Flatland: A Romance of Many Dimensions — John Shaqi
Flatland: A Romance of Many DimensionsAbbott, Edwin Abbott
Science
Flatland: A Romance of Many Dimensions
Abbott, Edwin Abbott
Fourth dimension
C (1)
|\ - _ D
| \ ||- _
| \ || - _
| <--- >|| -----------+(> Eye-glance
___C' (2) | / A|| _ -
___--- \ - _D' | / ||_ -
__--- \ || - _ |/ _ - E
| \ || - _ B
| \ || - _
| Eye-glance \ || - _
| <----------- A'>|| ------------------------+(>
| / || _ -
| / || _ -
|__ / || _ -
---___ / || _ -
---___/ _ -E'
B'
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 his 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 INTO 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 into 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 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
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.
Public-domain text, read in full here on John Shaqi.
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