fom
Posts:
1,037
Registered:
12/4/12
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Re: distinguishability - in context, according to definitions
Posted:
Feb 14, 2013 1:40 PM
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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))
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