How can the traingle be superior to the circle when it is bound by it?
A triangle has points of interests, relationships, views. A circle just is.
The expected dogmatic answers accrue.
But beyond this...
What is a circle?
Is it an amalgum of extreme polygonic acivity?
What is a triangle?
The pent, hex, etc., of evolving poygonic activity, be it regular complex or convex, at its seemingly endless math extreme, inevitably morphs into a circle.
Though, say photographically blow-up the circle, and closer inspection of its line reveals the un-eaveness of its true origins.
For example, a million sided polygon, when seen as a whole, is in all repects seen as a circle. Only under truly close-up scrutiny may its many straight-sided features be properly distinguished.
What I'm saying is, infinity may seem like a straight line, like a never-ending point a to b in space,but this is a false understanding, because infinity is in fact a point a to ? Neither is infinity an endless loop system of a circle, because the starting point inevitably becomes the end, pass that and we're into repeats, not authentic virgin linear infinity, which is our true mystery of the human condition and our ability to imagine this reality.
The mysteries of concepts of such things as infinity can not be explained by matters of faith.
It has been said that FAITH demands no proof, and this is so true of especially religious faith.
The philosphical historian and writer Jonathan Meades explains such belief systems as and interestingly developed social psychopathology, that's both understandable why many turn to such, and both a danger, especially where radicalisation is involved.
"I entirely lack the credulous gene. The idea that gods and prophets are anything more than low-level human inventions, seems to me so frail and so propostrous, that they're not worth considering as parts of a belief system. But as a psychopathology worthy of infinite investigation, there is nothing quite like them."
I tend to agree with him. A sanitised psychopathology has become the realm of the literal believer. To the objective observor, on the otherhand, it is a most interesting study of the power of the archetypes and the metaphoric significances of such religious sories, their varied developments, and how they have come to be so easily accepted by so many throughout the history of humankind.
Blind faith and conformity to such without question, especially in this day of highly evolving scientific understanding, reveals a psychopathology of incredulous proportions that certainly need to be much better understood and dealt with before it gets too out of hand.
Does a circle actually exist in nature or is it an artificial construct? It is the ellipse that is evident in the form of an imperfect circle. Calculating the path of a circle - that's easy. Calculating the path of celestial bodies, that proved much more complex - until 1676 when Sir Isaac Newton began working on what, at that time, he called "fluxional equations". I'm no mathematician but I think differential equations triangulation of a moving point.
As for Meade, he is referring (I think) to a predisposition that is evident in our species but gets expressed or perhaps fulfilled differently. What happens if we use as our working premise that gods and prophets are nothing more than low-level human inventions. We know that gods and prophets are found in all cultures throughout time. What impulse does Meade ascribe to this impulse and if certain individuals resist "low-level" inventions, are these substituted by a higher-level invention or inventions. And what might that be?
The explanation of reality through the use of gods, prophets and invention of religion seems to be a simple attempt to understand natural phenomena. What I find interesting is why some people believe that the explanation that they have accepted is perfect not only for them but for the broader community within which they exist.
Yes, there is a psychopathology which likely had primordial roots that appear in stark contrast to the requirements of our modern world.
I go back to the image of learning to swim as if you have webbed fingers as a means of achieving superior results. Are Olympic athletes that use such techniques operating on blind faith? In this case a stop watch becomes the metric. What metric do we have regarding those who operate as if their religion is perfect and complete? Some of these people might suggest burning at the stake is a logical outcome to posing questions like this.
So tell us more about what Meade has found or are his writings merely speculative?
Reverse the transitions from the many multi-sided polygons say down to a hexagon, then to its absolute possible - the triangle - as the most simple of of complete straight-lined shapes, or more realistically, their 3D equivalents within spheres, and then we can see how all straight-lined shapes have points of the fullest encapsulation by such.
Only math describes the clean line of the arc of a circle. Why, even the trajectory of a missile is naturally distorted by the conditions of the inevitable atmospheric soup through which it travells, and where math does not allow for such unpinable ebb-and-flow of interaction within the reality that exists.
So Yes! Kernel, as you say, it can be viewed as an 'artificial construct', even though something like it, from the micro to the macro, actually exists.
Roman, this sounds much like poetry...and is quite nice at that.
By Meade's own admission, he LACKS...as he sees it, a gene. Perhaps since he admits he does lack, then also his viewpoint is limited. It surprises me to some extent that he does not recognize this.
Along the way, when I realized I should go back to school, I stumbled into a book called, I Seem To Be A Verb, by Bucky Fuller. Interesting dude with very thick glasses. He did not see very well - or should I say he didn't see things the same way others did. The book changed by orientation.
He was the guy who explained to me what a point was of zero dimension. Then he explained that a line is a set of points that has one dimension - length. He took that line and explained that if moved in a direction perpendicular to itself it would cover a rectangular or 2 dimensional space. Then he showed that, when moved in a direction perpendicular to itself, it consumed a 3 dimensional space. There definitely seemed to be order in the universe when described by fuller. Not long thereafter, it occurred to me that infinity could be broken into greater and lesser infinities.
Fuller of course understood that the Hexagon was a convenient configuration for spherical formation and invented the Geodesic Dome as seen here while attending the Worlds Fair in Montreal.
The purity of imaginative vision is built upon the random moments of chaos. A pearl would not form if it were not for the irritation of grit within the shell.
Meades statement here, is both ironic and sarcy, where the 'lack' is thankfully seen as a process of evolutionary refinement in human discernment, and not a negative.
I like Meades because he's a true pragmatist. His pragmatism is not dependent upon a comporomised view, but instead on the greater efforts of being able to selectively detach himself from the usual emotively-led stances of the human condition, thus avoiding the dangers of bias.
That is my point, and I may be wrong in it, so forgive me if I am. If indeed he does view things as evolutionary refinement, as you say, then I see that as simply a different bias...with all the trappings that accompany it. Almost as though he has fooled himself in trying to be detached. Much like a sannyasi who leaves all his responsibilities to "find" god. But again, I may be wrong in how I see it...but maybe not.
Beautiful, and our muscles would not develop without resistance and our character would not develop without controversy..