Where does loop collide?

A control structure that runs a block of code repeatedly: the thread of control reaches the bottom, jumps back to the top, and executes the body again until a condition ends it. Böhm and Jacopini (1966) proved that sequence, selection, and iteration suffice to express any computation, and iteration is the loop; Knuth analysed loops and their invariants throughout The Art of Computer Programming (1968), while Dijkstra (1968) argued that disciplined loops make control flow legible where arbitrary jumps do not. The referent is a repetition inside a running program, and its unit is one pass through the body. What matters is the discipline and the termination condition, not any physical shape: an empty loop that never runs and an infinite loop that never stops are both well-defined. It shares the word with a feedback circuit and a closed curve but names a rule for repeating work.[1][2][3]

Unit

One execution of the loop body (an iteration)

Recovery means

Not applicable

Measured by

Iteration count, the loop invariant, and worst-case time per pass

A signal path that carries a system's output back to its input so the system can correct itself: the measured result is compared with the target, and the difference drives the next action. Maxwell (1868) opened the mathematics in On Governors, showing when such a loop settles and when it oscillates, and Black (1934) built the negative-feedback amplifier on the same principle, trading gain for stability. The referent is a closed signal path in a physical or dynamical system, and its unit is the flow of a signal from output back to the controller. Closing the loop is a design choice: an open-loop controller acts without feedback, and a closed-loop one watches its own output. It shares the word with the iteration construct and the topological curve but names a self-correcting circuit, measured by loop gain and stability, not by repetitions or by shape.[4][5]

Unit

A signal path from output back to the controller input

Recovery means

Not applicable

Measured by

Loop gain, phase margin, stability, and steady-state error

A closed path in a space: a continuous curve that starts and ends at the same point, or equivalently a continuous map from the circle into the space. Poincaré introduced the idea in Analysis Situs (1895), where loops based at a point, taken up to continuous deformation, form the fundamental group that distinguishes spaces; Hatcher (2002) gives the modern account. The referent is a purely geometric object, and its unit is a homotopy class of based loops. Nothing travels this loop and nothing repeats: what matters is whether it can be shrunk to a point, and a loop that cannot is what tells you a space has a hole. It shares the word with the code construct and the feedback circuit but names a shape, measured by contractibility and by the group its classes form, not by iterations or by gain.[6][7]

Unit

A homotopy class of based loops

Recovery means

Not applicable

Measured by

Contractibility, winding number, and the fundamental group

A run of unpaired bases in a folded nucleic acid, closed off by a base-paired stem: a single strand of RNA turns back on itself, the complementary stretches pair into a helix, and the bases at the turn form a hairpin loop. Tinoco, Uhlenbeck, and Levine (1971) assigned free energies to such loops so a fold could be scored, and Zuker and Stiegler (1981) folded whole sequences by minimising free energy over hairpin, bulge, and interior loops. The referent is a structural motif in a molecule, and its unit is a set of unpaired nucleotides bounded by a closing base pair. It does not iterate, correct a signal, or bound a hole; its size and free energy decide whether it appears in the folded shape. It shares the word with the other three loops but names a physical fold, measured in unpaired bases and kilocalories.[8][9]

Unit

Unpaired nucleotides bounded by a closing base pair

Recovery means

Not applicable

Measured by

Loop size in unpaired bases and its destabilising free energy