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Showing posts with label Venn. Show all posts
Showing posts with label Venn. Show all posts

Wednesday, May 16, 2012

Euler Diagram



An Euler diagram illustrating that the set of "animals with four legs" is a subset of "animals", but the set of "minerals" is disjoint (has no members in common) with "animals".
An Euler diagram is a diagrammatic means of representing sets and their relationships. The first use of "Eulerian circles" is commonly attributed to Swiss mathematician Leonhard Euler (1707–1783). They are closely related to Venn diagrams.

Venn and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement in the 1960s. Since then, they have also been adopted by other curriculum fields such as reading.[1]

Contents

Overview

Euler diagrams consist of simple closed curves (usually circles) in the plane that depict sets. The sizes or shapes of the curves are not important: the significance of the diagram is in how they overlap. The spatial relationships between the regions bounded by each curve (overlap, containment or neither) corresponds to set-theoretic relationships (intersection, subset and disjointness).
Each Euler curve divides the plane into two regions or "zones": the interior, which symbolically represents the elements of the set, and the exterior, which represents all elements that are not members of the set. Curves whose interior zones do not intersect represent disjoint sets. Two curves whose interior zones intersect represent sets that have common elements; the zone inside both curves represents the set of elements common to both sets (the intersection of the sets). A curve that is contained completely within the interior zone of another represents a subset of it.


Examples of small Venn diagrams (on left) with shaded regions representing empty sets, showing how they can be easily transformed into equivalent Euler diagrams (right).
Venn diagrams are a more restrictive form of Euler diagrams. A Venn diagram must contain all the possible zones of overlap between its curves, representing all combinations of inclusion/exclusion of its constituent sets, but in an Euler diagram some zones might be missing. When the number of sets grows beyond 3, or even with three sets, but under the allowance of more than two curves passing at the same point, we start seeing the appearance of multiple mathematically unique Venn diagrams. Venn diagrams represent the relationships between n sets, with 2n zones, Euler diagrams may not have all zones. (An example is given below in the History section; in the top-right illustration the O and I diagrams are merely rotated; Venn stated that this difficulty in part led him to develop his diagrams).

In a logical setting, one can use model theoretic semantics to interpret Euler diagrams, within a universe of discourse. In the examples above, the Euler diagram depicts that the sets Animal and Mineral are disjoint since the corresponding curves are disjoint, and also that the set Four Legs is a subset of the set of Animals. The Venn diagram, which uses the same categories of Animal, Mineral, and Four Legs, does not encapsulate these relationships. Traditionally the emptiness of a set in Venn diagrams is depicted by shading in the region. Euler diagrams represent emptiness either by shading or by the use of a missing region.
Often a set of well-formedness conditions are imposed; these are topological or geometric constraints imposed on the structure of the diagram. For example, connectedness of zones might be enforced, or concurrency of curves or multiple points might be banned, as might tangential intersection of curves. In the diagram to the right, examples of small Venn diagrams are transformed into Euler diagrams by sequences of transformations; some of the intermediate diagrams have concurrency of curves. However, this sort of transformation of a Venn diagram with shading into an Euler diagram without shading is not always possible. There are examples of Euler diagrams with 9 sets that are not drawable using simple closed curves without the creation of unwanted zones since they would have to have non-planar dual graphs.
 

History

 


Photo of page from Hamilton's 1860 "Lectures" page 180. (Click on it, up to two times, to enlarge). The symbolism A, E, I, and O refer to the four forms of the syllogism. The small text to the left says: "The first employment of circular diagrams in logic improperly ascribed to Euler. To be found in Christian Weise."

On the right is a photo of page 74 from Couturat 1914 wherein he labels the 8 regions of the Venn diagram. The modern name for these "regions" is minterms. These are shown on the left with the variables x, y and z per Venn's drawing. The symbolism is as follows: logical AND ( & ) is represented by arithmetic multiplication, and the logical NOT ( ~ )is represented by " ' " after the variable, e.g. the region x'y'z is read as "NOT x AND NOT y AND z" i.e. ~x & ~y & z.

Both the Veitch and Karnaugh diagrams show all the minterms, but the Veitch is not particularly useful for reduction of formulas. Observe the strong resemblance between the Venn and Karnaugh diagrams; the colors and the variables x, y, and z are per Venn's example.
As shown in the illustration to the right, Sir William Hamilton in his posthumously published Lectures on Metaphysics and Logic (1858–60) asserts that the original use of circles to "sensualize ... the abstractions of Logic" (p. 180) was not Leonhard Paul Euler (1707–1783) but rather Christian Weise (?–1708) in his Nucleus Logicoe Weisianoe that appeared in 1712 posthumously. He references Euler's Letters to a German Princess on different Matters of Physics and Philosophy1" [1Partie ii., Lettre XXXV., ed. Cournot. – ED.][2]
In Hamilton's illustration the four forms of the syllogism as symbolized by the drawings A, E, I and O are:[3]
  • A: The Universal Affirmative, Example: "All metals are elements".
  • E: The Universal Negative, Example: "No metals are compound substances".
  • I: The Particular Affirmative, Example: "Some metals are brittle".
  • O: The Particular Negative, Example: "Some metals are not brittle".
In his 1881 Symbolic Logic Chapter V "Diagrammatic Representation", John Venn (1834–1923) comments on the remarkable prevalence of the Euler diagram:
"...of the first sixty logical treatises, published during the last century or so, which were consulted for this purpose:-somewhat at random, as they happened to be most accessible :-it appeared that thirty four appealed to the aid of diagrams, nearly all of these making use of the Eulerian Scheme." (Footnote 1 page 100)

Composite of two pages 115–116 from Venn 1881 showing his example of how to convert a syllogism of three parts into his type of diagram. Venn calls the circles "Eulerian circles" (cf Sandifer 2003, Venn 1881:114 etc) in the "Eulerian scheme" (Venn 1881:100) of "old-fashioned Eulerian diagrams" (Venn 1881:113).
But nevertheless, he contended "the inapplicability of this scheme for the purposes of a really general Logic" (page 100) and in a footnote observed that "it fits in but badly even with the four propositions of the common Logic [the four forms of the syllogism] to which it is normally applied" (page 101). Venn ends his chapter with the observation that will be made in the examples below – that their use is based on practice and intuition, not on a strict algorithmic practice:
“In fact ... those diagrams not only do not fit in with the ordinary scheme of propositions which they are employed to illustrate, but do not seem to have any recognized scheme of propositions to which they could be consistently affiliated.” (pp. 124–125)
Finally, in his Chapter XX HISTORIC NOTES Venn gets to a crucial criticism (italicized in the quote below); observe in Hamilton's illustration that the O (Particular Negative) and I (Particular Affirmative) are simply rotated:
"We now come to Euler's well-known circles which were first described in his Lettres a une Princesse d'Allemagne (Letters 102–105). The weak point about these consists in the fact that they only illustrate in strictness the actual relations of classes to one another, rather than the imperfect knowledge of these relations which we may possess, or wish to convey, by means of the proposition. Accordingly they will not fit in with the propositions of common logic, but demand the constitution of a new group of appropriate elementary propositions.... This defect must have been noticed from the first in the case of the particular affirmative and negative, for the same diagram is commonly employed to stand for them both, which it does indifferently well". (italics added: page 424)
(Sandifer 2003 reports that Euler makes such observations too; Euler reports that his figure 45 (a simple intersection of two circles) has 4 different interpretations). Whatever the case, armed with these observations and criticisms, Venn then demonstrates (pp. 100–125) how he derived what has become known as his Venn diagrams from the "old-fashioned Euler diagrams". In particular he gives an example, shown on the left.
By 1914 Louis Couturat (1868–1914) had labeled the terms as shown on the drawing on the right. Moreover, he had labeled the exterior region (shown as a'b'c') as well. He succinctly explains how to use the diagram – one must strike out the regions that are to vanish:
"VENN'S method is translated in geometrical diagrams which represent all the constituents, so that, in order to obtain the result, we need only strike out (by shading) those which are made to vanish by the data of the problem." (italics added p. 73)
Given the Venn's assignments, then, the unshaded areas inside the circles can be summed to yield the following equation for Venn's example:
"No Y is Z and ALL X is Y: therefore No X is Z" has the equation x'yz' + xyz' + x'y'z for the unshaded area inside the circles (but note that this is not entirely correct; see the next paragraph).
In Venn the 0th term, x'y'z', i.e. the background surrounding the circles, does not appear. Nowhere is it discussed or labeled, but Couturat corrects this in his drawing. The correct equation must include this unshaded area shown in boldface:
"No Y is Z and ALL X is Y: therefore No X is Z" has the equation x'yz' + xyz' + x'y'z + x'y'z' .
In modern usage the Venn diagram includes a "box" that surrounds all the circles; this is called the universe of discourse or the domain of discourse.
Couturat now observes that, in a direct algorithmic (formal, systematic) manner, one cannot derive reduced Boolean equations, nor does it show how to arrive at the conclusion "No X is Z". Couturat concluded that the process "has ... serious inconveniences as a method for solving logical problems":
"It does not show how the data are exhibited by canceling certain constituents, nor does it show how to combine the remaining constituents so as to obtain the consequences sought. In short, it serves only to exhibit one single step in the argument, namely the equation of the problem; it dispenses neither with the previous steps, i. e., "throwing of the problem into an equation" and the transformation of the premises, nor with the subsequent steps, i. e., the combinations that lead to the various consequences. Hence it is of very little use, inasmuch as the constituents can be represented by algebraic symbols quite as well as by plane regions, and are much easier to deal with in this form."(p. 75)
Thus the matter would rest until 1952 when Maurice Karnaugh (1924– ) would adapt and expand a method proposed by Edward W. Veitch; this work would rely on the truth table method precisely defined in Emil Post's 1921 PhD thesis "Introduction to a general theory of elementary propositions" and the application of propositional logic to switching logic by (among others) Claude Shannon, George Stibitz, and Alan Turing.[4] For example, in chapter "Boolean Algebra" Hill and Peterson (1968, 1964) present sections 4.5ff "Set Theory as an Example of Boolean Algebra" and in it they present the Venn diagram with shading and all. They give examples of Venn diagrams to solve example switching-circuit problems, but end up with this statement:
"For more than three variables, the basic illustrative form of the Venn diagram is inadequate. Extensions are possible, however, the most convenient of which is the Karnaugh map, to be discussed in Chapter 6." (p. 64)
In Chapter 6, section 6.4 "Karnaugh Map Representation of Boolean Functions" they begin with:
"The Karnaugh map1 [1Karnaugh 1953] is one of the most powerful tools in the repertory of the logic designer. ... A Karnaugh map may be regarded either as a pictorial form of a truth table or as an extension of the Venn diagram." (pp. 103–104)
The history of Karnaugh's development of his "chart" or "map" method is obscure. Karnaugh in his 1953 referenced Veitch 1951, Veitch referenced Claude E. Shannon 1938 (essentially Shannon's Master's thesis at M.I.T.), and Shannon in turn referenced, among other authors of logic texts, Couturat 1914. In Veitch's method the variables are arranged in a rectangle or square; as described in Karnaugh map, Karnaugh in his method changed the order of the variables to correspond to what has become known as (the vertices of) a hypercube.

Example: Euler- to Venn-diagram and Karnaugh map

This example shows the Euler and Venn diagrams and Karnaugh map deriving and verifying the deduction "No X's are Z's". In the illustration and table the following logical symbols are used:
1 can be read as "true", 0 as "false"
~ for NOT and abbreviated to ' when illustrating the minterms e.g. x' =defined NOT x,
+ for Boolean OR (from Boolean algebra: 0+0=0, 0+1 = 1+0 = 1, 1+1=1)
& (logical AND) between propositions; in the mintems AND is omitted in a manner similar to arithmetic multiplication: e.g. x'y'z =defined ~x & ~y & z (From Boolean algebra: 0*0=0, 0*1 = 1*0=0, 1*1 = 1, where * is shown for clarity)
→ (logical IMPLICATION): read as IF ... THEN ..., or " IMPLIES ", P → Q =defined NOT P OR Q

Before it can be presented in a Venn diagram or Karnaugh Map, the Euler diagram's syllogism "No Y is Z, All X is Y" must first be reworded into the more formal language of the propositional calculus: " 'It is not the case that: Y AND Z' AND 'If an X then a Y' ". Once the propositions are reduced to symbols and a propositional formula ( ~(y & z) & (x → y) ), one can construct the formula's truth table; from this table the Venn and/or the Karnaugh map are readily produced. By use of the adjacency of "1"s in the Karnaugh map (indicated by the grey ovals around terms 0 and 1 and around terms 2 and 6) one can "reduce" the example's Boolean equation i.e. (x'y'z' + x'y'z) + (x'yz' + xyz') to just two terms: x'y' + yz'. But the means for deducing the notion that "No X is Z", and just how the reduction relates to this deduction, is not forthcoming from this example.
Given a proposed conclusion such as "No X is a Z", one can test whether or not it is a correct deduction by use of a truth table. The easiest method is put the starting formula on the left (abbreviate it as "P") and put the (possible) deduction on the right (abbreviate it as "Q") and connect the two with logical implication i.e. P → Q, read as IF P THEN Q. If the evaluation of the truth table produces all 1's under the implication-sign (→, the so-called major connective) then P → Q is a tautology. Given this fact, one can "detach" the formula on the right (abbreviated as "Q") in the manner described below the truth table.
Given the example above, the formula for the Euler and Venn diagrams is:
"No Y's are Z's" and "All X's are Y's": ( ~(y & z) & (x → y) ) =defined P
And the proposed deduction is:
"No X's are Z's": ( ~ (x & z) ) =defined Q
So now the formula to be evaluated can be abbreviated to:
( ~(y & z) & (x → y) ) → ( ~ (x & z) ): P → Q
IF ( "No Y's are Z's" and "All X's are Y's" ) THEN ( "No X's are Z's" )
The Truth Table demonstrates that the formula ( ~(y & z) & (x → y) ) → ( ~ (x & z) ) is a tautology as shown by all 1's in yellow column..
Square # Venn, Karnaugh region
x y z
(~ (y & z) & (x y)) (~ (x & z))
0 x'y'z' 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0
1 x'y'z 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1
2 x'yz' 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0
3 x'yz 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1
4 xy'z' 1 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0
5 xy'z 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 1
6 xyz' 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0
7 xyz 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1
At this point the above implication P → Q (i.e. ~(y & z) & (x → y) ) → ~(x & z) ) is still a formula, and the deduction – the "detachment" of Q out of P → Q – has not occurred. But given the demonstration that P → Q is tautology, the stage is now set for the use of the procedure of modus ponens to "detach" Q: "No X's are Z's" and dispense with the terms on the left.[5]
Modus ponens (or "the fundamental rule of inference"[6]) is often written as follows: The two terms on the left, "P → Q" and "P", are called premises (by convention linked by a comma), the symbol ⊢ means "yields" (in the sense of logical deduction), and the term on the right is called the conclusion:
P → Q, P ⊢ Q
For the modus ponens to succeed, both premises P → Q and P must be true. Because, as demonstrated above the premise P → Q is a tautology, "truth" is always the case no matter how x, y and z are valued, but "truth" will only be the case for P in those circumstances when P evaluates as "true" (e.g. rows 0 OR 1 OR 2 OR 6: x'y'z' + x'y'z + x'yz' + xyz' = x'y' + yz').[7]
P → Q , P ⊢ Q
i.e.: ( ~(y & z) & (x → y) ) → ( ~ (x & z) ) , ( ~(y & z) & (x → y) ) ⊢ ( ~ (x & z) )
i.e.: IF "No Y's are Z's" and "All X's are Y's" THEN "No X's are Z's", "No Y's are Z's" and "All X's are Y's" ⊢ "No X's are Z's"
One is now free to "detach" the conclusion "No X's are Z's", perhaps to use it in a subsequent deduction (or as a topic of conversation).
The use of tautological implication means that other possible deductions exist besides "No X's are Z's"; the criterion for a successful deduction is that the 1's under the sub-major connective on the right include all the 1's under the sub-major connective on the left (the major connective being the implication that results in the tautology). For example, in the truth table, on the right side of the implication (→, the major connective symbol) the bold-face column under the sub-major connective symbol " ~ " has the all the same 1s that appear in the bold-faced column under the left-side sub-major connective & (rows 0, 1, 2 and 6), plus two more (rows 3 and 4).

Gallery

Footnotes

  1. ^ Strategies for Reading Comprehension Venn Diagrams
  2. ^ By the time these lectures of Hamilton were published, Hamilton too had died. His editors (symbolized by ED.), responsible for most of the footnoting, were the logicians Henry Longueville Mansel and John Veitch.
  3. ^ Hamilton 1860:179. The examples are from Jevons 1881:71ff.
  4. ^ See footnote at George Stibitz.
  5. ^ This is a sophisticated concept. Russell and Whitehead (2nd edition 1927) in their Principia Mathematica describe it this way: "The trust in inference is the belief that if the two former assertions [the premises P, P→Q ] are not in error, the final assertion is not in error . . . An inference is the dropping of a true premiss [sic]; it is the dissolution of an implication" (p. 9). Further discussion of this appears in "Primitive Ideas and Propositions" as the first of their "primitive propositions" (axioms): *1.1 Anything implied by a true elementary proposition is true" (p. 94). In a footnote the authors refer the reader back to Russell's 1903 Principles of Mathematics §38.
  6. ^ cf Reichenbach 1947:64
  7. ^ Reichenbach discusses the fact that the implication P → Q need not be a tautology (a so-called "tautological implication"). Even "simple" implication (connective or adjunctive) will work, but only for those rows of the truth table that evaluate as true, cf Reichenbach 1947:64–66.

References

By date of publishing:
  • Sir William Hamilton 1860 Lectures on Metaphysics and Logic edited by Henry Longueville Mansel and John Veitch, William Blackwood and Sons, Edinburgh and London.
  • W. Stanley Jevons 1880 Elemetnary Lessons in Logic: Deductive and Inductive. With Copious Questions and Examples, and a Vocabulary of Logical Terms, M. A. MacMillan and Co., London and New York.
  • John Venn 1881 Symbolic Logic, MacMillan and Co., London.
  • Alfred North Whitehead and Bertrand Russell 1913 1st edition, 1927 2nd edition Principia Mathematica to *56 Cambridge At The University Press (1962 edition), UK, no ISBN.
  • Louis Couturat 1914 The Algebra of Logic: Authorized English Translation by Lydia Gillingham Robinson with a Preface by Philip E. B. Jourdain, The Open Court Publishing Company, Chicago and London.
  • Emil Post 1921 "Introduction to a general theory of elementary propositions" reprinted with commentary by Jean van Heijenoort in Jean van Heijenoort, editor 1967 From Frege to Gödel: A Sourcebook of Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA, ISBN 0-674-42449-8 (pbk.)
  • Claude E. Shannon 1938 "A Symbolic Analysis of Relay and Switching Circuits", Transactions American Institute of Electrical Engineers vol 57, pp. 471–495. Derived from Claude Elwood Shannon: Collected Papers edited by N.J.A. Solane and Aaron D. Wyner, IEEE Press, New York.
  • Hans Reichenbach 1947 Elements of Symbolic Logic republished 1980 by Dover Publications, Inc., NY, ISBN 0-486-24004-5.
  • Edward W. Veitch 1952 "A Chart Method for Simplifying Truth Functions", Transactions of the 1952 ACM Annual Meeting, ACM Annual Conference/Annual Meeting "Pittsburgh", ACM, NY, pp. 127–133.
  • Maurice Karnaugh November 1953 The Map Method for Synthesis of Combinational Logic Circuits, AIEE Committee on Technical Operations for presentation at the AIEE summer General Meeting, Atlantic City, N. J., June 15–19, 1953, pp. 593–599.
  • Frederich J. Hill and Gerald R. Peterson 1968, 1974 Introduction to Switching Theory and Logical Design, John Wiley & Sons NY, ISBN 0-71-39882-9.
  • Ed Sandifer 2003 How Euler Did It, http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2003%20Venn%20Diagrams.pdf

External links

Sunday, March 23, 2008

The Synapse is a Portal of the Thinking Mind

Life must be understood backwards; but... it must be lived forward.
Soren Kierkegaard


Penrose's Bermuda Triangle?

A long time ago I learnt about using avenues to free the mind by doing different things in the face of adversities. One can not always gauge their reaction to what life throws at them. I found this for me most certainly, and in face of the understanding of the "emotive struggle," it is moving "clarity to such thinking" of the thinking mind, that one would like to at least understand what influences these emotive consequences have on their thinking space.

The brain is a matter defined state of existence and is furthest from the source of expression. Yet, it houses avenues within the very nature of it's structure, to allow processes that may be comparative to me of what spaces can be created, as we create an open portal for all thinking minds avenues to new possible changes.




So I of course like to use a bubble in this context to to display the field around that thinking brain/Body to know that the emotive consequences lie within this field of expression.



It wasn't enough then that what was apparent to me, that the continued struggle I have of dealing with these emotive fluctuations is in our thinking minds, that the reactive states, were held in a place of a deeper repose while the collection of these things come from a history of living.

It was not enough that I knew of a map created by another of psychological stature and lead by scientific valuation, that it would lead to the understanding of Penfield's work on the structure of the brain.

Source:McGill University ArchivesWilder Graves Penfield, OM, CC, CMG, MD, FRS (January 25/26, 1891 – April 5, 1976) was an American-born Canadian neurosurgeon. See also:Wilder Penfield

So while I had given Stefan of Backreaction "a brief summary of it" there in the following quote below, it is in such a way this unfolds I had developed this understanding of "historical context" and now, work toward the future. This is why I like history, and why I used David Hilbert's quote. It signals "advancements in thinking" as we explore history in not only the context of who we are, but of our predecessor's mathematical development as well. The "gap created for such ingenuities" had to realize a "stop off point" for further developments. So we develop from that point, forward.

At 11:08 AM, March 13, 2008, Blogger Plato said. Historical Meme: Seven Things about Richard Carrington
Often we say things in our own lives not aware of the context and influence our parents have on us, yet, such concepts themself are transmitted and unknowingly we become the parent of our raising.

To change the cyclical nature of such events, and move to our own adult situations requires a deeper insight into who we are, that we might change the circumstance and reveal who it is, is talking, when acting in this role of our day to day.

That you may not have children now is not the issue and any young person might know then that we are also our parent, as well as, the child of that experience. It is how we shall choose as an adult to address society, each other, in these ways, that we change the future.


A lot of time if you are not aware of the internal structure this information is transmitted how would you know that it follows "another's mindmap" and you were not aware of it? So as glossy as this sounds "my writing" about our individual histories, we now know that we transmit part of our histories into the future.




Parent ego state


This is a set of feelings, thinking and behaviour that we have copied from our parents and significant others.


As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.


As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.


Adult ego state


The Adult ego state is about direct responses to the here and now. We deal with things that are going on today in ways that are not unhealthily influenced by our past.


The Adult ego state is about being spontaneous and aware with the capacity for intimacy. When in our Adult we are able to see people as they are, rather than what we project onto them. We ask for information rather than stay scared and rather than make assumptions. Taking the best from the past and using it appropriately in the present is an integration of the positive aspects of both our Parent and Child ego states. So this can be called the Integrating Adult. Integrating means that we are constantly updating ourselves through our every day experiences and using this to inform us.


In this structural model, the Integrating Adult ego state circle is placed in the middle to show how it needs to orchestrate between the Parent and the Child ego states. For example, the internal Parent ego state may beat up on the internal Child, saying "You are no good, look at what you did wrong again, you are useless". The Child may then respond with "I am no good, look how useless I am, I never get anything right". Many people hardly hear this kind of internal dialogue as it goes on so much they might just believe life is this way. An effective Integrating Adult ego state can intervene between the Parent and Child ego states. This might be done by stating that this kind of parenting is not helpful and asking if it is prepared to learn another way. Alternatively, the Integrating Adult ego state can just stop any negative dialogue and decide to develop another positive Parent ego state perhaps taken in from other people they have met over the years.


Child ego state


The Child ego state is a set of behaviours, thoughts and feelings which are replayed from our own childhood.


Perhaps the boss calls us into his or her office, we may immediately get a churning in our stomach and wonder what we have done wrong. If this were explored we might remember the time the head teacher called us in to tell us off. Of course, not everything in the Child ego state is negative. We might go into someone's house and smell a lovely smell and remember our grandmother's house when we were little, and all the same warm feelings we had at six year's of age may come flooding back.


Both the Parent and Child ego states are constantly being updated. For example, we may meet someone who gives us the permission we needed as a child, and did not get, to be fun and joyous. We may well use that person in our imagination when we are stressed to counteract our old ways of thinking that we must work longer and longer hours to keep up with everything. We might ask ourselves "I wonder what X would say now". Then on hearing the new permissions to relax and take some time out, do just that and then return to the work renewed and ready for the challenge. Subsequently, rather than beating up on ourselves for what we did or did not do, what tends to happen is we automatically start to give ourselves new permissions and take care of ourselves.


Alternatively, we might have had a traumatic experience yesterday which goes into the Child ego state as an archaic memory that hampers our growth. Positive experiences will also go into the Child ego state as archaic memories. The positive experiences can then be drawn on to remind us that positive things do happen.


The process of analysis's personality in terms of ego states is called structural analysis. It is important to remember that ego states do not have an existence of their own, they are concepts to enable understanding. Therefore it is important to say "I want some fun" rather than "My Child wants some fun". We may be in our Child ego state when we say this, but saying "I" reminds us to take responsibility for our actions.
Transactional Analysis theory was developed by Dr Eric Berne in the 1950's.

Intuitive Light Switches

So you can start off with thinking all about what Penrose had to say, and Max may have pushed this further, to wonder, how his structural interpretation may be compared to what the actual Mathematical Universe is saying. A Square? A soccer Ball. So today, it may be some Easter Egg interpretation?:)





See:

Venn Logic and TA

The Plato’s Cave Study: Does Bullshit Truly Baffle Brains?”

Thursday, February 08, 2007

Democritus had Passion and Heat?

It seems "humour" is pervading the internet today, so I thought I would add my take.


Democritus Laughing, by Hendrick ter Brugghen, 1628, in Rijksmuseum, Amsterdam
According to legend, Democritus was supposed to be mad because he laughed at everything, and so he was sent to Hippocrates to be cured. Hippocrates pointed out that he was not mad, but, instead, had a happy disposition. That is why Democritus is sometimes called the laughing philosopher


If one had never understood the entanglement process" might one have ever understood what could happen when you mix three circles/sphere of knowledge which overlap to become the "Venn logic of approach?"



Are men suppose to be "Illogical" and "Impassionate?" Maybe "that heat" can refer to the subjective analysis of all the things we might talk about in terms of "creativity?" Yet too, all the things that could involve the human being whilst it engages in the emotive memory induced entrapment of the world inside, which may disallow "clarity of the situation?"

The Art of Doodling

A graph induced analysis of the "boring lecture?" Whose point is the "climatic schedule of the hour," could have ripples following "all the power of that one moment?" While "witnessing this event" the deeper aspect of the student is engaged with things "rising from the unconscious."

Unbeknownst to them, having withdrawn into the dream world, they brought back with them, subjective desires of their soul? Impatience, and "being to the point" while all thing allowed them to journey a long distance from the classroom?

So having drawn this "three circles" or "introducing the "graph of boredom," the idea here is to explain what is "preoccupying the mind" when it should really be paying attention?:)

Democritus, known in antiquity as the ‘laughing philosopher’ because of his emphasis on the value of ‘cheerfulness,’ was one of the two founders of ancient atomist theory. He elaborated a system originated by his teacher Leucippus into a materialist account of the natural world. The atomists held that there are smallest indivisible bodies from which everything else is composed, and that these move about in an infinite void space. Of the ancient materialist accounts of the natural world which did not rely on some kind of teleology or purpose to account for the apparent order and regularity found in the world, atomism was the most influential. Even its chief critic, Aristotle, praised Democritus for arguing from sound considerations appropriate to natural philosophy.
In common with other early ancient theories of living things, Democritus seems to have used the term psychê to refer to that distinctive feature of living things that accounts for their ability to perform their life-functions. According to Aristotle, Democritus regarded the soul as composed of one kind of atom, in particular fire atoms. This seems to have been because of the association of life with heat, and because spherical fire atoms are readily mobile, and the soul is regarded as causing motion. Democritus seems to have considered thought to be caused by physical movements of atoms also. This is sometimes taken as evidence that Democritus denied the survival of a personal soul after death, although the reports are not univocal on this.

Saturday, May 20, 2006

Intuitive Self and Structure: My Past

One qubit at a time by the Economist

COMPUTING is about to hit a problem. In each new generation the components are smaller than they were in its predecessor, and the speed at which this miniaturisation is happening means that within 15 years or so a fundamental limit will be reached. At that point, not only will the strange effects of quantum mechanics hold sway, the components themselves will be on the scale of atoms and no further size-reduction will be possible. Which is why scientists and engineers are seeking new ways of building computers.

One route they are exploring, which was discussed at a meeting held recently at the Royal Society in London, is called quantum computing. Instead of trying to overcome quantum weirdness, this technique embraces and exploits it. The thing that distinguishes a quantum computer from the sort in use today is the number of calculations it can do in parallel. Both sorts of computer use binary arithmetic, but they do so in rather different ways. A classical computer employs bits—binary digits, either zero or one—to process and store information. But a bit must be one or the other; it cannot be both at the same time. A quantum computer does not suffer from this restriction.





Tabula rasa >(Latin: "scraped tablet", though often translated "blank slate") is the notion that individual human beings are born "blank" (with no built-in mental content), and that their identity is defined entirely by events after birth.


Yet it is in every moment that such information should have the ability to make it's way? The past allowable in what is created in that "one moment" has the potential to become the possibility of that future. They are inevitably liinked in you, as a receptacle of possibilites?

Quantum Phase Gate

The basic entanglement process of two quantum systems can be considered as an elementary function for quantum information processing, a "quantum gate". A lot of attention has been devoted in the last years to the realization and characterization of quantum gates, either in NMR, ion traps or cavity QED experiments.



Let's say we wanted to bring perspective to quantum processes in terms of computerization? There's this image in mind and the logic forming apparatus that issues from a Quantum Phase Gate.

While I see the historical past, I also see it's application in how information processing might be philsophical endowed within mind? Is it right, I am not sure, but looking at such spaces if we can call it that, while there seems to be "no separation between the two photons of Alice and BOb" and spooky is being interpreted here what value, if such interjections of information could appeal in that "space" of the quantum phase gate?

INteresting perspective on the term "mandorlas."

So a historical look then, and other research, that I am doing.

Vesica piscis(wikipedia 20 May 2006)

The symbol is formed from the almond-shaped area in the overlap between the circles, as shown in black in the diagram — for certain purposes also including the upper arcs as far as the edges of a rectangle whose sides coincide with the widest points of the almond (as shown in light blue in the diagram). The resulting figure looks like a stylized fish, or in the extended version like a flattened Greek letter alpha.


Seeing the earlier contribution made on Venn Logic and TA I couldn't help but see some similarities.



In regards to mandalas as well in terms of Liminocentric structures. A historical perspective and one I gained from understanding Jung.

While this terminology may seem foreign, it is well within context of this information, that such similarites were deduced in my own research. So, by producing these maps, it became interesting to know that if they arose from the deeper realms of the subconscious these will make themself known as emerging principals(bubbles of thought) from the waters, what said that such things could not have been part of the history of the soul, to have regained what it had once done by finding that wholenesss of being once before?

Such research and developement if followed, leads one to the deeper understanding of what emerges from the very source of one's being. Details, the schematic drawings of lines and circles as such, to have them become modern day models, while they were once part of our history as human beings. Once, represented the complete and gathering of all the native tribes.

So as ancient as these things are to the mind for consumption in today's world, the thought process is not tainted by that historical past, but leads one forward, from past accomplishements. Pave the way for new models to emerge in society? New models to emerge in science?

How could information enter the synapse, as it does in the gate? It's computational significance in "backreaction?" One would have to recognize the work of Josephson and what tunneling could do? RHIC investigation ain regards to Laval analogies?

Spintronics and implying channelling would have spin orientated possibilties? What signature would have revealled the nature of any elemental if the energy transferred through that tunnelling effect, came from the very beginnings of the universe?

Elements and Atoms: Chapter 11
An Unsystematic Foreshadowing: J. A. R. Newlands


Having revealed where I stand, I invite you to examine and assess Newlands' work on the subject. This selection includes four short papers of Newlands and a report of another paper which show him struggling toward and eventually formulating the system he dubbed the "law of octaves

Saturday, January 21, 2006

Drawing a Venn diagram: Entanglement Issues

Plectics, by Murray Gellman
It is appropriate that plectics refers to entanglement or the lack thereof, since entanglement is a key feature of the way complexity arises out of simplicity, making our subject worth studying.




The person above was kind enough to send information held in context of picture link for consideration, to help out with comprehension. I mean certain things hold us to consequences, that while I might have been thinking of Einsteins example of a pretty girl and a hot stove, this thinking did not pass my attention when one held the photon to certain enviromental influences as we gave these things thought processes. I context of "gravity as the square," is appropriate I think, about what combinations are realistic.



At the very heading of this post there is a link directly attached for consideration in context of all these possibilties. Some things come to mind in terms of Feynman's toy models, as strict interactive phase that we would like to keep track of. So what one might have done to say, hey, if we are given a possibility of scenarios about Entanglement issues, how shall we solve these interactive phases, as we try to build a multiphase integrative model held in context that perfect human being.

Entanglement applies to two or more particles even if one of them is used as input to the two slit experiment, it is not applicable to single particle experiments.


YOu know it is not that simple, but there are always grand designs on what we think something is nifty in society, as we progress our models of the future. As to how we will create the perfect models for apprehension about our universe, and how we interact with it.

Pictorial represenations can be very useful in presenting information or assisting reasoning. Venn diagram is an example. Venn diagrams are used to represent classes of objects, and they can also assist us in reasoning about the relations between these classes. They are named after the English mathematician John Venn (1834 - 1923), who was a fellow at Cambridge University.


While it is true that I am being fascinated by mathematical processes, and how they are used in our visionary quest for understanding, one would have to be a computer to remember all the interactive phases that could have manifested from a situation held in context of a "societal problem." One we might have encountered in our lifetimes.

It's statistical outcome that held to such micromanagement processes, would have been lost on all our minds, if we did not think some science process could have been touted with all these combinations.



Each time I am presented with this thinking, the elementals of the model for apprehension, it always seemed easier to me to just have a look and see what "buddhist principles" are telling us about how we have a hold of our world in all it's realisms. The choices we make, and how we are to conduct ourselves "becoming." Einstein used that term well I think.

So why such association and "combinations", that we have move the thinking here to what was gained in our emotive and abstract thinkings, as productive human beings? To see what a new foundational logic is being developed around our lives. Did we did not readily see the significance of the technologies involved. One had to dig a little deeper I think.

So here is a preview of what entanglement issue has been shown to help orientate views on this issue. Some diagram perhaps, to show the developing scenarios around such entanglement issues?



Quite early these indications about the possibilties of entangled states, raised all kinds of questions in my mind. Thinking of Hooft and others, about the issues of classical quantum processes, over top of these wide and incomprehensible statistical possibilties, seems held under the auspice of our reality model. That "square", given earthbound recognizitons, happily according to the basic pricniples, have so far held our views in gravitational model assumptions. IN essence, we have boxed the views on entanglement. As we have boxed Andrey Kravstov computerized model of the orignations of this universe in a supersymmetrical view of origination. What could have arisen from such situations. Probable outcomes?

Whether such a "quantum computer" can realistically be built with a value of L that is large enough to be of practical use is a topic of much debate. However, the mere possibility has led to an explosive renaissance of interest in the host of curious and classically counterintuitive properties associated with entangled states. Other phenomena that rely on nonlocal entanglement, such as quantum teleportation and various forms of quantum cryptography, have also been demonstrated in the laboratory

Friday, January 20, 2006

Venn Logic and TA

I always lke to inject a piece of my young child's perspective, becuase it helps explain things a bit about "the neighborshood." As we move through them. He asked me about the neighborhood that we were moving too, as if, that was the world. That was his question. "Is this the World," Dad? He was about 4 years old at the time. He's gone now, married, and leadng a very productive life.



The purpose of this picture above comes later down the length of this post. We are all not perfect, are we?

As a youth my first reading of this topic was from a book called, I'm Okay Your Okay, by M.D. Thomas A. Harris.

It helped in defining aspects of myself in context of what was happening in my environment, while being introspective. Is this always a good thing that we take stock of what is going on inside ourselves to wonder indeed what is all these parts of ourselves. How do we look at them in context of the way the "I" is being used.

These lessons were also derived from other places, so it becomes culminative in how one might look at society, and from it, a biased view forms no dfferent then one who has been transplanted from historical context of experience, moving from the lands of the Carribean to the UK society, held in context and views of the community in which they had lived, and live now. There were comparative features drawn from expeirence to consider here?

So as you move, you grow in perspective, all the while the pictures of mountains and similarities strike poises in our mind of of wnating recognition. Who was this person at the time of youth, who, like myself saw farms of a early history, to know that today this historical past is all but forgotten in the real world struggle of lives held in context of these farms? The picture today, contains the picture of our youth.


Parent ego state

This is a set of feelings, thinking and behaviour that we have copied from our parents and significant others.

As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.

As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.

Adult ego state

The Adult ego state is about direct responses to the here and now. We deal with things that are going on today in ways that are not unhealthily influenced by our past.

The Adult ego state is about being spontaneous and aware with the capacity for intimacy. When in our Adult we are able to see people as they are, rather than what we project onto them. We ask for information rather than stay scared and rather than make assumptions. Taking the best from the past and using it appropriately in the present is an integration of the positive aspects of both our Parent and Child ego states. So this can be called the Integrating Adult. Integrating means that we are constantly updating ourselves through our every day experiences and using this to inform us.

In this structural model, the Integrating Adult ego state circle is placed in the middle to show how it needs to orchestrate between the Parent and the Child ego states. For example, the internal Parent ego state may beat up on the internal Child, saying "You are no good, look at what you did wrong again, you are useless". The Child may then respond with "I am no good, look how useless I am, I never get anything right". Many people hardly hear this kind of internal dialogue as it goes on so much they might just believe life is this way. An effective Integrating Adult ego state can intervene between the Parent and Child ego states. This might be done by stating that this kind of parenting is not helpful and asking if it is prepared to learn another way. Alternatively, the Integrating Adult ego state can just stop any negative dialogue and decide to develop another positive Parent ego state perhaps taken in from other people they have met over the years.

Child ego state

The Child ego state is a set of behaviours, thoughts and feelings which are replayed from our own childhood.

Perhaps the boss calls us into his or her office, we may immediately get a churning in our stomach and wonder what we have done wrong. If this were explored we might remember the time the head teacher called us in to tell us off. Of course, not everything in the Child ego state is negative. We might go into someone's house and smell a lovely smell and remember our grandmother's house when we were little, and all the same warm feelings we had at six year's of age may come flooding back.

Both the Parent and Child ego states are constantly being updated. For example, we may meet someone who gives us the permission we needed as a child, and did not get, to be fun and joyous. We may well use that person in our imagination when we are stressed to counteract our old ways of thinking that we must work longer and longer hours to keep up with everything. We might ask ourselves "I wonder what X would say now". Then on hearing the new permissions to relax and take some time out, do just that and then return to the work renewed and ready for the challenge. Subsequently, rather than beating up on ourselves for what we did or did not do, what tends to happen is we automatically start to give ourselves new permissions and take care of ourselves.

Alternatively, we might have had a traumatic experience yesterday which goes into the Child ego state as an archaic memory that hampers our growth. Positive experiences will also go into the Child ego state as archaic memories. The positive experiences can then be drawn on to remind us that positive things do happen.

The process of analysing personality in terms of ego states is called structural analysis. It is important to remember that ego states do not have an existence of their own, they are concepts to enable understanding. Therefore it is important to say "I want some fun" rather than "My Child wants some fun". We may be in our Child ego state when we say this, but saying "I" reminds us to take responsibility for our actions.


Go ahead and Click on John Venn's picture


A painting of John Venn by Charles E. Brock. Photograph by Christopher Hurst, Hamilton-Kerr Institute, University of Cambridge


IN a strange world where such things are to become part of our analysis of subjective experience will we have created the perfect human being? Such models becme the logic structure of new computerized systems of thinking that will somehow recognize these factors in the human beings that we are, to have it done better in a traditional methods of logic, formed around and in computerized thinking.

Science and TA by Chris Boyd
Do we selectively ignore other models from artificial intelligence such as Zadeh's Fuzzy Logic? This is a logic used to model perception and used in newly designed "smart" cameras. Where standard logic must give a true or false value to every proposition, fuzzy logic assigns a certainty value between zero and one to each of the propositions, so that we say a statement is .7 true and .3 false. Is this theory selectively ignored to support our theories?


I had engaged this kind of exercise on my own, as I moved through different research avenues trying to piece together in my own mind, a process held in context of these neighborhoods, and such. How such interactive phases might have been thought about in science procedures. Looking at the basis of this logic, I was looking to find comparsions for this thinking in which the foundational perspectives might make sense.

Science and TA by Chris Boyd
If deduction is another way of knowing in TA, where and when is it applicable? Berne did use Venn diagrams, circles either distinct or overlapping, which were borrowed directly from symbolic logic to visually describe transactions. Perhaps TA in part can be considered a theory that analyzes ones own deductions based on childhood primitive assumptions. Perhaps it focuses on how people become irrational in decision making. In this case, TA provides critical thinking skills for human relations and can be considered a basis for analyzing the accuracy of our reality testing. Much as mathematics provides the language for science, TA may provide the logic for human relations and can be at least in part a deductive language.


Now as usual I did not have many to direct my thinking as I was developing thought processes, that the statements I highlighted were recognized as features I myself found along the journey to make sense of characteristic features we have of our thinking minds.

As you see clicking on John Venn's picture I would like to draw science into how I am seeing to support this "model of thinking." For clear and consise methods incorporating that clear mind.

Do we have to be robots with parts of ourselves missing from the supposed framework of that perfect being? This is what makes us unique in our perspectives as we move forward and share our point of views. We would have had to have been you to become who you are today. So it is never easy to see and be all that you want everyone to be.

Friday, October 07, 2005

Projective Geometries

Action at a Distance

Now ths statement might seem counterproductive to the ideas of projective geometry but please bear with me.


In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. This term was used most often with early theories of gravity and electromagnetism to describe how an object could "know" the mass (in the case of gravity) or charge (in electromagnetism) of another distant object.

According to Albert Einstein's theory of special relativity, instantaneous action-at-a-distance was seen to violate the relativistic upper limit on speed of propagation of information. If one of the interacting objects were suddenly displaced from its position, the other object would feel its influence instantaneously, meaning information had been transmitted faster than the speed of light.


Test of the Quantenteleportation over long distances in the duct system of Vienna Working group Quantity of experiment and the Foundations OF Physics Professor Anton Zeilinger

Quantum physics questions the classical physical conception of the world and also the everyday life understanding, which is based on our experiences, in principle. In addition, the experimental results lead to new future technologies, which a revolutionizing of communication and computer technologies, how we know them, promise.

In order to exhaust this technical innovation potential, the project "Quantenteleportation was brought over long distances" in a co-operation between WKA and the working group by Professor Anton Zeilinger into being. In this experiment photons in the duct system "are teleportiert" of Vienna, i.e. transferred, the characteristics of a photon to another, removed far. First results are to be expected in the late summer 2002.



One of the first indications to me came as I looked at the history in regards to Klein's Ordering of Geometries. Now I must admit as a layman I am very green at this understanding but having jumped ahead in terms of the physics involved, its seems things have been formulating in my head, all the while, this underatnding in terms of this "order" has been lacking.

In Euclidean geometry, the basic notions are distances and angles. The transformations that preserve distances and angles are precisely the rigid motions. Effectively, Klein's idea is to reverse this argument, take the group of rigid motions as the basic object, and deduce the geometry. So a legitimate geometric concept, in Euclidean geometry, is anything that remains unchanged after a rigid motion. Right-angled triangle, for example, is such a concept; but horizontal is not, because lines can be tilted by rigid motions. Euclid's obsession with congruent triangles as a method of proof now becomes transparent, for triangles are congruent precisely when one can be placed on top of the other by a rigid motion. Euclid used them to play the same role as the transformations favored by Klein.

In projective geometry, the permitted transformations are projections. Projections don't preserve distances, so distances are not a valid conception projective geometry. Elliptical is, however, because any projection of an ellipse is another ellipse.


So spelt out here is one way in which this progression becomes embedded within this hisotry of geometry, while advancing in relation to this association I was somewhat lifted to question about Spooky action at a distance. WEll if such projective phase was ever considered then how would distance be irrelevant(this sets up the idea then of probabilistic pathways and Yong's expeirment)? There had to be some mechanism already there tht had not been considered? Well indeed GHZ entanglement issues are really alive now and such communication networks already in the making. this connection raised somewhat of a issue with me until I saw the the phrase of Penrose, about a "New Quantum View"? Okay we know these things work very well why would we need such a statement, so I had better give the frame that help orientate my perspective and lead to the undertanding of spin.



Now anywhere along the line anyone can stop such erudication, so that these ideas that I am espousing do not mislead. It's basis is a geometry and why this is important is the "hidden part of dirac's mathematics" that visionization was excelled too. It is strange that he would not reveal these things, all the while building our understanding of the quantum mechanical nature of reality. Along side of and leading indications of GR, why would not similar methods be invoked as they were by Einstein? A reistance to methodology and insightfulness to hold to a way of doing things that challenegd Dirac and cuased sleepless nights?



Have a look at previous panel to this one.

While indeed this blog entry open with advancements in the Test in Vienna, one had to understadn this developing view from inception and by looking at Penrose this sparked quite a advancement in where we are headed and how we are looking at current days issues. Smolin and others hod to the understnding f valuation thta is expeirmentally driven and it is not to far off to se ehosuch measure sare asked fro in how we ascertain early universe, happening with Glast determinations.

Quantum Cryptography

Again if I fast forward here, to idealization in regards to quantum computational ideas, what value could have been assigned to photon A and B, that if such entanglement states recognize the position of one, that it would immediately adjust in B?

Spooky At any Speed
If a pair of fundamental particles is entangled, measuring an attribute of one particle, such as spin, can affect the second particle, no matter how far away. Entanglement can even exist between two separate properties of a single particle, such as spin and momentum. In principle, single particles or pairs can be entangled via any combination of their quantum properties. And the strength of the quantum link can vary from partial to complete. Researchers are just beginning to understand how entanglement meshes with the theory of relativity. They have learned that the degree of entanglement between spin and momentum in a single particle can be affected by changing its speed ("boosting" it into a new reference frame) but weren't sure what would happen with two particles.



So there is this "distance measure" here that has raised a quandry in my mind about how such a projective geometry could have superceded the idea of "spooky things" and the issues Einstein held too.

So without understanding completely I made a quantum leap into the idealization in regards to "logic gates" as issues relevant to John Venn and introduced the idea around a "relative issues" held in my mind to psychological methods initiated by such entanglement states.

As far a one sees here this issue has burnt a hole in what could have transpired within any of us that what is held in mind, ideas about geomtires floated willy Nilly about. How would such "interactive states" have been revealled in outer coverings.

The Perfect Fluid

Again I am fstforwding here to help portray question insights that had been most troubling to me. If suych supersymmetrical idealizations arose as to the source and beginning of existance how shall such views implement this beginning point?

So it was not to unlikely, that my mind engaged further problems with such a view that symmetry breaking wouldhad tohave signalled divergence from sucha state of fluid that my mind encapsulated and developed the bubble views and further idealizations, about how such things arose from Mother.

What would signal such a thing as "phase transitions" that once gauged to the early universe, and the Planck epoch, would have revealled the developing perspective alongside of photon developement(degrees of freedom) and released information about these early cosmological events.

So I have advance quite proportinately from the title of this Blog entry, and had not even engaged the topological variations that such a leading idea could have advanced in our theoretcical views of Gluonic perceptions using such photonic ideas about what the tragectories might have revealled.

So indeed, I have to be careful here that all the while my concepts are developing and advanced in such leaps, the roads leading to the understanding of the measure here, was true to form and revalled issues about things unseen to our eyes.

It held visionistic qualities to geometric phases that those who had not ventured in to such entanglement states would have never made sense of a "measure in the making." It has it's limitation, though and why such departures need to be considered were also part of my question about what had to come next.