Where does normal collide?

In Rene Descartes's 1637 La geometrie, a method was given for constructing the straight line that meets a curve at a right angle at a chosen point, the line now called the normal to the curve. Do Carmo's 1976 Differential geometry of curves and surfaces extended this to the normal vector of a surface, the direction that stands perpendicular to the flat plane touching the surface at a point. Here the normal is a direction in space, fixed purely by geometry and carrying no probability or force. It is unrelated to the bell-shaped spread of a set of measurements or to a block of rock that has slipped downward along a fracture.[1][2]

Unit

One perpendicular direction at a point on a curve or surface

Recovery means

Not applicable

Measured by

Computed as the direction orthogonal to the tangent line or tangent plane, often via the gradient or a cross product

Abraham de Moivre's 1733 approximation to the binomial, later circulated in his Doctrine of chances, first described the smooth bell-shaped curve that a sum of many small chance events settles into. Carl Friedrich Gauss's 1809 Theoria motus corporum coelestium tied the same curve to the pattern of measurement errors, which is why it is often called the Gaussian distribution, and Fischer's 2011 history traces how Laplace and later workers made it central to probability. Here the normal is a distribution of values, defined by a mean and a spread, that describes how measurements scatter. It has nothing to do with a line drawn perpendicular to a curve or with a downward slip of rock along a fault.[3][4][5]

Unit

A probability distribution set by a mean and a standard deviation

Recovery means

Not applicable

Measured by

Fitted by estimating its mean and variance, and checked against data by tests of normality such as Shapiro-Wilk

Ernest Masson Anderson's 1905 The dynamics of faulting, expanded in his 1951 book of the same name, set out the mechanics of the normal fault, a fracture along which the upper block, the hanging wall, drops down relative to the lower block, the footwall, as the crust is pulled apart. The term itself came earlier from British coalfield miners, for whom this was the ordinary or expected kind of fault. Here the normal names one class of geological fracture, identified by the downward slip of the hanging wall under extension. It bears no relation to a perpendicular line in geometry or to the bell curve of statistics.[6][7]

Unit

One dip-slip fracture with hanging-wall-down displacement

Recovery means

Not applicable

Measured by

Mapped in the field and quantified by the fault's dip, strike, and the amount of vertical throw