Poems of set paradox and spatial dimension

Universal Paradox     by Sandra DeLozier Coleman

     One gigantic set made of all that there is
     Boggles the mind with paradoxes.
     For it is greater than all, but smaller than this —
     The set which consists of the subsets of it.

     This little poem appeared in the Spring 2006 issue of The AMATYC Review -- a journal for which Coleman also served as Book Review Editor.  Below, from the Fall 2006 issue is "Points of Distinction" in which she describes mathematical progress from one to two to higher dimensions.  Currently Coleman is working on a dual language presentation of the poetry of noted Russian-born mathematician Sofia Kovalevskaya (1850-1891) -- whom she describes as "a mathematician with the soul of a poet."

Point of Distinction      by Sandra DeLozier Coleman

A point in space begins to move

creating endpoints -- clearly two!

A new dimension is defined

as point evolves into a line.

This segment, we shall call an edge,

and on its motion now will hedge

the growth of what we call a face,

as likewise edge a path doth trace.

But note, the path’s particular.

It must be perpendicular!

So, long before the face is through,

of matching edges there are two!

Two others grow as we progress,

but two are instantaneous!

With length that equals width attained

we change the way we move again,

and once more, right away, it’s clear,

two matching faces just appear.

Four more develop over time,

but two are instantly defined!

Extending to the hypercube,

assuming a new way to move,

the cube which has six matching faces,

a path analogous now traces,

where slightest motion yields in full

two separate cubes–identical!

These move apart in such a fashion,

their pathway we can scarce imagine,

but, by analogy, in time,

six other cubes will be defined.

At this point what results we call

a cube that’s four dimensional.

There’s nothing special about four.

There could be any number more.

We try within our space to learn

to see them through the twists and turns

and slices that don’t show the whole,

but rather how the form unfolds.

But always it would seem to me

the thing most difficult to see

is that small speck of space and time,

where separateness is first defined!