereas under present circumstances, ``by careful and constant experimental observation of comparative dimness and clearness, we are enabled to infer with great exactness the configuration of the object observed.'' It is a necessity of Flatland life to know the north (for instance, it is a point of good breeding to give a lady the north side of the way); this is determined in the absence of any heavenly bodies by a novel (we speak as a Spacedenizen) law of Nature, viz. the constancy of an attraction to the south; however, in temperate regions the southward attraction is scarcely felt, but here again Nature comes to the Flatlander's aid. If he is in an inhabited region, the fact that the houses (mostly regular pentagons; squares and triangles are only allowed in the case of powder-magazines, barracks, and such like, for sufficient reasons) have their roofs towards the north, so that the rain, which always comes from that quarter, may run off and not damage the houses, will help him to get his north point. If, however, he is out in the country far away from trees and houses, there is no help for him until a shower of rain comes. We must now give some description of the inhabitants. The women are all straight lines; the men are other regular figures (if there be hopeless irregularity, which the hospitals cannot cure, then the man is put to death). The lowest orders, policemen, soldiers, and the canaille, are isosceles triangles, their mental calibre being determined by the largeness of smallness of the vertical angle. It is possible for an isosceles triangle to be developed into an equilateral triangle, or the offspring after a few generations may be so developed; in this class are the respectable tradesmen. The professional men and gentlemen are Squares --- our author is a lawyer --- and Pentagons. The Circles (that is, approximations more or less closely to that figure) are the nobility.

Another law of Nature in Flatland is that ``a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility.'' Our author, as appears by the drawing on the cover, has four pentagonal sons and two hexagonal grandsons. We do not clearly gather where the one eye (for Flatlanders appear to be monoculi) is situated, and how locomotion is effected we are not told. It can hardly be by such means as were once suggested by Prof. Clerk Maxwell, for in Flatland you must go steadily forward or dire may be the disaster you will inflict upon your neighbour. There seems to be no lack of Board schools, and there is at least one university, that of Wentbridge (we had by force of habit written Cambridge), where instruction is given in mathematics. A knowledge of this branch of study is obligatory, for since a Flatlander's eye can only move in his world-plane, all the objects, human and otherwise, even the circular priests, appear to be straight lines, and the figure-angles have to be, at any rate approximately, correctly guessed at sight.

Before we close our notice we must return to the description of womankind. The women we have said are straight lines, hence they are very formidable, for they are like needles, and what makes them more to be dreaded is that they have the power of making themselves practically invisible, hence a Flatland female is ``a creature by no means to be trifled with.'' There are, however, certain regulations in force which diminish the dangers resulting from having a woman about the house. There is an entrance for her on the eastern side of the house, by which she must enter ``in a becoming and respectful manner''; she must also, when walking, keep up her peace-cry, under penalty of death, and if she has fits, is given to sneezing, or in any way is liable to any sudden movement, there is but one cure for such movements, and that is instant destruction. Though involuntary and sudden motions are thus summarily dealt with, yet if she is any public place she must keep up a gentle ``back-motion,'' and thus she is less liable to be invisible to her neighbours. Happily fashion exercises its potent sway in Flatland female society, as elsewhere, for we learn that ``the rhythmical, and, if I may so say, well-modulated undulation of the back in our ladies of circular rank is envied and imitated by the wife of a common Equilateral, who can achieve nothing beyond a mere monotonous swing, like the ticking of a pendulum.'' Owing to their unfortunate configuration they are inferior in all good qualities to the very lowest of the Isosceles, being entirely devoid of brain-power, and they have ``neither reflection, judgment, nor forethought, and hardly any memory.'' This is but a poor account, but we must bear in mind that it is an ex parte description by a Square who may at some time have suffered a disappointment at the hands of a lady. We shall be glad (though we can hardly expect such a result) --- now that tidings have come from this little-known country --- if some female will favour us with her view of the state of matters in Flatland. At birth a female is about an inch long, a tall adult woman reaches about a foot. The length of the sides of an adult male of every class may be said to be three feet or a little more.

The book consists of two parts --- This World, i.e. of Flatland, in twelve sections, and Other Worlds, in ten sections. The whole is very cleverly worked out, and many passages descriptive of events in the past history of the country at times force upon one the thought that after all the book may have been compiled by a Spacedenizen, and that he is quietly laughing in his sleeve and saying, ``de te Fabula narratur.'' However this may be, Flatlander or Spacelander, there is a slip in the note on p. 64, and for ``Flatland'' should be read ``Spaceland.''

We commend `A Square's' book to any of our readers who have a leisure hour from severer studies, and we believe when they have read it they will say ``the tenth part of the humour has not been suggested''2

R. Tucker

1From the secret Archives it appears that at the commencement of each millennium a Sphere descended into the midst of the Council of Circles proclaiming the great truth for the attempted teaching of which our author is in bonds.

2We may mention as specially humorous the chapters in which the Square is initiated into some of the mysteries of tri-dimensional space by the spherical stranger.