[Inquiry] Re: Differential Logic -- Series B

[Jon Awbrey]

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DLOG.  Note B13

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We were focussing on a particular figure of syntax,
presented here in both graph and string renditions:

o-------------------------------------------------o
|                                                 |
|                     x     y                     |
|                     o-----o                     |
|                      \   /                      |
|                       \ /                       |
|                        @                        |
|                                                 |
o-------------------------------------------------o
|                    ( x , y )                    |
o-------------------------------------------------o

In traversing the cactus graph, in this case a cactus
of one rooted lobe, one starts at the root, reads off
a left parenthesis "(" on the ascent up the left side
of the lobe, reads off the variable "x", counts off a
comma "," as one transits the interior expanse of the
lobe, reads off the variable "y", and then sounds out
a right parenthesiss ")" on the descent down the last
slope that closes out the clause of this cactus lobe.

According to the current story about how the abstract logical situation
is embodied in the concrete physical situation, the whole pool of units
that corresponds to this expression comes to its resting condition when
just one of the two units in {x, y} is resting and the other is charged.
We may think of the state of the whole pool as associated with the root
node of the cactus, here distinguished by an "amphora" or "at" sign "@",
but the root of the cactus is not represented by an individual agent of
the system, at least, not yet.  We may summarize these facts in tabular
form, as shown in Table 5.  Simply by way of a common term, let's count
a single unit as a "pool of one".

Table 5.  Dynamics of (x , y)
o---------o---------o---------o
|    x    |    y    | (x , y) |
o=========o=========o=========o
| resting | resting | charged |
o---------o---------o---------o
| resting | charged | resting |
o---------o---------o---------o
| charged | resting | resting |
o---------o---------o---------o
| charged | charged | charged |
o---------o---------o---------o

I'm going to let that settle a while.

Rock & Roll,

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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