So addressing the infinite universe with infinite stuff
Spacetime by default assumption is a continuum according to the pages and policies i read; here is a quick list of things i found that state this just incase there is any unstated rules that I'm unaware of;
as a "dimension" is stated by the wiki to be "a continuum of numbers.” There is even
a guideline for something to be considered a “Continuum” and even things like Timelines, Dimensions, Universes, etc are stated to be an equivalent. There is a couple whole section dedicated to how the wiki uses
set theory and
Dimensionality together, and this
does include the faq page.
Anyways I'll elaborate some more here.
“
ATOMS ARE LINKED TO ALL THINGS IN NATURE THEY MAKE UP EVERYTHING IN EXISTENCE. EVERYTHING IN THIS WORLD IS MADE OF ATOMS,” and that "
The universe has infinite stars.”, which logically means there is infinite atoms in the verse. These atoms in verse are not in any way or shape in a static or stationary state. And also by consequence that means there js an infinite # of 3D spatial coordinates that have atoms occupying them, and moving through 3D space.
But anyways let's look at these following statements which you knlw shows atoms take on unique states ahd have movement; “
TEMPERATURE IS IN FACT A MEASURE OF THE MOVEMENT OF ATOMS…”,
“
NOTHING THAT LIVES ON THIS EARTH STAYS STILL, EVEN FOR AN INSTANT.”,
“
ALL IS CONSTANTLY IN MOTION, CONSTANTLY CHANGING. THIS IS CALLED TRANSIENCE.”, and “
THE STARS THEY ARE ROTATING. THEY INTERTWINE SEVERAL TIMES AND FALL.” Everything in the universe is in constant motion, and when you combine this with the continuum of spacetime, this means that each atom, across the infinite universe, occupies an infinite number of distinct positions, and states at each moment/present/instant/Snapshot.
As i pointed out earlier, about the wiki and set theory so on and so on..........
The wiki states that Time is Uncountably infinite by default from a quote i found On the FAQ Page
3-Dimensional space on the wiki is also has an uncountably infinite number of spatial coordinates by default assumptions
As far as being larger than infinitely-sized objects or spaces goes, one must analyze the context of the feat in question to determine if it truly qualifies for Higher-Dimensional Existence. In terms of volume (Or, more generally, measure), the only way to be truly bigger than an object of infinite size is to have a non-zero size in a space of more dimensions than the object in question. However, portrayals of more expansive realms containing infinitely large things within themselves are not necessarily indicative of such.
A good construction to exemplify this is the topological space known as the long line. In essence, it is a space obtained by taking an uncountably infinite number of line segments and “gluing” them together end-to-end, and so it is in some sense much longer than the real line, which is comprised of only a countably infinite number of such line segments. Nevertheless, they are both 1-dimensional spaces.
The long line itself can also be generalized into 2-dimensional and 3-dimensional analogues, and as such the same principle holds for higher dimensions as well.
Mathematical Intuition
Speaking in more rigorous terms, a “dimension” in a system can be most effectively equated to the real number line, which is itself the most basic example of a 1-dimensional coordinate space (commonly denoted as simply as ℝ), and contains bounded subsets (smaller, finite lines if you will) whose exact measurements can be taken by “pointing” at a real number represented as a specific point in the line (Example: A line with length 3 is a subset of the real number line, whose length is infinite)
In this context, adding another dimension to a given space is effectively adding another real number line in a different, perpendicular position, which is mathematically represented by continuous cartesian products of ℝ. For example, 2-dimensional space is represented by ℝ^2 (ℝ x ℝ), 3-dimensional space by ℝ^3, and so on and so forth.
In this context, measurements of positions in space are once again obtained by directing oneself at arbitrary numbers contained in the axes of the given expanse, thus obtaining one's own coordinates in it. Simplifying this case, one could also informally state that the “Dimension” of a space is the exact number of coordinates needed to specify any position within it.
Likewise, any n-dimensional object can be thought of as being a subset of a real coordinate space of corresponding dimension. Here is a good illustrative example of that.
The Atoms in the verse are in constant motion because space is a continuum, as an atom moves from one spatial coordinate to another, it must pass through an uncountably infinite number of intermediate spatial coordinates. Consider an atom moving between any two distinct points, A and B. Due to the continuous nature of space, there isn't simply an empty gap between them; instead, there exists an uncountably infinite number of distinct spatial coordinates along the path from A to B. As the atom moves, it occupies each of these unique spatial coordinates that it moves through. Even over the smallest displacement that an atom traverses is an uncountably infinite number of distinct spatial coordinates.
The properties of an atom (such as spatial positioning, temporal positionning as it moves, momentum, and spin) possesses an infinite range of unique numerical values (Anything related to 3-Dimensional space and the one dimension of time.) These properties define an atom's existence within this universe. Because each spatial dimension is continuous, there are infinite unique numerical values describing each of those positions. To describe a single atom in this continuous space, we need to describe all of its spatial positions, and that means all of its values.
If we focus on the properties of an atom, we can use the same logic to demonstrate the sheer number of states each atom across the infinite universe will exist in. I'll designate the number of distinct states that each atom has at every instant as 'C', which in our case, is infinite. Consequently, for a single atom, there exist 'C' number of states (i'll just go with 1 countably infinite set here with baseline of infinite spatial coordinates, and there being infinite # of atoms). When we consider two atoms, the total number of state arrangements becomes C * C or C². Similarly, for three atoms, we have C³ state arrangements. Therefore, with an infinite number of atoms (ℵ), the number of total state arrangements at each instant is C^ℵ. Given that C is defined as infinite, this is equivalent to 2^ℵ (or C^ℵ).
This is important because this is a contribution to the totality and accumulation of all events in the universe per present/instant/moment/snapshot that contributes to the creation of uncountably infinite timelines.
Anyways now addressing "where are you getting atoms from" and where is "each atom is creating infinite branches?"
Macroscopic events, such as gusts of wind are the result of the
movements of air molecules, which as we should all know are made up of atoms like
oxygen and nitrogen.
Anyways; now where is "1 atom = 1 infinite # of branches?"
Anyways a scan mentions "the result of all these cumulative events" (未来とはそれらを重ねた結果なのです), its talking about the sum total of all atomic changes and configurations at each “present” which is just another alternative way of saying “snapshot.”
The idea that only macroscopic events influence the timeline overlooks that reality even at the macroscopic level with macroscopic events are the byproducts of atomic activity. Because "The future is built upon the events of the present" and "What we call time is the result of all these cumulative events," each of the 2^ℵ arrangements of atoms at any instant creates uncountably infinite timelines. Therefore, the perpetual atomic motion occurring in continuous spacetime produces 2^ℵ distinct futures.
Think of a beach. Each grain of sand contributes to the beach's ecosystem, structure, shape, etc. A single grain of sand alone doesn't determines the entire beach's uniqueness, but the combined effect of all the grains creates its unique form. So technically a single atom creating infinite branches is still correct.
The microscopic changes do create infinite branches but it's the accumulation And totality of all events at every snapshot that creates uncountably infinite # of timelines.
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Also, apart of those is
Dark Matter which is spreaded out across the universe in infinity and occupies all 3-Dimensional coordinates. Which by consequence should also ne included in this accumulation and totality that creates uncountably infinite branches at each snapshot.
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Basically my conclusion is this;
The totality of all events in the universe happening in the "present" (aka a snapshot) creates timelines based off those events. Which there is uncountably infinite events happening at every present and by wiki default assumption time is uncountably infinite as well. So uncountably infinite events happening across uncountably infinite snapshots, creating uncountably infinite timelines
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Disclaimer; I don't have a degree in advanced mathematics and physics so it's entirely possible I have a misunderstanding of things. I'm doing my best to understand the mathematical side of this.
Edit: I am struggling to put this into words.
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I'll wait for the OP, though I'm agreeing with Garrixian atm.
I think the OP is arguing that there is an infinitely expanding universe per every fundamental segment of matter from
this scan. It seems like it was said all kinds of minor and perpetually recurring events cause branching in the future, which I see the argument upon, though it explicitly said "cumulative events". I can't find any further explanations for those "cumulative events" in other scans. Overall, I see that the future can be changed and branched through those cumulative events, and it has branched infinitely, hence there are infinite occurrences of those cumulative events. However, that still isn't uncountable; either it explains the infinite branching of the future which makes it look likely, or there's like an infinite quantity of those cumulative events and per each cumulative event, there branches an infinite number of futures (a wacky explanation as I don't think the evidence provided can support the possibility of it being the latter). Even if the latter explanation was the case, it would still be infinite x infinite, which still lands in the pool of being countable.
Another argument I see is the infinite
branching of the future, which indicates an
exponential tree along with an image in the background of the first scan -- this can potentially get to uncountable infinity. If you can provide further context towards the first scan then I would consider merit for the proposal, but the scan alone isn't really enough to establish anything since the evidence is shaky and leaves considerable room for doubt.
