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Topic: distinguishability - in context, according to definitions
Replies: 43   Last Post: Feb 22, 2013 10:04 AM

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: distinguishability - in context, according to definitions
Posted: Feb 14, 2013 1:40 PM

On 2/14/2013 9:32 AM, Shmuel (Seymour J.) Metz wrote:
> In <qImdnYCz5tRmvITMnZ2dnUVZ_oWdnZ2d@giganews.com>, on 02/11/2013
> at 10:53 AM, fom <fomJUNK@nyms.net> said:
>
> You really need to step back, separate out the philosophy from the
> mathematics and define any terms that you aren't uisng in accordance
> with standard practice.
>

The name assignments that follow correspond to
the labels on the picture.

http://cmp.felk.cvut.cz/~navara/FOML/beran_no.png

There are only six labels in the first
coordinate. They correspond to switching
functions on the corners of the unit square
and reflect the "gluing" of edges and corners
in the quotient space construction of a toroidal
surface as can be found pictorially in Munkres
"Topology".

In notes not presented here, the name assigments
are coordinated with the complementary square of
the MOG array, and the interpretation is that of
a Turing machine state for a Turing machine reading
and writing to six Karnaugh maps simultaneously

The MOG array can be found here:

http://finitegeometry.org/sc/24/MOG.html

The MOG array has specific use for calculations
involving the 12-dimensional Golay Code

http://en.wikipedia.org/wiki/Binary_Golay_code

The MOG array also has an intimate relationship
with

http://en.wikipedia.org/wiki/Leech_lattice

It is probably best to view the names
which follow as letters for a possible
logic or computation model. For now,
they are nothing more than an alphabet.

--------------

The following ordered pairs are
labels for the free orthomodular
lattice on 2 generators.

01=((DENY),(NTRU))=((0110),(0000))
02=((DENY),(NOR))=((0110),(0010))
03=((DENY),(NIF))=((0110),(0001))
04=((DENY),(AND))=((0110),(1000))
05=((DENY),(NIMP))=((0110),(0100))
06=((DENY),(FLIP))=((0110),(0011))
07=((DENY),(LEQ))=((0110),(1010))
08=((DENY),(DENY))=((0110),(0110))
09=((DENY),(LET))=((0110),(1001))
10=((DENY),(XOR))=((0110),(0101))
11=((DENY),(FIX))=((0110),(1100))
12=((DENY),(IMP))=((0110),(1011))
13=((DENY),(NAND))=((0110),(0111))
14=((DENY),(IF))=((0110),(1110))
15=((DENY),(OR))=((0110),(1101))
16=((DENY),(TRU))=((0110),(1111))

17=((FLIP),(NTRU))=((0011),(0000))
18=((FLIP),(NOR))=((0011),(0010))
19=((FLIP),(NIF))=((0011),(0001))
20=((FLIP),(AND))=((0011),(1000))
21=((FLIP),(NIMP))=((0011),(0100))
22=((FLIP),(FLIP))=((0011),(0011))
23=((FLIP),(LEQ))=((0011),(1010))
24=((FLIP),(DENY))=((0011),(0110))
25=((FLIP),(LET))=((0011),(1001))
26=((FLIP),(XOR))=((0011),(0101))
27=((FLIP),(FIX))=((0011),(1100))
28=((FLIP),(IMP))=((0011),(1011))
29=((FLIP),(NAND))=((0011),(0111))
30=((FLIP),(IF))=((0011),(1110))
31=((FLIP),(OR))=((0011),(1101))
32=((FLIP),(TRU))=((0011),(1111))

33=((LEQ),(NTRU))=((1010),(0000))
34=((LEQ),(NOR))=((1010),(0010))
35=((LEQ),(NIF))=((1010),(0001))
36=((LEQ),(AND))=((1010),(1000))
37=((LEQ),(NIMP))=((1010),(0100))
38=((LEQ),(FLIP))=((1010),(0011))
39=((LEQ),(LEQ))=((1010),(1010))
40=((LEQ),(DENY))=((1010),(0110))
41=((LEQ),(LET))=((1010),(1001))
42=((LEQ),(XOR))=((1010),(0101))
43=((LEQ),(FIX))=((1010),(1100))
44=((LEQ),(IMP))=((1010),(1011))
45=((LEQ),(NAND))=((1010),(0111))
46=((LEQ),(IF))=((1010),(1110))
47=((LEQ),(OR))=((1010),(1101))
48=((LEQ),(TRU))=((1010),(1111))

49=((XOR),(NTRU))=((0101),(0000))
50=((XOR),(NOR))=((0101),(0010))
51=((XOR),(NIF))=((0101),(0001))
52=((XOR),(AND))=((0101),(1000))
53=((XOR),(NIMP))=((0101),(0100))
54=((XOR),(FLIP))=((0101),(0011))
55=((XOR),(LEQ))=((0101),(1010))
56=((XOR),(DENY))=((0101),(0110))
57=((XOR),(LET))=((0101),(1001))
58=((XOR),(XOR))=((0101),(0101))
59=((XOR),(FIX))=((0101),(1100))
60=((XOR),(IMP))=((0101),(1011))
61=((XOR),(NAND))=((0101),(0111))
62=((XOR),(IF))=((0101),(1110))
63=((XOR),(OR))=((0101),(1101))
64=((XOR),(TRU))=((0101),(1111))

65=((FIX),(NTRU))=((1100),(0000))
66=((FIX),(NOR))=((1100),(0010))
67=((FIX),(NIF))=((1100),(0001))
68=((FIX),(AND))=((1100),(1000))
69=((FIX),(NIMP))=((1100),(0100))
70=((FIX),(FLIP))=((1100),(0011))
71=((FIX),(LEQ))=((1100),(1010))
72=((FIX),(DENY))=((1100),(0110))
73=((FIX),(LET))=((1100),(1001))
74=((FIX),(XOR))=((1100),(0101))
75=((FIX),(FIX))=((1100),(1100))
76=((FIX),(IMP))=((1100),(1011))
77=((FIX),(NAND))=((1100),(0111))
78=((FIX),(IF))=((1100),(1110))
79=((FIX),(OR))=((1100),(1101))
80=((FIX),(TRU))=((1100),(1111))

81=((LET),(NTRU))=((1001),(0000))
82=((LET),(NOR))=((1001),(0010))
83=((LET),(NIF))=((1001),(0001))
84=((LET),(AND))=((1001),(1000))
85=((LET),(NIMP))=((1001),(0100))
86=((LET),(FLIP))=((1001),(0011))
87=((LET),(LEQ))=((1001),(1010))
88=((LET),(DENY))=((1001),(0110))
89=((LET),(LET))=((1001),(1001))
90=((LET),(XOR))=((1001),(0101))
91=((LET),(FIX))=((1001),(1100))
92=((LET),(IMP))=((1001),(1011))
93=((LET),(NAND))=((1001),(0111))
94=((LET),(IF))=((1001),(1110))
95=((LET),(OR))=((1001),(1101))
96=((LET),(TRU))=((1001),(1111))

Date Subject Author
2/10/13 fom
2/10/13 J. Antonio Perez M.
2/10/13 fom
2/11/13 Shmuel (Seymour J.) Metz
2/11/13 fom
2/14/13 Shmuel (Seymour J.) Metz
2/14/13 fom
2/14/13 fom
2/15/13 fom
2/15/13 Shmuel (Seymour J.) Metz
2/16/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/15/13 fom
2/15/13 fom
2/14/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/17/13 fom
2/17/13 Barb Knox
2/18/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/21/13 fom
2/22/13 Shmuel (Seymour J.) Metz
2/15/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/17/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/16/13 dan.ms.chaos@gmail.com
2/16/13 fom
2/17/13 dan.ms.chaos@gmail.com
2/17/13 fom
2/17/13 dan.ms.chaos@gmail.com
2/18/13 Shmuel (Seymour J.) Metz
2/20/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/16/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom