"Flat i (The Bivector Blues)" (Verse 1) Feynman drew a little clock hand, ticking in the plane, A scalar *i* to spin the phase and spin it back again, One universal imaginary, tidy and discreet — But a photon doesn't know which way its fields are gonna meet. (Pre-chorus) 'Cause when it hits the lattice and it scatters off at angle *k*, The E–B plane reorients — and the *i* just looks away. It's a ninety-degree rotation that forgot to say of what, And the algebra keeps smiling like it hasn't missed a lot. (Chorus) Oh, flat *i*, flat *i*, You rotate in a plane that you never specify. You'll do the math, you'll get the phase, You'll sum the paths and win the race, But you can't tell a bivector from a lie — Oh, flat *i*, flat *i*. (Verse 2) I wrote a scope paragraph to say what comes in Z-2, Then realized that Z-2 doesn't exist, and neither do Z-3 or Z-4, it's true. So I deleted all the sequels and I left the page alone — The roadmap to a paper that was never gonna be grown. (Pre-chorus) 'Cause the trap of the abstract is a promise you can't keep, A rotor in a bivector where the physics goes to sleep. Every object in my model is a force or a distance or a time — Except the *i*, and the *i* is where I draw the line. (Chorus) Oh, flat *i*, flat *i*, You rotate in a plane that you never specify. You'll do the math, you'll get the phase, You'll sum the paths and win the race, But you can't tell a bivector from a lie — Oh, flat *i*, flat *i*. (Bridge — slower, almost spoken) The clock hand spins at 10-to-the-16 radians a second, And you think you've captured it, but you haven't even reckoned That the hand's a field, the field's a plane, the plane's a turning blade — And a scalar can't remember all the angles it has made. So I'll keep the 83 megavolts, the 0.4-nanometre grid, And I'll leave the *i* there ticking — like a coffin with a lid. (Final chorus — key lift) Oh, flat *i*, flat *i*, You rotate in a plane that you never specify. You'll do the math, you'll get the phase, You'll sum the paths and win the race, But you can't tell a bivector from a lie — No, you can't tell a bivector from a lie — Oh, flat *i*… Goodnight, flat *i*.
