Where does weight collide?

The downward force that gravity exerts on a body, equal to the body's mass multiplied by the local gravitational acceleration, and measured in newtons like any other force. Because it is a force, this weight changes with location: the same body weighs less on the Moon than on Earth, even though the amount of matter in it, its mass, does not change. Galili's 2001 Weight versus gravitational force traced how physics and physics teaching have separated this force from mass and from the reading of a scale. The referent is a force in newtons set by gravity, not a coefficient in a formula, a trained parameter in a network, or the total mass of a living body.[1]

Unit

A force in newtons, equal to mass times gravitational acceleration

Recovery means

Not applicable

Measured by

Inferred from a mass and the local acceleration due to gravity, or read from a calibrated scale or force sensor

A number attached to an observation to set how much it counts in a calculation, so that a weighted mean or total gives some cases more influence than others. In survey sampling the weight is often the inverse of a unit's probability of being selected, so that a case standing in for many similar cases is counted up to represent them all. Horvitz and Thompson's 1952 A generalization of sampling without replacement from a finite universe gave the classic estimator built on these inverse probability weights. The referent is a dimensionless coefficient of importance chosen by the analyst or the sampling design, not a gravitational force, a trained network parameter, or the mass of a body.[2]

Unit

A dimensionless coefficient attached to an observation or term

Recovery means

Not applicable

Measured by

Set by the sampling design or the analyst, commonly as the inverse of a unit's selection probability, then applied in weighted sums

A learned number on a connection in a neural network that scales how much one unit's output contributes to the next unit's input: the collection of these weights is what the network stores and what training changes. Learning adjusts every weight a little at a time to reduce the error between the network's output and the target. Rumelhart, Hinton, and Williams's 1986 Learning representations by back-propagating errors showed how the error signal can be propagated backward to update these weights. The referent is a tunable parameter fitted by training, not a force from gravity, a fixed coefficient in a survey formula, or the mass of a body.[3]

Unit

A single learned parameter on one connection between units

Recovery means

Not applicable

Measured by

Initialised and then adjusted by gradient based training, and inspected as the numeric parameters of the fitted model

The total mass of a living body, one of the most basic measurements in clinical care, recorded in kilograms and tracked over time as a marker of growth, nutrition, and health. It is combined with height in the body mass index, defined as weight divided by height squared, to screen for underweight and obesity across populations. Keys, Fidanza, Karvonen, Kimura, and Taylor's 1972 Indices of relative weight and obesity evaluated such weight based indices and named the body mass index. The referent is the mass of a body on a clinical scale, not a gravitational force in newtons, a coefficient in a weighted average, or a parameter learned by a network.[4]

Unit

The mass of a whole body, in kilograms, as read on a scale

Recovery means

Not applicable

Measured by

Read directly on a calibrated clinical or bathroom scale, often combined with height as the body mass index