Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott: Part 1, Sections 6 - 7

Episode Transcript

Speaker 1 (00:00):
Part one, Sections six and seven of Flatland. This LibriVox
recording is in the public domain recording by Ruth Golding. Flatland,
A Romance of Many Dimensions by Edwin Abbot Abbot, Part one,
Section six of Recognition by Sight. I am about to

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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

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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

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only among the higher classes and in our more temperate climates,
that site recognition is practiced. 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

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with you in Spaceland and 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

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beneficent element. If fog were non existent, all lines would
appear equally and indistinct, wishably 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

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rich supply of fog, objects that are at a distant,
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

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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

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triangle and a pentagon. How am I to distinguish them?
Reader's note. The following paragraph makes reference to an accompanying diagram.
Diagram one is a rightwood pointing equilateral triangle, the vertical
left hand side of which is marked B C, the
other two sides being marked B, A and C A.

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Dotted lines are drawn from B and C to a
point further to the right to form an Isosceles triangle.
The far right hand point of this triangle represents the
eye of the observer, and a horizontal dotted arrow pointing
left from it indicates his eye glance. A broad vertical

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line DAE is drawn to indicate what the observer sees.
DAE is bright at the center and darkens sharply towards
its ends. End of Reader's note. It will be obvious
to every child in spacelanfe and who has touched the
threshold of geometrical studies, that if I can bring my

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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. C,
A and A B, so that I shall contemplate the
two impartially, and both will appear of the same size. Now,

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in the case of one 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

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A B recede rapidly into the fog, And what appear
to me as the merchant's extremities viz. D and E
will be very dim. Indeed, Note the following paragraph makes
reference to an accompanying diagram. Diagram two is a regular
pentagon sitting on a horizontal base, with C one at

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the apex, A one at middle right, and B one
at lower right. Longer dotted lines are drawn out towards
the right, upwards from B one and downwards from C
one to form an irregular pentagon. The far right hand
point of the extended pentagon represents the eye of the observer,

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and a dotted arrow pointing from it towards the center
of the lower left edge of the pentagon indicates his
eye glance. Again, a broad line D one A one
E one parallel to the lower left edge of the
pentagon is drawn to indicate what the observer sees. D

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one A one E one is bright at the center
and darkens very gradually towards its end end of reader's note.
On the other hand, in the case of two, the physician,
though I shall here also see a line D one
A one E one with a bright center A one,

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Yet it will shade away less rapidly into dimness, because
the sides A one, C one, A one, B one
recede less rapidly into the fog, And what appear to
me the physician's extremities is D one and E one
will be not so dim as the extremities of the merchant.

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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

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grasped this general cancer 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

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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

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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 as straight line or
in other words, a woman reader's note. The following paragraph

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makes reference to an accompanying diagram. The diagram shows a
hexagon with points at top and bottom. The vertical right
hand side is marked ab Dotted lines are drawn downward
from the topmost and upward from the bottomost points of
the hexagon, and extended to the right until they meet,

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forming an irregular pentagon. The far right hand point of
the pentagon represents the eye of the observer. The line
A B is extended to where it meets the dotted
lines to form a broad vertical line at C ab D.
The middle portion of this line AB is bright, and

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the outer portions darken towards C and D end of
Reader's note again, when I'm in the company of one
of my two hexagonal grandsons, contum plating one of his
sides A B full front, it will be evident from
the accompanying diagram that I shall see one whole line

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A B in comparative brightness, shading off hardly at all
at the ends, and two smaller lines C, A and
B D dim throughout and shading away into greater dimness
toward the extremities C and D. But I must not
give way to the temptation of enlarging on these topics.

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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,

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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 site recognition are regularly

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taught to large classes of the elite of the States,
it is only a few of the science 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 means standing and the grandfather of two most hopeful

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and perfectly regular hexagons, defined 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 site 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

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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

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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

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a word, to comport one's self with perfect propriety in
polygonal society, one ought to be a polygon one's self. 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 site recognition, is developed by the

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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

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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

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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 offense, and expulsion for the second. But among the

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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

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and an early vivacity, which contrast at first most favorably
with the inert, undeveloped, and listless behavior 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

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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

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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 useful tradesmen. The professions the public services

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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

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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

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by enacting that all who failed 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, Section seven

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of irregular figures. Throughout the previous pages, I have been
assuming what perhaps should have been laid down at the
beginning as a distinct and fundamental proposition, that every human
being in flatland is a regular figure, that is to say,
of regular construction. By this I mean that a woman

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must not only be a line, but a straight line.
That an artisan or soldier must have two of his
sides equal, that tradesmen must have three sides equal, lawyers,
of which class I am a humble member, four sides equal,
and generally, that in every polygon all the sides must

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be equal. The size of the sides would, of course
depend upon the age of the individual. A female at
birth would be about an inch long, while a tall
adult woman might extend to a foot. As to the
males of every class, it may be roughly said that
the length of an adult sides, when added together, is

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three feet or a little more. But the size of
our sides is not under consideration. I am speaking of
the equality of sides, and it does not need much
reflection to see that the whole of the social life
in Flatland rests upon the fundamental fact that nature wills
all figures to have their sides equal. If our sides

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were unequal, our angles would be unequal. Instead of its
being sufficient to feel or estimate by sight a single
angle in order to determine the form of an individual,
it would be necessary to ascertain each angle by the
experiment of feeling. But life would be too short for

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such a tedious groping. The whole science and art of
sight recognition would at once perish. Feeling, so far as
it is an art, would not long survive. Intercourse would
become perilous or impossible. There would be an end to
all confidence all forethought. No one would be safe in

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making the most simple social arrangements. In a word, civilization
would relapse into barbarism. Am I going too fast to
carry my readers with me to these obvious conclusions. Surely
a moment's reflection and a single instance from common life
must convince everyone that our whole social system is based

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upon regularity or equality of angles. You meet, for example,
two or three tradesmen in the street, whom you recognize
at once to be tradesmen by a glance at their
angles and rapidly bedimmed sides, and you ask them to
step into your house to lunch. This you do at

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present with perfect confidence, because everyone knows to an inch
or two the area occupied by an adult triangle. But
imagine that your tradesman drags behind his regular and respectable
vertex a parallelogram of twelve or thirteen inches in diagonal.
What are you to do with such a monster sticking

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fast in your house door? But I am insulting the
intelligence of my readers by accumulating details which must be
patent to everyone who enjoys the advantages of a residence
in spaceland. Obviously, the measurements of a single angle would
no longer be sufficient under such portentous circumstances. One's whole

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life would be taken up in feeling or surveying the
perimeter of one's acquaintances. Already, the difficulties of avoiding a
collision in a crowd are enough to tax the sagacity
of even a well educated square. But if no one
could calculate the regularity of a single figure in the company,

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all would be chaos and confusion, and the slightest panic
would cause serious injuries, or if there happened to be
any women or soldiers present, perhaps considerable loss of life.
Expediency therefore concurs with nature in stamping the seal of
its approval upon regularity of conformation. Nor has the law

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been backward in seconding their efforts. Irregularity of figure means
with us the same as or more than a combination
of moral obliquity and criminality with you, and is treated accordingly.
There are not wanting. It is true some promulgators of

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paradoxes who maintain that there is no necessary connection between
geometrical and moral irregularity. The irregular, they say, is from
his birth, scouted by his own parents, derided by his
brothers and sisters, neglected by the domestics, scorned and suspected

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by societ society, and excluded from all posts of responsibility, trust,
and useful activity. His every movement is jealously watched by
the police till he comes of age and presents himself
for inspection. Then he is either destroyed if he is
found to exceed the fixed margin of deviation, or else

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immured in a government office as a clerk of the
seventh class, prevented from marriage, forced to drudge at an
uninteresting occupation for a miserable stipend, obliged to live and
board at the office, and to take even his vacation
under close supervision. What wonder that human nature, even in

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the best and purest, is embittered and perverted by such surroundings.
All this very plausible reasoning does not convince me, as
it has not convinced the wisest of our statesmen. That
our ancestors erred in laying it down as an axiom
of policy, that the toleration of irregularity is incompatible with

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the safety of the state. Doubtless, the life of an
irregular is hard, but the interests of the greater number
require that it shall be hard. If a man with
a triangular front and a polygonal back were allowed to
exist and to propagate a still more irregular posterity, what

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would become of the arts of life? Are the houses
and doors and churches in flatland to be altered in
order to accommodate such monsters? Are our ticket collectors to
be required to measure every man's perimeter before they allow
him to enter a theater or to take his place
in a lecture room? Is it irregular to be exempted

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from the militia? And if not, how is he to
be prevented from carrying desolation into the ranks of his comrades? Again,
what irresistible temptations to fraudulent impostures must needs beset such
a creature? How easy for him to enter a shop

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with his polygonal front foremost, and to order goods to
any extent from a confiding tradesman. Let the advocates of
a falsely called philanthropy plead as they may, for the
abrogation of the irregular penal laws. I, for my part,
have never known an irregular who was not also what

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nature evidently intended him to be, a hypocrite, a misanthropist, and,
up to the limits of his power, a perpetrator of
all manner of mischief. Not that I should be disposed
to recommend at present the extreme measures adopted in some
states where an infant whose angle deviates by half a

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degree from the correct angularity is summarily destroyed at birth
some of our highest and ablest men, men of real genius,
have during their earliest days, labored under deviations as great
as or even greater than, forty five minutes, and the
loss of their precious lives would have been an irreparable

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injury to the state. The art of healing also has
achieved some of its most glorious triumphs in the compressions, extensions, japannings, collegations,
and other surgical or dietetic operations by which irregularity has
been partly or wholly cured. Advocating therefore a fear media,

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I would lay down no fixed or absolute line of demarcation,
but at the period when the frame is just beginning
to set, and when the medical board has reported that
recovery is improbable, I would suggest that the irregular offspring
be painlessly and mercifully consumed. End of Section seven. According

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by Ruce Golding,