Let us again examine the mode in which a plane-being represents a Block
of cubes with slabs. Take Block 1 of the 81 Set of cubes. The
plane-being represents this by nine slabs, which represent the Moena
face of the block. Then, omitting the solidity of these first nine
cubes, he takes another set of nine slabs to represent the next wall of
cubes. Lastly, he represents the third wall by a third set, omitting the
solidity of both second and third walls. In this manner, he evidently
represents the extension of the Block upwards and sideways, in the Z and
X directions; but in the Y direction he is powerless, and is compelled
to represent extension in that direction by setting the three sets of
slabs alongside in his plane. The second and third sets denote the
height and breadth of the respective walls, but not their depth or
thickness. Now, note that the Block extends three inches in each of the
three directions. The plane-being can represent two of these dimensions
on his plane; but the unknown direction he has to represent by a
repetition of his plane figures. The cube extends three inches in the Y
direction. He has to use 3 sets of slabs.
The Block is built up arbitrarily in this manner: Starting from Urna
Mala and going up, we come to a Brown cube, and then to a Light-blue
cube. Starting from Urna Mala and going right, we come to an Orange and
a Fawn cube. Starting from Urna Mala and going away from us, we come to
a Blue and a Buff cube. Now, the plane-being represents the Brown and
Orange cubes by squares lying next to the square which represents Urna
Mala. The Blue cube is as close as the Brown cube to Urna Mala, but he
can find no place in the plane where he can place a Blue square so as to
show this co-equal proximity of both cubes to the first. So he is forced
to put a Blue square anywhere in his plane and say of it: “This Blue
square represents what I should arrive at, if I started from Urna Mala
and moved away, that is in the Y or unknown direction.” Now, just as
there are three cubes going up, so there are three going away. Hence,
besides the Blue square placed anywhere on the plane, he must also place
a Buff square beyond it, to show that the Block extends as far away as
it does upwards and sideways. (Each cube being a different colour, there
will be as many different colours of squares as of cubes.) It will
easily be seen that not only the Gold square, but also the Orange and
every other square in the first set of slabs must have two other squares
set somewhere beyond it on the plane to represent the extension of the
Block away, or in the unknown Y direction.
Public-domain text, read in full here on John Shaqi.
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