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{{DISPLAYTITLE:Differential Analytic Turing Automata}}
 
{{DISPLAYTITLE:Differential Analytic Turing Automata}}
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==DATA.  Note 1==
    
<pre>
 
<pre>
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IDS -- DATA
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DATA.  Differential Analytic Turing Automata
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DATA.  Note 1
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For the purposes of the NKS Forum my aim is to chart a course from
 
For the purposes of the NKS Forum my aim is to chart a course from
 
general ideas about "transformational equivalence classes of graphs"
 
general ideas about "transformational equivalence classes of graphs"
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That should be enough to get started.
 
That should be enough to get started.
 +
</pre>
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==DATA.  Note 2==
−
 
  −
DATA.  Note 2
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
I will be making use of the "cactus language" extension of
 
I will be making use of the "cactus language" extension of
 
Peirce's Alpha Graphs, so called because it uses a species
 
Peirce's Alpha Graphs, so called because it uses a species
Line 108: Line 94:  
in hopes of making them as clear as they can be,
 
in hopes of making them as clear as they can be,
 
so please let me know if you have any questions.
 
so please let me know if you have any questions.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 3==
−
 
  −
DATA.  Note 3
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
I will draw on those previously advertized resources
 
I will draw on those previously advertized resources
 
of notation and theory as needed, but right now
 
of notation and theory as needed, but right now
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I'll leave you to muse on
 
I'll leave you to muse on
 
the possibilities of that.
 
the possibilities of that.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 4==
−
 
  −
DATA.  Note 4
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
I am preparing a more fleshed-out 1-variable example,
 
I am preparing a more fleshed-out 1-variable example,
 
but in the mean time, for anybody who's finished all
 
but in the mean time, for anybody who's finished all
Line 188: Line 170:     
DLOG D11.  http://stderr.org/pipermail/inquiry/2003-May/000489.html
 
DLOG D11.  http://stderr.org/pipermail/inquiry/2003-May/000489.html
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 5==
−
 
  −
DATA.  Note 5
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
For a slightly more interesting example, let's suppose that
 
For a slightly more interesting example, let's suppose that
 
we have a dynamic system that is known by its state space X,
 
we have a dynamic system that is known by its state space X,
Line 237: Line 217:     
DLOG D20.  http://stderr.org/pipermail/inquiry/2003-May/000498.html
 
DLOG D20.  http://stderr.org/pipermail/inquiry/2003-May/000498.html
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 6==
−
 
  −
DATA.  Note 6
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
One more example may serve to suggest just how much dynamic
 
One more example may serve to suggest just how much dynamic
 
complexity can be built on a universe of discourse that has
 
complexity can be built on a universe of discourse that has
Line 307: Line 285:     
Zoom^4 ...
 
Zoom^4 ...
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 7==
−
 
  −
DATA.  Note 7
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Here are the 4^th gear curves over the 1-feature universe
 
Here are the 4^th gear curves over the 1-feature universe
 
X = <|x|> arranged in the form of tabular arrays, listing
 
X = <|x|> arranged in the form of tabular arrays, listing
Line 355: Line 331:     
DLOG D24.  http://stderr.org/pipermail/inquiry/2003-May/000503.html
 
DLOG D24.  http://stderr.org/pipermail/inquiry/2003-May/000503.html
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 8==
−
 
  −
DATA.  Note 8
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
I am going to tip-toe in silence/consilience past many
 
I am going to tip-toe in silence/consilience past many
 
questions of a philosophical nature/nurture that might
 
questions of a philosophical nature/nurture that might
Line 424: Line 398:     
DLOG D73.  http://stderr.org/pipermail/inquiry/2003-June/000557.html
 
DLOG D73.  http://stderr.org/pipermail/inquiry/2003-June/000557.html
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 9==
−
 
  −
DATA.  Note 9
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
By virtue of Zipf's law -- yes, there is a dynamics to its economics --
 
By virtue of Zipf's law -- yes, there is a dynamics to its economics --
 
I have found myself forced, when it comes to matters that I've been
 
I have found myself forced, when it comes to matters that I've been
Line 506: Line 478:  
No more angels on pinheads,
 
No more angels on pinheads,
 
the brass tacks next time.
 
the brass tacks next time.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 10==
−
 
  −
DATA.  Note 10
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
It is time to formulate the differential analysis of
 
It is time to formulate the differential analysis of
 
a logical transformation, or a "mapping of discourse".
 
a logical transformation, or a "mapping of discourse".
Line 585: Line 555:  
let's return to particular cases, and carry out the first order
 
let's return to particular cases, and carry out the first order
 
analysis of the transformation F<u, v>  =  <((u)(v)), ((u, v))>.
 
analysis of the transformation F<u, v>  =  <((u)(v)), ((u, v))>.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 11==
−
 
  −
DATA.  Note 11
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
By way of getting our feet back on solid ground, let's crank up
 
By way of getting our feet back on solid ground, let's crank up
 
our current case of a transformation of discourse, F : U% -> X%,
 
our current case of a transformation of discourse, F : U% -> X%,
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the first basin and the orbit <1, 1> making
 
the first basin and the orbit <1, 1> making
 
up an isolated basin.
 
up an isolated basin.
 +
</pre>
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o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 12==
−
 
  −
DATA.  Note 12
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Way back in DATA Note 3, we guessed, or "abduced",
 
Way back in DATA Note 3, we guessed, or "abduced",
 
as a line of logicians from Aristotle to Peirce
 
as a line of logicians from Aristotle to Peirce
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I am going to take a nap to clear my head.
 
I am going to take a nap to clear my head.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 13==
−
 
  −
DATA.  Note 13
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
I think that it ought to be clear at this point that we
 
I think that it ought to be clear at this point that we
 
need a more systematic symbolic method for computing the
 
need a more systematic symbolic method for computing the
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I'll break this here in case anyone wants
 
I'll break this here in case anyone wants
 
to try and do the work for g on their own.
 
to try and do the work for g on their own.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 14==
−
 
  −
DATA.  Note 14
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
No doubt everybody who's still awake sacrificed
 
No doubt everybody who's still awake sacrificed
 
the few spare moments of their sleep last night
 
the few spare moments of their sleep last night
Line 1,025: Line 987:  
o---------------------------------------o
 
o---------------------------------------o
 
Figure 2.3.  Dg = g + Eg
 
Figure 2.3.  Dg = g + Eg
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 15==
−
 
  −
DATA.  Note 15
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
| 'Tis a derivative from me to mine,
 
| 'Tis a derivative from me to mine,
 
|  And only that I stand for.
 
|  And only that I stand for.
Line 1,084: Line 1,044:  
and these are the propositions that are commonly denoted:
 
and these are the propositions that are commonly denoted:
 
0, du, dv, du + dv, in other words, (), du, dv, (du, dv).
 
0, du, dv, du + dv, in other words, (), du, dv, (du, dv).
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 16==
−
 
  −
DATA.  Note 16
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
| for equalities are so weighed
 
| for equalities are so weighed
 
| that curiosity in neither can
 
| that curiosity in neither can
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Well, g, that was easy, seeing as how Dg
 
Well, g, that was easy, seeing as how Dg
 
is already linear at each locus, dg = Dg.
 
is already linear at each locus, dg = Dg.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 17==
−
 
  −
DATA.  Note 17
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
We have been conducting the differential analysis
 
We have been conducting the differential analysis
 
of the logical transformation F : [u, v] -> [u, v]
 
of the logical transformation F : [u, v] -> [u, v]
Line 1,259: Line 1,215:     
Take your pick, Gimli ...
 
Take your pick, Gimli ...
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 18==
−
 
  −
DATA.  Note 18
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Let's push on with the analysis of the transformation:
 
Let's push on with the analysis of the transformation:
   Line 1,508: Line 1,462:     
Exercise for the Reader.
 
Exercise for the Reader.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 19==
−
 
  −
DATA.  Note 19
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
I'd never rob readers of exercise ...
 
I'd never rob readers of exercise ...
 
but for my ain sense of an ending ---
 
but for my ain sense of an ending ---
Line 1,754: Line 1,706:  
|
 
|
 
| Leonard Cohen, "Teachers" (1967)
 
| Leonard Cohen, "Teachers" (1967)
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 20==
−
 
  −
DATA.  Note 20
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
In my work on "Differential Logic and Dynamic Systems",
 
In my work on "Differential Logic and Dynamic Systems",
 
I found it useful to develop several different ways of
 
I found it useful to develop several different ways of
Line 1,818: Line 1,768:  
that u and v are not both true at the same time, while
 
that u and v are not both true at the same time, while
 
du is equal in value to v, and dv is the opposite of u.
 
du is equal in value to v, and dv is the opposite of u.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 21==
−
 
  −
DATA.  Note 21
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
By way of providing a simple illustration of Cook's Theorem,
 
By way of providing a simple illustration of Cook's Theorem,
 
namely, that "Propositional Satisfiability is NP-Complete",
 
namely, that "Propositional Satisfiability is NP-Complete",
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The "tape-head" (that is, the "read-unit") will be called "H".
 
The "tape-head" (that is, the "read-unit") will be called "H".
 
The "registers" are also called "tape-cells" or "tape-squares".
 
The "registers" are also called "tape-cells" or "tape-squares".
 +
</pre>
   −
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==DATA.  Note 22==
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  −
DATA.  Note 22
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
To see how each finite approximation to a given turing machine
 
To see how each finite approximation to a given turing machine
 
can be given a purely propositional description, one fixes the
 
can be given a purely propositional description, one fixes the
Line 1,963: Line 1,909:  
   At the point-in-time p_i,
 
   At the point-in-time p_i,
 
   the tape-cell r_j bears the mark s_k.
 
   the tape-cell r_j bears the mark s_k.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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==DATA.  Note 23==
−
 
  −
DATA.  Note 23
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Given but a single free square on the tape, there are just
 
Given but a single free square on the tape, there are just
 
two different sets of initial conditions for Stunt(2), the
 
two different sets of initial conditions for Stunt(2), the
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   At time p_0, cell r_1 contains "1", and
 
   At time p_0, cell r_1 contains "1", and
 
   At time p_0, cell r_2 contains "#".
 
   At time p_0, cell r_2 contains "#".
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 24==
−
 
  −
DATA.  Note 24
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
A complete description of Stunt(2) in propositional form is obtained by
 
A complete description of Stunt(2) in propositional form is obtained by
 
conjoining one of the above choices for initial conditions with all of
 
conjoining one of the above choices for initial conditions with all of
Line 2,116: Line 2,058:  
   ( p1_q1  p1_r1  p1_r1_s#  ( p2_q*  p2_r0  p2_r1_s# ))
 
   ( p1_q1  p1_r1  p1_r1_s#  ( p2_q*  p2_r0  p2_r1_s# ))
 
   ( p1_q1  p1_r2  p1_r2_s#  ( p2_q*  p2_r1  p2_r2_s# ))
 
   ( p1_q1  p1_r2  p1_r2_s#  ( p2_q*  p2_r1  p2_r2_s# ))
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 25==
−
 
  −
DATA.  Note 25
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program
 
Interpretation of the Propositional Program
   Line 2,161: Line 2,101:  
   If M at p_1 is in state q_#, then M at p_2 is in state q_#, and
 
   If M at p_1 is in state q_#, then M at p_2 is in state q_#, and
 
   If M at p_1 is in state q_*, then M at p_2 is in state q_*.
 
   If M at p_1 is in state q_*, then M at p_2 is in state q_*.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 26==
−
 
  −
DATA.  Note 26
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program (cont.)
 
Interpretation of the Propositional Program (cont.)
   Line 2,195: Line 2,133:  
   At time p_2, M is in state q_#, or
 
   At time p_2, M is in state q_#, or
 
   At time p_2, M is in state q_*.
 
   At time p_2, M is in state q_*.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 27==
−
 
  −
DATA.  Note 27
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program (cont.)
 
Interpretation of the Propositional Program (cont.)
   Line 2,243: Line 2,179:  
   At each of the points in time p_i, for i in the set {0, 1, 2}
 
   At each of the points in time p_i, for i in the set {0, 1, 2}
 
   M can be in exactly one state q_j, for j in the set {0, 1, #, *}.
 
   M can be in exactly one state q_j, for j in the set {0, 1, #, *}.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 28==
−
 
  −
DATA.  Note 28
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program (cont.)
 
Interpretation of the Propositional Program (cont.)
   Line 2,266: Line 2,200:  
   At each of the points in time p_i, for i = 0, 1, 2,
 
   At each of the points in time p_i, for i = 0, 1, 2,
 
   H is reading exactly one cell r_j, for j = 0, 1, 2.
 
   H is reading exactly one cell r_j, for j = 0, 1, 2.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 29==
−
 
  −
DATA.  Note 29
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program (cont.)
 
Interpretation of the Propositional Program (cont.)
   Line 2,297: Line 2,229:  
   in each of the tape registers r_j, for j in {0, 1, 2},  
 
   in each of the tape registers r_j, for j in {0, 1, 2},  
 
   there can be exactly one sign s_k, for k in {0, 1, #}.
 
   there can be exactly one sign s_k, for k in {0, 1, #}.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 30==
−
 
  −
DATA.  Note 30
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program (cont.)
 
Interpretation of the Propositional Program (cont.)
   Line 2,372: Line 2,302:  
one such constraint on symbol changes for each combination of the
 
one such constraint on symbol changes for each combination of the
 
times p_0, p_1, registers r_0, r_1, r_2, and symbols s_0, s_1, s_#.
 
times p_0, p_1, registers r_0, r_1, r_2, and symbols s_0, s_1, s_#.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 31==
−
 
  −
DATA.  Note 31
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program (cont.)
 
Interpretation of the Propositional Program (cont.)
   Line 2,426: Line 2,354:  
   At time p_1, H is reading cell r_2, and
 
   At time p_1, H is reading cell r_2, and
 
   At time p_1, cell r_1 contains "1".
 
   At time p_1, cell r_1 contains "1".
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 32==
−
 
  −
DATA.  Note 32
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program (cont.)
 
Interpretation of the Propositional Program (cont.)
   Line 2,480: Line 2,406:  
to get the output of the program P is to read off the proper
 
to get the output of the program P is to read off the proper
 
part of the data from the expression of this interpretation.
 
part of the data from the expression of this interpretation.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Note 33==
−
 
  −
DATA.  Note 33
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
Interpretation of the Propositional Program (concl.)
 
Interpretation of the Propositional Program (concl.)
   Line 2,603: Line 2,527:  
the tape head H when and if the machine M reaches one of
 
the tape head H when and if the machine M reaches one of
 
its resting states, we get the result that Parity(1) = 1.
 
its resting states, we get the result that Parity(1) = 1.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Work Area==
−
 
  −
DATA.  Note 34
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
  −
 
  −
 
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
  −
 
  −
DATA.  Work Area 2
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
DATA 20.  http://forum.wolframscience.com/showthread.php?postid=791#post791
 
DATA 20.  http://forum.wolframscience.com/showthread.php?postid=791#post791
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|                                      |
 
|                                      |
 
o---------------------------------------o
 
o---------------------------------------o
 +
</pre>
    +
==DATA.  Discussion==
   −
 
+
<pre>
−
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
  −
 
  −
DATA.  Differential Analytic Turing Automata -- Discussion
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
  −
 
  −
DATA.  Discussion Note 1
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
  −
 
   
PD = Philip Dutton
 
PD = Philip Dutton
   Line 2,765: Line 2,671:  
last month without Google, is to archive a copy at one of the
 
last month without Google, is to archive a copy at one of the
 
other Google-visible discussion lists that I'm on at present.
 
other Google-visible discussion lists that I'm on at present.
 +
</pre>
   −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
+
==DATA.  Document History==
−
 
  −
DATA.  Discussion Note 2
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
  −
 
  −
 
  −
 
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
      +
<pre>
 
DATA.  Differential Analytic Turing Automata
 
DATA.  Differential Analytic Turing Automata
   Line 2,841: Line 2,741:  
32.  http://stderr.org/pipermail/inquiry/2004-June/001641.html
 
32.  http://stderr.org/pipermail/inquiry/2004-June/001641.html
 
33.  http://stderr.org/pipermail/inquiry/2004-June/001642.html
 
33.  http://stderr.org/pipermail/inquiry/2004-June/001642.html
−
34.
      
NKS Forum
 
NKS Forum
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32.  http://forum.wolframscience.com/showthread.php?postid=1489#post1489
 
32.  http://forum.wolframscience.com/showthread.php?postid=1489#post1489
 
33.  http://forum.wolframscience.com/showthread.php?postid=1490#post1490
 
33.  http://forum.wolframscience.com/showthread.php?postid=1490#post1490
−
34.
  −
  −
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
   
</pre>
 
</pre>
Jon Awbrey
12,122

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