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Isosceles      population      an   object    which     every    statesman      in  Flatland 

constantly      keeps    in  view。   On    the   whole    thereforealthough        I  am   not 

ignorant that�察�in many popularly elected School Boards�察�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�察�I trust�察�to shew that Recognition 

by  Feeling   is   not   so   tedious   or   indecisive   a   process   as   might   have   been 



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supposed�察     �and    it  is  obviously    more    trustworthy      than   Recognition      by 

hearing。 Still there remains�察�as has been pointed out above�察�the objection 

that this method is not without danger。 For this reason many in the Middle 

and Lower classes�察�and all without exception in the Polygonal and Circular 

orders�察�prefer a   third method�察 �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�察  �and   it   was   added   or   implied�察  �that   it   is   consequently   impossible   to 

distinguish   by   the   visual   organ   between   individuals   of   different   classes�此�

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�察�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�察�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�察�

blotting out the landscape�察�depressing the spirits�察�and enfeebling the health�察�

is by us recognized as a blessing scarcely inferior to air itself�察�and as the 

Nurse   of   arts   and   Parent   of   sciences。   But   let   me   explain   my   meaning�察�

without further eulogies on this beneficent Element。 

     If   Fog    were     non´existent�察    �all   lines   would     appear     equally    and 

indistinguishably   clear�察  �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�察�objects that are at a distance�察�say of 

three feet�察�are appreciably dimmer than those at the distance of two feet 

eleven inches�察�and the result is that by careful and constant experimental 



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observation of comparative dimness and clearness�察�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�察 �we   will   suppose�察 �a   Merchant   and   a   Physician�察 �or   in 

other     words�察    �an   Equilateral     Triangle     and   a   Pentagon�察     �how    am    I  to 

distinguish them�拭�

     It   will   be   obvious�察  �to   every  child   in   Spaceland  who   has   touched   the 

threshold   of   Geometrical   Studies�察  �that�察  �if   I   can   bring   my   eye   so   that   its 

glance may bisect an angle ��A�� of the approaching stranger�察�my view will 

lie as it were evenly between the two sides that are next to me ��viz。 CA 

and AB���察  �so   that   I   shall   contemplate   the   two   impartially�察  �and   both   will 

appear of the same size。 

     Now   in the   case   of   ��1��   the   Merchant�察  �what   shall   I see�拭  �I shall   see   a 

straight   line   DAE�察  �in   which   the   middle   point   ��A��   will   be   very   bright 

because   it   is   nearest   to   me�察  �but   on   either   side   the   line   will   shade   away 

RAPIDLY          TO    DIMNESS�察        �because     the   sides    AC    and    AB    RECEDE 

RAPIDLY   INTO   THE   FOG   and   what   appear   to   me   as   the   Merchant's 

extremities�察�viz。 D and E�察�will be VERY DIM INDEED。 

     On the other hand in the case of ��2�� the Physician�察�though I shall here 

also   see   a   line   ��D'A'E'��   with a   bright   centre   ��A'���察  �yet   it   will   shade   away 

LESS   RAPIDLY   to   dimness�察  �because   the   sides   ��A'C'�察  �A'B'��               RECEDE 

LESS RAPIDLY INTO THE FOG�此�and what appear to me the Physician's 

extremities�察�viz。 D' and E'�察�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�察�by the sense of sight。 If 

my Spaceland Patrons have grasped this general conception�察�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�察      �who    may     perchance      inferfrom     the    two   simple 

instances I have given above�察�of the manner in which I should recognize 

my Father and my Sonsthat Recognition by sight is an easy affair�察�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�察    �when     my   Father�察   �the  Triangle�察    �approaches      me�察  �he 

happens to present his side to me instead of his angle�察�then�察�until I have 

asked him to rotate�察�or until I have edged my eye around him�察�I am for the 

moment   doubtful   whether   he   may   not   be   a   Straight   Line�察  �or�察  �in   other 

words�察  �a   Woman。 Again�察  �when   I   am   in   the   company   of   one   of   my   two 

hexagonal   Grandsons�察  �contemplating   one   of   his   sides   ��AB��   full   front�察  �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�察  �which   present   themselves   to   the   well´ 

educatedwhen   they   are         themselves      in  motion�察   �rotating�察   �advancing     or 

retreating�察�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�察�as for example in a ball´room or conversazionemust be of a 

nature to task the angularity of the most intellectual�察�and amply justify the 

rich endowments of the Learned Professors of Geometry�察�both Static and 

Kinetic�察�in the illustrious University of Wentbridge�察�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�察�who 

are    able    to  give    the   time    and    money      necessary     for   the   thorough 

prosecution of this noble and valuable Art。 Even to me�察�a Mathematician 

of    no   mean    standing�察    �and   the   Grandfather      of  two    most    hopeful    and 

perfectly   regular   Hexagons�察  �to   find   myself   in   the   midst   of   a   crowd   of 



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rotating   Polygons   of   the   higher   classes�察  �is   occasionally   very   perplexing。 

And of course to a common Tradesman�察�or Serf�察�such a sight is almost as 

unintelligible     as   it

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