Where does rotation collide?

The practice of growing different crops in a planned succession on the same land, so that soil fertility, pests, and weeds are managed across seasons rather than in a single repeated planting. The Roman writer Columella described it in the first century in De re rustica, recommending that legumes be alternated with grain to restore the soil. Bullock's 1992 review Crop rotation gathered the modern agronomic evidence on how the ordering of crops affects yield and soil health. Here the word names a sequence of plantings over time on one field, not the turning of a solid body, the reorienting of statistical axes, or the movement of money between market sectors.[1][2]

Unit

One planned sequence of crops grown on a field over successive seasons

Recovery means

Soil nutrients and structure recover during phases planted to restorative crops such as legumes

Measured by

Assessed by crop yield, soil nutrient levels, and pest and weed pressure across the sequence

The turning of a rigid body about an axis, so that every point traces a circle about that axis while the distances between points stay fixed. Euler set out the mechanics of such motion in his 1765 Theoria motus corporum solidorum seu rigidorum and proved in 1775 that any change of orientation of a body can be achieved by a single turn about a fixed axis. The construct is described by an angle, an axis, and an angular velocity, and is treated in modern texts such as Goldstein's Classical mechanics. Here the word names a physical turning of matter in space, not a cycle of crops, a reorientation of factor axes, or a shift of investment between sectors.[3][4]

Unit

An angular displacement about an axis, in radians or degrees

Recovery means

Not applicable

Measured by

Quantified by angle, axis orientation, and angular velocity or angular momentum

In factor analysis, the reorientation of the reference axes in the space of extracted factors so that each variable loads strongly on only a few factors, making the pattern easier to interpret. Thurstone introduced this idea of turning the axes toward a simple structure in his 1947 Multiple-factor analysis. Kaiser's 1958 The varimax criterion for analytic rotation in factor analysis gave an objective rule for choosing the orientation, the varimax method still in wide use. Here the word names a mathematical reorientation of coordinate axes over a set of loadings, not a physical spin, a cycle of crops, or a movement of capital between sectors.[5][6]

Unit

One orientation of the factor axes, given by a rotation matrix applied to the loadings

Recovery means

Not applicable

Measured by

Chosen by criteria such as varimax that maximise the simplicity of the loading pattern

An active investment strategy that shifts holdings from one industry or style group to another to profit from their changing relative performance over the business and market cycle. Sorensen and Burke set out a systematic version in their 1986 Portfolio returns from active industry group rotation, testing the returns from moving between industry groups on ranked signals. Here the word names the periodic reallocation of capital across market segments, not the turning of a solid body, a succession of crops, or the reorienting of statistical axes.[7]

Unit

One reallocation of a portfolio across sectors or style groups

Recovery means

Not applicable

Measured by

Evaluated by portfolio return and risk relative to a benchmark after each reallocation