The Architect (Nov. 15, 1884), pp. 326--327.
In this book we have an account of a country that is not to be found on any atlas hitherto
published, and is unknown to the enterprising followers of Messrs. Cook & Sons. But as
the author, Mr. Square, is a native of Flatland, we can consider his account to be as
veracious as the descriptions of other remarkable places which have been written by
Lemuel Gulliver. The peculiarity of Flatland is that everything in it is absolutely
deficient of a third dimension. There are only two dimensions. Men, women, cattle,
trees, houses, are, like the subjects of Euclid's six books, either lines or surfaces. Mr.
Square tells us-and we have no reasons to doubt his statement-that statesmen in Flatland
are circles, professors are squares, tradesmen are triangles (the equilateral being
considered the most respectable), soldiers are isosceles triangles, each having a narrow
base and sharp apex. Pope says that most women have no character at all, and the
Flatland ladies are only straight lines. There is, however, compensation in everything,
and, by the peculiarity of their organization, they are made most dangerous to the men,
for whether seen in front or from behind, they are aware of the presence of danger. To
prevent accidents, all kinds of wise precautions have to be taken against womankind.
Two doors are made to the houses, a large one for the men, a narrow one for the women;
extremely small rooms are also provided for the latter, in order that their male friends
may be comparatively safe. In the houses there are many peculiarities besides doors.
Flatland architects are great in planning, and it is a pity that one of them was not induced
to study the conditions of the competition for the Admiralty and War Offices. We do not
suppose that the contest would attract the least eminent practitioner in Flatland, but some
of the younger members might have been inspired to send over a few suggestions.
Considering that in Flatland it is impossible to see the shape of anyone for as one's self
and one's friends would be both on one plane, each must seem only as straight lines to
the other, whatever be their normal form. May we not therefore conclude that the author
can only have discovered the appearance of his neighbors by a philosophical course of
experience, that is, by having in the jostling of life had to feel (for length and breadth can
surely have feelings) their various sides and angles? If, however, we admit the test of
experience we might be tempted to say that Mr. Square is not so impartial as he professes
to be and his statement that the female sex consists of straight lines, dangerously acute at
each end, is probably evidence that Mr. Square is rather advanced in years, and has been
jilted more than once. Unless mathematical truth, as it is expounded in Cambridge, does
not hold in Flatland, we see no reason why the women should not be described as ellipses
instead of lines. They would thus be more perfect than the circular statesmen who have but one centre to their being, whereas an elliptical woman would have two foci and an endless variety of outline. Beings may shrink with age in Flatland as elsewhere, and although Mr. Square probably was constituted of honest right angles when he was young, his sides may have since become concave, his angles, more acute, and who knows if he has not reached the formation of a cross? In that case he is, when at home, no doubt more than a match for his wife, offering four dangerous points to her two. We might even go so far as to say that the origin of the narrow doors in Flatland houses arose from the necessity of giving facility for escape of women when pursued by their irate lords. But we speak under correction, and shall be glad to hear what Mr. Square has to say on this subject. Mr. Square is also a traveller, and has visited Lineland, a country which consists of a straight line. The inhabitants are also straight lines of various dimensions, moving backwards and forwards in their linear world. Mr. Square relates how, on one occasion, he frightened the King of Lineland by his appearance. No inhabitant of Lineland could conceive, far less explain, the existence of such a form; their was no word in their language to express such a surface, the idea of two dimensions being absolutely foreign to their nature. Spaceland, the land in which we live (consult Stieler's atlas), was also visited. Mr. Square cannot by any effort of his intellect comprehend the third dimension which forms solids, and therefore he labours under some difficulty in travelling among us. But our land appears to him like some dream of light, of a brilliancy surpassingly great and magnificent, but inexpressible. The encomiums of a man of his experience are flattering. Nevertheless, he has no doubt of the reality of Spaceland. When he was professor of mathematics in Flatland Mr. Square taught that quantities exist not only in their first or second powers, which are accounted for by lines and surfaces, but that they can be elevated to an infinity of powers. Therefore, although he cannot conceive anything beyond surfaces to represent mathematical results, yet he cannot resist the conclusion that there are other dimensions, other worlds, other realities besides those his brain is capable of comprehending. His speculations on mathematics are accordingly far more notable than those of Sir William Rowan Hamilton when he predicted the form which objects
must assume when seen through a mineral of a certain form. There are readers who may
hesitate to accept everything that is said by Mr. Square, especially if they only once read
his book. Hamlet tells us there are more things in heaven and earth than are dreamt of in
our philosophy, but while we repeat the lines glibly we hardly accept them as words of
wisdom. The inhabitants of Flatland, in spite of their good sense, may likewise hesitate
in believing all Mr. Square can tell them about ourselves. Meanwhile we recommend all
our friends to read Flatland. They will find in it as limitless fields for their thought as in Carlyle's Sartor Resartus, with the great advantage that Flatland is written in good English instead of debased German.