嗔秤戻幣�哉膵�云利匈嬉蝕湊蛸賜�塋床四衲���萩晦編報炎嘔囚^泡仟 ̄云利匈��
栽怩弌傍利 卦指云慕朕村 紗秘慕禰 厘議慕尺 厘議慕禰 TXT畠云和墮 〆辺茄欺厘議箝誓匂〇

flatland(献棲蒙声)-及20何蛍

酔楯荷恬: 梓囚徒貧圭�鮗� ○ 賜 ★ 辛酔堀貧和鍬匈 梓囚徒貧議 Enter 囚辛指欺云慕朕村匈 梓囚徒貧圭�鮗� ● 辛指欺云匈競何! 泌惚云慕短嗤堋響頼���誅卒亮茂�俊彭堋響��辛聞喘貧圭 "辺茄欺厘議箝誓匂" 孔嬬 才 "紗秘慕禰" 孔嬬��



than he was offering to me。 

     ;Pardon me�察─�said I�察 �O Thou Whom I must no longer address as the 

Perfection of   all   Beauty�察�but   let   me beg   thee to vouchsafe thy  servant   a 

slight of thine interior。; 

     Sphere。 My what�拭�

     I。 Thine interior�此�thy stomach�察�thy intestines。 

     Sphere。   Whence   this   ill´timed   impertinent   request�拭  �And   what   mean 

you by saying that I am no longer the Perfection of all Beauty�拭�

     I。   My   Lord�察  �your   own   wisdom  has   taught   me   to   aspire   to   One   even 

more   great�察  �more   beautiful�察  �and   more   closely   approximate   to   Perfection 

than   yourself。  As   you   yourself�察  �superior   to   all   Flatland   forms�察  �combine 

many Circles in One�察�so doubtless there is One above you who combines 

many  Spheres in   One   Supreme   Existence�察  �surpassing   even   the   Solids   of 

Spaceland。 And even as we�察�who are now in Space�察�look down on Flatland 

and   see   the   insides   of   all   things�察  �so   of   a   certainty  there   is   yet   above   us 

some higher�察�purer region�察�whither thou dost surely purpose to lead meO 

Thou Whom   I   shall   always   call�察  �everywhere   and   in   all   Dimensions�察  �my 

Priest�察   �Philosopher�察     �and   Friendsome       yet   more    spacious     Space�察   �some 

more   dimensionable   Dimensionality�察  �from   the   vantage´ground   of   which 

we shall look down together upon the revealed insides of Solid things�察�and 

where   thine   own   intestines�察  �and   those   of   thy   kindred   Spheres�察  �will   lie 

exposed to the view of the poor wandering exile from Flatland�察�to whom 

so much has already been vouchsafed。 

     Sphere。   Pooh�   �Stuff�   �Enough   of   this   trifling�   �The   time   is   short�察  �and 

much   remains   to   be   done   before   you   are   fit   to   proclaim   the   Gospel   of 

Three Dimensions to your blind benighted countrymen in Flatland。 

     I。 Nay�察�gracious Teacher�察�deny me not what I know it is in thy power to 

reform。 Grant me but one glimpse of thine interior�察�and I am satisfied for 

ever�察�remaining henceforth thy docile pupil�察�thy unemacipable slave�察�ready 

to receive all thy teachings and to feed upon the words that fall from thy 

lips。 

     Sphere。 Well�察�then�察  �to   content and   silence   you�察  �let   me   say  at   once�察  �I 



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would shew you what you wish if I could�察�but I cannot。 Would you have 

me turn my stomach inside out to oblige you�拭�

     I。 But my Lord has shewn me the intestines of all my countrymen in 

the   Land   of   Two   Dimensions   by   taking   me   with   him   into   the   Land   of 

Three。 What therefore more easy than now to take his servant on a second 

journey   into   the   blessed   region   of   the   Fourth   Dimension�察  �where   I   shall 

look down with him once more upon this land of Three Dimensions�察�and 

see the inside of every three´dimensioned house�察�the secrets of the solid 

earth�察�the treasures of the mines of Spaceland�察�and the intestines of every 

solid living creature�察�even the noble and adorable Spheres。 

     Sphere。 But where is this land of Four Dimensions�拭�

     I。 I know not�此�but doubtless my Teacher knows。 

     Sphere。   Not   I。   There   is   no   such   land。   The   very   idea   of   it   is   utterly 

inconceivable。 

     I。   Not    inconceivable�察     �my    Lord�察   �to   me�察  �and    therefore    still  less 

inconceivable   to   my   Master。   Nay�察  �I   despair   not   that�察  �even   here�察  �in   this 

region   of   Three   Dimensions�察  �your   Lordship's   art   may   make   the   Fourth 

Dimension   visible   to   me�察  �just   as   in   the   Land   of   Two   Dimensions   my 

Teacher's skill would fain have opened the eyes of his blind servant to the 

invisible presence of a Third Dimension�察�though I saw it not。 

     Let me recall the past。 Was I not taught below that when I saw a Line 

and inferred a Plane�察�I in reality saw a Third unrecognized Dimension�察�not 

the same as brightness�察�called ;height;�拭�And does it not now follow that�察�

in this region�察�when I see a Plane and infer a Solid�察�I really see a Fourth 

unrecognized   Dimension�察  �not   the   same   as   colour�察  �but   existent�察  �though 

infinitesimal and incapable of measurement�拭�

     And besides this�察�there is the Argument from Analogy of Figures。 

     Sphere。 Analogy� �Nonsense�此�what analogy�拭�

     I。 Your Lordship tempts his servant to see whether he remembers the 

revelations imparted to him。 Trifle not with me�察�my Lord�察�I crave�察�I thirst�察�

for    more     knowledge。      Doubtless      we    cannot     SEE    that   other    higher 

Spaceland now�察�because we have no eye in our stomachs。 But�察�just as there 

WAS   the   realm   of   Flatland�察  �though   that   poor   puny   Lineland   Monarch 



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could   neither   turn   to   left   nor   right   to   discern   it�察  �and   just   as   there   WAS 

close   at   hand�察  �and   touching   my   frame�察  �the   land   of   Three   Dimensions�察�

though I�察�blind senseless wretch�察�had no power to touch it�察�no eye in my 

interior to discern it�察�so of a surety there is a Fourth Dimension�察�which my 

Lord perceives   with the inner eye   of thought。 And that it must   exist   my 

Lord   himself   has   taught   me。   Or   can   he   have   forgotten   what   he   himself 

imparted to his servant�拭�

     In One Dimension�察�did not a moving Point produce a Line with TWO 

terminal points�拭�

     In   Two   Dimensions�察  �did   not   a   moving   Line   produce   a   Square   with 

FOUR terminal points�拭�

     In Three Dimensions�察�did not a moving Square producedid not this 

eye of mine behold itthat blessed Being�察�a Cube�察�with EIGHT terminal 

points�拭�

     And in Four Dimensions shall not a moving Cubealas�察�for Analogy�察�

and   alas   for   the   Progress   of   Truth�察  �if   it   be   not   soshall   not�察  �I   say�察  �the 

motion   of   a   divine   Cube   result   in   a   still   more   divine   Organization   with 

SIXTEEN terminal points�拭�

     Behold the infallible confirmation of the Series�察�2�察�4�察�8�察�16�此�is not this 

a   Geometrical   Progression�拭  �Is   not   thisif   I   might   quote   my   Lord's   own 

words;strictly according to Analogy;�拭�

     Again�察�was I not taught by my Lord that as in a Line there are TWO 

bounding Points�察�and in a Square there are FOUR bounding Lines�察�so in a 

Cube      there   must    be   SIX    bounding      Squares�拭     �Behold     once    more    the 

confirming   Series�察  �2�察  �4�察  �6�此  �is   not   this   an Arithmetical   Progression�拭�And 

consequently does it not of necessity follow that the more divine offspring 

of the divine Cube in the Land of Four Dimensions�察�must have 8 bounding 

Cubes�此�and is not this also�察�as my Lord has taught me to believe�察 �strictly 

according   to Analogy;�拭  �O�察  �my   Lord�察  �my   Lord�察  �behold�察  �I   cast   myself   in 

faith    upon    conjecture�察    �not   knowing      the   facts�察  �and   I  appeal     to  your 

Lordship   to   confirm   or   deny   my   logical   anticipations。   If   I   am   wrong�察  �I 

yield�察�and will no longer demand a Fourth Dimension�察�but�察�if I am right�察�

my Lord will listen to reason。 



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     I ask therefore�察�is it�察�or is it not�察�the fact�察�that ere now your countrymen 

also have witnessed the descent of Beings of a higher order than their own�察�

entering closed   rooms�察 �even   as   your   Lordship   entered   mine�察 �without the 

opening of doors or windows�察�and appearing and vanishing at will�拭�On the 

reply to this   question I  am ready  to stake everything。  Deny it�察 �and I  am 

henceforth silent。 Only vouchsafe an answer。 

     Sphere ��AFTER A PAUSE��。 It is reported so。 But men are divided in 

opinion as to the facts。 And even granting the facts�察�they explain them in 

different   ways。   And   in   any   case�察  �however   great   may   be   the   number   of 

different   explanations�察  �no   one   has   adopted   or   suggested   the   theory   of   a 

Fourth Dimension。 Therefore�察�pray have done with this trifling�察�and let us 

return to business。 

     I。   I   was   certain   of   it。   I   was   certain   that   my   anticipations   would   be 

fulfilled。 And   now  have   patience   with   me   and   answer   me   yet   one   more 

question�察�best of Teachers� �Those who have thus appeared no one knows 

whenceand         have    returnedno     one    knows     whither     have    they    also 

contracted       theirSECTIONs          and    vanished      somehow        into   that   more 

Spacious Space�察�whither I now entreat you to conduct me�拭�

     Sphere      ��MOODILY��。         They     have    vanished�察    �certainlyif    they   ever 

appeared。 But most people say that these visions arose from the thought 

you will not understand mefrom the brain�察�from the perturbed angularity 

of the Seer。 

     I。 Say they so�拭�Oh�察�believe them not。 Or if it indeed be so�察�that this 

other   SPace   is   really  Thoughtland�察  �then   take   me   to   that   blessed   Region 

where I in Thought shall see the insides of all solid things。 There�察�before 

my   ravished   eye�察  �a   Cube   moving   in   some   altogether   new   direction�察  �but 

strictly according to Analogy�察�so as to make every particle of his interior 

pass through a new kind of Space�察�with a wake of its ownshall create a 

still more perfect perfection than himself�察�with sixteen terminal Extra´solid 

angles�察�and Eight solid Cubes for his Perimeter。 And once there�察�shall we 

stay our upward course�拭�In that blessed region of Four Dimensions�察�shall 

we linger at the threshold 
卦指朕村 貧匯匈 和匯匈 指欺競何 壘��0�� 家��0��
酔楯荷恬: 梓囚徒貧圭�鮗� ○ 賜 ★ 辛酔堀貧和鍬匈 梓囚徒貧議 Enter 囚辛指欺云慕朕村匈 梓囚徒貧圭�鮗� ● 辛指欺云匈競何!
梁椣戻幣�� 梁心弌傍議揖扮窟燕得胎��傍竃徭失議心隈才凪万弌誌育断蛍�輌臆惨軼僑〃�燕慕得珊辛參資誼持蛍才将刮襲潜��範寔亟圻幹慕得 瓜寡追葎娼得辛參資誼寄楚署衛、持蛍才将刮襲潜填��