Circles, squares, triangles, and the mix. Why?, I am not good at titles...

A thought that struck me after a recent thread by StevenA has left me somewhat unsatisfied.
His thread and question was about the existence of Pi in nature.

The question that was raised in my head was about the human obsession with perfect shapes.

Why when we look at a circle on paper do we imagine it is perfect? When we look at the edge of a leaf, we imagine the curve to be perfect, or the points to be perfect. We even go as far as to imagine that a simple formula for it exists.

I don't think the answer to this is because of the structure of modern mathematics. Even in the Lascaux caves, paintings from 30,000 years ago, rectangles and other geometrically perfect shapes can be found.

I suppose it comes down to symmetry...but the question remains, why? What in our evolutionary history forced our brain to think in symmetrical figures?

Is it the way we put together integers in our heads? Or might it go way back to the times before hominoids?

I recall reading something in a book in which a sociologist/psychologist had tried to explain the seemingly random abstract shapes found in ancient caves. He described the stages in which the brain gets 'high'. During one of them, apparently we would see such shapes: zig-zags, curls, straight lines etc, projected in front of our eyes. The person explained that the ancient cave dwellers drew those as they got high from crude drugs and hyperventilation in shamanic rituals and then drew these.

~~~
Also, in a book I'm reading right now, ("How the mind words" by Steven Pinker), Steven points out how amazing it is that not only can our brain interpret communicatives (such as vocal sounds, visuals of facial expressions etc) to mean what the person originating them wants them to mean, but also how one idea from someone else can cause another person to come up with a completely new and independent idea. As is the case here. Amazing ain't it?

In ST:Deep Space Nine is/was a shape changer named Odo. A TV critic once commented why would anyone who can look like a filmstar want to look ugly (as he thought Odo did)? The point the critic missed was that all Odo's people can look as handsome as they want so beauty had no meaning. Their ideal was in perfection of whatever form they took.

When people or even animals choose a mate, one consideration is perfection. That indicates that a person is healthy and so will produce healthy offspring. We see perfection as a sign that all is well. That is why we seek perfection in all things, whether shiny and new cars or picture perfect living rooms. That strays into other fields, that we also want perfection there, that a circle when drawn looks like a circle and not something vaguely the right shape.

Look at old pottery and you see handpainted designs on them. Not always good but the people tried their best with what they had at hand. It is the same with these cave paintings. They were often symbols to their gods of a good hunt or good weather and they wanted to plaese the gods so gain favour with them.

Perhaps a reading of the book "The Naked Ape" by Desmond Morris would offer insight into the world of sentient aesthetics.

I am wondering if glitches in our perception do not contribute to this phenomenon. Look at the way optical illusions work, our brain does not see what is actually there, but rather an interpretation. The illusions work because our brain will actually alter our perceptions to fit pre-conceived notions. In other words, our brain tries to idealize that which it sees. Perhaps our brain applies this pattern to other thought processes too.

That's an interesting idea Kaneda, but I tend to distinguish the part of us that wants a perfect living room, and the part of us that imagines perfect squares. The reason being that I think one evolved way before the other. The former plays an important part in sexual selection, and that is what tells me that their is a difference in their evolutionary age. But that does not disprove your theory and it is still a good idea. I'll give it more thought.

fizzeksman, I have my hands full with school work and three other books I am reading right now, plus about 5 more I can't wait to get done with. But I'll add on your book too and hopefully get to it soon. Thanks for the suggestion.

Rusty, you are right in what you point out, but I think that again, the idea of having the ability of image is older than that. Infact that is what would predefine the 'pre-conceived notions' you are speaking of.

It surely does. I think that is what gives us the ability to understand moving pictures, and computer graphics, and even virtual reality. Otherwise it would just be scribbly noise to us.

Maybe it is because the system we live in has symmetry.

I can't post a URL link at the moment so I passed it via personal message.

"I am wondering if glitches in our perception do not contribute to this phenomenon. Look at the way optical illusions work, our brain does not see what is actually there, but rather an interpretation. The illusions work because our brain will actually alter our perceptions to fit pre-conceived notions. In other words, our brain tries to idealize that which it sees. Perhaps our brain applies this pattern to other thought processes too."

What "illudes" us about some "optics" is in fact the interpretation that our conscious minds make up for some images. However, if a theory of mind is going to get involved, we have to wonder if our minds, being made of universal fabric, **invented** triangles and circles. No chance. If we are made up of the fabric of the universe there is no reason to believe that our minds are not made of the same matters. Assuming otherwise would give us a mind that is made of extra-universal matter and that would be problematic. Triangles and circles are real entities, and not only that: our minds are made up of the fabric of the universe, and use --and appropriate-- geometrics for themselves through our sense of "I"ness. We "tend to distinguish the part of us that wants a perfect living room, and the part of us that imagines perfect squares. The reason being that (...) one evolved way before the other." (ImmortalCoil)

Kaneda: "Why when we look at a circle on paper do we imagine it is perfect? When we look at the edge of a leaf, we imagine the curve to be perfect, or the points to be perfect. We even go as far as to imagine that a simple formula for it exists." Philosophically, it is actually **perfection** that lets us imagine it, thus aproximating our mind machine to itself. The fabric of the universe would exist with or without us, but once we have decided that we are made up of it we have inverted the roles and are now at the receiving end of the realm of perfect ideas and not at the imagining/making uprules for the universe.

"I suppose it comes down to symmetry...but the question remains, why? What in our evolutionary history forced our brain to think in symmetrical figures?" you are already answering the question: because asymmetry is not mindly. Add that up with "one evolved way before the other" and you have "mind" coming up from the "chaos" with symmetry already built in way before our own sense of self.

"Is it the way we put together integers in our heads? Or might it go way back to the times before hominoids?" Yes to both.

Yes, it is the way we put integers together, and they -and their putting-together-- already existed before there were **people** to put them together. Which leads us to: mind existed before life-as-we-know it. Therefore the complete theory of mind already existed much before there was ever any life to use it. If it were otherwise, by putting together integers mind would be bringing into the universe the extra-universal, a logical impossibility. This in no way reflects on your having or not having a "soul", at least in well-combed, non-ragged Spiritualism, as it takes for granted that you are already perfect and that everything that you can describe is circumscribed, within the fabric of the universe itself... long story... gets boring too, but briefly, your "soul" is matter is matter is matter and is matter, and your "spirit" is not because it is above what can be described...

And yes, it goes back to way before any humanoids or any life at all existed. It goes right down to the fabric of the atom, which already has photonic capability already built into its architecture. Since photons require that electrons be at certain places in order to have an effect, this is the minimal quantization of the sense of vision --that one sense of vision that we appropriated/stole from the fabric of the universe! That one. It ain't ours. However, this would be a "platonic atom", if such a thing exists, and not the one from physics. The platonic atom is superior as a model of reality because it stands in many different contexts. A triangle is a platonic atom. A circle too. (A square may be just a derivation of a triangle and I don't quite count as an "atom" yet.)

Forgive me for just jumping in, as (I) have not had the computer time to read all of this thread yet, but (I) thought that as one who has done art work (I) could contribute my 0.2 cents worth.....

Like this.......

So why the perfect triangle, circle, and square?

Simple enough they are the "Ideals" from whence the Universe itself is born.

The differentiation between the "Ideals" and the "Reals" or reality follows somewhat like this, we take the word 'tree' and (I) ask you to draw me a picture of a 'tree' but low and behld you cannot, (It is an 'Ideal') as the very first thing you must do to present me with the Image of the real is to decide between the types of trees, Coniferous or Deciduous, or the exception to the Rule the deciduous Conifer that is the Larch or Tamarack tree a Confer that sheds it's needles in the fall.

That is what the Perfect Circle idea is all about and, is about us humans, as we have intellectual access to the Idea of Ideals and Ideal states, NO other animal has that, (least ways no one can prove they do, or that they don't, but we will, for the purpose of this discourse, assume that they do not) such that we have a level of thought that allows us to explore this Universe (and beyond) with an understanding that permits us to realize, even though we cannot see it, that somehow, somewhere, there exists the Ideal or perfect state.

That we are living in a state that to the judgment of most humans in NOT Ideal or perfect, is simply a lack of understanding of this place as this place operates as if it were the Ideal State inasmuch as the rule (an Ideal) of Cause and effect always follows through.

That the Universe Follows 'rules' in and of itself, is remarkable, as that demonstrates a basis of initiation that must have somehow derived from, and continued on upon a state of rule(s).

So we seek the perfection that is hinted at existing from the very thoughts in our minds, looking and seeking it out as to see if we can determine the origin of us, and to know the hows and the whys of the nature of this 'place' embodied corporeal existence, as that is where all of us actually exist, inside of ourselves.

Realistically there is a pathway of bridging the Ideal to the real, it is solved by a simply riddle: "If there is 'an exception to every rule' (and there is) then, for that to be held as 'valid' across all regimes, there must be an exception to that rule, so what is the 'exception to the rule' that states: "there is an exception to every rule"?"

Solve that one, the riddle, and you will understand better why there are things (Ideas) like 'perfect circles'...even thought you could never draw me one.

A clue, the solution is Perfect.

BTW it is an old question, how could a 'perfect being' (A God) create such a, seemingly, im-perfect world.

The idea that we understand and know of "Ideals" tells us that the origin of this place is, as born from Perfection, Born from the Ideal. (AKA a 'thought' a Perfect thought)

Solve the riddle?

These shapes are a projection of the way the personality software behind human nature is set up. That is why the same types of symbols appear in almost all cultures, independently. The circle is the inner self, which is the unity of the software, sort of the jukebox. It the part of us that will play the fight-flight software to help the ego get away. The ego can't generate this much adrenaline by itself at will, but needs the inner self to get full octane. The inner self connection to the circle is why angles have halos, or kings have crowns (circles) it shows a mind unified with divinity, which can be the inner self if you factor out the symbols of religion.

The triangle or trinity shows three aspects of the software. It has its basis in the nuclear family; father, mother, child. If you sit a triangle on its base with an apex at top, the child is at the top with the two parents offering support, the mother emotional and the father intellectual (traditionally).

The Jewish star of David is two triangles or two trinities. One for the material realm and one for the spiritual realm. The mother and father teach things of the spirit and the needs of the world to the child.

The square has four sides, like the Christian cross. This shows the software going from 3 to 4 aspects, with one aspect dividing from another. In practical terms, it implies intellect, emotion, intuition and instinct. These are the four ways various humans judge reality. Some are pure intellect, some are more emotional, some act on impulse and instinct, others are more intuitive. Most people will specialize in one but can use all four.

The left hand is emotion, the right hand is intellect, the two legs are instinct (right leg) and biochemistry (left leg). The head is intuition and the color yellow, like the sun. The color blue is intellect; thoughts (as deep as the ocean; blue sky research, etc.) The color red is emotion, while the color green is biochemical nature and natural instinct.

Since green is made of blue and yellow it is a blend of thought and intuition. In other words, if one gets hungry they have this gut intuition that is then translated into the idea of hunger. The split from 3 to 4 came from the green, or instinct, allowing yellow to appear separate from blue. Up to the old testament culture was procedure oriented with yellow only for prophets. But after Christ the symbolism of leaving behind a comforter, and the repressed instinct of the dark ages allowed the yellow to differentiate.

The pyramids were four triangles on a square base coming to a point. They anticipated the whole shebang. The four triangles or trinities were a male-female connection added to spirit/material influence of the parents, grounded on the four attributes, i.e., intuition, intellect, emotion and instinct. Very good balance, which is why it is still around to this day, i.e., hasn't happened yet but would lead to very balanced children. Maybe the Pharaoh was able to reach that level due to the huge support staff.

Wow, I didn't think this topic would be fodder for such abstract thoughts.

Sorry MDT, IAMores, and Mr. Parsons....I can't agree with you.
Though, it seems that some of you didn't read my question correctly.

IAMores, you're brandishing some new brand of quantum science that don't fit in very well with my view of the universe, and also logic and evidence.

Mr. Parsons, what I think your post comes down to is:
these 'ideals' have been preprogrammed into us from the universe itself and that is because that's how god made it?
And also your riddle doesn't make much sense in science. That 'rule' is a common phrase in the English language and has no bearing to reality. Only perception.

MDT, as usual, your presentation does not sit well with me. Mostly because it is something you made up without any science involved.

And FrankMak....the link you PMed me: http://vip.ocsnet.net/~ancient/TrianglePair-SI.pdf
says nothing about anything.

Show me where I brandished some new sort of quantum science on the post above because --since I was just being reductionist-- I don't see it. Show me where my statements don't sit very well with logic. Or evidence.

Triangles and circles are real entities?
Why are all planets/stars/comets/asteroids/nebulae and whatever else in this universe roundish? Why don't we see planets that are triangles?
The same principle that works on the construction of a large body works on micro-structures. The reason why a molecule would also be roundish is because energy tends to balance itself out as evenly as possible with all the combined forces. That is the very nature of energy in our universe. The most stable structure of a molecule with say 6 atoms would be spherical.

Again, the universe is not 'perfect' in the same sense in which you refer to it.

Even if the universe were 'perfect' in your sense...our perception of matter and space is much more complex than the physical construct of our brain. So unless you have an explanation of how those 'real entities' actually constructed our brain's perception based on it's own physical structure...I don't think it is appropriate to make such claims.

This is not supported by QM. You don't find me much at the QM sub-forums cause I don't know much about it, but from what I do know, the Heisenberg uncertainty principle requires the electrons to not be at "certain places".

Assuming that you derived the term 'platonic atom' from platonic solids, can you actually envision a stable structure as a 'platonic pyramid'? It is impossible for that to exist in a natural enviornment for longer than a split second.

Anyway I'm not one of those ppl who enjoy getting into personal battles (unless I'm really pissed off, like at tlocity)...so just to let you know, I didn't mean anything personal. If for some reason my tone sounded too harsh earlier, I apologize, but I didn't mean it.

Not quite the subject. Your questions concerned the perception of perfection at the basic and elementary level of human senses, the visual sense, not at the basis of planetary formation. I said that that would require a complete theory of mind and proceeded to pretend to have it in order to make the point that if the mind **created** a single geometric -say, triangle- that already didn't exist in the universe then it would be bringing into existence the extrauniversal. Planets and molecules are not triangular in their spherical aspects because spherical aspects emulate a platonic **point**, a zero-dimensional platonic "atom", and it is what happens to points that defines triangles. At its simplest, everything loses dimensionality to become a point wannabe:

So that the universe is not perfect in "my" sense even though you think that the same principle works on the construction of large bodies and microstructues!

You can't simultaneously say that "perception of matter and space is much more complex than the physical construct of our brain" -no matter how right- and call an inbuilt human sense of perfection an "inappropriate claim". You asked why symmetry: "What in our evolutionary history forced our brain to think in symmetrical figures?" I said asymmetry is not mindly. It may in fact, perfectly, be brainly but it is not mindly. If it were, the act of perception would not be possible.

I stand corrected: the requirement is that they *not* be at certain places for photon absorption. That is what I am calling the smallest-possible sense of vision.

Yes, I can because you follow that question with the answer, namely a one-sentence description of a big bang:

All meanings and all things collapse into a single point. A point is the pyramid you want. Within infinitesimals lie all geometric shapes. If they didn't, thinkers would be painting themselves into a corner: we would have to believe that the first 3 points of the universe were the creators of the triangle, that their future as a triangle was somehow a cosmic surprise, and that triangularity was **not*** contained within the future possibilities of the primordial point. That is an impossibility, and would only work if life, thus mind, didn't exist in order to compute. A "mindless" universe would be in a constant state of surprise with itself(;-)) at every new geometric that it formed. What is the difference between that and the traditional religious concept of God?

k...maybe there's some miscommunication going on.

Here's what I understood from your original post....correct me if I'm wrong:
You said that the reason we envision say perfect triangles is because they exist in the universe naturally. And also that it would be impossible for us to do so if they did not exist naturally because that would be 'extrauniversal'.

When you say

Could you genuinely say that this is accepted science?

read what I said again

What I said was "perception of matter and space is much more complex than the physical construct of our brain", so if you wish to make the claim that since triangles are emulated as 'platonic points' of spherical structures (whatever that means), then you have to have a good explanation for the evolution of that. Meaning you cannot make a claim as wild as that without explaining to me how the physical 'emulation' of a triangle went from being what it was to being visualized by us even when we have our eyes closed.

yeah um....I said stable, so no.

See again, regardless of what you believe, you cannot claim that this is widely accepted science.

that has nothing to do with what I said.

Actually the idea of these shapes being a projection from within the human mind is supported by the engineering marvel of the pyramids. These ancient people were more unconscious than conscious (semi-dream state). What they thought they were doing was pleasing the gods with these divinely inspired structures. In modern terms, they were projecting from within, and making it become manifest in reality, so others could benefit by its tangible nature. Sort of like Kubule's dream of snakes in a circle that anticipated the structure of benzene, allowing his to advance chemistry. After these shapes were created by the Egyptians, they inspired awe in all who saw them, sort of pushing buttons inside other brains.

One would be hard pressed to find many perfect triangles or squares in nature, beyond imaginary lines in crystals. You would be even more hard pressed to find good approximations, in the ancient time. Their geometric perfection came after humans; millenium later humans saw them in crystals. It was already anticipated by the human mind, even before they knew what it was. It was a projection of the human mind that gave hints as to how the unconscious mind was layed out.