View Full Version : Lines, Circles, Cycles & Spirals

04-14-2014, 08:46 AM
Everything is a cycle.

Problem is when the cycle is larger than our own petty existence... sometimes it can be hard to see the curve up ahead. This is where faith can be useful; faith that things will eventually turn around.

But circular doesn't mean things won't move forward, that things will always end up as they began. I don't think it is like that. Metaphorically perhaps.

We don't have a good mathematical structure that can show the reality of the circular nature of reality. Some sort of interconnected system of circular spirals flowing forward into the future perhaps?

Then again on a small scale a circle looks like a very straight line forward...


04-14-2014, 12:54 PM
I agree with that Dev; as we can build something we want straight using a spirit level, but as the structure gets longer it has to go with the curve of the tiny planet earth, but to us it appears perfectly straight.

I guess a theodolite overcomes this...I think...does it?

There are much bigger curves than our planet.


04-14-2014, 06:31 PM
Well Dev ...

You've alluded to part of the concept. Our teenie-tiny-eentsie-beansy little brains -- and I include myself since I have one -- have a hard time wrapping themselves around the idea of cyclical thinking.

But frankly, it's not that hard.

It's easy to feel disconnected, which would be the basis for linear thinking ... separation ... a beginning, middle, and end disconnected. Our bodies are not physically connected to "something else" like the roots of a tree. Our brains are not connected to other brains, like the Internet. We "feel" separated.

But by the simplest of observations, we know this not to be true.

Problem is ... largely ... that there are people who would LOVE for us never to feel connected to anything, so they perpetuate the concept of a lack of connection.

If you've read my other writings, I've made this suggestion in other ways. One of those ways has been discussing Western (European) Culture, and as far as I'm concerned -- I'll just come out and say it forthright -- it's a culture founded on mental disease.

One rudimentary way of putting it is the unstable, unprovable, inaccurate and outright false condition of "compartmentalization."

This is an extremely primitive intellectual condition ...

... largely because it is utterly false.

Now, it's not hard to see how the perspective developed if you examine European history. For a time, separating yourself (as a nation/culture, or even village to village) was an advantage in European history. The Plague was a strong contributor to this ... and there were several waves of it across Europe. Merely letting a stranger into your village could get you all killed. But also, imperialism itself has its roots in separation ... compartmentalization ... specialization ... a serf did this and a noble did that and there was no intermixing. One could not become the other.

Keep in mind that this was a perception, and in fact there was no separation at all in the overall functioning of the society. The society functioned as a whole.

The problem was [and is] the fact that it's unsustainable and self-defeating to attempt to perpetuate any separation whatsoever. It is a temporary condition. It is a condition of false perception, largely over the fact that nothing can ever be separated from anything else.

Note the fact: Nothing Can Ever Be Separated From Anything Else.

Germany cannot be separated from France. Neither can Germany absorb France and annihilate its existence. Chemistry cannot absorb Physics and neither can Chemistry annihilate Physics. Your liver cannot dominate your physical body and replace your lungs. None can -- in the end -- dominate the other. None can -- in the global peripheral all-encompassing wholistic view -- hold a more important place than the other. The male is no more or less important than the female ... the plant no more important than the mineral ...

Each element of the Universe regardless of its size or prominence is no less or more important than the other ... quantum, microscopic, macroscopic, global, solar or galactic, all interrelate.

Holding a shell in one hand and a quartz crystal in the other, one is a seashell and the other is a rock -- neither "being" the other -- but they are related.

The perception of "separation" or compartmentalization is the key. Believing that there is separation is "linear thinking."

And there ain't no such thing.

04-15-2014, 10:03 AM
Temporarily leaving aside European/Western history, the fragmentation of Knowledge and 'past' concepts in general, I'd like to address this topic from the perspective of the stuff we're being taught to take for granted in school, like for example Euclidean Geometry.

Quoth Wikipedia:

Euclidean geometry is an axiomatic system (http://en.wikipedia.org/wiki/Axiomatic_system), in which all theorems (http://en.wikipedia.org/wiki/Theorems) ("true statements") are derived from a small number of axioms.

Near the beginning of the first book of the Elements, Euclid gives five postulates (http://en.wikipedia.org/wiki/Postulate) (axioms) for plane geometry, stated in terms of constructions (as translated by Thomas Heath):

"Let the following be postulated":

"To draw a straight line (http://en.wikipedia.org/wiki/Straight_line) from any point (http://en.wikipedia.org/wiki/Point_%28geometry%29) to any point."
"To produce [extend] a finite straight line (http://en.wikipedia.org/wiki/Line_segment) continuously in a straight line."
"To describe a circle (http://en.wikipedia.org/wiki/Circle) with any center and distance [radius]."
"That all right angles are equal to one another."
The parallel postulate (http://en.wikipedia.org/wiki/Parallel_postulate): "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."

Although Euclid's statement of the postulates only explicitly asserts the existence of the constructions, they are also taken to be unique.

The Elements also include the following five "common notions":

Things that are equal to the same thing are also equal to one another (Transitive property of equality).
If equals are added to equals, then the wholes are equal (Addition property of equality).
If equals are subtracted from equals, then the remainders are equal (Subtraction property of equality).
Things that coincide with one another are equal to one another (Reflexive Property).
The whole is greater than the part.

Parallel postulate (Main article: Parallel postulate (http://en.wikipedia.org/wiki/Parallel_postulate))

To the ancients, the parallel postulate seemed less obvious than the others. They were concerned with creating a system which was absolutely rigorous and to them it seemed as if the parallel line postulate should have been able to be proven rather than simply accepted as a fact. It is now known that such a proof is impossible. Euclid himself seems to have considered it as being qualitatively different from the others, as evidenced by the organization of the Elements: the first 28 propositions he presents are those that can be proved without it.

Many alternative axioms can be formulated that have the same logical consequences (http://en.wikipedia.org/wiki/Logical_consequence) as the parallel postulate. For example Playfair's axiom (http://en.wikipedia.org/wiki/Playfair%27s_axiom) states:
In a plane (http://en.wikipedia.org/wiki/Plane_%28geometry%29), through a point not on a given straight line, at most one line can be drawn that never meets the given line.How is all this facing the concept of non-linear perception/reality? Is this Geometry 'wrong'?

Or is it 'wrong' to teach it in schools? Is there an alternative? Or a way to complement it educationally?

It does, after all, shape the way we think and perceive from an early age...

Does this Geometry apply to limited/contained systems only, thus negating the 'As Above So Below' Hermetic Law of Correspondence?

04-15-2014, 12:53 PM
Happily leaving history aside, let's look at it in terms of The Observer, one of which we all are.

From which vantage point do we choose to make these mathematical observations?

Yes, one could state that these facts are simply facts and they stand on their own, with or without our observation of them.

Then again, the question arises, "If a bear shits in the woods, does it stink?"

Obviously, the answer to that question is always yes. But the "real" question is how relevant is it to the massive, nearly inconceivably complex ecosystem of the woods?

What is your perspective? What is your "normal"? How deeply are you locked into dissecting and analyzing the quantum/micro/macroscopic workings of the Universe? Once we/you/I have examined every dimension of that finite straight line, what then? Does your view become broadened? Or narrowed?

Your questions are answered in your data:

"5. The whole is greater than the part."

Of course, one must define "greater." Better? Or simply larger?

Even if not better, the simple concept of "part" spurs investigation of more parts. Once one discovers one part, certainly there must be more.

In my experiences with Lakota philosophy, I learned one critical difference of perspective between that under which I was raised and that from which they see things.

That difference is illustrated with the two concepts of "Knowledge" and "Understanding." Note that there are two entirely different words for two entirely different concepts. We'll ignore the fact that they are related for the time-being, and examine why they are separate concepts.

There are three ways to approach a perception of these concepts:

1. Knowledge first, seeking the acquisition of Understanding through the accumulation of Knowledge.
2. Understanding first, with a subsequent accumulation of Knowledge to affirm and confirm the theorized Understanding.
3. An acceptance of the ultimate incomprehensibility of both Knowledge and Understanding coupled with the investigation of both, at the same time, merely for the exercise of personal fulfillment.

Let's examine these approaches from an inspection of the body you inhabit.

The first stumbling block is to get past the idea that you are that body, something that many people can't fathom. They identify to a compulsion with their physical being ... to the point of panic when even the suggestion is made that their "true self" may have little to do with the physical body. Steeped to an obsession with their physical appearance, experience and even behavior, acknowledging "self" beyond the physical is essential in developing a wider view.

An understanding ... or knowledge ... either is valid ... of the two concepts of "brain" or "mind" or similarly "think" and "know" should help step you out of a perception strictly physically based. There are things your brain can think -- as a calculator or computer can think -- that your mind comes to know and understand that are beyond the thoughts themselves ...

... which proves beyond doubt that something beyond the physical exists.

Something beyond that finite straight line exists.

So ...

From where do you take your perspective? From the vantage point of the finite straight line? From the still-finite perspective of mathematics? Or from a "wholistic" perspective of Universal Unity?

There is a choice. In fact, you must choose. That is the literal definition of "perspective" if and when perspective is anything but a default.

For a conscious, cognizant being, perspective is not a default, but a choice. A plant, a bird, a rock or a cloud (or even a mathematical law) has a "default perspective." There is no choice in the method by which they participate in Creation.

You possess choice.

You may choose to view and participate in Creation from your default perspective, that finite straight line, or you may choose a wider view.

To put it in terms taken from The Emerald Tablet, I neither choose to take my perspective from either Above or Below, but choose to step back and observe both at the same time.

Does any of this help?