Where does normalization collide?

Rescaling a quantum state's wavefunction so that the total probability of finding the particle anywhere equals one. Born's 1926 paper Zur Quantenmechanik der Stoßvorgänge read the squared magnitude of the wavefunction as a probability density, which forces the integral of that density over all space to be one, and normalization is the act of dividing the wavefunction by a constant so this holds. Here the referent is a mathematical scaling of a physical state's amplitude, its unit fixed so that a probability integrates to one, and it has nothing to do with breaking a database into tables, softening a data range, or a group treating a behaviour as ordinary.[1]

Unit

A scaling constant applied to a wavefunction so its probability density integrates to one

Recovery means

Not applicable

Measured by

Computed by integrating the squared magnitude of the wavefunction over all space and dividing by the square root of that integral

Restructuring the tables of a relational database into successive normal forms so that stored facts are not duplicated and updates cannot leave the data inconsistent. Codd's 1970 paper A relational model of data for large shared data banks introduced the relational model and the first normal form, and his 1972 Further normalization of the data base relational model defined the higher normal forms that split a table whenever one column depends on another in a way that would otherwise repeat information. The referent is a design transformation on tables and their dependencies, its unit a normal form a schema either satisfies or does not, and it is unrelated to scaling a wavefunction, rescaling a feature range, or a society treating conduct as normal.[2][3]

Unit

A normal form (1NF, 2NF, 3NF and so on) that a table's structure either satisfies or fails

Recovery means

Not applicable

Measured by

Checked by examining functional dependencies among columns against the definition of each normal form

The process by which institutions measure people against a standard of the normal and, over time, make ideas or behaviours that were once treated as deviant appear ordinary and unremarkable. Foucault's 1975 Surveiller et punir described how schools, clinics, and prisons exert power through a normalizing judgment that ranks individuals against a norm and pulls them toward it. The referent is a social and historical shift in what a group takes for granted, its unit the changing boundary between normal and deviant, and it is not a scaling of amplitudes, a database restructuring, or a numerical rescaling of data.[4]

Unit

A historical shift in what a group treats as normal rather than deviant

Recovery means

Not applicable

Measured by

Traced through historical and qualitative study of institutions, discourse, and shifting standards of the normal

Rescaling the numbers flowing through a model, either input features or the intermediate activations of a network, so they sit on a comparable scale and training stays stable. Ioffe and Szegedy's 2015 Batch normalization standardised each layer's activations to zero mean and unit variance within a mini-batch, then let the model learn a scale and shift, which sped up and steadied deep network training. The referent is a numerical transformation of a model's values, its unit a rescaled quantity such as a z-scored activation, and it is a different act from normalizing a wavefunction, decomposing database tables, or a society coming to treat conduct as normal.[5]

Unit

A rescaled value, for example an activation standardised to zero mean and unit variance

Recovery means

Not applicable

Measured by

Applied and monitored through the statistics (mean, variance) used to rescale activations and its effect on training loss

In disability studies, normalization refers to making the patterns and conditions of ordinary life available to people with disabilities. This meaning comes from Wolfensberger (1972) in The principle of normalization in human services.[6]

Unit

Recovery means

Measured by