flatland(弗莱特兰)-第5章
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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 monthwhich 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 thereforealthough 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
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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 nextSECTION。
SECTION 6 Of Recognition by Sight
I am about to appear very inconsistent。 In the previousSECTIONs 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
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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
incredibleI shall have attained all I can reasonably expect。 Were I to
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attempt further details I should only perplex。 Yet for the sake of the young
and inexperienced； who may perchance inferfrom the two simple
instances I have given above； of the manner in which I should recognize
my Father and my Sonsthat 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…
educatedwhen 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 conversazionemust 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
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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 Artor I may almost ca
