Changes

|}

|}

Table 5 accumulates an array of notation that I hope will not be too distracting.  Some of it is rarely needed, but has been filled in for the sake of completeness.  Its purpose is simple, to give literal expression to the visual intuitions that come with venn diagrams, and to help build a bridge between our qualitative and quantitative outlooks on dynamic systems.

Table 5 accumulates an array of notation that I hope will not be too distracting.  Some of it is rarely needed, but has been filled in for the sake of completeness.  Its purpose is simple, to give literal expression to the visual intuitions that come with venn diagrams, and to help build a bridge between our qualitative and quantitative outlooks on dynamic systems.

{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%"

|+ '''Table 5. A Bridge Over Troubled Waters'''

 

|- style="background:ghostwhite"

{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; width:90%"

| align="center" | <math>\mbox{Linear Space}\!</math>

|+ <math>\text{Table 5.}~~\text{A Bridge Over Troubled Waters}</math>

| align="center" | <math>\mbox{Liminal Space}\!</math>

|- style="background:#f0f0ff"

| align="center" | <math>\mbox{Logical Space}\!</math>

| align="center" | <math>\text{Linear Space}\!</math>

| align="center" | <math>\text{Liminal Space}\!</math>

| align="center" | <math>\text{Logical Space}\!</math>

|-

|-

|

|

= & [\mathbb{B}^n]                                    \\

= & [\mathbb{B}^n]                                    \\

\end{matrix}</math>

\end{matrix}</math>

|}<br>

|}

 

<br>

The left side of the Table collects mostly standard notation for an <math>n\!</math>-dimensional vector space over a field <math>\mathbb{K}.</math>  The right side of the table repeats the first elements of a notation that I sketched above, to be used in further developments of propositional calculus.  (I plan to use this notation in the logical analysis of neural network systems.)  The middle column of the table is designed as a transitional step from the case of an arbitrary field <math>\mathbb{K},</math> with a special interest in the continuous line <math>\mathbb{R},</math> to the qualitative and discrete situations that are instanced and typified by <math>\mathbb{B}.</math>

The left side of the Table collects mostly standard notation for an <math>n\!</math>-dimensional vector space over a field <math>\mathbb{K}.</math>  The right side of the table repeats the first elements of a notation that I sketched above, to be used in further developments of propositional calculus.  (I plan to use this notation in the logical analysis of neural network systems.)  The middle column of the table is designed as a transitional step from the case of an arbitrary field <math>\mathbb{K},</math> with a special interest in the continuous line <math>\mathbb{R},</math> to the qualitative and discrete situations that are instanced and typified by <math>\mathbb{B}.</math>