Scientific Romances (First Series)Hinton, Charles Howard
Philosophy
Scientific Romances (First Series)
Hinton, Charles Howard
Fourth dimension
If, now, the same cubes be taken, and the attempt be made to build up
the looking-glass image of the block with them, it will be found that
there will be a disadjustment. If the blue sides are made to go to the
right, as they must, to form an image block, then some other sides will
be in different places to what they should be in order to produce an
image of the original block. Although considered as an arrangement of
cubes the new block will be an image of the original block, still,
looking at the individual cubes of which it is composed, it will be seen
that the new block is not an exact image of the old block.
If, however, we take the other starting-point, and, not assuming any
fixed fundamental cube, look only at the act of arrangement, the two
Blocks, III. and IV., are found to be identical in every internal
relationship.
For, taking the act of arrangement as the basis, if, when we have built
up the Block IV., we look upon each of the cubes as an arrangement of
the same kind as the whole, then the cube 1 in Diag. IV. is represented
in Diag. VI. And it is evident that if Diag. IV. is built up out of
cubes like Diag. VI., the small cubes, 1, 4, 7, lie in the same edge as
the cubes 1, 4, 7, in Diag. IV. Thus it will be found for every
relationship in Diag. III. there is an exactly similar relationship in
Diag. IV.
In this case if, for the sake of material illustration, we use marked
cubes, it seems that we must not suppose each particular cube to have a
fixed marking of its own, but that we must suppose the markings to
spring up on the sides of the cubes in accordance with the places into
which they are put.
There is another manner of regarding the matter which may help to bring
out the point at issue.
If we suppose that we are putting up the cubes in one room while another
person is putting up cubes in an adjoining room; if we can tell him what
we are doing, using the words right and left, he will be able to put up
a block exactly like ours. But if we do not allow ourselves to use the
words right and left, but speak to the other person as if he were simply
an intelligence without having the same kind of bodily organization as
ourselves, we should find that, supposing he could put up the block of
cubes, it would be a mere matter of chance whether he had put up the
block as we had put it, or whether he had put it up in an image way. And
the same with regard to any shape. We could tell him that the cubes
should be put together, and we could tell him the relationship which
they should have with regard to one another; but the figure he put up
would just as likely be an image of our shape as not.
And we could go on for ever building more and more complicated shapes
and telling him to do the same, and no hitch or difficulty would come.
But at the end all his shapes might be ours just reversed, as if seen in
a mirror.
Public-domain text, read in full here on John Shaqi.
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