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===Note 20===
 
===Note 20===
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<pre>
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<blockquote>
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| the way of heaven and earth
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<p>the way of heaven and earth</p>
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| is to be long continued
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<p>is to be long continued</p>
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| in their operation
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<p>in their operation</p>
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| without stopping
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<p>without stopping</p>
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|
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| i ching, hexagram 32
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You may be wondering what happened to the announced subject of "Differential Logic".
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<p>i ching, hexagram 32</p>
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If you think that we have been taking a slight excursion my reply to the charge of
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</blockquote>
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a scenic rout would be both "yes and no".  What happened was this.  We chanced to
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make the observation that the shift operators E_ij form a transformation group
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that acts on the set of propositions of the form f : B^2 -> B.  Group theory
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is a very attractive subject, but it did not have the effect of drawing us
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so far off our initial course as one might at first think.  For one thing,
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groups, in particular, the special family of groups that have come to be
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named after the Norwegian mathematician Marius Sophus Lie, turn out to
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be of critical importance in the solution of differential equations.
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For another thing, group operations afford us examples of 3-adic
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relations that have been extremely well-studied over the years,
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and thus they supply us with no small bit of guidance in the
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study of sign relations, another class of 3-adic relations
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that have significance for logical studies, in our brief
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acquaintance with which we have scarcely even begun to
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break the ice.  Finally, I could not resist taking up
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the connection between group representations, which
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constitute a very generic class of logical models,
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and the all-important pragmatic maxim.
     −
Biographical Data for Marius Sophus Lie (1842-1899):
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You may be wondering what happened to the announced subject of "Differential Logic".  If you think that we have been taking a slight excursion my reply to the charge of a scenic rout would be both "yes and no".  What happened was this.  We chanced to make the observation that the shift operators E<sub>''ij''</sub> form a transformation group that acts on the set of propositions of the form ''f''&nbsp;:&nbsp;'''B'''<sup>2</sup>&nbsp;&rarr;&nbsp;'''B'''.  Group theory is a very attractive subject, but it did not have the effect of drawing us so far off our initial course as one might at first think.  For one thing, groups, in particular, the special family of groups that have come to be named after the Norwegian mathematician Marius Sophus Lie, turn out to be of critical importance in the solution of differential equations.  For another thing, group operations afford us examples of 3-adic relations that have been extremely well-studied over the years, and thus they supply us with no small bit of guidance in the study of sign relations, another class of 3-adic relations that have significance for logical studies, in our brief acquaintance with which we have scarcely even begun to break the ice.  Finally, I could not resist taking up the connection between group representations, which constitute a very generic class of logical models, and the all-important pragmatic maxim.
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http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Lie.html
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</pre>
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[http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Lie.html Biographical Data for Marius Sophus Lie (1842–1899)]
    
===Note 21===
 
===Note 21===
Jon Awbrey
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