The Nature of Fractals – Part III: Our Chaotic Reality

The Nature of Fractals – Part III: Our Chaotic Reality

This is Part III of a three part series on the Nature of Fractals. Readers can view the first two installments here: Part I and Part II.


In the previous part of this series, I introduced the thought that quantum mechanics are related to fractals. That combination further implies the idea that quantum objects represent the combination of spirit and matter, which themselves exhibit fractal properties.

The Hebrew Letter Kaf

A concept alluding to a transition akin to that seen in quantum mechanics can be found in mystic  interpretations of the Hebrew alphabet. The word “kaf” is made up of two symbols from the first letters of two other words – koach, meaning potential, and poel: “…suggesting that Kaf enables the latent power of the spiritual (the potential) to be made actual in the physical…”1  The symbol kaf represents a palm with a Yod in its middle where potential becomes reality and hearkens back to the concept of a quantum object collapsing into its matter form.

The combination of spirit and matter (see featured image) further suggests a direct link between Humanity and God. Our very thoughts may be thought of as quantum objects and underlie our reality, bringing into existence that which we interact with on a daily basis.

Imagine a being, a being so advanced and evolved, that he is One with the Word – he is indistinguishable from the Word. His thoughts are very special – they appear in his mind as quantum mechanical potential energy and take on a life of their own. Within the thought, there is Life – spirit and matter combine to form consciousness, one facet of the being as described in the dual-aspect theory.

In this manner, Sungsang and Hyungsang interact and form a human being. The thoughts or beings exist in the Universe of his mind, evolving themselves until they have each “had their due” and dissolve into nothingness. In this manner, each thought works to merge with the Word – thus further purifying the being. Thoughts beget thoughts of their own. which become fractal tessellations perpetuated throughout eternity. Fractals are left behind throughout the infinite hierarchy as evidence of the being’s work. At the End of Time, the being himself dissolves into nothing, a passing thought in a greater being’s mind.

Along similar lines, both the Bible and Mormonism support beliefs that are consistent with the previous paragraph. In the Bible we read in Romans (8:16-17):

“The Spirit itself beareth witness with our spirit, that we are the children of God and if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together.”

In the Mormon faith, it is the belief that each individual can progress to the point to inheriting a universe of their own. 

“…Each one of you has it within the realm of his possibility to develop a kingdom over which you will preside as its king and god. You will  need to develop yourself and grow in ability and power and worthiness, to govern such a world with all of its people.”2

Lorentz Attractor

From a different perspective, fractal mathematics are a representation of chaos. “Fractals are related to chaos because they are complex systems that have definite properties.”3 It was discovered that there is indeed a pattern to chaotic systems. Using a number of different initial points for a given chaotic system and running the system for quite some time (a chore perfectly suited to automation), they all eventually resolve into a two-dimensional projection of a butterfly shape called the Lorentz Attractor. 4

When one thinks about the Earth and the moon revolving around each other due to gravitational attraction, the Earth is an attractor for the moon. In chaos theory, the “orbital” patterns seen in the butterfly shape seem to form orbits around what are called “strange attractors.” The butterfly shape is described in terms of fractal dimensions, which means that the shape’s dimensionality is not an integer (2-D, 3-D, etc.), but a fraction between two integers.

“…So, a fractal image is a visual representation of a strange attractor (or fractal space) that defines the orbit of a deterministic system that behaves chaotically…”5

So when we consider that fractals represent a form of order ubiquitous throughout Nature, it can be seen that they are indeed the embodiment of Ordo ab Chao – Order out of Chaos.


1 The Letter Kaf/Khaf, n.d.

2 “. . . the Matter of Marriage” [address delivered at University of Utah Institute of Religion, 22 Oct. 1976])  (Will Exalted Mormons Get Their Own Spirit Children and Worlds?, n.d.

3 Blumenthal, n.d.

4 Chaos VII : Strange Attractors, n.d.

5 Wrigley, 2017.

Being Blackballed – Part 2

Being Blackballed – Part 2

This is a continuation of a blog published in April 2018, and located here. In that post, we discussed the history and responsibility of balloting. Here, we’ll continue with the idea of being blackballed and the repercussions of such an event.

There are diverse attitudes to being blackballed. Some rebel to the idea that any one or any group can “shun” or “refuse” them what they seek. The idea of being blackballed is considered archaic, as if there is anything that could stop someone in our modern age from achieving what they want to achieve. To be blackballed is a singularly terrible event that should never, ever happen. There’s the view that being blackballed is akin to a formal shunning or being ostracized, whence some of this history derives, and to be blackballed is a stain on your character. Another point of view is that there is a “gang” of people who may be against you, actively working to stop you from achieving your goals. How many times have we heard, “the election is rigged?”

In other words, being blackballed is rarely caused by the person being blackballed; it is a misperception of their character, deliberate malice to stop a rising star, or punishment for some sort of wrong doing. The person blackballed sees themselves as blameless as they didn’t do the actual casting of the ballot. That is, the reason for the blackballing or the loss is viewed through their very personal lens. Modern conventional wisdom holds that ostracism is usually meant to hurt or punish people rather than support the good of society. In modern times, it is viewed as bad for the morale of a group; in ancient times, the good of the society was paramount. In short, it’s fair to say that most modern people feel that being blackballed is a very bad thing.

Perhaps we can throw a wrench in this. Perhaps we can look at being blackballed as something positive. Stanford University recently did a news story on a recent study focused on being ostracized. Interestingly enough, the researchers found that the exclusion, or being ostracized, allowed individual groups to stop bullying, stop the exploitation of “good” people, and generally allowed the group to reform the one being excluded.

The study concluded that gossip and ostracism are part of human nature and that without them, we might not as easily reform the behavior of people who don’t play well with others. In fact, those who want to be part of the group but don’t play well with others might benefit from this blackballing and learn. Being “blackballed” might have some positive effects.

There is a frame of mind that rebels at the implications of this. Should everyone conform? Should everyone play nice with others to gain some of cooperative achievements? It smacks of Big Brother or a police state; stay in line, and no one gets hurt. Perhaps in the workplace, but what about in a fraternal organization? Perhaps it is the way we go about ostracism and as stated above, how we handle our personal view of the act of exclusion that makes the difference.

Many groups are exclusionary and require requirements for admission, and not all groups should be open to all people. However, we, and I include Freemasonry in this, rarely take the time to work with people who want desperately to be part of the group. We cling to the idea that they must improve or they can’t join, and they need to do it on their own. Why should I help someone with so negative an attitude or abhorrent behavior work to become part of my “in crowd?”

Because it is not about us. It is not about ostracism but about inclusion. If we are ever to work in perfecting humanity, wouldn’t we want to step forward and help people become better? Are we, who really want to improve the world, all talk and no action? I don’t think so. I once knew a woman Freemason who said “why do all the weirdos come to us?” She was whining that everyone in her group was “not normal.” The truth is, none of us is normal, and I think that most of us want to believe that people want to improve.

If that’s the case, why wouldn’t we help people really work hard to improve themselves to make the “grade” and become one of the leaders of the perfecting of humanity? Freemasonry is about bringing together, not tearing apart. Ordo ab Chao is inclusion, not exclusion.

I listened to a recent podcast on “Whence Came You” discussing “guarding the west gate.” It was heartening to hear that all organizations, including Freemasons, have challenges about admitting quality people. There is nothing to stop us from assisting those who might not yet be worthy to become worthy. 

I have seen many people who come to Freemasonry who have a true passion for the Craft, or what they know of it, and, for whatever reason, they might not meet our “qualifications.” If someone struggles with reading or writing, why wouldn’t we work with that person/applicant to bring them up to the level where they will feel comfortable and equitable in being a member? It might mean working with them on reading, or assigning them papers to write, or book reports. It might mean encouraging them to go to a college course or Toastmasters. Rather than getting to the point of blackballing or blind acceptance, we should care enough about the people who are joining us to make those efforts to help them be comfortable and share their talents.

This kind of work, though, isn’t comfortable. It takes a strong sense of leadership and communication to be the facilitator in these types of situations. The leader must know how and why they act, how to communicate well, and how to bring people to acceptance rather than denial. It takes Lodge leaders with clear direction and sense of purpose for the good of the Order, not their personal or even singular Lodge gain. It also takes a strong character of the applicant to listen to the criticism and make appropriate lifestyle changes to improve. These are the kinds of people we want to be Freemasons: those who love the craft and want to be true service workers in the name of humanity. If we can both, the facilitator and the mentee, let go of ego and stigma, there can be true growth.

What happens when we ignore this kind of calling? I was one participating in a ballot where the person was clearly not qualified for the group they were joining. They had self-esteem issues and had problems controlling their emotional responses. They were ill-prepared for what awaited them. Unfortunately, they were balloted on and approved unanimously. Unanimously. Nothing could have been more harmful for that person and for ourselves. I was left with a huge sense of guilt for throwing this person into a situation they were ill-equipped to deal with. I was left with a sense of letting down my institution, because I did not do my duty and attend to this person’s needs rather than ego. I figured, what did I know? Who was I to deny this person? In the end, it was my responsibility to care for them and for my group, letting go of my need to be “approved of” by the group or this person. I will never forget this lesson. I will now always stand up for the truth of what I see and feel, and will take that responsibility for helping my fellow man. I’ve learned that as part of the group; it is my duty.

Should it ever get to blackballing, I would hope that the person being blackballed would have the grace, virtue, courage, and zeal to listen to the criticism with an open mind and heart, and grow from that experience. I would hope they exhibit the kind of leadership that should grow into being an outstanding Freemason and contributor to humanity. I would hope that the leadership of said group would also see it as an opportunity to grow rather than to shun, to live up to their ideals, rather than work from their sense of ego, fear, or discrimination.

Blackballing should not be shunning; quite the opposite. Blackballing should be an opportunity for Freemasons, and others, to express their truth and to help improve the person being blackballed to become better than they are. If we take the stance that we do everything we can before the ballot is cast, and perhaps that ballot is the last wake up call, then it seems we have done our duty in working on ourselves and in perfecting humanity.