Flatland: A Romance of Many Dimensions
helps. It is with us a Law of Nature that the brain of the Isosceles
class shall begin at half a degree, or thirty minutes, and shall
increase (if it increases at all) by half a degree in every generation;
until the goal of 60 degrees is reached, when the condition of serfdom
is quitted, and the freeman enters the class of Regulars.
Consequently, Nature herself supplies us with an ascending scale or
Alphabet of angles for half a degree up to 60 degrees, Specimens of
which are placed in every Elementary School throughout the land. Owing
to occasional retrogressions, to still more frequent moral and
intellectual stagnation, and to the extraordinary fecundity of the
Criminal and Vagabond Classes, there is always a vast superfluity of
individuals of the half degree and single degree class, and a fair
abundance of Specimens up to 10 degrees. These are absolutely
destitute of civic rights; and a great number of them, not having even
intelligence enough for the purposes of warfare, are devoted by the
States to the service of education. Fettered immovably so as to remove
all possibility of danger, they are placed in the class rooms of our
Infant Schools, and there they are utilized by the Board of Education
for the purpose of imparting to the offspring of the Middle Classes
that tact and intelligence of which these wretched creatures themselves
are utterly devoid.
In some States the Specimens are occasionally fed and suffered to exist
for several years; but in the more temperate and better regulated
regions, it is found in the long run more advantageous for the
educational interests of the young, to dispense with food, and to renew
the Specimens every month--which is about the average duration of the
foodless existence of the Criminal class. In the cheaper schools, what
is gained by the longer existence of the Specimen is lost, partly in
the expenditure for food, and partly in the diminished accuracy of the
angles, which are impaired after a few weeks of constant "feeling".
Nor must we forget to add, in enumerating the advantages of the more
expensive system, that it tends, though slightly yet perceptibly, to
the diminution of the redundant Isosceles population--an object which
every statesman in Flatland constantly keeps in view. On the whole
therefore--although I am not ignorant that, in many popularly elected
School Boards, there is a reaction in favour of "the cheap system" as
it is called--I am myself disposed to think that this is one of the
many cases in which expense is the truest economy.
But I must not allow questions of School Board politics to divert me
from my subject. Enough has been said, I trust, to shew that
Recognition by Feeling is not so tedious or indecisive a process as
might have been supposed; and it is obviously more trustworthy than
Recognition by hearing. Still there remains, as has been pointed out
above, the objection that this method is not without danger. For this
reason many in the Middle and Lower classes, and all without exception
in the Polygonal and Circular orders, prefer a third method, the
description of which shall be reserved for the next section.
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?
[ASCII approximation follows]
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.
[ASCII approximation follows]
/\ - _ 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,