The Hidden Messages

In a world cloaked in the irony of simplicity, the supermarket checkout line becomes the ultimate oracle, whispering secrets of the universe through the static of barcode symphonies.

Have you ever stood behind the woman with 47 items in the 12-or-less aisle and pondered her numerical destiny? Each item a cipher, unraveling existential truths, hidden in plain sight.

Meanwhile, the cashier's smile—an enigma wrapped in a greeting. Transcendental yet elusive, it speaks volumes in a language that scholars have yet to decode.

Decipher the following:
Δ1^7 - π3σ√i = ?
Hint: Look beneath the surface of mundane routines.