clifford_a-_pickover_surfing_through_hyperspacebookfi-org

94 surfing through hyperspace
and time. We ordinary humans could only see the event with limited
vision on an unfolded tesseract."
Sally holds the unfolded hypercube in her slender hands. "We've
talked about how a cubical prison couldn't trap a 4-D being. But could a
tesseract prison hold such a creature? Perhaps we could trap the creature
that took the president in a hypercube."
You nod. "That's correct."
"What would a hypercubical prison look like in our world?"
"Sally, again let's reason by analogy and consider what a cubical prison
would look like to a Flatlander. Let's pretend that the prison is a hollow
cube made of steel. As the prison was pushed down through Flatland,
the Flatlander would first see a solid square face. This is the floor of the
prison. Next, the walls would be pushed down, forming a hollow square
on Flatland. Finally, the Flatlander would see a solid square face corresponding
to the jail's ceiling. If the president were in this cubical jail
while it was pushed down into Flatland, we'd first see cross sections of his
feet, then body, then head, until he disappeared."
"If we pushed down the cubical prison at odd angles, we might see
other intersections with Flatland."
You motion Sally over to the water tub in your office—the one you use
for understanding intersections of 3-D objects with Flatland. "Sally,
you're right as usual. In my example, I pushed the prison at right angles so
it had a square cross section. But if we tip the prison so that one of its corners
faces down, we'd first see a single point, then a triangle, then a sixsided
figure (a hexagon), then a triangle, and finally a point." You slowly
push a glass cube into the water, corner first, to show Sally the various
cross sections (Fig. 4.9).
"Now let's consider a hypercube prison containing the president and also
the Omegamorph that abducted him. If the hypercube were pushed delta
into our space, we might first see its 'cubical floor.' This floor would be a
solid cube of steel corresponding to the steel face of the 3-D prison. Next
we'd encounter hollow steel cubes, and finally the solid steel cube 'ceiling.'
If the cube were made of glass so we could see inside, the president might
materialize all at once in the same way that a Flatlander aligned parallel to
Flatland might materialize all at once as he intersected Flatland."
"The 4-D Omegamorph would look like hair or skin blobs as the 4-D
prison was lowered into our world, and the tesseract intersecting our
world could look like an ordinary hollow cube."