Changes

===Note 8===

===Note 8===

Before going on, it would probably be a good idea to remind ourselves of just why we are going through with this exercise.  It is to unify the world of change, for which aspect or regime of the world I occasionally evoke the eponymous figures of Prometheus and Heraclitus, and the world of logic, for which facet or realm of the world I periodically recur to the prototypical shades of Epimetheus and Parmenides, at least, that is, to state it more carefully, to encompass the antics and the escapades of these all too manifestly strife-born twins within the scopes of our thoughts and within the charts of our theories, as it is most likely the only places where ever they will, for the moment and as long as it lasts, be seen or be heard together.

Before going on -- in order to keep alive the will to go on! --

it would probably be a good idea to remind ourselves of just

why we are going through with this exercise.  It is to unify

the world of change, for which aspect or regime of the world

I occasionally evoke the eponymous figures of Prometheus and

Heraclitus, and the world of logic, for which facet or realm

of the world I periodically recur to the prototypical shades

of Epimetheus and Parmenides, at least, that is, to state it

more carefully, to encompass the antics and the escapades of

these all too manifestly strife-born twins within the scopes

of our thoughts and within the charts of our theories, as it

is most likely the only places where ever they will, for the

moment and as long as it lasts, be seen or be heard together.

With that intermezzo, with all of its echoes of the opening overture,

With that intermezzo, with all of its echoes of the opening overture, over and done, let us now return to that droller drama, already fast in progress, the differential disentanglements, hopefully toward the end of a grandly enlightening denouement, of the ever-polymorphous <math>Q.\!</math>

over and done, let us now return to that droller drama, already fast

in progress, the differential disentanglements, hopefully toward the

end of a grandly enlightening denouement, of the ever-polymorphous Q.

The next transformation of the source proposition q, that we are

The next transformation of the source proposition <math>q,\!</math> that we are typically aiming to contemplate in the process of carrying out a ''differential analysis'' of its ''dynamic'' effects or implications, is the yield of the so-called ''difference'' or ''delta'' operator <math>\operatorname{D}.</math>  The resultant ''difference proposition'' <math>\operatorname{D}q</math> is defined in terms of the source proposition <math>q\!</math> and the ''shifted proposition'' <math>\operatorname{E}q</math> thusly:

typically aiming to contemplate in the process of carrying out a

"differential analysis" of its "dynamic" effects or implications,

is the yield of the so-called "difference" or "delta" operator D.

The resultant "difference proposition" Dq is defined in terms of

the source proposition q and the "shifted proposition" Eq thusly:

   | Dq  =  Eq - q  =  Eq - eq.

   | Dq  =  Eq - q  =  Eq - eq.

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