Posts Tagged duals
At dawn, separated by twenty two paces,
their vertices pointed in each other’s faces,
the cube and its foe Octahedron stood still,
as fair Tetrahedron urged ‘fire at will!’
For Cube fought with earth, Octahedron with air,
and to win Tetrahedron with fire’s not fair.
“Fight fire with fire, that’s what we agreed on!”
said seconds, Dodeca- and Icosahedron.
But they paused, and they wavered, and called, “Toi ou moi?
Who’ll live for now, and who forever, like Galois?”
They each made a face, for they’d each made a point.
Was dying or living the upper adjoint?
The Galois connection was hard to ignore;
he’d dueled over shapely wee solids before,
and though he was shot, we can’t name his opponent,
while Galois’ last writings became a component
of fields (and of groups) of mathematics that show
among other things, what these two solids should know:
That Cube and its friend Octahedron are dual,
and no four-faced loner should cause them to duel.
At once, the two shook off their anthropomorphism,
and saw from their faces to points, isomorphism.
“You cannot kill me,” they each said to the other,
“For if I am a martyr, then so are you, brother,
and even though I’d be like Évariste too,
I’d rather not share such an honour with you.”
So they and their seconds proposed to their bride
that four eager suitors could each pick a side.
The pyramid’s answer was sweet but ironic:
“Of course you can share, but my love is Platonic.”