A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Discussion of the nature of Ultimate Reality and the path to Enlightenment.
Pam Seeback
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by Pam Seeback »

Contact with "circle" keeps the condition of objectifying one's subjectivity turning eternally. This is why man's mental world can never be a foundation upon which to rest one's being. There can be no peace while man hunts for truth in idea. Which means "a unifying theory" is a contradiction of terms. I am assuming, of course, that the author of this thread considers "unity" and "peace" to be the same thing.
The Blessed One said: "And what is the origination of the world? Dependent on the eye & forms there arises eye-consciousness. The meeting of the three is contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. From craving as a requisite condition comes clinging/sustenance. From clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. This is the origination of the world.
Put three scientists into a room to discuss their theories of reality and see the sparks fly! Pure objectivity? No greater myth abides than this.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by Pam Seeback »

One only needs to go within themselves to discover that without the attachment of meaning to a form, it serves no purpose. And where there is attachment, a sense of purpose, there is not objectivity or purity of form.

This is not a theory, but an experiential realization.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by Pam Seeback »

chikoka wrote:
movingalways wrote:You are right, you are not an abstraction about abstractions, so why then, do you abstract about abstractions? Why do you choose to identity with what you are not, rather than with what you are?
Its fun.
Indeed. But not unifying as per your original thesis.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by cousinbasil »

jufa wrote:The central point here is whether a square or circular circle exist and are real or not.

Is a square circle real or not, is what I put to you?
Let me address the first point, which I hope answers the second.

In another thread, I cited Roger Penrose's postulation of three kinds of existence. This is not original with him, but I am following the approach because it seems to avoid ambiguities - like the one brought up by your first point. Squares and circles exist in a Platonic realm, or Platonic sense. All squares are equivalent. All circles are equivalent. The ancient Greeks studied the properties of circles and squares - the circles and squares we studied in grade school are those very ones. They do not change. The properties of a circle or square are not invented; rather, they are discovered. They do not change, although many properties of each may very well remain to be unearthed.

So the answer is yes, a circle exists and a square exists, both in this timeless fashion. Physical objects may exist, but not in a Platonic or timeless sense, as physical objects are subject to physical change. Whether an object changes over time is not the point - the point is that it can, whereas a circle cannot, say.

Since both a square and a circle exist in this sense, they can be said to be real.

But since they are not real in a physical sense, there seems to be some misunderstanding in this thread as to whether one can declare that a "square circle" also exists. Whatever you choose to imagine or envision which you decide to call a square circle cannot have the all the properties of both a square and a circle. For instance, that would mean it had four angles and it had no angles, which is a logical contradiction.

To harp on the square circle or insist it is not impossible is foolish, since you are therefore contending that there is no such thing as a logical contradiction. You would be in effect saying impossibilities are impossible, which is itself a logical contradiction.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by Pam Seeback »

Squares and circles exist in a Platonic realm, or Platonic sense. All squares are equivalent. All circles are equivalent.
Agreed.
The ancient Greeks studied the properties of circles and squares - the circles and squares we studied in grade school are those very ones. They do not change. The properties of a circle or square are not invented; rather, they are discovered.
Agreed. The discovery of properties, however, is of no value unless subjective meaning is attached. Of what value is the property "round" if "round" does not enter the affective realm? No effective/affective attachment = circular imaging.
They do not change, although many properties of each may very well remain to be unearthed.
It is because one's body is of the earth that one takes a platonic form and becomes attached to its shape. Look at how many men are attached to the form "triangle" and how many women are attached to the form "cylinder." :-)
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by jufa »

You keep mentioning Platonic realm of thought, and this is a theory of doubt, not certainty. Such being the case, your platform is that of quicksand, which, in this case, is the force of suction pulling you deeper and deeper into a quagmire which will only allow you to go up or down, but never find a position other than assumption.

Your acknowledgment the square and circles existence should be the end of this subject from a logical or illogical position. This is evident in the reality of their existing properties which you revealed to be visible and invisible [invisible waiting to be discovered by thought].

This is the reality of this thread: That which one is unaware of does not exist to them. But when one leaves a room, does the room no longer exist? Or does the room exist because you are aware of it by thought?

You see, existence is thought awareness. What is not logical is existence itself. So when dealing with objects or subjects in an existence which has no logic to be, all thoughts within are effects of assumption because there is no causation to be had.

Never give power to anything a person believes is their source of strength - jufa
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by cousinbasil »

jufa wrote:You keep mentioning Platonic realm of thought, and this is a theory of doubt, not certainty.
What could you possibly be talking about? The Platonic realm of thought is not a "theory" of any kind. It is that portion of one's awareness which does not change, except to become more deeply realized the more one is exposed to it. It is precisely where doubt not only does not exist, but cannot exist.
Such being the case
It's not the case
your platform is that of quicksand, which, in this case, is the force of suction pulling you deeper and deeper into a quagmire which will only allow you to go up or down, but never find a position other than assumption.
The quagmire that is a logical proof, you mean? Are you sure this is the right forum for you?
This is the reality of this thread: That which one is unaware of does not exist to them. But when one leaves a room, does the room no longer exist? Or does the room exist because you are aware of it by thought?
"That which one is unaware of does not exist to them." Them is plural. One is singular. So who are you speaking about, exactly?
So when dealing with objects or subjects in an existence which has no logic to be, all thoughts within are effects of assumption because there is no causation to be had.
No causation to be had. Good one. Exactly which "existence" are you referring to?
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by jufa »

cousinbasil wrote
What could you possibly be talking about? The Platonic realm of thought is not a "theory" of any kind. It is that portion of one's awareness which does not change, except to become more deeply realized the more one is exposed to it. It is precisely where doubt not only does not exist, but cannot exist.

It is stated: Plato's theory of Forms or theory of Ideas asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality. When used in this sense, the word form is often capitalized. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato's own views are much in doubt [Watt, Stephen (1997). "Introduction: The Theory of Forms (Books 5-7)". Plato: Republic. London: Wordsworth Editions. pp. xiv–xvi. ISBN 1853264830.]. Plato spoke of Forms in formulating a possible solution to the problem of universals.
cousinbasil wrote
The quagmire that is a logical proof, you mean? Are you sure this is the right forum for you?
You have no logic proof to keep you from sinking. You only have assumptive theories, based on assumptive theories.
cousinbasil wrote
"That which one is unaware of does not exist to them." Them is plural. One is singular. So who are you speaking about, exactly?
Now you want to play word comprehension. Good way to avoid the thrust here, which you totally ignored, was put to you in question form which I repeat when one leaves a room, does the room no longer exist? Or does the room exist because you are aware of it by thought?
cousinbasil wrote
No causation to be had. Good one. Exactly which "existence" are you referring to?
Playing word comprehension again. The gist here, as you know, was your attempt to apply logic to effect when there was no logic to be had for the existence of the effect.


Never give power to anything a person believes is their source of strength - jufa
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by chikoka »

cousinbasil wrote:Except n-dimensional space is logically consistent and a square circle is not, by definition. You are acting as if the axiom of identity has been felled. If so, when did that happen - ?
Its not been felled , basicaly because it was never really up.
It was simply assumed (def. of axiom = assumption).

Agrippas trilema goes on to show that axioms are not provable but build a theory that says "if this (axiom) then that."

Please acknowledge the "if" in the last statement.Its not "this ..then that"

cousinbasil wrote:I am unaware of any fruitful field of research or inquiry that totally abandons the usually implicitly agreed upon "axiom of identity."
I introduce you to this one.
cousinbasil wrote:In English, anything is all-encompassing and need not refer to things at all.
When its not reffering to things what is it reffering to?
cousinbasil wrote:You are postulating the possibility of a "zeta," which has four sides AND does not have four sides.
Theres no "which" when it comes to "zeta's" , that term does not make sense in zeta notation.
Its an era to use "thing notation" (e.g. the english language) to discuss zetas.Use zeta notation which is where i hope we get to after the initial hurdle (of justifying it) is over.
cousinbasil wrote:Quote:
Also if the univerese is flat and infinite then it is a square and a circle and any shape imaginable at the same time

And composed entirely of Banana Peels...
No.
As you increase the radius of a circle the circumference becomes flatter ,(thats why the earth was first thought to be flat).
At infinity radius the sides are totally flat , just like the sides of a square.
cousinbasil wrote:The properties of a circle or square are not invented; rather, they are discovered.
I disagree.Circles and squares are based on things that by defn. cannot exist.
The point. (dimensionless), and the line (one dimensional) anything with length but no width cannot exist.
Except maybe as a zeta.Which i like the sound of.
cousinbasil wrote:For instance, that would mean it had four angles and it had no angles, which is a logical contradiction.
The circle just by itself is already a logical contradiction.Its made of a "widthless" line.
cousinbasil wrote:To harp on the square circle or insist it is not impossible is foolish, since you are therefore contending that there is no such thing as a logical contradiction. You would be in effect saying impossibilities are impossible, which is itself a logical contradiction
My defn of a logical contradiction is a saying 2/3 is a "natural" number.
That does not mean it still isnt a (generic) number.
Another one is a square circle that is a "thing".
That does not mean it still isnt a (generic) thing (zeta).
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by eyekwah »

Image

Adding a programmer's perspective here:

Logic is funny like that. Once things get irrational and illogical, no further arguments work. It's like entering in wrong numbers into a calculator and expecting them to give the right answers. Surprisingly, sometimes it might even work, though that doesn't make it meaningful.

And I think limiting sets to finite collections is lame. Hasn't anyone heard of a symbolic link in linux? If you don't worry so much about how many objects you have in your set, I think we could do that much more in mathematics with such a set.
Life is wasted on the living.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by cousinbasil »

Its not been felled , basicaly because it was never really up.
It was simply assumed (def. of axiom = assumption).

Agrippas trilema goes on to show that axioms are not provable but build a theory that says "if this (axiom) then that."

Please acknowledge the "if" in the last statement.Its not "this ..then that"
Acknowledged. But so what? I find "if...then" to be basic to learning. As in IF you abandon A=A THEN you cannot construct a logical statement.
chikoka wrote:
cousinbasil wrote:In English, anything is all-encompassing and need not refer to things at all.
When its not reffering to things what is it reffering to?
It could refer to "anything," such as ideas, emotions, events, schemes... The set of things it cannot refer to is this one: { }.
As you increase the radius of a circle the circumference becomes flatter ,(thats why the earth was first thought to be flat).
At infinity radius the sides are totally flat , just like the sides of a square.
You are saying that as a circle becomes bigger, at some point it starts to have sides. That would mean some parts of its circumference were further away from its center than others, would it not? If so, it would no longer be a circle.
The circle just by itself is already a logical contradiction.Its made of a "widthless" line.
You are correct in that one has to specify whether one is talking about a bounded or unbounded circle. Boundary-value arguments are some of the most profoundly fascinating ones in any area of math. But you seem to be getting confused by the idea (Platonic) of a circle, and the thing the teacher draws freehand on the blackboard that is supposed to represent it.
My defn of a logical contradiction is a saying 2/3 is a "natural" number.
How about 6/3? Is that a natural number?
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by jupiviv »

Curves can't exist either as Platonic ideas or physical objects(and please, no jokes about Kim Kardashian being curvy.)

Draw points on the circumference of a circle, and you'll have a polygon. It appears curved only because we don't/can't see all the straight lines. It may be said that the Platonic idea of a circle is the inability/refusal to see all the straight lines in it on the part of the subject.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by jupiviv »

chikoka wrote:I beleive that we could have a set of all things (or every-thing) that is closed when using certain operations (of which i will speak later on).
When we are talking about "all things", the concept of a boundary becomes meaningless, because there is nothing else.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by jufa »

jupiviv wrote:Curves can't exist either as Platonic ideas or physical objects(and please, no jokes about Kim Kardashian being curvy.)

Draw points on the circumference of a circle, and you'll have a polygon. It appears curved only because we don't/can't see all the straight lines. It may be said that the Platonic idea of a circle is the inability/refusal to see all the straight lines in it on the part of the subject.
Should curves be non-existence, how then are you referencing curves? Moreover how can points be drawn on the circumference of a circle being the circle does not exist? Polygon deals with two dimensional straight lines which angles never reach 180 degrees. What are the degrees of a curve?

Your position that
Curves can't exist either as Platonic ideas or physical objects
falls short for this very simply logic. The computer you are aware of at this present came forth from an invisible thought and manifested as - need i say it? yea - as all the curves and angles you now find pleasure of usage.

In the beginning the computer was a theory. How did the theory become objectified being it does not exist?

Reality is the thought. To think anything is its reality. That which comes forth from thought is effect. The question is what is the logic behind the reality of the thought?

Never give power to anything a person believes is their source of strength - jufa
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by chikoka »

Quote
----
The circle just by itself is already a logical contradiction.Its made of a "widthless" line.You are correct in that one has to specify whether one is talking about a bounded or unbounded circle. Boundary-value arguments are some of the most profoundly fascinating ones in any area of math. But you seem to be getting confused by the idea (Platonic) of a circle, and the thing the teacher draws freehand on the blackboard that is supposed to represent it.
----

You have it backwards.
The thing a teacher draws on the black board is made of a line which *does* have width.
The ideal circle (platonic) is made of a line with no width.

I want to stick to this point till we exhaust it since it is very important for my proof.



Quote
-----
My defn of a logical contradiction is a saying 2/3 is a "natural" number.
How about 6/3? Is that a natural number?
-----

Yes it is.It is equivalent to the natural number 2.
2/3 is not equivalent to any natural number.

I would really like to see you show that my definition or understanding of logical contradictions is flawed in a way that yours is not.
If you do that then you would have succeeded in puting an end to this thread.
Please dont run away from this one.
We seem to have different understandings of what a "logical contradiction" is, which is where *ALL* the problems we are having stem from.

Again, please dont run away (evade) this one.

My Understanding:
========
My definition for logical impossible is not_having_closure_in_its_realm.
So some things realy are logicaly impossible when the domain of the entiteis under consideration , together with the operation under consideration lead to results that dont lead to closure in that domain (as range).

E.g. If you use the natural numbers as the domain and co domain and the function is division say, then a result such as 2/3 is absurd (as in reducto absurdum).

If we lived in a "natural" world , then any proof leading to irrational numbers would be considered absurd just as you think zeta's are absurd.


and simplified:


My defn of a logical contradiction is a saying 2/3 is a "natural" number.
That does not mean it still isnt a (generic) number.
Another one is a square circle that is a "thing".
That does not mean it still isnt a (generic) thing (zeta).
=====



Quote
----
chikoka wrote:
cousinbasil wrote:
In English, anything is all-encompassing and need not refer to things at all.
When its not reffering to things what is it reffering to?
It could refer to "anything," such as ideas, emotions, events, schemes... The set of things it cannot refer to is this one: { }.
---

The examples you gave are all of things.Ideas, emotions,events,schemes..are all things.I want you to say what it could reffer to if it werent reffering to things.




quote
----
chikoka wrote:
I beleive that we could have a set of all things (or every-thing) that is closed when using certain operations (of which i will speak later on).

When we are talking about "all things", the concept of a boundary becomes meaningless, because there is nothing else.
----

agreed there is nothing (no thing) else.But there could be some zeta's.

Its like saying there are (no_hats) in the box,but there still could be socks.


Quote
----
You would be in effect saying impossibilities are impossible, which is itself a logical contradiction
---

So impossibilities are what; possible? And THAT isnt a logical contradiction?

I know where the solution to this paradox lies.
I assumed that the impossibility is the thing and not the statement about the thing ,which you did when you made up your statement.
I'm strawmaning you back.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by Pam Seeback »

This thread is about a unifying theory of the totality and the all. Knowing that forms are equal in their non-interpreted or neutral state explains why the all is a unified field, but it does not explain how one unifies their interpretative existence [A does not equal A] with their non-interpretative [A equals A] existence.

Is this not the suffering of every man, of knowing the perfection of A = A, but that he does not live this perfect knowledge? Some say reason and logic is the living of this perfection, implying that it is not connected to the prejudice or relative attachment of sentience, but to me, this is the final delusion a man must acknowledge before he can find the reality of unification, which is the unification of imperfection to perfection. In other words, unity in his mind, heart or conscience.

If one does not know peace, does anything else matter?
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by cousinbasil »

chikoka wrote:You have it backwards.
The thing a teacher draws on the black board is made of a line which *does* have width.
The ideal circle (platonic) is made of a line with no width.
But you are the one who has a problem with this! You said above:
The circle just by itself is already a logical contradiction.Its made of a "widthless" line.
How is the definition of a circle a contradiction? What is it contradicting? Unless you are confusing it with its representation, there is no contradiction that I can see.
I want to stick to this point till we exhaust it since it is very important for my proof.
I am already exhausted!
chikoka wrote:
cousinbasil wrote:It could refer to "anything," such as ideas, emotions, events, schemes... The set of things it cannot refer to is this one: { }.
The examples you gave are all of things.Ideas, emotions,events,schemes..are all things.I want you to say what it could reffer to if it werent reffering to things.
It refers to things and whatever else you are supposing are not things by its definition. You can change the definition of any word if it suits you, but going that route means there is not much we can talk about.

You are saying there are things and there are zetas. This is only so if you restrict what is meant by things. For then why can't I say no, there are things, there are zetas, and there are epsilons, and that those three are mutually exclusive?
When we are talking about "all things", the concept of a boundary becomes meaningless, because there is nothing else.
So impossibilities are what; possible? And THAT isnt a logical contradiction?
No it's not, in that it is possible to arrive at a logical contradiction. But all logical contradictions are therefore equivalent. When I refer to what I call a logical contradiction, what would you have me call it instead? You are saying 2/3 is not a natural number, and I agree that be definition of what a natural number is, 2/3 is not a natural number. Why then is it suddenly incorrect to call a square circle a logical contradiction? Why does that have to be a zeta instead?

Honestly, I am not sure what point you are trying to make here. Instead of introducing more terminology (zetas), what is wrong with the terminology we have? I simply used Marvin because you are insisting the square circle is not impossible. I am not saying there is no such thing as non-euclidean geometry. But even within say Lobachevsky geometry, a square and a circle are defined in such a way that square circles do not exist.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by cousinbasil »

jupiviv wrote:Curves can't exist either as Platonic ideas or physical objects(and please, no jokes about Kim Kardashian being curvy.)
Scurvy is more like it.
Draw points on the circumference of a circle, and you'll have a polygon. It appears curved only because we don't/can't see all the straight lines. It may be said that the Platonic idea of a circle is the inability/refusal to see all the straight lines in it on the part of the subject.
Or to let the number of those straight lines approach infinity, or the length of each to approach zero in a limit procedure, which is by now a very well-understood method, co discovered by Newton.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by jupiviv »

cousinbasil wrote:Or to let the number of those straight lines approach infinity, or the length of each to approach zero in a limit procedure, which is by now a very well-understood method, co discovered by Newton.
All of that would fall under the Platonic idea of "refusal to see etc."
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by cousinbasil »

jupiviv:
Not sure why the idea of a circle is open to such things as refusal, denial, or inability. In its essence it is one of the most stable and useful Platonic ideals, absolutely replete with ramifications such as Trigonometry. The ability to construct a unit circle on a complex plane leads to the theory of residues which enable elegant exact solutions to otherwise seemingly intractable problems.

But does a circle - or can a circle - exist in any precise physical way? I am not sure it can, since it is based on Euclidean idealized space which may or may not reflect true space.
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by jufa »

Religion, science, philosophy and math are the primers for mankind's awareness, but that is all they are. However, mankind thinks and believes they are the basis for their living, achievements, success, good and bad endeavors, and on, and on, and on. But as all situations, circumstances, conditions, and even the environ, they come and go fluently in all individuals lives unnoticed because the attitude of memory keeps one locked into that which was. Repetition of all we do is repetitive of all that is.

I stated sometime ago, the Zero is absolute only because the definition of the circle is recognized. It is that definition which makes the void within it, and outside of it appears not to be the equal of the circle. But it is the circle which is the form and the definition of one observing the voids within and without the circle. Had there been no definition, then there would be no Zero. Definition is only because of thought awareness. So it is the definition of the circle which is the reality, and that reality is comprehended when it is realized there is only ONE circle and it is equal to nothing, not even itself. It is that definitive circle which gives the void within and without it definition and dimensions. Yet the void is unmeasurable. Take away the definition of the circle and you have nothing. But you can't take the circle always and become relative even to yourself. Circle does not = circle. Circle is the definition of circle.

It is the attempt to remove the circle of definition which causes the chaotic quantum world of dualism, angles and Platonic theories. For religion, science, and philosophy and mathematicians to says that which is within and without the definitive circle has or does not have meaning, or is not real, when the reality of the matter is, all things relate to the circle because they are an emanation of the circle. When trilateral angles forbid consideration of the 180 degrees which defines a subject or object existence in pure form, the trilateral divide void itself from that which is the very cause of its existence and expansion.

What are you saying jufa? This attempt to eliminates the circle, which is the center of that within and without, is denying the Four Square Circle -time, space, distance and matter- of sentient intelligence. This is the basis for "the restless mind, pulse Platonic realm, and theories of a trilateral division. All find existence and are definable only because of the existence of the circle. No mind, pulse Platonic realm, or theories of a trilateral division can be separated from the whole. Neither can they borrow energy from temporal parts of the circle because the circle is one continuum of the continuum of itself...this is the truest state of The Totality And The All.

Never give power to anything a person believes is their source of strength - jufa
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by cousinbasil »

What are you saying jufa?
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by jufa »

cousinbasil wrote:
What are you saying jufa?
I am saying when anything is brought forth by emanation of thought and expressed, it exist.

When one says there is no reality to anything, the instant of thought identification makes it a reality. Nothing is the reality of thought by identification. Identification is the reality of nothing by thought.

That to fraction the thought into fragments, then argue a particular fragment represents "the totality and the all" of the thought is reality, one has to be?

Never give power to anything a person believes is their source of strength - jufa
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by Pam Seeback »

cousinbasil: But does a circle - or can a circle - exist in any precise physical way? I am not sure it can, since it is based on Euclidean idealized space which may or may not reflect true space.
Whether the circle is based on Euclidean idealized space does not change the fact that it is the thinking upon the circle that keeps it alive in one's consciousness. And what is the circle but the turning image-thoughts of oneself? Welcome to the reason for dualism.
cousinbasil
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Re: A UNIFYING THEORY OF THE TOTALITY AND THE ALL

Post by cousinbasil »

ma wrote:And what is the circle but the turning image-thoughts of oneself? Welcome to the reason for dualism.
You are entering the affective realm again. I don't think that is necessary, but you may find it productive - I find discussing Platonic realities oddly soothing as opposed to metaphysical discourse.

My point was in the very well understood Platonic sense, the circle is the set of all points in a plane that are equidistant from a given point. This distance, which is called the radius of the circle, entirely defines the circle. All circles differ only in their radii, ignoring the location of the circle, since it really is always in one's head. Without loss of generality, the study of the circle is usually done with letting the radius r=1. From this, all of the Trigonometry functions spring. Since we are always letting r=1, the units do not matter.

The ratio of 2C/r (=2C since r=1) where C is the circumference or "distance around" this unit circle is given the name π. It turns out that π cannot be expressed as a repeating decimal, so therefore is an irrational number. Another way of saying this is that π cannot be expressed as the ratio of two whole numbers, although 22/7 is somewhat close.

The irrational unit-less quantity π is also the area of the unit circle.

This may be only true if space itself is Euclidean. If not, then the actual physical area of a circle might be different from π and may not be irrational after all! Just a guess...
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