Section 6. 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 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 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?
<>
<>
C (1)
|\ - _ D
| \ ||- _
| \ || - _
| <--- >|| -----------+(> Eye-glance
___C' (2) | / A|| _ -
___--- \ - _D' | / ||_ -
__--- \ || - _ |/ _ - E
| \ || - _ B
| \ || - _
| Eye-glance \ || - _
| <----------- A'>|| ------------------------+(>
| / || _ -
| / || _ -
|__ / || _ -
---___ / || _ -
---___/ _ -E'
B'
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 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
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.
<>
<>
/\ - _ C
/ \ || _
/ \ || - _
/ \|| - _
| A || - _
| || -+(> (Eye)
| B || _ -
\ /|| _ -
\ / || _ -
\ / || -
\/ _ - 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 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 lipspeech 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 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.
