Where does rectification collide?

The practice of making words match the realities they name, so that titles, roles, and terms are used truthfully and consistently. Confucius set it out in the Analects (Book 13, Chapter 3, from teachings of about 500 BCE): if names are not correct, then language does not fit the truth of things, and affairs cannot be carried to success, so a ruler must first rectify the names. In later scholarship this teaching became known in English as the rectification of names. Here the referent is an ethical and political discipline over language, not the length of a curve, the correcting of a legal document, or the conversion of electric current.[1]

Unit

One name or title, judged by whether its use fits the reality it points to

Recovery means

Not applicable

Measured by

Judged qualitatively by whether a term's use is consistent with the role or reality it names, not by any numeric scale

The determination of the exact length of a curved line, that is, finding a straight segment equal in length to a given arc. William Neile carried this out in 1657 for the semicubical parabola, the first algebraic curve to have its length found, a result John Wallis published in 1659, the same year Hendrik van Heuraet gave a general method for turning a curve into a straight line of equal length. Emilia Florio's 2022 study traces how Wallis framed the problem of rectifying the parabola. Here the referent is a geometric calculation of arc length, not a discipline over words, a court's correction of a document, or a change in electric current.[2][3]

Unit

One arc length, a straight segment equal to the curve, in units of length

Recovery means

Not applicable

Measured by

Computed by integrating the arc-length formula, or historically by geometric transformation of the curve into a straight segment

An equitable remedy in which a court corrects the written words of a document, such as a contract, deed, or settlement, so that it records what the parties actually agreed when a mistake left the writing wrong. English courts of equity exercised this power by the mid eighteenth century: in Henkle v Royal Exchange Assurance Co (1749) the Court of Chancery accepted that it could correct a policy that did not reflect the bargain, and Paul Davies's 2016 study sets out how the modern doctrine corrects common and unilateral mistakes without rewriting the parties' agreement. Here the referent is a court's correction of a legal instrument, not a calculation of length, a discipline over words, or the conversion of current.[4][5]

Unit

One instrument corrected by court order to match the true agreement

Recovery means

Not applicable

Measured by

Established in court by clear evidence of the parties' true common intention and of the mistake in the writing

The conversion of alternating current, which reverses direction many times a second, into direct current, which flows one way, by a device that lets current pass in one direction far more easily than the other. Ferdinand Braun reported the physical basis in 1875, finding that certain metal sulfide contacts conduct much better in one direction than the reverse, the asymmetric conduction later built into point-contact and semiconductor rectifiers. Here the referent is an electrical process that reshapes a current, not a geometric length, a court's correction of a document, or a discipline over words.[6]

Unit

A current waveform turned from alternating to one-directional, rated in volts and amperes

Recovery means

Not applicable

Measured by

Characterised by the ratio of forward to reverse conduction and by how fully the output current is made one-directional