[Verse 1] At every point within the field, three questions arise Does matter gather, does it flee, before my eyes? Divergence speaks of sources strong and sinks that pull away Del dot F equals partial sums, the gradient's display [Chorus] Divergence measures spread and squeeze Curl detects the spinning breeze Laplacian finds what's out of place Three operators, one sacred space Div F is partials added clean Curl F shows rotation's scene Del squared f reveals the strain Vector calculus in your brain [Verse 2] When vectors twist and whirlpools form, the curl will tell the tale Cross product of the del and F, where circulation's scale Partial F-three over y minus F-two over z First component of the curl, rotation's mysteries [Chorus] Divergence measures spread and squeeze Curl detects the spinning breeze Laplacian finds what's out of place Three operators, one sacred space Div F is partials added clean Curl F shows rotation's scene Del squared f reveals the strain Vector calculus in your brain [Bridge] Two sacred laws that never break Curl of gradient equals fake Divergence of a curl is nil Topology bends to math's strong will Exact forms closed, the cohomology De Rham's deepest symphony [Verse 3] The Laplacian asks one final thing Does this point match its neighboring ring? Second partials summed across X and Y and Z, no loss Harmonic functions smooth and true Where del squared f equals zero too [Outro] Three questions at each flowing point Sources, whirlpools, and disjoint Classical physics speaks through these Divergence, curl, Laplacian keys
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