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Directory:Jon Awbrey/Papers/Cactus Language (view source)
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, 05:14, 10 January 2009→The Cactus Language : Stylistics: markup
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In this picture <math>Q\!</math> is a certain set and <math>X\!</math> is the universe of discourse that is relevant to a given discussion. Since a stricture does not, by itself, contain a sufficient amount of information to specify the number of sets that it intends to set in place, or even to specify the absolute location of the set that its does set in place, it appears to place an unspecified number of unspecified sets in a vague and uncertain strait. Taken out of its interpretive context, the residual information that a stricture can convey makes all of the following potentially equivalent as strictures:
In this picture, Q is a certain set, and X is the universe of discourse
that is relevant to a given discussion. Since a stricture does not, by
itself, contain a sufficient amount of information to specify the number
of sets that it intends to set in place, or even to specify the absolute
location of the set that its does set in place, it appears to place an
unspecified number of unspecified sets in a vague and uncertain strait.
Taken out of its interpretive context, the residual information that a
stricture can convey makes all of the following potentially equivalent
as strictures:
"Q", "XxQxX", "XxXxQxXxX", ...
{| align="center" cellpadding="8" width="90%"
|
<math>\begin{array}{ccccccc}
^{\backprime\backprime} Q ^{\prime\prime}
& , &
^{\backprime\backprime} X \times Q \times X ^{\prime\prime}
& , &
^{\backprime\backprime} X \times X \times Q \times X \times X ^{\prime\prime}
& , &
\ldots
\\
\end{array}</math>
|}
With respect to what these strictures specify, this
With respect to what these strictures specify, this leaves all of the following equivalent as straits:
leaves all of the following equivalent as straits:
{| align="center" cellpadding="8" width="90%"
|
<math>\begin{array}{ccccccc}
Q
& = &
X \times Q \times X
& = &
X \times X \times Q \times X \times X
& = &
\ldots
\\
\end{array}</math>
|}
Within the framework of a particular discussion, it is customary to
Within the framework of a particular discussion, it is customary to set a bound on the number of places and to limit the variety of sets that are regarded as being under active consideration, and it is also convenient to index the places of the indicated relations, and of their encompassing cartesian products, in some fixed way. But the whole idea of a stricture is to specify a strait that is capable of extending through and beyond any fixed frame of discussion. In other words, a stricture is conceived to constrain a strait at a certain point, and then to leave it literally embedded, if tacitly expressed, in a yet to be fully specified relation, one that involves an unspecified number of unspecified domains.
set a bound on the number of places and to limit the variety of sets
that are regarded as being under active consideration, and it is also
convenient to index the places of the indicated relations, and of their
encompassing cartesian products, in some fixed way. But the whole idea
of a stricture is to specify a strait that is capable of extending through
and beyond any fixed frame of discussion. In other words, a stricture is
conceived to constrain a strait at a certain point, and then to leave it
literally embedded, if tacitly expressed, in a yet to be fully specified
relation, one that involves an unspecified number of unspecified domains.
A quantity of information is a measure of constraint. In this respect,
A quantity of information is a measure of constraint. In this respect, a set of comparable strictures is ordered on account of the information that each one conveys, and a system of comparable straits is ordered in accord with the amount of information that it takes to pin each one of them down. Strictures that are more constraining and straits that are more constrained are placed at higher levels of information than those that are less so, and entities that involve more information are said to have a greater ''complexity'' in comparison with those entities that involve less information, that are said to have a greater ''simplicity''.
a set of comparable strictures is ordered on account of the information
that each one conveys, and a system of comparable straits is ordered in
accord with the amount of information that it takes to pin each one of
them down. Strictures that are more constraining and straits that are
more constrained are placed at higher levels of information than those
that are less so, and entities that involve more information are said
to have a greater "complexity" in comparison with those entities that
involve less information, that are said to have a greater "simplicity".
<pre>
In order to create a concrete example, let me now institute a frame of
In order to create a concrete example, let me now institute a frame of
discussion where the number of places in a relation is bounded at two,
discussion where the number of places in a relation is bounded at two,