Victor Steinbok aardvark66 at GMAIL.COM
Tue Oct 11 16:45:37 UTC 2011

I'm just sitting here, scratching my head. Here's a bunch of OED
definitions for math and computer use of "domain" (I'm leaving out the
logic ones, as well as the more general and legal ones):

> 4. c. Math. 'In the theory of Functions, the portion of the z-plane
> within a circle which just does not include a singular point is called
> the domain of its centre' (H. T. Gerrans).
> 1893    A. R. Forsyth Theory Functions Complex Variable 55   If the
> whole of the domain of b be not included in that of a.
>  d. Math. An algebraic system with two binary operations defined by
> postulates stronger than those for a ring but weaker than those for a
> field; esp. (more fully * integral domain*), a commutative ring in
> which the cancellation law holds for multiplication of non-zero
> elements and (with most writers) which has a unit element for
> multiplication.
> 1896
> 1904
> 1937
> 1941
> 1958
> 1965
>  e. Math. The set of values that an independent variable of a function
> can take; the graphical representation of this set; the set comprising
> all the first elements of the ordered pairs constituting some given set.
> 1902
> 1914
> 1937
> 1955
> 1967
> ...
>  g. Math. An open connected set of at least one point.
> 1906
> 1906
> 1957
> ...
> Draft additions March 2001
> Computing. A subset of locations on the Internet or other network
> which share a common element of their IP address (indicating a
> geographical, commercial or other affiliation), or which are under the
> control of a particular organization or individual; freq. in   *domain
> name* n. the part of a network address which identifies it as
> belonging to a particular domain.
> 1982
> ...

The Gerrans definition in 4.c. is essentially meaningless, when taken
out of context. What Gerrans described is commonly identified as
"neighborhood" of the point (and need not be literally a circle, nor
need the point be "the center"). I'm also wondering if the Forsyth quote
does not actually belong under 4.g.--but, without context, it's
impossible to tell. It does speak of "domain of b" (which is not a
subdomain of a), so maybe it's a correct ID--but, whatever the case,
this usage was very short-lived, which is why only one citation is
given. [In my recollection, 4.g. is the correct use for general open
connected sets. When these are tied to specific points, they are
identified as "neighborhoods of" these points.]

On the other hand,  4.e. is too narrowly defined (independent variable
values--yes; ordered "pairs"--no!). 4.d. is partially gibberish--trying
to make complicated math comprehensible in a non-mathematical
dictionary--why not just pull a definition from a math encyclopedia and
modify it to avoid plagiarism? A domain is a kind of ring with specific
additional properties (not "stronger than a ring").

And what's with "esp. more fully 'integral domain'"? This is one KIND of
domain in algebra, not "especially" referred to as "domain". What about
the Euclidean domain? Principal ideal domain? Are these "nothing
special" next to "integral domain"? [Wiki is better--see below.]

The computing definition does not "define" domain at all--it's a
description of something, but it's not a definition, certainly not a
definition of a "domain" (aside from the "control" part, which is
essential--but is the range 74.126.45.[0-99] a domain? or is it 100
domains? Does it matter if they are all controlled by the same entity?
What if two domain names are resolved to the same address? Is that one
domain or two?). Also note that "domain name" is normally shortened to
"domain", further entangling the already flawed lemma.

How bad is it? Subdomain is not defined at all--not for math, not for
computing. With definitions given above, it's not surprising--there is
really no plausible way to distinguish between a domain and a subdomain.

Apparently, Belgian judges were reading the OED definition when they
ordered blocked (along with a number of other
www-prefixed "domains"). The catch?
> So obviously in defiance of that, people testing their dns servers go
> to the domain, except, thepiratebay doesn't have
> the www domain turned on. At one point it redirected to the main page
> at the url, now it doesn't probably because of
> negligence from the admins. What's interesting is that the court only
> ordered the block of the www subdomains so if an isp wants to make a
> fuss they should be able to avoid the penalties until a later ruling.

It's a mess.

Of on-line dictionaries, only Wiktionary has "subdomain", but even there
it only limits it to computing--nothing for math, nothing for biology or
generalized taxonomy (note that these two are missing from the OED
entirely for domain as well):

> subdomain (plural subdomains)
> 1.    (computing, Internet) a domain name that has been prefaced with
> additional parts, each part ending in a period
>     * 1987 November, P. Mockapetris, Domain Concepts and Facilities,
>     RFC1034, also known as STD0013
>         A domain is a subdomain of another domain if it is contained
>         within that domain. This relationship can be tested by seeing
>         if the subdomain's name ends with the containing domain's
>         name. For example, A.B.C.D is a subdomain of B.C.D, C.D, D,
>         and " ".
>     * BIND 9 Administrator Reference Manual (9.3.2), Copyright © 2004,
>     2005 Internet Systems Consortium, Inc. ("ISC"), Copyright ©
>     2000-2003 Internet Software Consortium,
>         Every name in the DNS tree is a domain, even if it is
>         terminal, that is, has no subdomains. Every subdomain is a
>         domain and every domain except the root is also a subdomain.
> 2.    (computing, Internet) Any lower-level part of a domain name.
>     * In, en is a subdomain.

Note that BIND9 definition resembles a taxonomic one, which, in fact, it
is (no one talks about internet domain name taxonomy, however). There is
also a Usage Note:

> The technical community that created the terminology uses the first
> sense of a "domain name prefaced with additional parts".

Wikipedia is a bit briefer:

> In the Domain Name System (DNS) hierarchy, a subdomain is a domain
> that is part of a larger domain.

As I said, biological senses of "domain" are completely missing, which
is why there is no entry for "protein domain" either. From Wiki,

> A protein domain is a part of protein sequence and structure that can
> evolve, function, and exist independently of the rest of the protein chain

Thee can also have "subdomains" as constituent parts.

Wiki also has an entry on the taxonomic use of "domain":

> In biological taxonomy, a domain (also superregnum, superkingdom,
> empire, or regio) is the highest taxonomic rank of organisms, higher
> than a kingdom.

It's worth checking the entire Wiki list--some of it is kind of blah,
but most is quite good:

FarLex actually says something interesting:

> A lower-level component of a domain name. For example,
> and are subdomains of
>, which is known as a "second level domain." See naked
> domain, zone and root domain.

The "subdomain" is a component of a "domain name", not a "domain". Is
that right? glossary makes another important distinction:

> Subdomain is a way to divide your site into sections with short and
> easy to remember names.

This is true, but, unfortunately, it's not a definition--subdomains ay
include a number of websites (e.g., if a hosting service grants specific
sites to its users that are marked like folders, e.g., faculty pages at
university domains). A domain is not a site and vice versa. Nor is it a
server or an address.

AHD has greatly simplified listing for "domain":

> Mathematics:
> *    The set of all possible values of an independent variable of a
> function.
> *    An open connected set that contains at least one point.
> Computer Science: A group of networked computers that share a common
> communications address.

Not perfect, but much better than the alternative in the OED. Still
missing a few...


PS: I left out the other definitions, but note that "eminent domain" is
a legal concept, not a general one--and there is no "Law" notation in
domain 2.a., even though the first citation (bracketed) is to Grotius.
Longfellow used it poetically, but it's still a legal concept.

PPS: Another missing definition is of a magnetic domain as the region of
uniform magnetization. This is fairly standard, so should be covered.

The American Dialect Society -

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