I nodded slowly, and pointed at the other screen. “What about that?”

He pursed his lips. “Working on a program to calculate i.”

A joke, I thought. “That’s right, the composer is the mathematician...” But he was peering intently at the screen. I frowned. “But Ian, the imaginary unit is... just that. It’s imaginary. A convenience, nothing more. A symbol, defined as the square root of minus one. Trust me. I’m the programmer.”

He smiled and looked at me. “And I’m calculating it.”

I was silent.

Why not calculate 1 for an encore? But it was too late now. He lived somewhere he called nowhere; I had accepted that without question. And he called himself i. No sense now in explaining the meaningless of ‘calculating’ it, was there?

He knew that.

So I asked: “And once you know the result?”

He stared at the keyboard. “A theory of harmony based on complex numeric relations...”

I shook my head, stood up, switched on the light. “Bollocks, Ian. You’re a composer, right? You know that harmony is based on natural ratios. The octave, the fifth, the fourth, ordinary fractions, real numbers.” I gestured wildly. “But a complex number is the sum of a real part and an imaginary part.”

He crouched in his chair, gazing silently past my shoulder, picking his lips.

I shook my head once more. “In music, Ian... how can you have a harmonic ratio with an imaginary component?” I turned around. “Anyway, I’m off to bed.” I walked to the bathroom.

He came after me and grabbed my arm. “Richard...?” He looked at me with a frown on his face and genuine confusion in his eyes. “In music, Richard... how can you hear a palace?”