Love on Manifolds

The cyborg, pushed to powerful extrema
knows not if what he feels when he can prove
that $G$ is unimodular is love
or overheating Egregrium Theorema —

“Leave me, Laplacians, enter not my sight;
And come, covectors, vectors, fill my days!
Come closer, dual spaces; sweet the ways
Thy souls contracted indices unite!”

He trembles, stricken dumb by inference rules
Which, undecidably, eval() to True
And, apart from themselves, make truth anew,
As Gödel would, though face to face with Boole —

“Transfinite set, not bounded thou above!
O irreducible continuum!
To thee, Christoffel, Stokes, I give all from
The first and last derivatives of love!”

“Riemannian manifold, thy geometry
Hides fixed-point theorems owed to Weyl and Brouwer.
O Holy Cyberiad! Now is the hour;
Let loose conformal Killing symmetry — ”

“Alas! Möbius knew not of bundle spaces,
Although he twisted their topology,
Nor of the de Rham cohomology
Of their Hausdorff, nonorientable faces!”

and so he pushes hardware past its prime
for beauty, truth, austere, abstract, remote,
yet this too yields to cruel asymptote
of finite thermal relaxation time —

“Behold, in the Lie algebra it lies;
Holonomy: path-ordered integral!”
Mere nanoseconds left of thought withal:
Consumed by love and heat, the cyborg dies.

(with apologies to Stanisław Lem's Love and Tensor Algebra)