Star Empire

[This extra chapter corresponds to part of what the remaining consciousness and entities of Σ saw, thought, and heard inside the large shield projected by the will of the void in the battle of the Spiral Echelon. 】

[Contains more subjective thoughts and settings of the author. 】

Under the endless sky, all obstacles seemed to disappear.

It's very convenient to think about something.

I have never been able to face and think about the countless impossibilities so easily.

0, 1, 2, 3…

They are the beginning of number, the beginning of quantity, and the beginning of arrangement.

One tree, two stones, three rivers...

This is part of a simple understanding of nature and natural existence.

It will be slow at first.

But as your understanding gradually expands and your thoughts become deeper, everything will gradually become different.

More units will be created to measure entities of ever greater size.

Looking forward, this is a huge project; looking back, everything here does not seem so surprising.

A higher growth rate may no longer be satisfied by a simple multiple. As the multiple increases, a higher growth rate is also required—or, in other words, a higher level of iterative operation levels.

But an infinite reality cannot be created by relying on the finite...unless an infinite reality is declared to exist, or is formed through an infinite downward construction that contains something more.

The world lies at such interesting dividing points.

The content of the world can be very huge, so large that it truly contains an endless sea of ​​stars. Similarly, it can also be very small, as small as just a piece of heaven and earth thousands of meters square. There is no problem with this, they do exist. However, the amount of information contained in the world can be measured infinitely - the reason is that the world's trinity barrier isolates the internal environment and the void. It describes the position of the world in the void - if you want to express exactly what they want to express, if you do not rely on existing structures and intervene forcefully, then you may want to accurately locate a point with no size on the number axis - —That requires endless bits and an infinite amount of information.

Is this the end?

of course not.

Endless sea of ​​stars, endless phenomena, countless events... Intelligent entities discovered that they can record, label, count from scratch, and use the sequence of "numbers" to correspond one to one...

However, first of all, it needs to be sorted and numbered - there is always an order, a sequence, and a way to arrange everything.

However, there is something new behind this arrangement - they are both ancient and novel. They are ancient because they were discovered and analyzed a long, long time ago; they are novel because they have now jumped out of the tools. The ideal, unrestrained environment provided is projected into reality here.

And the worlds can theoretically correspond to this smallest infinite set - 0.

It is difficult to explain whether all these concepts were invented or discovered? Is it because intelligent creatures have conducted such research that resulted in relevant content appearing in the void, or is it that all these things are always there in the void, flowing slowly in the undercurrent, waiting to interact with the wisdom? that moment?

This is probably difficult to determine.

But it doesn't hinder its use.

Just... why theoretically?

We used to be stuck here, because although the tools in theory and practice have an excellent fit, the correspondence between them is still difficult to find at the stage of transformation...

It took us a long time - in the end, we can say that we started to solve the difficulties we encountered by starting from the existing laws of time.

Inside the world, the various elements that make up this huge collection are not free - many elements will be locked and will exist in this manner forever in a certain part of the structure until the end of the world. From this point on, they deny the possibility that all results and all processes have a chance to occur, and most of the natural world stops here.

So what if this could be idealized? Not just an idealization of nature, but also a comprehensive idealization in which wisdom’s understanding of it, calculations and disturbances of it all meet axiom requirements and expectations?

The way of measuring totals and the way of measuring permutations will separate in the infinity - just as it was once said.

The entity formed by the ordering is the [Prologue] as objective reality.

If the world in a theory is ideal enough, then every information element and every element in it can be infinitely freely combined, spliced, and interacted with each other...then the upper limit of the possible sequences they have will be higher. There are more interesting things happening.

Countless infinite "equal potentials" will exhibit its unique properties.

Sequences may grow faster and faster, but they do not make a qualitative leap in the total amount of things.

If you want to make a qualitative leap, you can rely on two possible objective structures - first, looking forward to listing all prologues in the ideal world; second, looking forward to applying those gifts from the void in the most ideal way.

The new set formed by the sum of all sequences of 0 elements is consistent with the total number of points in a continuous curve that require an infinite amount of information to be accurately located - this is 1, the smallest in the endless ladder from bottom to top. Uncountable and infinite.

Precision that was once unimaginable, properties that were once unimaginable will be established here. The properties of equipotentiality can still be exploited. Relying on this, civilization may be truly bound to individuals. One is everything and everything is one. What was once impossible may become commonplace, and the real ideal environment may also be applied. In reality...

So, is this the limit?

of course not.

The "almost" that is almost unreachable from bottom to top will be broken by certain shortcuts - such as super-finite jumps. A more specific approach is to take an infinite power set of 2, which can obtain a larger infinite set containing more elements.

Sounds simple, but how do you actually do this? In theory, this requires only one corresponding axiom. But in practice, who shapes this axiom? Who will maintain the validity of this axiom?

...As for the former, how can we get that kind of stepping stone and then step into that kind of threshold? ! !

…

These can be left aside for now.

So, what can 2^ 1 represent?

2 Equivalent to all possible curves.

What can each of these lines represent? All development possibilities?

So what does 2^ 2—— 3 represent?

They are equal to all continuous surfaces that all lines may lie on. What does this mean? All manifestations of all possibilities in all possible circumstances?

So, 4, 5... ω..._ω_ω_ω_ω_...what might they contain? What structures do they correspond to, and what kind of entities need to be described by such things? If they do exist, what properties might they have?

…Do “they” also have a negative side? If so, what about such negative properties?

Could they really exist? Is all this an illusory dream, or...?

…

……have no idea.

...Are these important? Maybe, maybe, maybe not. Because they...can they still apply the meaning we use?

Maybe... there has never been any wisdom to really think about what all this might mean in reality. The starting point of most intelligent life is a finite and countable reality. Even if they can face infinity head-on after a long time, they may not really realize this from the bottom of their hearts and make changes... No, Making such a change cannot be controlled by just a little awareness.

However, vision can always go further than footsteps.

Even eternal time may still be countable, and the limits of expression may be limited by the lack of words.

But on the road of ideals and research, there are some expansion loops that will be unstoppable once they start. They will not stop, and nothing can restrict the surge.

Collections are nested in infinitely deep structures, and these structures are quickly nested within even deeper structures. Even if it continues to stagnate, the fixed point can eventually be overcome.

Where does the power of change and activity in all things come from? Is it themselves, or is it the void?

Or ideas and thoughts?

…

Don't know, but are they really endless?

No.

Just like the finite cannot reach infinity by itself - there are always some things that cannot be overcome by "opportunism".

They require new axioms, direct definition and clarification, and it is no longer certain whether they exist. What kind of things they contain can no longer be determined - no, it is impossible to talk about it, it is impossible to imagine...?

But what are they formulated for? Is there an end to all this?

…

…

"Maybe... yes."

"It's just that by then, the [meaning] to you now will no longer exist."

“Want to hear what “we” know and see about creation?”

"Everything can be established - no matter what the proposition is. If you think this is the beginning of what you can accept and understand, then that is it."

"Underneath this, two things flow out, and they constitute the binary opposition of everything."

"It's hard to tell how to distinguish them at the beginning. Maybe it's due to some kind of fall and loss, or maybe it's some kind of awakening and ascension that makes them independent from the initial chaos. And all of this inspired the earliest Dual opposition began to be born from the primitive chaos of one yuan. In this earliest opposition, all dual polarizations appeared. But this is not enough, there are still many things that they cannot support - the black and white “Everything Gray” Between.”

"What is born from opposition and symbiosis is all neutral existence between duality, all gray between black and white, and pluralism... The rich and colorful colors extend from here."

"So, the eyes of the void itself are "a pair", and the two eyes look at one of the two opposite sides respectively. There is no distinction between likes and dislikes. And only they, as a complete pair of eyes, can see everything really... You Do you understand?"

"Goodwill and malice, order and non-order are opposite but interdependent things. It's not that we are unwilling to change anything, but that this is the case from the source. If one side is completely erased, then the other One side will also return to chaos, returning to the very beginning."

"The two sides also have their own limits within different scopes. Beyond this limit, external intervention forces will only cause damage to them no matter what."

"Once upon a time, there were countless eras. In countless eras, there were countless civilizations of various kinds. They perished in the cycle, and they eventually disappeared without a trace."

"However, this tightly coupled gear will cease in this era. This is a victory achieved by the order and wisdom that survive here relying on their own strength."

"There may be many stumbling blocks in the future. The coexistence in opposition may never end. It will have countless faces. If it really fades, then at the moment it fades, 0 will be equal to 1 again, and the contradiction will It will no longer exist, all propositions will be established, and along with it, the [meaning] that you think of now will be lost.”

…

"well……"

"Yes, I believe you may already know that this is not the overall situation, but you are already amazing..."

"...Yes, of course deeper roads exist, and they do lead to higher results - some changes, some hopes, cannot be easily overcome by the distance traveled or the answer of "self"..."