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Of Recognition By Sight

From: Flatland

I am about to appear very inconsistent. In the previous sections I
have said that all figures in Flatland present the appearance of a
straight line; and it was added or implied, that it is consequently
impossible to distinguish by the visual organ between individuals of
different classes: yet now I am about to explain to my Spaceland
critics how we are able to recognize one another by the sense of sight.

If however the Reader will take the trouble to refer to the passage in
which Recognition by Feeling is stated to be universal, he will find
this qualification--"among the lower classes." It is only among the
higher classes and in our more temperate climates that Sight
Recognition is practised.

That this power exists in any regions and for any classes is the result
of Fog; which prevails during the greater part of the year in all parts
save the torrid zones. That which is with you in Spaceland an unmixed
evil, blotting out the landscape, depressing the spirits, and
enfeebling the health, is by us recognized as a blessing scarcely
inferior to air itself, and as the Nurse of arts and Parent of
sciences. But let me explain my meaning, without further eulogies on
this beneficent Element.

If Fog were non-existent, all lines would appear equally and
indistinguishably clear; and this is actually the case in those unhappy
countries in which the atmosphere is perfectly dry and transparent.
But wherever there is a rich supply of Fog, objects that are at a
distance, say of three feet, are appreciably dimmer than those at the
distance of two feet eleven inches; and the result is that 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.

An instance will do more than a volume of generalities to make my
meaning clear.

Suppose I see two individuals approaching whose rank I wish to
ascertain. They are, we will suppose, a Merchant and a Physician, or
in other words, an Equilateral Triangle and a Pentagon; how am I to
distinguish them?

It will be obvious, to every child in Spaceland who has touched the
threshold of Geometrical Studies, that, if I can bring my eye so that
its glance may bisect an angle (A) of the approaching stranger, my view
will lie as it were evenly between the two sides that are next to me
(viz. CA and AB), so that I shall contemplate the two impartially, and
both will appear of the same size.

Now in the case of (1) the Merchant, what shall I see? I shall see a
straight line DAE, in which the middle point (A) will be very bright
because it is nearest to me; but on either side the line will shade
away RAPIDLY TO DIMNESS, because the sides AC and AB RECEDE RAPIDLY
INTO THE FOG and what appear to me as the Merchant's extremities, viz.
D and E, will be VERY DIM INDEED.

On the other hand in the case of (2) the Physician, though I shall here
also see a line (D'A'E') with a bright centre (A'), yet it will shade
away LESS RAPIDLY to dimness, because the sides (A'C', A'B') RECEDE
LESS RAPIDLY INTO THE FOG: and what appear to me the Physician's
extremities, viz. D' and E', will not be NOT SO DIM as the extremities
of the Merchant.

The Reader will probably understand from these two instances how--after
a very long training supplemented by constant experience--it is
possible for the well-educated classes among us to discriminate with
fair accuracy between the middle and lowest orders, by the sense of
sight. If my Spaceland Patrons have grasped this general conception,
so far as to conceive the possibility of it and not to reject my
account as altogether incredible--I shall have attained all I can
reasonably expect. Were I to attempt further details I should only
perplex. Yet for the sake of the young and inexperienced, who may
perchance infer--from the two simple instances I have given above, of
the manner in which I should recognize my Father and my Sons--that
Recognition by sight is an easy affair, it may be needful to point out
that in actual life most of the problems of Sight Recognition are far
more subtle and complex.

If for example, when my Father, the Triangle, approaches me, he happens
to present his side to me instead of his angle, then, until I have
asked him to rotate, or until I have edged my eye around him, I am for
the moment doubtful whether he may not be a Straight Line, or, in other
words, a Woman. Again, when I am in the company of one of my two
hexagonal Grandsons, contemplating one of his sides (AB) full front, it
will be evident from the accompanying diagram that I shall see one
whole line (AB) in comparative brightness (shading off hardly at all at
the ends) and two smaller lines (CA and BD) dim throughout and shading
away into greater dimness towards the extremities C and D.

But I must not give way to the temptation of enlarging on these topics.
The meanest mathematician in Spaceland will readily believe me when I
assert that the problems of life, which present themselves to the
well-educated--when they are themselves in motion, rotating, advancing
or retreating, and at the same time attempting to discriminate by the
sense of sight between a number of Polygons of high rank moving in
different directions, as for example in a ball-room or
conversazione--must be of a nature to task the angularity of the most
intellectual, and amply justify the rich endowments of the Learned
Professors of Geometry, both Static and Kinetic, in the illustrious
University of Wentbridge, where the Science and Art of Sight
Recognition are regularly taught to large classes of the ELITE of the

It is only a few of the scions of our noblest and wealthiest houses,
who are able to give the time and money necessary for the thorough
prosecution of this noble and valuable Art. Even to me, a
Mathematician of no mean standing, and the Grandfather of two most
hopeful and perfectly regular Hexagons, to find myself in the midst of
a crowd of rotating Polygons of the higher classes, is occasionally
very perplexing. And of course to a common Tradesman, or Serf, such a
sight is almost as unintelligible as it would be to you, my Reader,
were you suddenly transported to my country.

In such a crowd you could see on all sides of you nothing but a Line,
apparently straight, but of which the parts would vary irregularly and
perpetually in brightness or dimness. Even if you had completed your
third year in the Pentagonal and Hexagonal classes in the University,
and were perfect in the theory of the subject, you would still find
there was need of many years of experience, before you could move in a
fashionable crowd without jostling against your betters, whom it is
against etiquette to ask to "feel," and who, by their superior culture
and breeding, know all about your movements, while you know very little
or nothing about theirs. In a word, to comport oneself with perfect
propriety in Polygonal society, one ought to be a Polygon oneself.
Such at least is the painful teaching of my experience.

It is astonishing how much the Art--or I may almost call it
instinct--of Sight Recognition is developed by the habitual practice of
it and by the avoidance of the custom of "Feeling." Just as, with you,
the deaf and dumb, if once allowed to gesticulate and to use the
hand-alphabet, will never acquire the more difficult but far more
valuable art of lip-speech and lip-reading, so it is with us as regards
"Seeing" and "Feeling." None who in early life resort to "Feeling" will
ever learn "Seeing" in perfection.

For this reason, among our Higher Classes, "Feeling" is discouraged or
absolutely forbidden. From the cradle their children, instead of going
to the Public Elementary schools (where the art of Feeling is taught,)
are sent to higher Seminaries of an exclusive character; and at our
illustrious University, to "feel" is regarded as a most serious fault,
involving Rustication for the first offence, and Expulsion for the

But among the lower classes the art of Sight Recognition is regarded as
an unattainable luxury. A common Tradesman cannot afford to let his
son spend a third of his life in abstract studies. The children of the
poor are therefore allowed to "feel" from their earliest years, and
they gain thereby a precocity and an early vivacity which contrast at
first most favourably with the inert, undeveloped, and listless
behaviour of the half-instructed youths of the Polygonal class; but
when the latter have at last completed their University course, and are
prepared to put their theory into practice, the change that comes over
them may almost be described as a new birth, and in every art, science,
and social pursuit they rapidly overtake and distance their Triangular

Only a few of the Polygonal Class fail to pass the Final Test or
Leaving Examination at the University. The condition of the
unsuccessful minority is truly pitiable. Rejected from the higher
class, they are also despised by the lower. They have neither the
matured and systematically trained powers of the Polygonal Bachelors
and Masters of Arts, nor yet the native precocity and mercurial
versatility of the youthful Tradesman. The professions, the public
services, are closed against them, and though in most States they are
not actually debarred from marriage, yet they have the greatest
difficulty in forming suitable alliances, as experience shews that the
offspring of such unfortunate and ill-endowed parents is generally
itself unfortunate, if not positively Irregular.

It is from these specimens of the refuse of our Nobility that the great
Tumults and Seditions of past ages have generally derived their
leaders; and so great is the mischief thence arising that an increasing
minority of our more progressive Statesmen are of opinion that true
mercy would dictate their entire suppression, by enacting that all who
fail to pass the Final Examination of the University should be either
imprisoned for life, or extinguished by a painless death.

But I find myself digressing into the subject of Irregularities, a
matter of such vital interest that it demands a separate section.

Next: Concerning Irregular Figures

Previous: Of Our Methods Of Recognizing One Another

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