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===Commentary Note 8.5===

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~~<pre>~~

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Since multiplication by a 2-adic relative term is a logical analogue of matrix multiplication in linear algebra, all of the products that we computed above can be represented in terms of logical matrices and logical vectors.

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Since multiplication by a 2-adic relative term

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is a logical analogue of matrix multiplication

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in linear algebra, all of the products that we

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computed above can be represented in terms of

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logical matrices and logical vectors.

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Here are the absolute terms again, followed by

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Here are the absolute terms again, followed by their representation as "coefficient tuples", otherwise thought of as "coordinate vectors".

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their representation as "coefficient tuples",

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otherwise thought of as "coordinate vectors".

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1 = B +, C +, D +, E +, I +, J +, O

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: 1 = B +, C +, D +, E +, I +, J +, O

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= <1, 1, 1, 1, 1, 1, 1>

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:: = <1, 1, 1, 1, 1, 1, 1>

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b = O

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: b = O

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= <0, 0, 0, 0, 0, 0, 1>

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:: = <0, 0, 0, 0, 0, 0, 1>

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m = C +, I +, J +, O

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: m = C +, I +, J +, O

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= <0, 1, 0, 0, 1, 1, 1>

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:: = <0, 1, 0, 0, 1, 1, 1>

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w = B +, D +, E

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: w = B +, D +, E

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= <1, 0, 1, 1, 0, 0, 0>

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:: = <1, 0, 1, 1, 0, 0, 0>

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Since we are going to be regarding these tuples as "column vectors",

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Since we are going to be regarding these tuples as "column vectors", it is convenient to arrange them into a table of the following form:

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it is convenient to arrange them into a table of the following form:

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<pre>

| 1 b m w

---o---------

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J | 1 0 1 0

O | 1 1 1 0

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</pre>

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Here are the 2-adic relative terms again, followed by

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Here are the 2-adic relative terms again, followed by their representation as coefficient matrices, in this case bordered by row and column labels to remind us what the coefficient values are meant to signify.

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their representation as coefficient matrices, in this

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case bordered by row and column labels to remind us

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what the coefficient values are meant to signify.

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'l' = B:C +, C:B +, D:O +, E:I +, I:E +, O:D =

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: 'l' = B:C +, C:B +, D:O +, E:I +, I:E +, O:D =

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<pre>

'l'| B C D E I J O

---o---------------

Line 718: Line 710:

J | 0 0 0 0 0 0 0

O | 0 0 1 0 0 0 0

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</pre>

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's' = C:O +, E:D +, I:O +, J:D +, J:O =

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: 's' = C:O +, E:D +, I:O +, J:D +, J:O =

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<pre>

's'| B C D E I J O

---o---------------

Line 730: Line 724:

J | 0 0 1 0 0 0 1

O | 0 0 0 0 0 0 0

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</pre>

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Here are the matrix representations of

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Here are the matrix representations of the products that we calculated before:

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the products that we calculated before:

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'l'1 = "lover of anybody" =

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: 'l'1 = "lover of anybody" =

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<pre>

| 0 1 0 0 0 0 0 | | 1 | | 1 |

| 1 0 0 0 0 0 0 | | 1 | | 1 |

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| 0 0 0 0 0 0 0 | | 1 | | 0 |

| 0 0 1 0 0 0 0 | | 1 | | 1 |

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</pre>

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'l'b = "lover of a black" =

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: 'l'b = "lover of a black" =

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<pre>

| 0 1 0 0 0 0 0 | | 0 | | 0 |

| 1 0 0 0 0 0 0 | | 0 | | 0 |

Line 753: Line 750:

| 0 0 0 0 0 0 0 | | 0 | | 0 |

| 0 0 1 0 0 0 0 | | 1 | | 0 |

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</pre>

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'l'm = "lover of a man" =

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: 'l'm = "lover of a man" =

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<pre>

| 0 1 0 0 0 0 0 | | 0 | | 1 |

| 1 0 0 0 0 0 0 | | 1 | | 0 |

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| 0 0 0 0 0 0 0 | | 1 | | 0 |

| 0 0 1 0 0 0 0 | | 1 | | 0 |

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</pre>

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'l'w = "lover of a woman" =

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: 'l'w = "lover of a woman" =

+

<pre>

| 0 1 0 0 0 0 0 | | 1 | | 0 |

| 1 0 0 0 0 0 0 | | 0 | | 1 |

Line 773: Line 774:

| 0 0 0 0 0 0 0 | | 0 | | 0 |

| 0 0 1 0 0 0 0 | | 0 | | 1 |

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</pre>

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's'1 = "servant of anybody" =

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: 's'1 = "servant of anybody" =

+

<pre>

| 0 0 0 0 0 0 0 | | 1 | | 0 |

| 0 0 0 0 0 0 1 | | 1 | | 1 |

Line 783: Line 786:

| 0 0 1 0 0 0 1 | | 1 | | 1 |

| 0 0 0 0 0 0 0 | | 1 | | 0 |

+

</pre>

−

's'b = "servant of a black" =

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: 's'b = "servant of a black" =

+

<pre>

| 0 0 0 0 0 0 0 | | 0 | | 0 |

| 0 0 0 0 0 0 1 | | 0 | | 1 |

Line 793: Line 798:

| 0 0 1 0 0 0 1 | | 0 | | 1 |

| 0 0 0 0 0 0 0 | | 1 | | 0 |

+

</pre>

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's'm = "servant of a man" =

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: 's'm = "servant of a man" =

+

<pre>

| 0 0 0 0 0 0 0 | | 0 | | 0 |

| 0 0 0 0 0 0 1 | | 1 | | 1 |

Line 803: Line 810:

| 0 0 1 0 0 0 1 | | 1 | | 1 |

| 0 0 0 0 0 0 0 | | 1 | | 0 |

+

</pre>

−

's'w = "servant of a woman" =

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: 's'w = "servant of a woman" =

+

<pre>

| 0 0 0 0 0 0 0 | | 1 | | 0 |

| 0 0 0 0 0 0 1 | | 0 | | 0 |

Line 813: Line 822:

| 0 0 1 0 0 0 1 | | 0 | | 1 |

| 0 0 0 0 0 0 0 | | 0 | | 0 |

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</pre>

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'ls' = "lover of a servant of ---" =

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: 'ls' = "lover of a servant of ---" =

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<pre>

| 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 |

| 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 |

Line 823: Line 834:

| 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 1 | | 0 0 0 0 0 0 0 |

| 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 |

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</pre>

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'sl' = "servant of a lover of ---" =

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: 'sl' = "servant of a lover of ---" =

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<pre>

| 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 |

| 0 0 0 0 0 0 1 | | 1 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 |

Jon Awbrey

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