Chapter 1164: Dimensionality Reduction Analysis and the Impact of Modification

Tower of Time, Plane Exploration Layer, inside the Operation Room dedicated to Plane Scholars.

Xia Duo performed a series of operations to set the Plane Exploration Array to active exploration, targeting the 【Yellow Sand Semi-Plane】 already anchored by the Tower of Time, and ordered the tower spirit to project the results.

A moment later, six sets of data appeared in the center of the Operation Room; each set of detection data was a cluster composed of over 1,200 simplified Arcane Geometry Diagram symbols, with boundaries between them.

Such a data set could be called a "1,200-dimensional data set" on Earth; the Plane Exploration Array uses these 1,200-plus dimensions to describe the space-time state detected by the Perception Field in the Ether Interlayer.

Hidden within this is information related to the Plane; of course, this single piece of data certainly contains more than just Plane-related information, as it may also reflect part of the essence of this world.

Naturally, it is primarily related to the Plane, as it is, after all, data collected by the Plane Exploration Array!

Just as one can describe a person's state using the three dimensions of height, weight, and a love for sweets, there can be more.

Describing the space-time state of the Ether Interlayer can certainly have more dimensions, not limited to just over 1,200.

Of course, these 1,200 dimensions only exist because Xia Duo crudely treated each of the 1,200-plus Arcane Geometry Diagrams as a single dimension.

Perhaps there are only 120 dimensions inside, with each dimension using 10 Arcane Geometry Diagrams to describe specific parameters.

As for what the reality actually is, Xia Duo cannot draw a conclusion yet, but treating it as a 1,200-dimensional data set for now is certainly not a problem.

The process of data analysis is essentially the process of dimensionality reduction; it is just a bit tedious right now.

On Earth, let alone 1,200-dimensional data, even higher dimensions would not be rare, but since Earth has computers to utilize, Xia Duo can only perform manual dimensionality reduction here.

But it is not so complex that it cannot be done; one only needs to grasp the main threads, just like what he is about to do—

The six sets of data reflecting the space-time state of the Ether Interlayer were all recorded by the Perception Field projected by the Plane Exploration Array in the Ether Interlayer, containing data on the 【Yellow Sand Semi-Plane】; what is relatively easy to discover among them are the manifest characteristics of the 【Yellow Sand Semi-Plane】 in the Ether Interlayer.

After removing the data deviations caused by the semi-plane's autonomous migration in the Ether Interlayer, what is obtained are the more stable manifest characteristics of the 【Yellow Sand Semi-Plane】 in constant space-time!

Xia Duo currently does not have much interest in the Ether Interlayer, or one could say he currently lacks the ability to study it; he is more concerned with the Plane itself.

Therefore, after performing dimensionality reduction on these six sets of 1,200-dimensional data, what remains is actually the manifest characteristic data of the Yellow Sand Semi-Plane in constant space-time; this is a brand-new data set with only 672 dimensions.

This data is still very complex, but Xia Duo is not trying to study the full correspondence between these 672 feature points and the Yellow Sand Semi-Plane right now.

He only wants a portion of it!

Next, Xia Duo took out a notebook from his Personal Space that he had long finished using; this was where he had recorded the manifest characteristic data of the Yellow Sand Semi-Plane in constant space-time before the Green Field Plane War.

Or to put it more bluntly, it was the manifest characteristic data of the Yellow Sand Semi-Plane in constant space-time before the Plane modification.

By comparing the two, he directly excluded more than half of the feature points he could not yet understand; the remaining hundred-plus feature points were the changes in the Yellow Sand Semi-Plane in the Ether Interlayer caused by the Plane modification.

From 1,200-dimensional data to 100-plus-dimensional data, it was simplified by more than just a little.

In fact, Xia Duo could conduct more targeted modification experiments to determine the Plane Root fluctuations corresponding to more feature points.

This is just the Yellow Sand Semi-Plane; later there could be the 【Blue Crystal Plane】, or whatever other Plane.

And after this series of experiments, a clearer correlation between the Plane and the space-time state of the Ether Interlayer can be derived, leading to a more accurate and practical model of Plane manifest characteristics, thereby increasing the efficiency of discovering new Planes!

……

After finding the key feature points for the state changes of the 【Yellow Sand Semi-Plane】 in constant space-time during this period of Plane modification, Xia Duo substituted them into the ever-changing space-time state of the Ether Interlayer.

Thereby seeking the positional changes of this 100-plus-dimensional data set within that original 1,200-dimensional data set, which is the actual impact of the Plane modification on the Yellow Sand Semi-Plane in the Ether Interlayer.

Or to use Earth terminology, it is finding the physical meaning behind the data changes!

Data analysis itself is dull, but if one links it to various concrete things, it becomes interesting; at the very least, it is a way to find joy in hardship.

While retrieving information about the Perception Field of the Plane Exploration Array from the Tower of Time blueprints in his mind, he combined this information with the corresponding space-time state of the Ether Interlayer to analyze the actual significance of that 100-plus-dimensional data set.

This process lasted until the end of the month; of course, during this period, Xia Duo did not forget to record the brand-new manifest characteristic data of the Yellow Sand Semi-Plane in the Ether Interlayer every day after performing Root Modification on it.

Through such long-term and uninterrupted data collection and research analysis, at the end of the month, Xia Duo finally reached a preliminary conclusion regarding Plane modification—

Plane modification, especially Root Modification, has a very profound impact on a Plane; it directly changes the space-time relationship of the Plane in the Ether Interlayer!

But such modification does not change the anchoring state of the Semi-plane itself.

Simply put, the state of the Plane does indeed change, but the migration laws of the modified Plane do not change.

It is similar to how a change in the mass of a planet in the Earth's universe would cause its orbital path within the star system to change, but the fact that it revolves around the star itself does not change.

The Tower of Time anchoring a Semi-plane is not to restrict its autonomous migration—although it could indeed do so—but the anchoring of the Yellow Sand Semi-Plane is merely to calculate its migration laws.

Its relationship with the Main Plane in the Ether Interlayer is similar to the relationship between a planet and a star; as long as the migration laws are determined, its exact position can be located at any time.

The anchoring of a Sub-plane is similar; it is recording the position.

The difference is that a Sub-plane is similar to the Main Plane and does not undergo autonomous migration; the changes in its space-time position in the Ether Interlayer are more due to changes in the Ether Interlayer itself.

Therefore, the anchoring of a Sub-plane is actually simpler than that of a Semi-plane; as long as the Six-dimensional Coordinate of the Sub-plane relative to the Elemental Plane is recorded, it will not easily change. (This is not the Six-dimensional Coordinate of internal position, but the Plane itself, macroscopically; as long as the space-time distance to the Main Plane in the Ether Interlayer is determined, it is equivalent to having a relatively fixed Plane Coordinate.)

Actual teleportation will also be simpler than for a Semi-plane, though this only refers to the difficulty of teleportation between two Planes at the same space-time distance.

Generally, the space-time level distance between a Sub-plane and the Main Plane in the Ether Interlayer is "further," while a Semi-plane is closer; some even have their autonomous migration restricted directly, fixing them in a connection with the Main Plane.

Cross-Plane Teleportation Spells mostly start at the 8th Circle, while for a Semi-plane, if it completely overlaps with the Main Plane, one can even just walk in without needing any Spells.

Even if they do not completely overlap, as long as its autonomous migration characteristics are restricted, generally only a 5th Circle Spell is needed to complete Cross-Plane Teleportation, or if it is even "closer," a 3rd Circle Spell is barely feasible.