Where does progression collide?

Euclid's Elements (ca. 300 BCE) treated ordered lists of numbers in which each term grows from the one before it, including geometric progressions where each term is a fixed multiple of the last, and the summing of such lists. Later mathematics named two standard forms: an arithmetic progression, in which a constant amount is added at each step, and a geometric progression, in which a constant factor multiplies at each step. The referent is a numbered sequence built by a fixed rule of addition or multiplication, fixed by its first term and its step or ratio, not a movement of chords in music or the worsening of a disease in a patient.[1]

Unit

One ordered sequence of numbers, set by its first term and its common difference or common ratio

Recovery means

Not applicable

Measured by

Given by its defining rule, the first term with the common difference or common ratio, from which any term or the sum of terms is computed

Rameau's Traité de l'harmonie réduite à ses principes naturels (1722) set out a theory in which chords move from one to the next under a governing bass, so that harmony is heard as an ordered motion rather than isolated sounds. Piston's Harmony (1941) later taught this as harmonic progression: the succession of chords through a passage, described by the roman numerals of the chords and the way each resolves toward the next. The referent is a chord-to-chord movement within a key, named by the chords it passes through, and it is unrelated to a rule-built number sequence or the advance of a disease.[2][3]

Unit

One ordered succession of chords within a key

Recovery means

Not applicable

Measured by

Written out as a series of roman numerals or chord symbols and analysed by the function of each chord and how it resolves to the next

Foulds's The experimental study of tumor progression (1954) described progression as the stepwise change by which a tumor takes on more aggressive properties over time, advancing through a succession of stages. Nowell's The clonal evolution of tumor cell populations (1976) refined this as the outgrowth of successive cell variants, and in clinical practice the word also names disease progression as an endpoint, with progression-free survival being the time a patient lives without the disease worsening (Booth and Eisenhauer, 2012). The referent is the worsening or advance of a disease in a body, tracked by imaging, markers, and survival time, and it is neither a number sequence nor a movement of chords.[4][5][6]

Unit

One patient's disease advance over time, or the time lived without it worsening

Recovery means

Progression names the worsening; a later reversal is termed response or remission rather than progression

Measured by

Assessed by imaging and clinical criteria such as RECIST, by biomarker levels, and by endpoints like progression-free survival