Where does trace collide?

Cayley's 1858 A memoir on the theory of matrices defined square arrays of numbers and the operations on them; within that algebra the trace of a square matrix is the sum of the entries on its main diagonal. This number also equals the sum of the matrix's eigenvalues and does not change when the basis is changed, which makes it a basic invariant of the linear map the matrix stands for. Here the referent is a single number read off a table of coefficients, and it has nothing to do with a stored memory, a faint chemical quantity, or the mark of an absent term.[1]

Unit

A single scalar: the sum of the n diagonal entries of an n-by-n matrix

Recovery means

Not applicable

Measured by

Computed by adding the diagonal entries, equivalently as the sum of the eigenvalues

Semon's 1904 Die Mneme named the lasting physical change that an experience leaves in the nervous system the engram, the memory trace that can later be reactivated to reproduce something of the original experience. Josselyn and Tonegawa's 2020 Memory engrams: Recalling the past and imagining the future reviewed how particular populations of neurons hold such traces and how switching those neurons back on can drive recall. Here the referent is a durable change in living brain tissue that stores a memory, not a number from a matrix, a small chemical quantity, or a philosopher's mark of difference.[2][3]

Unit

One retained change in neural tissue that encodes a single memory

Recovery means

The trace can be reactivated so the stored memory is recalled

Measured by

Inferred from retention and recall in behaviour, and localised by tagging and reactivating the neurons that hold it

Underwood's 1956 Trace elements in human and animal nutrition gathered the elements that occur in living tissue at very small concentrations, the trace elements such as iron, zinc, copper, and iodine, many of which are essential in tiny amounts yet harmful in excess. Fraga's 2005 Relevance, essentiality and toxicity of trace elements in human health reviewed how these low-concentration elements act in the body and where the line between too little and too much falls. Here a trace is a quantity of matter so small that it sits near the lower limit of what can be reliably measured, unlike a number from a matrix, a stored memory, or a mark of an absent term.[4][5]

Unit

The concentration of an element that is present only in tiny amounts, for example parts per million

Recovery means

Not applicable

Measured by

Quantified by trace analysis such as atomic absorption or mass spectrometry at very low concentrations

Derrida's 1967 De la grammatologie (translated as Of Grammatology in 1976) used the trace for the way any element of language carries within it a mark of the other elements it is not, so that meaning depends on what is absent as much as on what is present. On this account no sign is fully self-contained: each one bears the trace of the differences that set it apart from every other. Here the referent is a structural mark of absence within a system of signs, and it is unrelated to a number from a matrix, a stored memory, or a faint chemical quantity.[6]

Unit

Not applicable: a structural feature of any sign, not a counted quantity

Recovery means

Not applicable

Measured by

Not measured; identified through close reading and textual interpretation