🚀 go-pugleaf

I was a bit sloppy in the construction of my arguments in my original post.
Prof. Birnbaum has pointed out a number of weaknesses, some of which reflect
inaccuracies in my writing, and some of which indicate that I had not given
enough thought to the issues.  Kyongsok Kim has picked up on one of the
issues that reflects both failings.

I have yet to see Prof. Birnbaum's response posted, although I have
an e-mail copy.  When it appears, I will post some clarifications regarding
issues that he raised, and I look forward to hearing from others about
the basic socio-political difference between our respective positions.

kkim@plains.NoDak.edu (kyongsok kim) writes:

> As far as I know, #integers is NOT finite; however, #characters is FINITE
> (although it may be VERY LARGE), isn't it?  I have hard time figuring out
> a parallelism here.  Please correct me if I am missing something here?

My intention was only to illustrate that we do make abstractions that are
geared towards making implementations reasonable.  However, I might argue
that the analogy is fairly close: the set of characters is finite, but of
unknown extent and with no provable upper bound on it's membership. This
being the case, it is not possible to specify a maximum 'size' (either for
a bit encoding, a byte-sequence encoding, a Turing machine, or any other
mechanism) of a single character.

I don't have trouble believing that the set of characters has no provable
upper bound on membership.  I also argue that even if there is a provable
boundary today, that it is not static.  I would contend that the size of the
set must be monotonically increasing as new "written culture" (cf. DB's post)
is created and/or discovered but (thanks to Historians, Linguists,
Archaeologists, et al.) not often irrevocably lost.  My argument on
this point is lacking somewhat in intellectual rigor [ that's what
eight years of implementation work can do to you :-) ], but I doubt
I can be proven incorrect.

I do not mean to imply that no abstraction can be devised to represent any
member of an infinite set.  If I recall correctly, X.409 / ASN.1 encoding
provides an elegant method for representing arbitrary size integers.  My
intention was to illustrate that it is always possible to choose a member of
the set of size sufficient to overflow available space in an implementation
of any abstraction, either by exceeding fixed limits implied in the
abstraction itself, or by exceeding limits on resources.

For characters, this is as true as it is for integers.  In a fixed-width
bit encoding method, eventually one can always devise enough characters
to exhaust the available values.  In a completely open-ended variable-width-
byte-sequence encoding, it is possible to construct a character that overflows
storage limits.  In a scheme in which a limited sequence of members of a subset
of the fixed-width characters (i.e., diacritics) can be applied to a single
member of a different subset of the fixed-width characters (i.e., base
symbols), the base subset and diacritic subset are both instances of
fixed-width bit encodings, ergo the available values of both may eventually
be exhausted.

So, yes, the analogy as I stated it initially is weak.  Never-the-less, I
believe that if we accept that the set of characters is finite but of
unknown extent, the analogy does hold.  And the purpose that I had in
mind was to demonstrate that the pragmatic concerns of implementors are not
only legitimate... they are inevitable.

rich schwartz   (All views expressed are my own, and not Wang Labs, Inc.'s.)
 rschwartz@office.wang.com      VOICE (508) 967 5027     FAX (508) 967 0947
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