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Hi Mickel and others,
Let me share my knowledge with you on basic boolean algebra and since we are in
an age where computers are the norm sooner or later more people will learn
about logic.
Lets keep to the basic and introduce the 2 operations that Dennis also uses,
AND and OR.
AND
The AND operation is written as a dot '.' and works as follows:
A . B
0 . 0 = 0
1 . 0 = 0
0 . 1 = 0
1 . 1 = 1
So only when both A and B are 1 is the output 1. Let me show the '.' (dots) In
the equation that Dennis gave us:
x.y + x.(1-y) + y.(1-x) + (1-x).(1-y) = 1
OR
The OR operation is written as a plus '+' and works as follows:
A + B
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 1
So if only one of them is 1 the output already becomes 1. You can see the plus
signs in the equation:
x.y + x.(1-y) + y.(1-x) + (1-x).(1-y) = 1
INVERSE or NOT operation
Dennis writes the NOT operation simply as (1-x) but could be written as ӯ, that
is a character with a - on top.
_ _
(1-x).(1-y) is the same as writing x.y
It's operation is just to make a 0 a 1 and a 1 a 0.
Ok, that is it for now, hope it helps some of you to understand logic a little
bit better.
Best
Jurgen
From: Mickel
Sent: Tuesday, September 01, 2009 7:30 PM
To: The Resolution of Mind list
Subject: Re: [TROM1] Trom and Boolean Algebra
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Dear Pete
After ploughing my way through that lot I think I am going to inquire as to if
the medical fraternity has got around to doing brain transplants yet, I might
see if I can get an exchange for one that actually works.
It's a very interesting subject and one I am determined to get a very good
understnding of, the reason why follows.
Like many people I have had days or moments when the bank, mind and masses that
I am immersed in have suddenly dropped away, a major keyout is probably what it
is called in Scientology.
I know for a fact that like Dennis says when he could find no more items or
charge in the mind that a person finds there is no where else to go, it's a
clear state, a joyful state, magic appears to happen, it's completely
effortless, a person moves above time or causality.
It can be seen that there is no timetrack that we normally are aware of and
many other things, a view for instance of your own immortality.
Anyway, the point I am trying to make here is that a person who has this type
of experience finds there is no where else to go, where can you go other than
where you are right now, there is no higher state, this type of thing can last
for minutes years or a lifetime.
So for me I came to the conclusion a long time ago that either that's it,
that's the end, there is nothing else to attain or I have to search for someone
who had found something beyond that point of what might be called a Oneness
with everything, Dennis came to the same conclusion when he had flattened
everything.
There is no other path I can take, it's either what I am calling Spiritual
postulates, goals packages or it's what the non duality philosophy finds.
That is the reason I want to get a good understanding of this Boolean Algebra.
So Thanks, I am going to save this in my TROM folder and read it as I go along.
Best
Mike
----- Original Message -----
From: Pete McLaughlin
To: TROM
Sent: Tuesday, September 01, 2009 2:16 AM
Subject: [TROM1] Trom and Boolean Algebra
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Hi Mickel
I kept thinking about you question on “Common Classes” realized I still had
something misunderstood on the Logical Notes section of TROM. On reviewing
that section I found what I had missed and here is the result.
Dennis uses Boolean algebra to make sure he considered all the possible ways
two individuals could interact concerning a goal. It took me a while to
understand what he was doing with the algebraic formulas so I thought it might
help to show what they are about.
Logical Notes
This section can be glossed over if desired. The purpose of the section is to
demonstrate to those interested that the subject of the goals package rests
upon a firm logical foundation.
The subject of logic rests upon two fundamental axioms:
1. The common class of a concept and its absence does not exist. (x(1-x))=0.
This equation is only satisfied when x is either zero or unity. Thus, in the
algebra of classes (Boolean algebra) (symbolic logic) the symbols can only have
the value of zero or unity.)
(((A “Common Class” is a group of items that share characteristics of two
parent classes. View this as two circles overlapping. The area of overlap is
the common class as it is part of both circles.
(x(1-x))=0 View this formula as a bucket full of black marbles and white
marbles. If you pull out one marble it can be either white or black. There are
no other possibilities so this equation says “Can I pull out a marble that is
both black and white? The answer is no so in Boolean algebra you put the value
for false which is zero.)))
2. The universe can be divided into any concept and its absence. (x + (1-x)
=1.)
(((Using the same bucket of black and white marbles this statement says that
if you pull out a marble it will be either black or white. The equation then
reads if I pull out a marble it must be either black or white and the answer is
the Boolean value for true which is the number 1.)
From these two basic axioms all other logical propositions are derived. One
of these propositions states that the types of possible classes that can exist
with two concepts, x, y, are four. Their sum equals the universe: unity.
xy + x(1-y) + y(1-x) + (1-x)(1-y) = 1
(1 and 2 above dealt with one value and its absence. Now we have two values
and their absences. Lets picture two buckets. The first has black marbles and
white marbles to represent X and its absence 1-X the second bucket has red and
blue marbles to represent Y and its absence 1-Y. if we pull out one marble at
random from each bucket we can get the combinations of black and red, black and
blue, red and white and white and blue. Those are the only possible
combinations so the equation states these 4 combinations of two values and
their absences are all of the possible combinations we can get in this
situation and the answer is true or the Boolean value 1.)))
Any goals package contains two concepts; these plus their absences
(negatives) constitute the four legs of the package.
The ‘To know’ package is such a package. If we represent ‘To know’ by x, and
‘To be known’ by y, we can see from the above equation regarding two concepts
that the four possible classes are:
xy This is the class To know and To be known. These are complementary
postulates, and are a no-game class.
x(1-y) This is the class To know and To not be known. These are conflicting
postulates, and are a game class.
y(1-x) This is the class To be known and To not-know. These are conflicting
postulates, and are a game class.
(1-x)(1-y) This is the class To not-know and To not be known. These are
complementary postulates, and are a no- game class.
The sum of these four classes is the totality of the universe of the two
concepts. “To know” and “To be known”. Within these four classes, then, the
whole subject of knowing and being known is contained. When we consider each of
these four classes from the viewpoint of ‘self’ and ‘others’ we arrive at 2x4=8
classes. When we consider each of these 8 classes from the viewpoint of
‘origin’ and ‘receipt’ we arrive at 2x8=16 classes. These 16 classes are the 16
levels we find when we examine the ‘To know’ goals package. We can equally, of
course, cut the universe into any two purposes in the form ‘To -’ and ‘To be
-’, and arrive at the same conclusion viz: That the whole universe of the two
concepts is within that package.
(At this point I made the mistake of thinking that Dennis was talking about
the Level 5 chart. He is not. The level 5 chart only deals with the two games
conditions between two opponents which is the middle two values above (x(1-y)
and y(1-x)) the other two are “no game” conditions and not on the level 5
chart.
So what Dennis is showing here is that on any goal an individual can
interact with another in only 4 ways. Two of these will be friendly no games
conditions and two will be conflicts between opposing goals. When you add in
the 4 combinations from the others point of view you get 8 points of view of
this goal and when you consider who started in interaction, self or other, this
would make 16 different combination of how self and other could interact on
this goal.
Stated a little different there are:
4 ways self can pursue a goal with other
4 ways other can pursue a goal with self
And either self or other started the current effort toward a goal
Thus a total of 4x4x2=16 different ways to pursue a goal.
Since these are ALL the ways these two could interact we can be assured that
while we are taking apart a goals package in the mind we are not leaving
something undone. Dennis proves here that he has considered all the
possibilities. )
Thus, we have proven within the rigors of strict logical reasoning that any
goals package contains the full universe of its component concepts, and that no
part of life is external to the package. In the language of the mathematician
the 16 levels of the goals package are necessary and sufficient for our
purposes.
Hope this helps
Keep on TROMing
Pete
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