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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 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； 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 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 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 seriou