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Directory:Jon Awbrey/Papers/Futures Of Logical Graphs (view source)
Revision as of 13:44, 28 July 2009
, 13:44, 28 July 2009→Introduction: fix format for variables
The outermost region of the plane-embedded graph is singled out for special consideration and the corresponding node of the dual graph is referred to as its ''root node''. By way of graphical convention in the present text, the root node is indicated by means of a horizontal strike-through.
The outermost region of the plane-embedded graph is singled out for special consideration and the corresponding node of the dual graph is referred to as its ''root node''. By way of graphical convention in the present text, the root node is indicated by means of a horizontal strike-through.
Extracting the dual graph from its composite matrix, we get this picture:
Extracting the dual graph from its composite matrix gives the following picture:
{| align="center" cellpadding="10"
{| align="center" cellpadding="10"
Nodes in a graph depict ''records'' in computer memory. A record is a collection of data that can be thought to reside at a specific ''address''. For semioticians, an address can be recognized as a type of index, and is commonly spoken of, on analogy with demonstrative pronouns, as a ''pointer'', even among computer programmers who are otherwise innocent of semiotics.
Nodes in a graph depict ''records'' in computer memory. A record is a collection of data that can be thought to reside at a specific ''address''. For semioticians, an address can be recognized as a type of index, and is commonly spoken of, on analogy with demonstrative pronouns, as a ''pointer'', even among computer programmers who are otherwise innocent of semiotics.
At the next level of concreteness, a pointer-record structure may be represented as follows:
At the next level of concreteness, a pointer-record structure is represented as follows:
{| align="center" cellpadding="10"
{| align="center" cellpadding="10"
|}
|}
This portrays the pointer <math>\operatorname{index}_0</math> as the address of a record that contains the following data:
This portrays the pointer <math>\mathit{index}_0\!</math> as the address of a record that contains the following data:
{| align="center" cellpadding="10"
{| align="center" cellpadding="10"
| <math>\operatorname{datum}_1, \operatorname{datum}_2, \operatorname{datum}_3, \ldots,</math> and so on.
| <math>\mathit{datum}_1, \mathit{datum}_2, \mathit{datum}_3, \ldots,\!</math> and so on.
|}
|}