Godzilla Singular Point Cosmology Blog

Godzilla Singular Point Cosmology Blog

Dimensions

I previously mentioned that Riemannian manifolds can be extended to infinite dimensions, but this isn’t entirely reliable. While it is true that Riemannian manifolds can be extended to infinite dimensions through certain methods, doing so disrupts the smoothness of the topological structure, and each dimension would no longer be uncountably infinite.

However, a crucial detail is often overlooked. In the first episode of the anime, weren’t there many formula-like notes? Those were notes left behind by Ashihara during his research on singular points. They were handwritten by Enjoe Toh, the anime’s screenwriter and scientific advisor. Among them was a formula like this:

The key section is here:

To explain this formula, it is necessary to first clarify another formula, though this equation does not originate from a singular point.

‖ψ‖ = ∫E³ |ψ(x)|² dx¹ ∧ dx² ∧ dx³,

‖ψ‖ = 1.

"This equation represents the quantum mechanical normalization condition in three-dimensional Euclidean space, indicating that the total probability over the entire E³ equals 1. The meaning here is that by integrating the square modulus of the wave function i.e., the probability density we obtain the total probability. The differential notation appended to the integral corresponds to the expression in Grassmann algebra, where x₁, x₂, x₃ denote three differential quantities representing the volume element of three-dimensional Euclidean space. This is where it relates to singular points.

"Here we encounter an integral where the lowercase g denotes the metric tensor, and √|g| represents the square root of the determinant of this metric tensor. In Euclidean geometry, this value reduces to 1 because the Euclidean metric tensor is the identity matrix (whose determinant is 1)—hence its absence in the earlier Euclidean space expression. This integral fundamentally calculates the higher-dimensional volume in a spacetime with metric g. In this segment’s expression, you again observe such an integral, similarly followed by a suffix denoting a higher-dimensional volume element..."

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Therefore, by identifying what this differential notation represents, we can determine the minimum dimensionality of the singularity's cosmological structure.

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The initial writing was ambiguous, but we conclusively determined it to be M. This differential notation reappears in the formula sheet, confirming the singularity’s cosmology must possess at least M dimensions. Crucially, note it’s uppercase M, not lowercase m. This constitutes the most explicit evidence that the singularity’s universe is infinite-dimensional. Within standard mathematical analysis frameworks, m denotes an integer, any finite natural number, but never infinity. M, however, belongs to non-standard analysis: it represents a hyperinteger, an unlimited infinite natural quantity.

Simply put, we can determine the 'volume' of this universe meaning the number of dimensions comes from the differential terms following dx. For example:

• dx₁ ∧ dx₂ ∧ dx₃ → 3 dimensional directions

• dx₁ ∧ ⋯ ∧ dx₁₀₀₀ → 1000 dimensions

According to this formula, the universe of the singular point has M (capital, not lowercase) dimensional directions. Here, M denotes an infinitely large natural number, implying that the singular point's universe possesses at least infinite dimensions."

This should at least qualify for High1-B. I’ m not yet certain whether this can push it further, but it should undoubtedly be an unimaginable feat. Regarding this same formula: It indicates that all dimensions are described by a single spacetime metric g.

  

Additionally, this passage means that Kumonga's tendrils connect three spatial dimensions of the universe, one flowing temporal dimension (t), and countless orthogonally extended dimensions. Here, the 'flowing dimension' refers to the time dimension t. This indicates that the cosmology of the singular point is an infinite-dimensional spacetime continuum formed by infinite spatial dimensions plus one temporal dimension. All dimensions share a single timeline. This significantly enhances Ultima's monumental undertaking.

それらの体から伸びる触手は、この世界を構成する縦横斜にき三つの次元と流れゆく一つ の次元のみならず、それらと直交して伸びる無数の次元とも接続していた。それらは地表を 探りつつ、そして可能性のあらゆる可能性の流れながら活動していた。

The tentacles extending from their bodies were connected not only to the three horizontal, vertical and diagonal dimensions and the one flowing dimension that make up this world, but also to the countless dimensions extending perpendicular to them. They were working, probing the surface and flowing with all the possibilities of possibility. 

Firstly, the Omega Point has been elevated. The VB page's claim that the Omega Point is 4-dimensional is clearly erroneous as it should be infinite-dimensional. Moreover, the future possible universes generated via hypercomputation at the singular point are also infinite-dimensional, since all dimensions are permeated by a single temporal dimension. Parallel universes arising from timeline splits would likewise naturally be infinite-dimensional.

These universes are both simulated by the singular point and real, because the singular point computes using time and space itself. Moreover, the number of possible universes can now be determined in which they are also uncountably infinite.

Watch this:

This diagram is used by Perro II to represent the branching of all future possibilities. The vertical axis represents time. You will observe that the rate of branching accelerates over time in the anime, it is described as exponential growth. If the binary tree model depicted in this chart continues splitting infinitely with exponentially increasing speed, it can completely fill the entire real number line within a finite time, forming a dense set. This implies uncountably infinite possible universes, each of infinite dimensionality.

These universes will collide with one another as singular points compete to determine which future is genuine, ultimately converging to form the Omega Point. The Omega Point is a chaotic spacetime where all possible futures occur simultaneously. Universes will be annihilated by vacuum decay arising from paradoxes. Ultima will then treat it as an egg, metaphorically incubating within it until transcending all possibilities, hatching from it, and repeating this cycle in the next universe.

Simply put, IT's dream consists of uncountably infinite parallel timeline universes, each of infinite dimensionality. Ultima will completely transcend them and proceed to the next dream. Here, 'dream' refers to the past and future specifically, the universe corresponding to each point on the timeline. Thus, there exist uncountably infinite dreams. This is why IT can never awaken. For IT, Ultima is it's past, future, and present. Ultima will ceaselessly destroy universes, defeat formidable adversaries, and evolve until ultimately becoming IT slumbering at time's end. Meanwhile, IT's dreams (i.e., memories) create Ultima. They share a bond of mutual causality, akin to the droplet experiment. IT serves as Ultima's ultimate fate anchor: so long as IT exists, Ultima cannot die only fail because the future has already been determined and has occurred.

Dreams Within Dreams

The dream of Godzilla, by the nature of the Omega Point, constitutes an uncountably infinite set of infinite-dimensional possible parallel universes. Furthermore, based on descriptions from Jet Jaguar and 'all conceivable possibilities,' this dream aligns with expansive modal realism. Yet this dream itself is merely a subset of a larger ultima's dream which is a recursion where dreams nest within greater dreams ad infinitum. The ontological primacy resides beyond all dreams at the ultimate apex.

To demonstrate this, one must first clarify what 'dream' signifies:

現実は記憶であって、記憶は現実と変わるところが何もなかった。

Reality is memory, and memory is no different from reality.

《それ》は、過去の夢を見ており、過去において未来の夢を見ており、過去において未来の 夢を見るという夢を未来において見続けていた。

"IT" saw the past in the dream, saw the future in the past, and continued to dream about seeing the future in the future.

From this we understand that dreams are IT's memories. IT is Ultima's past, future, and present.

The spacetime framework of the singular point's cosmology allows the future to precede the past. Ultima and IT exist in mutual causality. Through ceaseless combat and destruction, Ultima grows, experiences all possibilities, and advances toward the future until it transcends all possibility and impossibility to become IT, slumbering at time's foundation. Meanwhile, IT dreams its own past into being.

The second sentence implies infinite dream hierarchy: every ultima is another ultima's dream, with each dream layer containing infinite nested dreams.

《それ》は夢から醒さめる夢から醒め、またその夢から醒める夢を見ていた。夢の中で夢を見てまた夢見ていた。どこまでいってもその繰り返しに果てはなく、《それ》が見ているものは決して醒めることのできない夢で、誰も入り込むことのできない夢とも言えた。

“It” wakes up from the dream of “waking up from a dream”, and then continues to dream of “waking up from a dream”. There are dreams within dreams, and dreams within dreams. This cycle will never end. What “it” sees is a dream that it can never wake up from, and a dream that no one can set foot in.

This passage signifies that dreams are endless even 'awakening' constitutes part of the dream. Given that the Omega Point serves as a vessel transporting Ultima to another universe, 'awakening' entails rupturing the Omega Point to traverse universes. Yet this too remains merely a fragment of another Ultima's dream.

This should demonstrate that the distinction between dream layers transcends quantitative difference, constituting instead a qualitative transcendence. Such qualitative leaps extend through at least infinite layers. IT is at the apex of it all, seeing it all as a dream, and can view all possible futures and pasts simultaneously.

Adding that IT exists at time's end a state of transcendental supremacy perceiving all this as a dream (even dreams within dreams), with the gap between lower and higher dimensional entities resembling the chasm between TV characters and their viewers (an R>F hierarchy), this cosmology should qualify for 1-A or  High 1-A.