Of Recognition by Sight

I am about to appear very inconsistent. In 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 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 nonexistent, 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 a 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 his 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 into 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 into 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 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 round 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 ballroom 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 States.

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 into our 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 that
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
second.

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 competitors.

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 shows 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.