Category Archives: Knowledge

~The Möbius Strip~

“The Möbius strip or Möbius band is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.

August Ferdinand Möbius (November 17, 1790 – September 26, 1868) was a German mathematician and theoretical astronomer.

He is best known for his discovery of the Möbius strip, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space. It was independently discovered by Johann Benedict Listing around the same time. The Möbius configuration, formed by two mutually inscribed tetrahedra, is also named after him. Möbius was the first to introduce homogeneous coordinates into projective geometry.

A model of the Möbius strip can be easily created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. In Euclidean space there are two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise. That is to say, it is a chiral object with “handedness” (right-handed or left-handed).

The Möbius band (equally known as the Möbius strip) is not a surface of only one geometry (i.e., of only one exact size and shape), such as the half-twisted paper strip depicted in the illustration to the right. Rather, mathematicians refer to the (closed) Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any closed rectangle with length L and width W can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in 3-dimensional space, and others cannot. Yet another example is the complete open Möbius band. Topologically, this is slightly different from the more usual — closed — Möbius band, in that any open Möbius band has no boundary.

While the idea of Mobius strip architecture has been tackled before, perhaps no scheme has been so ambitious as Vincent Callebaut’s “Swallow’s Nest,” a proposed arts and literature center for the Taiwanese city of Taichung seen below.

Composed of a series of isosceles triangles gradually rotated around an ellipse, the building creates a dramatic division between interior and exterior while allowing the integration of public space into the center of the building by means of “the Infinite Patio.” The twisting of the structure also allows for three large vaulted spaces for the display of art objects.”

Source ~ https://www.google.com/amp/s/germanculture.com.ua/famous-germans/mobius-strip-and-its-inventor/amp/

~Perpetual Curiosity~

Curiosity comes in many forms or flavors, and they are not always motivated by the same factors. Perceptual curiosity is a term that has been coined. That’s the kind of interest we have when something surprises us or doesn’t quite fit with what we know or believe we know. This is perceived as an uncomfortable state, an adversity state. It’s like an itch that has to be scratched. That is why we attempt to learn more to satisfy that sort of curiosity

~Cultural Relativism~

Cultural relativism refers to not judging a culture to our own standards of what is right or wrong, strange or normal. Instead, we should try to understand cultural practices of other groups in its own cultural context.

“Accepting this moral wrong because of moral relativism based on culture is dangerous as it leads to indifference. If we cannot judge and moral rightness depends on certain cultures, then “anything goes”. Moral relativism leads to moral paralysis and indifference.” ~ https://sevenpillarsinstitute.org/moral-relativism-and-its-effects/

Quotes {133} ~ The Denial Of Ambiguity

“There runs through the fundamentalist belief system a deep dread of ambiguity, disorder, and chaos. Accordingly, the cult of masculinity keeps all ambiguity — especially sexual ambiguity — in check. It fosters a world of binary opposites: God and man, saved and unsaved, church and world, Christianity and secular-humanism, male and female. These tidy pairings keep life from slipping back into a complicated nightmare. Reality thus defined, is made predictable and understandable — something deeply comforting to believers — who’ve had trouble coping with the messiness of human existence. There is, in this Christian worldview, clearly demarcated order and disorder. Behaviors that do not conform, such as homosexuality, are forms of disorder, tools of Satan, and must be abolished. A world that can be predicted and understood, a world that has clear boundaries, can be made rational, it can be managed and controlled. The petrified, binary world of fixed immutable roles is a world where people — many of them damaged by bouts with failure, despair, and their own ambiguities, can bury their chaotic and fragmented personalities and live with the illusion that they are strong, whole, and protected. The decline of America is described as the result of the decline of male prowess. This decline has led to weakness and moral decay. It has resulted in a bewildering human and social complexity that — often seen as feminine — is the work of Satan. By submitting to a Christian leader and powerful male God who will destroy those who misbehave, followers avoid dealing with life. The movement seeks, above all, to banish mystery — the very essence of faith. Not only is the binary world knowable and predictable, but finally God is knowable and predictable. Since life has a way of not respecting these artificial lines — since ambiguity, inconsistency, and irrationality are part of human existence — the only way believers can push forward is to pretend that these troubling aspects of our internal and external reality do not exist. They create a parallel reality, one that allows them to escape… into a world of their own creation. Unconscious motives, longings, and fears are denied and responsibility for them is abandoned as fundamentalism makes a pretense of being all about cut-and-dried truth, and clear and recognizable feelings.” ~ Chris Hedges, American Fascists

~Does It Spark Joy?~

“The popular tidying guru, Marie Kondo, has a simple method for how to de-clutter your home. You hold an item in your hands — like an old sweater — and ask of it, “Does it spark joy?” If it does, you keep it. If it doesn’t, you throw it away. In this way you minimize your material possessions to the most essential items.

But never mind de-cluttering your house — that’s peanuts. The elephant in the room is asking this question of your life activities as a whole. Imagine designing a life in which most of the activities you do every day are ones that spark the greatest joy in you. Imagine what that would be for you. Now imagine a life where all the activities you do don’t spark joy. Which life do you want?

Of course the problem is that most people have no clear idea of what activities spark the greatest joy for them. And the second problem is that they don’t believe they can design a life which aligns with those. Well, you can figure both of those out. In fact you’ll need to in order to have a good life. That’s what my Life Purpose Course is designed to help you do.

But for now, just spend the next week asking yourself, “What sparks the greatest joy in my life?” Make a list. And then start to wonder how you can turn one of these activities into a career. That which sparks the greatest joy in you is a tiny kernel of the career you will one day build. For more specifics on how to go about this, see my Life Purpose Course.”

Source ~ https://www.actualized.org/insights?p=10

~Flood The Zone With Shit~

“I love how transparent Steve Bannon is about his devilry:

“The real opposition is the media. And the way to deal with them is to flood the zone with shit.”

– Steve Bannon

In a sense this makes him an ineffective devil because he’s too honest about his devilry. Devilry can’t survive long in transparency. It has to be opaque.

But anyway, that is precisely how devilry works. It perpetuates falsehood simply by muddying the waters so much that average people cannot tell the difference between truth and falsehood. This is a broader tactic of devils that takes place not only in politics but with religion and spirituality. Many people these days are so sour on religion, spirituality, and anything smacking of the New Age because these important zones have been flooded with shit over the centuries. This makes it very difficult for people to find Truth/God. The zone has been so flooded with shit that most people think that Truth and God a myth. And in such a state, the devil wins. The devil doesn’t need a proper victory — in fact he can never get one because devilry is falsehood — but he can squeak out a short-term psuedo-victory by muddying the waters.

Be on the lookout for those in society who make careers out of muddying the waters. Don’t become pawns in their game. To have a high-functioning society it’s crucial that public figures don’t manipulate truth for personal gain.”

Source ~ https://www.actualized.org/insights?p=16

~Nationalism~

“Much of the political turmoil we see today in the world can be simply explained as a battle between nationalism vs globalism. For thousands of years mankind has lived in communities separated from each other via geography, language, religion, race, culture, etc. But today, thanks to technology, each year, mankind is becoming more and more interconnected as one global community. This trend is inevitable and irreversible. But much of the world’s population is running on the age-old nationalist operating system, thus resisting global integration. It’s an matter of identity. Global integration requires relinquishing one’s old, limited national identity — which feels threatening and uncomfortable for many people. So they invent all sorts of defense mechanisms to avoid it. These defense mechanisms include: judgment, blame, scapegoating, gaslighting, strawmanning, demonization, projection, denial, propaganda, lashing out, conspiracy theories, ridicule, righteous anger, violence, and fear.

I recommend you acquaint yourself with what the term “nationalism” means. It’s good to have an explicit definition of it in your mind. It will explain a lot of what you will see going on around you during your lifetime.”

Source ~ https://www.actualized.org/insights?p=11