I thought for this article, that I would take you on a little thought experiment combining some of the more orthodox beliefs in science, particularly mathematics, and combining them with philosophy and inner alchemy.

In particular, I would like to discuss the interesting news that mathematicians are saying that two different types of infinity have been discovered. This is highly interesting to me as an inner alchemist, a logician, and a philosopher.

Now, the inner alchemist and the logician go together (at least as I interpret it) being that many of the inner alchemy principles when it comes to cubing (explained in detail in the book, The Way of The Projectionist) require a deep and thorough understanding of causality and logical progression, including the creation of large mind palaces.

But the philosopher aspect is one that is born of the fact that on some occasion, I have had reason to debate the existence of certain possibilities with people that sometimes find themselves within a very rigid reality tunnel. In doing so, as a philosopher of inner alchemy let us say, I may be tasked with the difficult prospect of integrating modern scientific understanding with an older science that I have sometimes referred to as Mind Science.

Generally, as this kind of philosopher I will need to juxtapose the leading research in mathematics, physics, psychology, psychiatry, with what might be termed more mystical ideas, creating a conglomeration of all existing data in order to prove the possibility of things that were common knowledge to ancient practitioners of Mind Science…that is, inner alchemists (sorcerers) of the ancient and now forgotten past.

So, let’s dive into the fascinating world of infinity and its philosophical implications, especially for those who might not be math experts.

Two new types of infinity have been discovered: exact cardinals and ultra-exact cardinals.

Mathematicians at the University of Vienna have introduced two new types of infinity, termed exact cardinals and ultra-exact cardinals, which challenge traditional mathematical frameworks for understanding infinite sets. To put into more simple terms:

Exact Cardinals

Exact cardinals are infinite sets that contain exact replicas of their entire structure within themselves. Think of it as a self-contained infinity that can “mirror” itself perfectly.
For example, imagine an infinite library where every shelf contains a smaller library that is an exact copy of the entire original library. The focus here is on the self-similarity and completeness of the structure.

Ultra-Exact Cardinals

Ultra-exact cardinals take this idea further by not only containing exact replicas of their structure but also including the rules or instructions that define how the structure is built. This self-awareness adds an extra layer of complexity. It’s like having an infinite library where every shelf contains not only a smaller copy of the library but also the blueprint for constructing that library.
The addition of the blueprint to this infinity model means that this newly proposed infinity set has a deeper level of self-reference and structural understanding.

A more philosophical understanding of infinity

These cardinals (which are abstract mathematical objects that represent the size or “cardinality” of a collection of things) are not the usual interpretation of infinity from a more philosophical point of view.

Usually, from a more humanist understanding, infinity is usually SEEN or perceived as a direction of motion that never ends. Another way to see infinity would be to see it as a vast expanse without limit, which then again would capture the attention of someone witnessing that infinity and create a natural motion into that infinity.

Infinity in that sense could be thought of as a black hole, like a literal black hole that seems to lead to nowhere or everywhere. From a distant point of view, you could think of this as a cartoon blackhole. Just like in a cartoon, where a protagonist draws a black hole with black paint, you could think of infinity as somebody drawing something like this in three-dimensional space. And totally defying the laws of nature, characteristic of a cartoon reality, this blackhole could somehow allow a three-dimensional thing to pop straight into it and disappear forever.

And being that this blackhole represents infinity, meaning that as you go through it you can then go into it forever without end, this blackhole due to the sheer fact that it is infinity, has gravity. There is within it this pulling power that seems to suck everything into it. In other words, this literal cartoon blackhole seems to be pulling things into it, it has a gravitational pull.

This pull is so great, infinity is so powerful that the moment that you look at this cartoon blackhole, it seems to instantly grow in size before you, until it obliterates all reality and all that you can see is the blackhole itself, only the blackhole. The moment that you pay attention to it, you have been pulled (you have entered) into infinity and you are cascading down, what from your point of view is a long tunnel that can quite literally lead to infinite possibilities.

As such, from what I am in this article calling a philosophical point of view, infinity equals motion. Infinity quite literally presupposes motion, which is something that mathematics (at least as far as I understand it) has not been able to grasp yet.

But as I will point out in this article, even though it is not understood at the moment, this discovery of a new kind of infinity has started a new understanding of multiple timelines and parallel universes as they are conceived by quantum mechanics.

New Infinity suggests amazing philosophical and theoretical implications!

Instead of going straight into my philosophical controversy as it were, let’s consider some of the implications of these two new infinity models, strictly from a modern point of view. After doing so I can further outline what may not be completely apparent to mathematicians right now.

So, these new infinities challenge our understanding of mathematics and reality. They don’t fit neatly into the usual hierarchy of infinities that mathematicians have used for years. It’s as if we discovered a new color that doesn’t quite fit on the rainbow.

The introduction of exact cardinals and ultra-exact cardinals has significant theoretical implications, particularly in the areas of mathematical ontology and the nature of infinity. These new types of infinity challenge existing theoretical frameworks and raise intriguing questions about the foundations of mathematics.

Ontological Considerations

The existence of these new types of infinity calls for a reevaluation of what we consider to be “real” in mathematics. Modern theorists have long debated the ontological status of mathematical objects, and these new infinities add complexity to this discussion. The requirement for exact cardinals to contain exact copies of their structure, and for ultra-exact cardinals to also contain the rules governing their structure, raises questions about the nature of mathematical existence and self-reference.

Conceptual Boundaries of Infinity

These new infinities challenge our conceptual understanding of what infinity means. They suggest that there may be more nuanced and complex forms of infinity than previously thought, potentially expanding the philosophical discourse on the nature and limits of mathematical concepts.

Foundations of Mathematics

The introduction of these new infinities may necessitate a reconsideration of the foundational principles of mathematics. They could potentially impact how we view set theory and the iterative conception of sets, which has been a cornerstone of mathematical philosophy.

Epistemological Questions

The discovery of these new types of infinity raises epistemological (Theory of Knowledge) questions about how we come to know and understand mathematical objects. It challenges our intuitions about infinity and may require new modes of thinking to fully grasp their implications.

Potential Effects on Philosophical Debates

Platonism vs. Nominalism

The existence of these new infinities could reignite debates between mathematical Platonists, who believe in the independent existence of mathematical objects, and nominalists, who view mathematical entities as useful fictions. The self-referential nature of ultra-exact cardinals, in particular, might be seen as supporting Platonist views.

Relationship Between Mathematics and Reality

The discovery of these new infinities may prompt philosophers to reconsider the relationship between mathematical structures and physical reality. It could lead to new perspectives on how abstract mathematical concepts relate to our understanding of the universe.
The introduction of exact cardinals and ultra-exact cardinals has the potential to significantly impact philosophical discussions surrounding mathematics, infinity, and the nature of existence. These new concepts challenge existing frameworks and open up new avenues for philosophical inquiry into the foundations and implications of mathematical thinking.

The implications from a philosophical or inner alchemy point of view

So that is just the implications of this new infinity model from a generally orthodox and modern point of view. This means that these are relatively safe and what might be termed rational concepts and ideas that naturally become evident when we contemplate the idea of these new infinity models.
But from an inner alchemy point of view there are incredible new possibilities opening up in the modern understanding of reality, that are starting to align more and more with ancient mystical understanding, and what I have referred to as the SEEING of ancient inner alchemists that practice a far different but far more powerful form of science, that I referred to as Mind Science.
These are:

1. That mathematics is not the language of the universe, that reality is not mathematical per se, but that mathematics is simply one way of perceiving reality using the perceptive mechanisms inherent in humanity at this time in history.
2. That within the scope of humanity there isn’t just the known and the unknown, but that there is also the unknowable.

Let me explain

The recent discoveries of exact cardinals and ultra-exact cardinals in mathematics offer profound insights that challenge our traditional understanding of reality and our place within it. These new concepts of infinity, with their intricate self-referential structures, reveal limitations in our mathematical frameworks and, by extension, in our ability to fully comprehend the universe.

Firstly, these new infinities strongly suggest that mathematics may not be the fundamental language of the universe, but rather a human construct for perceiving reality. The fact that we’ve discovered mathematical entities that defy our existing categorizations implies that our mathematical systems are incomplete and possibly arbitrary. Just as we’ve created new mathematical concepts to describe these infinities, it’s likely that our entire mathematical framework is a human invention, tailored to our specific cognitive abilities and perceptual limitations.

Consider how exact cardinals contain perfect copies of their entire structure within themselves, a concept that stretches our ability to visualize or fully comprehend. This suggests that reality might be far more complex and interconnected than our current mathematical models can represent. Our mathematics, then, appears to be a simplified lens through which we view a much more intricate universe, rather than the universe’s inherent language.

Ultra-exact cardinals take this a step further by containing not just their structure but also the rules governing that structure. This self-referential nature hints at levels of complexity in reality that our current mathematical systems struggle to describe adequately. It’s as if we’ve stumbled upon evidence that the universe operates on principles far more sophisticated than our mathematical models can capture.

These new infinities also powerfully demonstrate that within the scope of human knowledge, there exists not just the known and the unknown, but also the unknowable. The very concept of ultra-exact cardinals, with their nested layers of self-reference and rule-containment, pushes against the limits of human comprehension. We can define these mathematical entities, but fully grasping their implications and visualizing their structure remains beyond our cognitive reach.

This revelation of the unknowable is not a defeat but an exciting frontier. It suggests that the universe is far richer and more mysterious than we previously imagined. Just as these new infinities exist beyond our intuitive understanding, there may be aspects of reality that will forever remain beyond human comprehension, not due to a lack of effort or intelligence, but because of fundamental limitations in human cognition.

In embracing these implications, we open ourselves to a more humble yet awe-inspiring view of the cosmos. Mathematics, rather than being the ultimate truth of reality, becomes a beautiful and useful tool – one of many possible ways to interpret the world around us. This perspective encourages us to remain open to other forms of understanding and perception, recognizing that our current scientific and mathematical models are not the end-all of knowledge, but stepping stones in an endless journey of discovery.

Exact cardinals and ultra-exact cardinals serve as powerful indicators that reality is far more complex than our mathematical models suggest. They point to mathematics being a human construct for perceiving reality rather than its fundamental language, and they reveal the existence of concepts that may forever remain beyond our full comprehension. Far from being discouraging, these implications invite us to approach the universe with renewed wonder, humility, and an openness to the vast unknowns that surround us.

Proof of multiple timelines? This is where it gets interesting!

The concepts of exact cardinals and ultra-exact cardinals offer a fascinating new perspective on infinity that aligns remarkably well with theories of multiple timelines and parallel universes in quantum mechanics. These mathematical discoveries provide a compelling framework for understanding the nature of reality on both a cosmic and quantum scale.

From the philosophical point of view that I am using in this particular article, exact cardinals represent a form of infinity that moves in a single, sustained direction. Each element in this type of infinity contains within itself all that came before, allowing for an unending progression along a single path. This concept mirrors our traditional understanding of time and causality – a linear flow from past to present to future. It’s as if the universe is following a single, albeit infinite, timeline.

Ultra-exact cardinals, however, introduce a revolutionary new layer to our understanding of infinity. These mathematical entities not only contain all that came before but also possess an intrinsic understanding of their own structure. This self-awareness, so to speak, grants them the potential to generate new directions, new paths of infinity. It’s as if they can spawn entirely new timelines from any given point.

This multi-directional capability of ultra-exact cardinals provides a mathematical analog to the Many-Worlds Interpretation of quantum mechanics. In quantum theory, each quantum event potentially creates a branching of reality, leading to multiple timelines or parallel universes. Ultra-exact cardinals, with their ability to create new infinities in multiple directions, offer a mathematical foundation for this mind-bending concept.

Consider the implications: If our universe operates on principles similar to ultra-exact cardinals, then at every moment, there exists the potential for reality to branch into multiple timelines. Each quantum decision, each possibility, doesn’t just lead to a new state along a single timeline, but potentially creates an entirely new infinity – a new universe running parallel to our own.

This perspective adds an exhilarating new dimension to our understanding of infinity. It’s no longer just about endless progression in one direction, but about an infinite number of infinite progressions, all existing simultaneously. Our reality, then, could be viewed as a vast, ever-expanding web of timelines, each one an infinity unto itself, all interconnected at the quantum level.

The parallel between ultra-exact cardinals and quantum mechanics goes even deeper. Just as ultra-exact cardinals contain the rules of their own structure, quantum mechanics suggests that the fundamental laws of physics might be intrinsic to each universe. This self-contained nature of physical laws within each timeline resonates with the self-referential quality of ultra-exact cardinals.

Moreover, this framework provides a mathematical basis for the multiverse theory. If infinity can exist in multiple directions simultaneously, as suggested by ultra-exact cardinals, then the existence of multiple universes becomes not just possible, but mathematically elegant. Each universe could be seen as its own ultra-exact cardinal, containing within it the potential for infinite progression and the spawning of new realities.

In essence, the discovery of ultra-exact cardinals has given us a new language to describe the intricate, multi-layered nature of reality suggested by quantum mechanics. It bridges the gap between abstract mathematics and the physical world, offering a unified view of infinity that encompasses both the macro scale of multiple universes and the micro scale of quantum possibilities.

This perspective invites us to see our reality not as a single, linear progression, but as an infinitely branching tree of possibilities, each branch an infinity unto itself. It suggests that every moment, every decision, every quantum fluctuation, carries within it the seeds of entire universes.

This convergence of advanced mathematics and cutting-edge physics points to a universe far more vast, intricate, and wondrous than we ever imagined – a cosmos of infinite possibilities, branching and expanding in all directions, forever.

Anyway, I hope that my philosophical interpretation of cutting-edge mathematics might open new possibilities within your mind. Certainly, science is progressing in its slow methodical way towards the final understanding of something that ancient mystics knew long ago. But you don’t have to wait for its slow and cumbersome progression, you can use your own inner feeling sense (also described in detail in the book mentioned at the start of the article) to explore these topics and find connections and new discoveries, as we did in this article. This alone can completely alter your psyche and therefore your reality by creating a new and greatly expanded idea of the world, an expanded mind palace, that can withstand even infinity!