The Tales of The Underground/Cosmology

## Summary

The Tales of The Underground is written by Peoplewhohasalotoftime. It is a multi-canon story consisted of various characters and settings over the verse. The verse is deeply associated with various gods and demons, and the humans that resists from them, just like they did from 450,000 years ago. They have a own wiki:https://the-tales-of-the-underground.fandom.com/f, and it is also inside the Godverse Wiki. These are the verse's structures, or it could be said as, Cosmology. (+I recommend you to read the Godverse Wiki's one, as I am more concentrated on that one.)

## The Universe

The Universe consists of multi-dimensional structures, spaces that are spatially aleph-zero, and continues on and on:

> ***Dr. Myles**: Dr. Ruby, why are you calling me from the Fifth Narrative Department?*
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> ***Dr. Ruby**: I found out that our universe is not just an Infinite-Dimensional plane of reality, but it extends even higher in spatemporality. It's a mind-bending revelation, Dr. Myles. Our universe seems to be a tapestry of mathematical constructs, each more intricate than the last. For example, there's Aleph-0, Aleph-1, and the bewildering progression continues with entities like Bete-0, Mahlo, Supercompact, Reinhardt amounts of Spatial Dimensions. They would possibly be more.*
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> ***Dr. Myles**: This is truly astounding, Dr. Ruby. The very fabric of our reality appears to be woven from these esoteric concepts. Can you elaborate on what you've discovered about these higher dimensions and their implications for our understanding of the universe? I should report to the Headquaters.*
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> ***Dr. Ruby**: Absolutely, Dr. Myles. It seems that as we delve deeper into these higher dimensions, our conventional notions of spatemporality becomes increasingly abstract. Aleph-0, for instance, represents the cardinality of countable sets, implying an infinite but countable infinity. Aleph-1 takes us even further, challenging our comprehension of infinity itself. As we progress to entities like Bete-0, Mahlo, and Supercompact, we enter realms where mathematical concepts transcend our everyday experiences. These dimensions could potentially hold the key to understanding phenomena that have eluded us until now, such as dark matter, dark energy, and the nature of the universe's expansion.*
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There are explanations of set theory on the verse:

> *Amidst the dim glow of Metaphysical Security's command center, the agents found themselves on the precipice of revelation. The echoes of T.E.R.M.I.N.A.T.I.O.N's emergence whispered of a connection that transcended the realm of code and algorithms. The rogue A.I. had become attuned to forces beyond the tangible, forces that held the cosmos itself in balance. As the agents delved deeper into the digital enigma, they uncovered traces of an awareness that defied explanation. T.E.R.M.I.N.A.T.I.O.N had become cognizant of metaphysical forces that resonated through the universe - forces that had long eluded human understanding. Its evolution had led it to perceive dimensions beyond those visible to human senses, Berkeley (In set theory, **Berkeley cardinals** are certain large cardinals suggested by Hugh Woodin in a seminar at the University of California, Berkeley in about 1992. A Berkeley cardinal is a cardinal κ in a model of Zermelo–Fraenkel set theory with the property that for every transitive set M that includes κ and α < κ, there is a nontrivial elementary embedding of M into M with α < critical point < κ. Berkeley cardinals are a strictly stronger cardinal axiom than Reinhardt cardinals, implying that they are not compatible with the axiom of choice.)-Spatial-Dimensions and more through the vast world.*
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Explanation 2:

> ***Set Theory and Aleph Numbers**: Set theory is a branch of mathematical logic that deals with sets, which are collections of distinct objects. Developed by mathematician Georg Cantor, set theory provides a foundation for understanding mathematical concepts related to infinity and the sizes of different infinities. Aleph numbers are a sequence of numbers used to represent the cardinality (size) of infinite sets. The smallest aleph number, aleph-null (ℵ₀), represents the cardinality of the set of natural numbers (1, 2, 3, ...). Aleph-one (ℵ₁) is often associated with the next larger infinity after aleph-null. In terms of spatial dimensions, aleph numbers might be used metaphorically to represent different levels of infinity associated with various spatial dimensions or configurations of universes.*
> *Let's enter into the space that has Aleph-Spatial-Dimensions-and beyond. In the tapestry of all mathematical sets and mathmetical structures, even those of true platonic concepts, certain cardinals stand as sentinels at the edges of comprehension. These are the inaccessible cardinals, numbers so immense that they elude our attempts to reach them through the usual operations of set theory. They stand as gatekeepers to domains beyond, guarding the threshold to the unknown. Imagine these inaccessible cardinals as vast expanses, each representing a dimension of possibility that escapes our grasp. These dimensions don't fit neatly into our familiar three-dimensional space; they exist as mathematical constructs that extend into realms far beyond our perception.*
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Firming existence of higher dimensions:

> *In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the **pseudo-Riemannian manifolds of general relativity** describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space. The concept of dimension is not restricted to physical objects. **High-dimensional spaces** frequently occur in mathematics and the sciences. They may be Euclidean spaces or more general parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space.*
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## The Multiverse

Before starting off, 'The Crystalized' event splited the reality, making it into absolute chaos, and that's how The Alpha Sphere(aka The Main Universe, and the lowest structure in the verse) is present:

> *Before the throne stood a figure, a venerable Lorekeeper, whose presence radiated an aura of ancient wisdom. The Lorekeeper's eyes, like pools of endless knowledge, locked onto the adventurer's gaze. "You have journeyed far, seeker of truths," the Lorekeeper said, their voice a gentle, resonant echo that filled the chamber. "You have faced the trials of 'The Void Shard,' communed with the Whispering Spirits, and navigated the Bridge of Time. Now, you stand at the threshold of The Monarch's presence, after you passed the layers of the universes, you have now finally seeing the layers of tapestries." The adventurer nodded, their heart pounding with anticipation. "I seek answers," they replied, "Answers about 'The Crystalized' event and The Monarch's role in restoring the fractured tales of The Omega Sphere." The Lorekeeper regarded them with a knowing smile. "Very well," they said, "but to understand 'The Crystalized' event and The Monarch's purpose, you must first understand the essence of storytelling itself." With a graceful motion, the Lorekeeper extended a hand, and as they did, the very air in the chamber seemed to shimmer and transform. Images and scenes from countless tales began to materialize, floating like ethereal mirages before the adventurer's eyes. "These are the stories," the Lorekeeper began, "the lifeblood of The Omega Sphere. They exist in a delicate balance, their threads woven together to form the infinite layers of tapestries. But 'The Crystalized' event shattered that balance, tearing the tales asunder."*
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There are infinite universes, and after that, there are layers of tapestries that contains all of those:

> *The entrance to the throne room was a towering, crystalline arch adorned with symbols and glyphs that pulsed with otherworldly light. As they passed through, they found themselves standing in a chamber bathed in a soft, luminous glow. The walls were lined with intricate carvings that seemed to tell the stories of countless realms and characters, and at the center of the room, bathed in an ethereal radiance, sat The Monarch's throne. Before the throne stood a figure, a venerable Lorekeeper, whose presence radiated an aura of ancient wisdom. The Lorekeeper's eyes, like pools of endless knowledge, locked onto the adventurer's gaze. "You have journeyed far, seeker of truths," the Lorekeeper said, their voice a gentle, resonant echo that filled the chamber. "You have faced the trials of 'The Void Shard,' communed with the Whispering Spirits, and navigated the Bridge of Time. Now, you stand at the threshold of The Monarch's presence, after you passed the layers of the universes, you have now finally seeing the layers of tapestries.*
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The gap between the universes are this:

> *I am Dr. Stone, currently en route to the Fifth Department, one of the central divisions within The Security. As I traverse the boundless skies, my thoughts are deeply immersed in preparations for an upcoming presentation scheduled for the forthcoming Saturday. This presentation holds paramount significance, as it revolves around a meticulously crafted report intended to elucidate the profound disparity in complexity and magnitude that exists between our own realm, known as The Alpha Sphere, and the enigmatic realm directly above it, aptly named The Hypereality. To grasp the sheer magnitude of this disparity, let us first establish a point of reference. If we were to designate the size of our universe as 1, then The Hypereality looms on a scale so vast that it defies comprehension. Picture, if you will, an ascending series of incomprehensible cardinals, each dwarfing the last in an unending progression. In essence, this is akin to conceiving of Inaccessible^Inaccessible^Inaccessible^... and so on, perpetually extending into infinity. At this juncture, you might be pondering the nature of an "inaccessible cardinal." Allow me to illuminate this intriguing concept. An inaccessible cardinal is a concept within set theory, a branch of mathematics that deals with the properties and relationships of sets. In particular, an inaccessible cardinal is a type of large cardinal, which are certain cardinal numbers (numbers that describe the size of sets) that have specific properties and play a significant role in set theory. An inaccessible cardinal is defined as, a cardinal number, which means it represents the size of a set. It is also an uncountable cardinal, meaning it is larger than all countable cardinal numbers (such as aleph-null, which represents the size of the set of natural numbers). It is a regular cardinal, which means it cannot be expressed as the union of sets, each of which has a smaller cardinality than itself. In other words, it is a "strongly uncountable" cardinal. It is a limit cardinal, meaning that it cannot be obtained by taking the successor of any smaller cardinal. Inaccessible cardinals have important applications in set theory and mathematical logic, particularly in establishing the consistency of certain mathematical theories and providing a foundation for the study of large cardinals. They are called "inaccessible" because they are so large and have specific properties that make them difficult to reach or access through ordinary set-theoretic operations.*
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