canonical

(Historically, "according to religious law")

1. mathematics A standard way of writing a formula. Two

formulas such as 9 + x and x + 9 are said to be equivalent

because they mean the same thing, but the second one is in

"canonical form" because it is written in the usual way, with

the highest power of x first. Usually there are fixed rules

you can use to decide whether something is in canonical form.

Things in canonical form are easier to compare.

2. jargon The usual or standard state or manner of

something. The term acquired this meaning in computer-science

culture largely through its prominence in Alonzo Church's

work in computation theory and mathematical logic (see

Knights of the Lambda-Calculus).

Compare vanilla.

This word has an interesting history. Non-technical academics

do not use the adjective "canonical" in any of the senses

defined above with any regularity; they do however use the

nouns "canon" and "canonicity" (not "canonicalness"* or

"canonicality"*). The "canon" of a given author is the

complete body of authentic works by that author (this usage is

familiar to Sherlock Holmes fans as well as to literary

scholars). "The canon" is the body of works in a given field

(e.g. works of literature, or of art, or of music) deemed

worthwhile for students to study and for scholars to

investigate.

The word "canon" derives ultimately from the Greek "kanon"

(akin to the English "cane") referring to a reed. Reeds were

used for measurement, and in Latin and later Greek the word

"canon" meant a rule or a standard. The establishment of a

canon of scriptures within Christianity was meant to define a

standard or a rule for the religion. The above non-technical

academic usages stem from this instance of a defined and

accepted body of work. Alongside this usage was the

promulgation of "canons" ("rules") for the government of the

Catholic Church. The usages relating to religious law derive

from this use of the Latin "canon". It may also be related to

arabic "qanun" (law).

Hackers invest this term with a playfulness that makes an

ironic contrast with its historical meaning. A true story:

One Bob Sjoberg, new at the MIT AI Lab, expressed some

annoyance at the incessant use of jargon. Over his loud

objections, GLS and RMS made a point of using as much of

it as possible in his presence, and eventually it began to

sink in. Finally, in one conversation, he used the word

"canonical" in jargon-like fashion without thinking. Steele:

"Aha! We've finally got you talking jargon too!" Stallman:

"What did he say?" Steele: "Bob just used "canonical" in the

canonical way."

Of course, canonicality depends on context, but it is

implicitly defined as the way *hackers* normally expect things

to be. Thus, a hacker may claim with a straight face that

"according to religious law" is *not* the canonical meaning of

"canonical".

(2002-02-06)