"A Habitrail Refuted"
lyrics by Benjamin Newman
ttto: "A Habitrail Named Klein" by Blake Hodgetts

(capo 2)

( G D C D )

/: G Bm D Em / C - G (D) :/

Walter's was a story that could never have occurred
And in this song I aim to prove it
For a habitrail to multiply a hamster is absurd
No matter where or how you move it

	/ Em - Bm - / C - - D /

	Such a tale can't be attributed to loops or bends or twists
	What follows is a proof that no such manifold exists

		/ G Bm C G / C G C D / 1st / C G D G /

		O Walter, we falter, we fail in our math
		To conclude you were cloned when you followed a path
		We reason in circles by not thinking straight
		Topology can't be the cause of your fate

A manifold of n-space can, no matter how complex
Be sewn together out of patches
Each patch, considered locally, however it connects
Is homotopical to flat space

	So if k hamsters enter, and then more than k emerge
	There must be at least one patch in which the hamster paths diverge

		O Walter, we falter, we fail in our math...

A path that maps an interval of R onto a range
Is thus the image of a function
But in each patch in which the hamster count is seen to change
The path must have an end or junction

	The manifold's topology must leave these unexplained
	A local fact accounts for every hamster lost or gained

		O Walter, we falter, we fail in our math...

If we suppose, in spite of this, that Walter's tale is true 
What are the local facts in question?
I must confess to bafflement, just as, I'm sure, will you
Though I am open to suggestions

	But physics or biology seems likelier to yield
	A true account of hamster duplication in the field

		O Walter, we falter, we fail in our math...