Where does decay collide?

The spontaneous transformation of an unstable atomic nucleus into another nuclide, releasing particles or radiation. Rutherford and Soddy set out the law in their 1903 paper Radioactive Change: the number of atoms disintegrating in a given moment is a fixed fraction of those present, so the population falls off exponentially and is summarised by a half-life. The referent is a population of nuclei, the unit is a probability of transformation per atom per unit time, and the event is random for any single atom and exact only in the aggregate. Nothing here concerns a mind, a mouth, or a city; the decay is a property of matter, indifferent to environment and unaffected by rehearsal, hygiene, or investment.[1]

Unit

An unstable nucleus transforming per unit time

Recovery means

Not applicable

Measured by

The decay constant or half-life, inferred from the count rate of emitted particles

The fading of a memory trace as time passes without rehearsal, offered as an explanation of forgetting. Brown in 1958 and Peterson and Peterson in 1959 showed that recall of a short item drops sharply over a retention interval filled with a distractor task, and read the loss as a trace weakening with elapsed time. The referent is a stored representation in one mind, the unit is a decline in recall over the seconds since encoding, and the claim is contested: interference theory holds that later material displaces the trace rather than time erasing it, which is why decay here is defined against interference. Unlike a nucleus, a trace can be held by rehearsal, and its loss is a fact about cognition, not about matter.[2][3]

Unit

A memory trace weakening over elapsed time

Recovery means

Rehearsal before the trace fades holds it; a trace already gone is not recovered

Measured by

Percent correct recall as a function of the retention interval

The progressive dissolution of a tooth's mineral surface by acids that bacteria in dental plaque produce from dietary sugars. Selwitz, Ismail, and Pitts, reviewing dental caries in 2007, describe it as a dynamic imbalance between demineralisation and repair that, left unchecked, cavitates the enamel and dentine. The referent is a hard biological tissue, the unit is lesion depth advancing over months and years, and the driver is a bacterial and dietary process, not a random transformation and not a fading representation. It shares only the plain meaning of deterioration with the other constructs; measured, it is a clinical lesion, and early loss can be reversed by remineralisation while a cavity cannot.[4]

Unit

A tooth's mineral surface dissolving over time

Recovery means

Early lesions can remineralise if the acid challenge stops; a cavity is not reversible

Measured by

Clinical and radiographic lesion depth and the DMFT index across a population

The deterioration of a city as population and demand fall, leaving housing, infrastructure, and neighbourhoods to decline. Glaeser and Gyourko, in their 2005 model Urban Decline and Durable Housing, explain why decline is slow and sticky: houses are durable and outlast the demand that built them, so a city that loses its economic base empties gradually and keeps cheap housing and poorer residents for decades. The referent is a built environment and its market, the unit is a fall in population, prices, and occupancy over years, and the mechanism is economic and physical durability. Unlike a nucleus or a trace, this decay is shaped by policy and investment, and it can be reversed when demand returns.[5]

Unit

A city's housing and built stock deteriorating

Recovery means

Renewed demand or redevelopment can reverse it, but durable housing decays only slowly

Measured by

Population loss, vacancy rates, and house prices below construction cost