Ratio

Ratio (pronounced rey-shoh (U) or rey-shee-oh (non-U))

(1) The relation between two similar magnitudes with respect to the number of times the first contains the second.

(2) The proportional relation; rate.

(3) In finance, the relative value of gold and silver in a bimetallic currency system.

(4) In mathematics, a quotient of two numbers or quantities.

(5) In western legal systems, the slang for ratio decidendi, the substantive part(s) of the judgment.

(6) In the metrics of the internet, the number of comments to a post or other expression on social media relative to the number of likes (a high ratio assumed to suggests disagreement with the contents of the original post).

1630–1640: From the Latin ratiō (a doublet of ration and reason) (a reckoning, account, numbering, derivation, calculation) from the base of rērī (to judge, think).  The original meaning in English, dating from the 1630s (reason, rationale, calculation, reckoning, numbering, calculation, judgment) mirrored the Latin practice while the mathematical sense "relationship between two numbers" is attested from the 1650s.  The use in theological texts in the sense of "reason, rationale" was a tribute to the original meaning in Latin (a reckoning, account, numbering, derivation, calculation), hence also the idea of "a business affair; course, conduct, procedure".  From this also emerged (in a transferred sense and applying to mental action), the meaning "reason, reasoning, judgment, understanding, that faculty of the mind which forms the basis of computation and calculation" (the ultimate origin of this being rat-, the past-participle stem of reri (to reckon, calculate (and also "to think, judge, believe), from the primitive Indo-European root re- (to think, reason, count).  The Latin ratio often was used to represent or translate the Greek logos (computation, account, esteem, reason) in works of philosophy, though the range of senses in the two do not wholly overlap because ratio lacks the essential "speech, word, statement" meaning which exists in the logos.  The familiar modern meaning "corresponding relationship between things not precisely measurable" had become common by the early nineteenth century.

Ratio Decidendi and Obiter Dictum

The ratio decidendi is a phrase in legal Latin meaning "reason (or rationale) for the decision” and the professional oral & verbal shorthand is ratio.  It’s the ratio decidendi which justifies the judgment and expresses the legal principle(s) which determine the outcome.  The ratio decidendi either creates or is consistent with legal precedent and in the common law’s hierarchical system, lower courts are required to follow precedents established by higher courts.

Obiter dictum the complimentary legal Latin phrase meaning "by the way" and the legal slag is variously dicta or (more commonly) obiter.  The obiter is the collective term for other substantive material in the judgment but not part of the reasoning for the decision, the remarks or observations made by a judge that do not form a necessary part of the decision.  There exists an informal test called the Wambaugh Inversion to determine whether a judicial statement is ratio or obiter.  This involves asking whether the decision would have been different, had the statement been omitted.  If so, the statement is crucial and is ratio; if not, it is obiter.  The rarely used plural for ratio is rationes decidendi whereas, because of the rules of Latin, obiter is used almost always in the plural as obiter dicta.  The difference between the ratio and the dicta is a most useful distinction but would be more helpful if judges could be prevailed upon to make if clear which is which; even bullet-point summaries would be handy.  One suspects many judges think themselves fine stylists of the language, a view not always shared by their captive audience.

B2BR: The bitemporal to bizygomatic ratio

Lindsay Lohan's bitemporal to bizygomatic ratio (B2BR), calculated by pinkmirror.com.  Her admirable B2BR ratio of 1.07 contributed to her overall beauty score of 8.5 (out of 10), putting her in the "beautiful" category.  The above image is rendered in the 1:2 aspect ratio of the DL envelope, favored by architects because the result is thought pleasing to the eye.  

Architects and engineers use all sorts of ratios in their calculations, some to improve aesthetic appeal and some to optimize specific strength.  In internal combustion engines, ratios are commonly used (compression ratio, connecting rod-to-stroke ratio et al) and in building design, the "DL envelope ratio" (1:2) references the standard DL envelope (110 x 220 mm; 4⅓ x 8⅔") which, when applied in architecture, is considered to produce a shape pleasing to the eye, apparently because it closely corresponds with the natural field of human vision.  In the beauty business there are also ratios, used predictably to compartmentalize various aspects of women's appearance so their degree of attractiveness can be reduced to a number.  The site pinkmirror.com helpfully provides an interactive analysis page, one component of which is the bitemporal to bizygomatic ratio (B2BR), a measure used in facial anthropometry (the study of facial measurements and proportions) and cosmetic and restorative surgery.  The B2BR compares the distance between the two temporal bones (bitemporal distance) with the distance between the two zygomatic bones (bizygomatic distance) in the face.  Notionally, the B2BR is set at 1:1 (a baseline for calculation purposes rather than an ideal) and if bitemporal distance is greater than that of the bizygomatic, the ratio will be greater than 1, indicating a relatively narrow midface whereas if the bizygomatic distance is greater, the ratio will be less than 1, indicating a relatively wide midface.  In medicine the B2BR is used as an indicative diagnostic tool which can be helpful in assessing certain genetic conditions that affect facial structure and in cosmetic & restorative surgery its used as one of the measures of facial proportions when planning treatments.  Some advanced systems in cosmetic facial surgery no use CAD (computer assisted design) software and 3D printing (essentially "prototyping" the "new" face) and the B2BR is one of the critical metrics used in both.