75: Chapter 75 The First Language

Throughout the entire autumn of the twenty-sixth year, Jiang Lin was doing something that looked very strange.

Looking at that lonely current sheet of Sweet-Parker Model, like a cold scar spanning across the history of Physics.

Looking at Petschek's X-marked geometry, elegant yet possessing an idealized fragility.

Looking at Plasmoid's string of green magnetic island markers, like a string of boiling, fractured beads.

Looking at Hall's position, marked as an untouchable high point.

Looking at the line of red text next to turbulent reconnection that proactively chose not to be patched, exuding a sort of helpless compromise.

Looking at the smallest and darkest new marker in the southwest corner — [? - Multi - Loop - Coupled].

Looking at that smaller line of text — [Substation engineering specifications abnormal. Nameplate remaining characters: TM -, grid, power distribution, Great Wall. Meaning unknown.]

Every time he finished looking, his gaze would ultimately stop at that new marker.

Those remanent magnetism data brought back from the substation ruins were like tiny barbs, piercing into the theoretical framework he had established over the past few decades.

One afternoon in October of the twenty-sixth year, he finally did something.

He sat down at the desk, spread out a large piece of blank paper, and wrote a word right in the center of the paper.

[Magnetic Reconnection]

Then he started drawing around it.

Of course there was better drawing software on the workstation, with more precise topological modeling tools, but this time he didn't want software to help him sort out his thoughts.

The underlying logic of software was a deterministic algorithm, whereas what he needed at this moment was for his thoughts to grow on their own.

The first line went upward from the center, with Sweet-Parker written at the end of the line.

The second line went up and to the right, with Petschek written at the end.

The third line went to the right, Plasmoid magnetic island string.

The fourth line went down and to the right, Hall reconnection.

The fifth line went downward, collisionless reconnection.

The sixth line went down and to the left, turbulent reconnection.

The seventh line went to the left, tearing mode / sawtooth collapse.

The eighth line went up and to the left, ? - Multi - Loop - Coupled.

Eight lines, eight schools.

Each of them was a specific implementation of magnetic reconnection under certain boundary conditions.

If in a university lecture hall in the Real World, textbooks would arrange these eight schools into a clear historical timeline.

Starting from 1Parker, proposing the long current sheet model.

To 1hek, introducing slow shock waves to accelerate the reconnection rate.

To the Plasmoid of 2007, discovering the secondary instability of the long current sheet.

To the MMS detector in 2016 obtaining measured data in the electron diffusion region.

...

Sorted by time, by discovery order.

In this narrative, the appearance of one school was often understood as surpassing or correcting another school.

Later generations were always closer to truth than predecessors.

But after Jiang Lin finished reading eighty-two core Class A papers over the past decade, he knew this sorting method was too single-threaded.

It was suitable for teaching, not for describing the simultaneous opening of multi-scale mechanisms in a real disaster scene.

The substation's remanent magnetism data told him that in a real disaster scene, the eight schools might not all appear completely at the same time.

But a real physical system would never choose just one mechanism like doing a multiple-choice question.

Under different scales, different boundaries, and different dissipation conditions, it would make different mechanisms open successively, overlap, and compete.

Nesting into each other, interfering with each other, neither surpassing nor replacing the other.

If one extrapolated the 12,000-square-meter local wreckage system of the substation to the conductive network of the entire Wasteland planet, or even to the macroscopic space where the solar wind intersects with Earth's magnetosphere.

Most mechanisms were likely to open successively, overlap, and compete at different scales.

They might not all appear completely at the same time, but a real system would never choose just one of them.

Sweet-Parker's slow current sheet might exist in some macroscopic background scale, silently accumulating energy.

Petschek's X-shaped geometry might appear at an energy release point on another secondary scale.

Plasmoid's string of magnetic islands might split apart like a string of firecrackers on a third, smaller scale.

The Hall effect began to make the motions of electrons and ions diverge near the ion inertial length; further down, the electron diffusion region was truly the untouchable high point.

Turbulence might be like a never-ending storm, running through all scales from macroscopic to microscopic.

Tearing mode described some local collapse behaviors constrained by boundaries and resonant surfaces; in tokamaks, it was especially clear.

They were all present, simultaneously present, forming a multi-channel, multi-scale, mutually nested system.

And Jiang Lin, even having turned the history of Physics upside down, clearly found that all these schools combined were still not enough.

Because there was still one school that didn't even have a complete definition on the research history map on his north wall.

That smallest and darkest [? - Multi - Loop - Coupled].

What it meant was, what would happen when the boundary conditions of the system were no longer an idealized infinite plasma, but an entire closed conductor network as intricate as the human power grid?

This was like asking, when lightning strikes a huge wire mesh, how would this mesh retaliate against the sky?

Textbooks did not discuss this question.

At least among those Class A core papers he had read to pieces, not a single one took this question as its main axis.

Academia preferred clean plasma chambers rather than rusted substation ruins.

But the substation data, in the form of cold physical evidence, interrogated this question.

Staring at this octagonal diagram, Jiang Lin realized for the first time, vaguely yet with incomparable intensity, that what he needed was not to take another step forward on a certain line to produce a slightly more accurate new model.

What he needed was a new language.

A new language capable of describing how these eight schools operated simultaneously and how they coupled with each other.

When this thought arose in his mind and he wrote down these words, even he himself was a bit surprised.

He didn't know what this language looked like; was it some variant of tensor calculus?

Or some brand new topological algebra?

He only knew this language should exist, because the real Physics happening on the Wasteland was right there.

If a certain language did not exist, it was definitely not because it was impossible, but simply because no one had invented it yet.

Thus, Jiang Lin began to look for this language.

Searching for the language of Physics often could not start from pure theory.

He decided to stop all paper reading and laboratory analysis, first returning to engineering, returning to those tangible, rotatable, heat-generating metal creations.

Spending six to eight hours every day sitting at the workbench, facing wind turbine no. 2 outside the window and Observation Point A in the distance, drawing structural diagram after structural diagram.

Although these diagrams varied in form, the title was always the same.

[Multi-Channel Structure of the Outpost Power System]

wind turbine no. 2 was itself an excellent multi-channel coupled system.

The impeller captured the wind energy raging across the Wasteland — the first channel: the aerodynamic channel.

The impeller directly drove the low-speed permanent magnet generator rotor through the hub and main shaft — the second channel: the electromechanical conversion channel.

The generator output unstable three-phase AC power, which was converted into ripple-bearing DC through the rectifier bridge — the third channel: the power conversion channel.

Through the intelligent distribution of the controller, part of the DC power was charged into the battery (energy storage channel), part flowed to the load (consumption channel), and part flowed to the dumping resistor (energy dissipation channel).

Every channel had its own characteristic time scale.

Aerodynamic channel: the time scale of wind speed changes, from seconds to minutes, slow and grand.

Electromechanical conversion: the response time of the motor electromagnetic torque, from milliseconds to seconds.

Power conversion: the switching frequency of semiconductor switches, microseconds to milliseconds, extremely fast.

Energy storage: the charge and discharge time of battery chemical reactions, from minutes to hours, or even days.

Consumption: the real-time switching of loads, seconds to minutes.

Energy dissipation: the thermal equilibrium and heat dissipation time of the dumping resistor, seconds to minutes.

Six channels, six distinct time scales, simultaneously affecting the overall behavior of the power system.

When textbooks wrote about wind power generation systems, they never clearly drew all six channels on a single diagram and discussed their coupling.

Either they only talked about aerodynamics, which was the scope of fluid mechanics classes filled with Navier-Stokes equations.

Or they only talked about electromechanics, which was electrical machinery, discussing flux linkage and Ampere's force.

Or they only talked about power electronics, which was power devices classes, full of conduction losses and switching losses of power switching devices.

Or they only talked about control logic, which was systems engineering classes, playing with PID algorithms.

Every class, like blind men touching an elephant, only talked about one channel.

The multi-channel nonlinear behavior of the entire system in a real environment — very few introductory textbooks put these channels in the same diagram to seriously discuss their coupling near failure boundaries.

But Jiang Lin, in the process of establishing, maintaining, and repairing wind turbine no. 2 at the Outpost, had personally seen and handled the multi-channel coupling of this system.

When wind speed suddenly changed, the aerodynamic channel responded first, and the impeller speed fluctuated violently.

Speed fluctuations were transmitted to the generator end through the electromechanical channel, causing three-phase voltage fluctuations.

Voltage fluctuations passed through the power conversion channel, causing the DC bus voltage to jump.

The jump passed through the energy storage channel, causing the battery charging current to change.

The change passed through the controller logic, triggering or not triggering energy dumping.

The entire chain, from wind to the heating of the dumping resistor, all channels were active simultaneously.

And what determined whether the system ultimately operated stably and safely or burned down violently in overload was never any single channel.

Rather, it was the coupling relationship between them.

Which channel responded fast, which channel responded slow.

Which channel's output overflow would trigger another channel's collapse threshold?

Which channel's overload would be absorbed by another channel's redundant capacity?

Which channel had hardware protection, and which channel was fragile and exposed?

This was a real engineering system.

Jiang Lin hung the multi-channel structural diagram of the power system next to the research history map.

Thus, he had two diagrams.

One was the sixty-year research history of the magnetic reconnection field.

One was the engineering structure of the Outpost power system.

One side was plasma astrophysics, the other side was low-end electrical engineering; they looked worlds apart, but in terms of multi-channel coupling, both were talking about the exact same thing.

Deep winter of the twenty-sixth year.

Amidst raging wind and snow, inside the solid fortress of the Stone House, Jiang Lin began trying to apply the multi-channel thinking of the Outpost power system to magnetic reconnection.

The first attempt was: if magnetic reconnection was also a multi-channel system, how many channels did it have?

What specific plasma Physics process did each channel correspond to?

What was the characteristic scale of each channel?

How exactly were the channels coupled?

He created a new folder in the workstation.

[Multi-Channel-Framework]

Inside the folder, there was currently only a pitiful text file.

[draft_v1.txt]

The first line of the file was — [Multi-Channel Decomposition Attempt of Magnetic Reconnection V1]

Moving down, like Cook Ding dismembering an ox, he listed the candidate channels one by one.

[Channel One: Large-Scale MHD Power Supply Channel]

Characteristics: Massive magnetic energy from external large-scale systems (such as solar corona, Earth's magnetosphere) continuously input into the reconnection region like a reservoir releasing water.

Characteristic scale: System macroscopic scale L.

Corresponding theoretical model: The large-scale part of Sweet-Parker Model.

[Channel Two: Mesoscale Plasmoid Spallation Channel]

Characteristics: When the energy transported by the MHD channel overwhelms the long current sheet, the current sheet itself undergoes tearing instability, fracturing into a long string of structures called magnetic islands.

Characteristic scale: A fraction of the current sheet length.

Corresponding theoretical models: Loureiro (2007) chain instability, Bhattacharjee (2009) fast reconnection mechanism.

[Channel Three: Small-Scale Hall Transition Channel]

Characteristics: At extremely tiny scales, heavy ions cannot keep up with the pace of light electrons, decoupling the two in the magnetic field and producing a strong Hall electric field, which changes the geometric topology of the reconnection region.

Characteristic scale: Ion inertial length d_i.

Corresponding theoretical models: Mechanism confirmed by GEM Challenge, Burch (2016) MMS detector measured data.

[Channel Four: Cross-Scale Turbulence Channel]

Characteristics: Disordered turbulence of the magnetic field itself, like a pot of boiling water, makes a large number of micro-scale reconnection events occur randomly and simultaneously throughout the space, greatly increasing dissipation.

Characteristic scale: The entire inertial cascade interval from the macroscopic energy injection scale all the way to the microscopic energy dissipation scale.

Corresponding theoretical model: Lazarian-Vishniac (1999) stochastic turbulent reconnection model.

[Channel Five: Boundary Closed Channel]

Characteristics: In artificial or specific closed geometries (such as the toroidal chamber of a tokamak device), the magnetic field is forcibly maintained with certain topological constraints by the container, and reconnection can only occur on specific resonant surfaces.

Characteristic scale: Characteristic scale of the boundary container.

Corresponding theoretical model: Tearing mode inside tokamak devices.

[Channel Six: Multi-Loop Collective Response Channel]

Characteristics: Multiple closed artificial or natural conductor loops are nested within each other. Under extreme electromagnetic perturbations, they act like a massive LC oscillation network, producing collective responses and magnetization imprints.

Characteristic Scale: The macroscopic scale of the entire conductive network (potentially covering the entire planetary surface).

Corresponding Theoretical Model: None yet.

The last line carried a glaring question mark.

Below [draft_v1], Jiang Lin added another line of text.

"Six channels; the first five all have existing, mature theories to support them. The sixth is a cruel hint given to me by the remnant magnetism of the substation ruins, but in human theoretical Physics, this remains a suffocating blank."

After finishing and saving, he closed the editor and rubbed his sore brows.

The framework had been set up, but it was merely the first step of a Long March.

Year 27, Spring.

The ice and snow melted, and the Moss burst with vitality.

However, Jiang Lin fell into a quagmire of trying to articulate the coupling relationships among these six channels.

For the coupling between every pair of channels, he attempted to draw a small diagram on draft paper.

These diagrams were not simple connecting lines, but physical flowcharts containing strict logical causality.

He analyzed the coupling between Channel One (MHD) and Channel Two (Plasmoid): large-scale MHD inputs magnetic energy and stretches the current sheet.

When the aspect ratio of the current sheet exceeds the critical value, instability occurs, and the Plasmoid is generated.

This was a one-to-one, very classic serial coupling.

He analyzed the coupling between Channel One (MHD) and Channel Three (Hall).

Large-scale MHD fluid motion would never directly drive the microscopic Hall effect.

The Hall effect would only spontaneously ignite at extremely small scales such as the ion inertial length.

But large-scale MHD held the power of life and death.

It determined whether the Hall effect had the chance to appear.

If the current sheet squeezed out by the large scale was too short and thick, before the Hall scale had time to form, the entire system would have already degenerated into slow Sweet-Parker reconnection through resistive dissipation.

This was an insidious, indirect, and conditional coupling.

...

Drawing to the end, only Channel Six remained—multi-loop collective response.

Holding his pen, Jiang Lin hovered it in mid-air for a long time, hesitating and unable to put it down.

For this channel, he could not draw any coupling diagram.

He did not know how the massive artificial surface network should couple with the microscopic Hall effect inside the plasma.

He could not even mathematically prove whether it truly existed as a dominant variable of reconnection.

Sighing, he drew a huge dashed box on the column for Channel Six on the blueprint, leaving it blank for a potentially smarter self in the future, or for the next more dangerous expedition.

Throughout the spring of Year 27, Jiang Lin spent his time drawing these coupling diagrams.

As he drew more and more diagrams, he realized that textual descriptions were pale.

If he could not nail down these coupling relationships with mathematical language, then everything he did was just a bunch of metaphysics.

For each group of coupling relationships, he began attempting to characterize its physical threshold with a set of dimensionless numbers.

The coupling threshold between Channel One and Channel Two was determined by the aspect ratio of the current sheet.

The coupling threshold between Channel One and Channel Three was determined by the ratio of the current sheet length to the ion inertial length.

The coupling threshold between Channel Two and Channel Three was determined by the ratio of the Plasmoid size to the ion inertial length.

The penetration strength of Channel Four was determined by the plasma turbulence intensity.

The closure degree of Channel Five was determined by the open/closed ratio of the boundary conditions.

Channel Six remained a frustrating unknown.

Every dimensionless number corresponded to a clear physical intuition.

Every intuition was extracted by Jiang Lin from the literature and engineering experience of the past decade.

He knew very well that he had not invented any of the dimensionless numbers in here.

L/d_i was clearly written in Bhattacharjee's paper, and the turbulent Mach number could be found everywhere in Lazarian's formula.

They were all in the vast ocean of literature.

However, piecing them together precisely like Lego blocks to form a complete network capable of describing the multi-channel state of the entire plasma system was something no paper had ever done in human-known academic literature.

The closest thing to this grand vision was a famous review published by Cassak in 2006.

In that review, Cassak proposed a 0.1 reconnection rate problem that fascinated the Physics community.

That is, why in Solar Flares, the Earth's magnetotail, or even in laboratories, did those systems defined as fast reconnection—regardless of whether the underlying physical mechanism was the Hall effect or Plasmoid—always mysteriously have their dimensionless reconnection rate values fall around the magnitude of 0.1?

Cassak discussed this magical convergence, but his article did not give Jiang Lin the multi-channel network framework he wanted.

However, it provided Jiang Lin with tremendous inspiration.

Behind different scales and different mechanisms, there must exist some higher-dimensional, common rate-selection constraint.

Much like all rivers flowing into the sea.

Jiang Lin stood up and solemnly circled the location of Cassak's 2006 paper with a red pen on the densely packed research history map on the north wall.

In the summer of Year 27, temperatures soared, and the Wasteland entered the hottest and most agonizing season of the year.

As for Jiang Lin, inside the steamer-like Stone House, he began attempting to do something extremely ambitious and extremely dangerous in the theoretical Physics community.

He wanted to use a single number, merely a dimensionless number.

To characterize the critical geometric conditions of the entire complex multi-channel system instantly shifting from slow resistivity-dominated to violent rapid reconnection-dominated.

This number had to be an exquisite combination of the coupling relationships of the six channels (or the five known channels).

It should not be any single existing old dimensionless number; otherwise, it would be redundant.

In the history of Physics, sitting in front of a blackboard and scratching one's head to invent a new dimensionless number was very easy—just find a few parameters to multiply and divide.

But inventing a new dimensionless number with profound physical significance that could truly predict unknown real physical phenomena was as difficult as ascending to heaven.

Throughout history, the vast majority of dimensionless numbers created by ambitious scholars were eventually found, after ruthless peer review, to either be simple algebraic transformations of some existing number with zero novelty.

Or they were just mathematical games that could not correspond to any measurable physical phenomena in experiments.

Jiang Lin reminded himself: try first, interrogate second.

If the attempt failed, he would unhesitatingly admit defeat and never be infatuated with his own creation.

If the attempt seemed successful, he would immediately look for the trickiest counterexamples to attack it.

He started working.

For his first attempt, he weighted and added five quantities: the Lundquist number S, the current sheet aspect ratio L/a, the ion inertial length ratio L/d_i, the turbulence intensity σ, and the boundary open ratio η.

Taking the logarithm of each quantity, he obtained a combined number and named it G_1.

He turned on the workstation, pulled up the known sample database, and used G_1 to fit those classical events that had undergone countless observations.

Solar Flares, Earth's magnetospheric substorms, tearing mode disruptions in tokamak devices, and experimental data from small reconnection devices in university laboratories.

After the results came out, G_1 gave seemingly very close values across all samples.

But this was precisely the biggest problem: being close did not equal physical consistency.

Solar Flare G_1 ≈ 2.3.

Magnetospheric substorm G_1 ≈ 2.7.

Tokamak G_1 ≈ 1.9.

Laboratory device G_1 ≈ 1.4.

If the parameter G_1 truly accurately described the essence of the system's transition between fast and slow, then the G_1 of all fast reconnection systems should be greater than some extremely clear critical value G_c, while the G_1 of slow systems should all be less than G_c.

From a classification standpoint, Solar Flares and magnetospheric substorms definitely belonged to fast reconnection, tokamak tearing modes barely counted as medium, and laboratory devices were definitely slow.

Their G_1 values indeed showed a trend of fast > medium > slow.

But what use was this?

And where was the critical value G_c?

If G_c = 2.0, then the laboratory device (1.4) and the tokamak (1.9) were both classified as slow, while the magnetospheric substorm (2.7) and the Solar Flare (2.3) were classified as fast.

This classification barely held up statistically, but physically, Jiang Lin looked at this pile of numbers and felt very unsatisfied.

It was not because the numerical distribution wasn't pretty enough, but because the definition of G_1 itself lacked any solid physical foundation.

Why were five quantities weighted and added together? By what right was the weight distribution set to this proportion, and why take logarithms instead of exponents or other nonlinear functions?

He could not answer any of these.

G_1 looked more like a hindsight-fitted mathematical tool created just to get a result, rather than a physical quantity defined a priori based on first principles.

Post-hoc fitting tools were very dangerous.

Like a tailor-made lie, it could perfectly fit any known old sample you gave it, but once it encountered an unseen new sample, it would immediately collapse and fail to make any effective predictions.

Jiang Lin unhesitatingly threw aside the dozen pages of manuscripts filled with the derivation process of G_1.

He decided to abandon this method of weighted splicing of existing dimensionless numbers and derive from the physical processes themselves, starting from the most fundamental causal relationships.

Every channel of the wind turbine had a characteristic driving time and a characteristic response time.

Driving time—referring to the timescale required for this channel to receive externally applied perturbations.

Response time—referring to the time required for the internal mechanisms of this channel to provide feedback and take action against this perturbation.

If the driving time was much greater than the response time (external changes were slow while its own actions were fast), this channel could effortlessly dominate the situation.

If the driving time was much smaller than the response time (external changes were extremely fast while its own actions couldn't keep up), this channel would lag severely or even be discarded.

This was precisely the criterion for the stable operation of the wind turbine.

Wind speed changes (driving, a few seconds) were much greater than the yaw motor's action time (response, hundreds of milliseconds), so the wind turbine could always steadily face the wind.

But if a bizarre microsecond-level gust blew across the Wasteland (driving time extremely small), the yaw mechanism would have no time to respond at all (response time too large), and the wind turbine would be beaten passively or even snap its shaft.

Jiang Lin realized that if the magnetic reconnection channels were also disassembled in this way, the driving/response time ratio of each pair of channels would be a dimensionless number with clear physical significance.

He began calculating.

If he paired and compared the six channels listed previously, according to combinations and permutations, he would get a full fifteen pairs of driving/response ratios.

Theoretically, the high-dimensional matrix formed by these fifteen ratios was the truly complete coupling network description.

It was not some crude weighting, but fifteen independent, flesh-and-blood physical ratios.

But problems followed.

Fifteen numbers were too many.

The human brain simply could not directly process phase transition processes in a fifteen-dimensional parameter space.

This might be mathematically beautiful, but in engineering and prediction, it had zero practical value.

Jiang Lin wondered whether he could perform a principal component analysis within this massive fifteen-dimensional matrix.

Could he extract one or two crucial ratios that played a decisive role, serving as the throat representative for the system's fast-slow transition?

He re-examined the theoretical derivation of these fifteen ratios.

And then he found that some of these ratios were infinitely close to 1 in all samples, whether from stars or laboratories.

This meant that these two mechanisms were always synchronized, and the coupling between them did not constitute a bottleneck hindering the system's evolution and could be ignored.

Some ratios were extremely large or extremely small in all samples, meaning that a certain channel was always in a state of absolute suppression or absolute dormancy, far from the critical point of fast-slow phase transitions, and could also be ignored.

After nearly a month of brutal screening and computational stripping, only a few ratios showed drastic and significant order-of-magnitude differences across different sample environments.

That is to say, only these few ratios were the critical hubs that truly choked the system's neck, determining whether it died in slow dissipation or erupted in violent reconnection.

He carefully picked out these three critical ratios.

The first: the ratio Π_1 = L/L_c of the current sheet length L to the Plasmoid secondary instability critical excitation length L_c.

It determined whether the system would fragment into magnetic islands.

The second: the ratio Π_2 = L/d_i of the current sheet length L to the ion inertial length d_i.

It determined whether the system could touch collisionless Hall Physics.

The third: the ratio Π_3 = σ/σ_c of the plasma turbulence intensity σ to a certain critical turbulence intensity σ_c.

It determined whether the background noise added fuel to the fire or overshadowed the main act.

Three ratios, each with rock-solid physical significance, each corresponding to the driving/response matching survival condition of a critical channel.

Jiang Lin began combining these three ratios into a highly condensed algebraic topological form.

Gate Index, G.

Gating index.

To handle the non-monotonic effect of turbulence, he introduced a normalized response function F(σ/σ_c).

This function peaks when the turbulence intensity is moderate, and declines simultaneously at both the excessively weak and excessively strong ends.

The V0.1 form of G was temporarily written by him as—

[ Plasmoid term + Hall accessibility term + turbulence response term ]

The specific algebraic form would not enter the main text for now, only entering the work log.

In Physics, the first log is equivalent to a mathematical switch, corresponding to whether the Plasmoid channel is forcibly opened.

The second log corresponds to whether the microscopic Hall channel is accessible at the current scale.

The third log with a negative sign precisely describes whether the turbulent background has become strong enough to suppress all other single reconnection mechanisms.

The negative sign appearing in the formula, as well as the seemingly strange fractional structure χ / ( 1 - χ ) in the brackets, were not conjured out of thin air by Jiang Lin.

That is because the influence of turbulence is non-monotonic in Physics; moderate turbulence increases dissipation and helps rapid reconnection occur.

Jiang Lin had seen a similar derivation form of this subtle non-monotonic algebraic structure in an inconspicuous appendix of that classic paper published by Lazarian and Vishniac in 1999.

He never considered himself a god who created things out of nothing; he was merely borrowing the bricks of giants and modifying the recipe for the cement.

The definition of the G parameter was finally born.

Highly excited, Jiang Lin forced himself to calm down and entered the cruel cross-validation stage.

He used the new G parameter to re-fit those known samples.

Solar Flare: G ≈ 4.1.

Magnetospheric substorm: G ≈ 3.8.

Tokamak tearing mode: G ≈ 1.2.

Sawtooth collapse: G ≈ 1.5.

Laboratory small-scale reconnection device: G ≈ - 0.3.

Watching these numbers, Jiang Lin's heartbeat began to accelerate.

If the critical value G_c = 2.0 is set.

Those with G > 2.0 were indisputably all cosmic-scale rapid reconnections (Solar Flare, magnetospheric substorms, with values as high as about 4).

Those whose G fell into the [1, 2] interval were all events in a critical state with intermittent characteristics (tokamak disruption phenomena).

Those with G < 1 or even negative numbers were those lifeless slow events (laboratory devices).

This classification result was countless times clearer and sharper than the previously cobbled-together G_1.

More importantly, the definition of G had a profound Physics foundation.

Those three log terms each corresponded to the asymptotic expansion of the specific channel-coupled Physics equations, and were by no means constants cobbled together afterwards just to look good.

Looking at this set of beautiful fitting data, Jiang Lin did not excitedly jump up and cheer.

Because he knew this was merely the first step; he had not yet actively sought out counterexamples to attack it.

If the G gating index truly described the truth of the rapid-slow transition of plasma in the universe, it must and had to satisfy the following three harsh conditions, without a single one missing.

First, it must be able to accurately predict new samples.

Applying G to new experimental or observational data that he had never seen when previously defining the formula, it must still be able to give the correct Physics classification.

It must not die the moment it sees the light of day.

Second, it must possess Physics sensitivity to parameter changes.

If the external parameters of a system were artificially adjusted from the slow interval to the fast interval, the numerical value of G must mathematically change from small to large accordingly, and the trend of change must conform to the monotonicity expectations of calculus.

Third, it must be compatible with existing classical observational phenomena.

For example, the famous 0.1 reconnection rate phenomenon proposed by Cassak should naturally emerge as a mathematical corollary near G ≈ G_c (the critical threshold).

Over the next twenty-seventh year, an entire summer and autumn, Jiang Lin spent all his time like an indefatigable machine on these three cruel tests.

First test: Blind testing of new samples.

He meticulously removed all training data previously used to construct the G parameter from the database.

Then, from the category C index library, he randomly selected a dozen or so obscure observational papers that he had barely looked at closely before.

These included several unusually high-resolution microscopic reconnection events detected by the MMS satellite at the Earth's magnetopause, a few papers statistically analyzing different burst power levels of Solar Flares, and a few niche statistics regarding reconnection occurring in controlled nuclear fusion devices under special magnetic field configurations.

He forcefully plugged the Physics parameters of these brand-new samples one by one into the G parameter formula for blind calculation.

A specific reconnection event observed by MMS: G ≈ 3.5.

According to the paper's description, this event erupted extremely rapidly, consistent with the fast classification of G > 2.0.

A certain ultra-large X-class Solar Flare: G ≈ 4.4.

Obviously extremely fast, consistent.

A certain smaller M-class flare: G ≈ 2.8.

Still fast, consistent.

A special configuration tokamak experiment with deliberately suppressed instability: G ≈ 0.7.

The paper described its evolution as extremely slow, consistent with the slow classification of G < 1.0.

A highly controversial new reconnection claim experiment proposed by a certain laboratory: G ≈ 2.1.

This happened to be stuck on the edge of the critical value, which explained why this experiment triggered a huge controversy in the academic community over whether it was fast or slow.

Among the dozen or so completely blind-tested new samples, the vast majority accurately hit G's prediction interval.

Only one or two extreme boundary cases required finer re-determination due to measurement errors.

Second test: Monotonicity scanning of the parameter space.

Utilizing the pitifully low computing power of the Stone House workstation, Jiang Lin wrote a script and performed a series of brute-force parameter space scans.

In the code, he fixed all other parameters, and then continuously changed the Lundquist number, current sheet length, and turbulence intensity one by one, observing the three-dimensional surface trend of the G value changing accordingly.

The results showed:

G exhibited monotonic increase with the increase of the Lundquist number S.

The larger S was, the more ideal the fluid was, the higher the probability of secondary instabilities leading to rapid reconnection, and the larger G was, which matched Physics intuition.

The variation of G with the macroscopic length L of the current sheet was also monotonically increasing, consistent with theoretical expectations.

The variation of G with turbulence intensity σ was non-monotonic, presenting on the surface that non-monotonic parabolic dome structure he deliberately designed.

G reached its maximum when σ was at a moderate value, assisting reconnection; G decreased rapidly when σ was extremely oversized or undersized.

This fitted the facts of complex plasma Physics.

Third test: Compatibility of historical unsettled cases.

He extracted all experimental and observational samples in the database that calculated G ≈ G_c (hovering near the critical value 2.0) separately, to check the dimensionless reconnection rate values actually reported in these papers.

A miracle appeared.

The reconnection rate values reported by these samples in a critical state were densely concentrated in a narrow band region between 0.05 and 0.15.

This reconciled the 0.1 reconnection rate mystery in Cassak's review that had plagued the academic community for many years.

In contrast, for those samples where G was much greater than G_c, such as Solar Flares, the reconnection rate significantly exceeded 0.15 like a wild horse off the reins.

For samples where G was much less than G_c, the reconnection rate was significantly lower than 0.05 like stagnant water.

None of the three tests provided a fatal counterexample.

The next morning, sunlight shone through the lattice window onto the screen.

Having not slept all night, Jiang Lin rubbed his stiff cheeks and wrote a paragraph in the digital log with a restrained and even warning-toned brushstroke.

[ September 17th of the Twenty-Seventh Year ]

[ The definition of the G parameter (gating index) is out, and all three harsh Physics cross-validations have passed. ]

[ But it must be remembered: passing the tests does not equal this being the truth at all. ]

[ The current G is most likely only an advanced phenomenological law established within the limited sample range currently known and accessible to me. ]

[ Once entering more extreme relativistic parameter spaces such as black hole accretion disks or neutron star surfaces, G is very likely to fail instantly. ]

[ When facing different, especially open cosmic boundary conditions, the equation form of G may require extremely painful topological corrections. ]

[ The current G can only be called Version 1. ]

[ It is merely a footing starting point for mankind on the road to understanding complex system phase transitions, and is definitely not the final answer. ]

Finished writing and saving the log, he walked over to the east wall, and beneath [RECON-VC-01] (substation remanent magnetism observation) which had changed his cognitive trajectory, he newly wrote a line of characters.

[ THEORY-G-01: Gating Parameter (G-Index) Definition V1, Three Cross-Validations Passed. ]

[ Scope of Application: Conventional magnetic reconnection plasma systems with multi-channel coupling characteristics. ]

[ Unresolved Achilles' Heel 1: The mathematical form of Channel Six (macroscopic multi-loop network collective response) is too complex and has not yet been successfully incorporated into G's logarithmic framework. ]

[ Unresolved Achilles' Heel 2: The critical threshold G_c is merely derived based on statistical fitting, and extremely lacks rigorous mathematical Physics derivation from first principles. Why is it 2.0 instead of π or e? ]

[ Unresolved Achilles' Heel 3: The asymptotic behavior of G under extreme parameters approaching infinity or infinitesimal is unknown. ]

Four lines: the first line was a dazzling victory result, while the subsequent three lines were all new pits dug for the G parameter itself.

This was probably the norm of scientific research. Whenever a truly valuable new theoretical tool was invented, while solving an old problem, it would often open up even more new problems in one breath, like Pandora's box.

However, in Jiang Lin's view, a good scientific tool should inherently hack open new battlefields while cutting off old mazes.

If a Physics theory was only responsible for perfectly solving current problems without deriving any new unknowns, then either it had hidden logical fallacies, or it was a moribund dead learning abandoned by the times.

Only tools that could continuously give birth to and simultaneously open up brand-new Physics pictures were sharp weapons truly capable of driving humanity's cognitive boundaries forward.

The G parameter might not be perfect, and could even be said to be riddled with holes.

Perhaps a hundred years later, it would be ruthlessly swept into the dustbin of history by a more elegant, higher-dimensional new tensor tool invented by later generations.

But at least at this moment, in this desolate Wasteland Outpost, it brazenly opened up three brand-new directions of Physics.

Based on this point alone, it was worth continuing to pursue.

In October of the twenty-seventh year, the autumn wind gradually rose.

Jiang Lin entered a long and trivial sorting-out period.

He digitally archived in chronological order all the channel coupling diagrams he had drawn during countless sleepless nights over the past full year, all those G_1 manuscripts crumpled into balls after being proven wrong by him, all the underlying data tables for each cross-validation of the G parameter, and those interrogation record logs wracking his brains against counterexamples.

He established a huge main archive folder: [ THEORY-G-01 ]

Subfolder structure—

[ 01 _ Six-Channel Phenomenon Decomposition ]

[ 02 _ Coupled Response Matrix Deduction ]

[ 03 _ Failed Attempts _ Ruins of G_1 ]

[ 04 _ Algebraic Definition of G Parameter Version 1 ]

[ 05 _ Three-Item Cross Blind-Test Validation Dataset ]

[ 06 _ Abnormal Counterexample Interrogation and Defense Records ]

[ 07 _ List of Unresolved Fatal Issues ]

Inside every subfolder, detailed derivation processes and records of intermediate states of thought were attached.

After finishing the organization, he placed the folder [ THEORY-G-01 ] right in the center of the workstation desktop, in the most conspicuous position.

Below this central folder, theoretical folders of six old schools were arranged like stars surrounding the moon.

[ MR-SP-01 ], [ MR-PK-02 ], [ MR-NUM-03 ], [ MR-PLM-04 ], [ MR-EDR-05 ], [ MR-TURB-06 ].

In the upper right corner of the screen, the Physics origin of all crazy ideas hung aloof— [ RECON-VC-01 ] (substation remanent magnetism observation).

The new [ THEORY-G-01 ] sat squarely in the center.

This was not just the placement of icons, but an externalized projection of the cognitive architecture of Physics in Jiang Lin's brain.

At the center was the brand-new theoretical attempt born in the Wasteland; below it was all the human scientific heritage it relied on, absorbed, and attempted to unify.

The upper right corner was the silent cosmic nature, giving him true revelations through the ruins of disaster.

With his hands crossed behind his head, Jiang Lin quietly looked at the layout structure full of internal logical tension on the screen.

He did not arrogantly feel that he had already solved the century-old problem of magnetic reconnection that had plagued humanity for more than half a century.

But he had a genuine sense of groundedness; he felt that for the first time on this research map, he had left a pencil mark of his own.

Time flies.

From the twenty-eighth year to the thirty-second year.

A full five years quietly elapsed in the wind and sand of the Wasteland.

During these five years, Jiang Lin displayed hair-raising scientific concentration.

He did not eagerly and impatiently go straight to hard-crack the three extremely tempting unresolved mathematical problems left by the G parameter.

Instead, he chose to settle his mind and do a piece of coolie work that seemed extremely clumsy to smart people, but was the most fundamental in the construction of a rigorous scientific system.

He was going to forcibly apply the G-gated index to every single magnetic reconnection observation and experimental literature sample published in human history that could be scraped from the literature library of the hard drive, conducting the wildest universal stress test.

Not a dozen or so.

Nor dozens.

It was everything, an exhaustive analysis leaving no blind spots.

Eighty-two Class A core papers, four hundred and twenty-one Class B key papers, plus the massive Class C index library, as long as every case record whose physical parameters could be pieced together and traced through the lines.

After an initial rough screening, the statistical table of Jiang Lin shockingly piled up over 1800 real physical occurrence scenarios.

Flares of various levels erupting from the solar chromosphere.

Complex magnetospheric substorms triggered by the compression of the magnetotail of the Earth by the solar wind.

Dozens of tiny electron diffusion region reconnection events detected by the MMS constellation satellites at the magnetopause of the Earth.

Tearing modes erupting in dozens of tokamak devices around the world.

Sawtooth collapse phenomena occurring in the core of fusion plasmas.

Experimental reports of two-dimensional reconnection devices generated by pulsed discharge in major university laboratories.

High-resolution Plasmoid numerical simulation grid data run by supercomputing centers consuming millions of machine hours.

Physics experiments of reconnection under a turbulent background with artificially applied external disturbances.

All these phenomena from all corners of the world, spanning from astronomical scales to workbench scales, were ruthlessly thrown by Jiang Lin into a huge index database table driven by Python.

Facing this massive amount of data, Jiang Lin did not eagerly let the computer directly draw a unified scatter plot.

A chart drawn that way would be polluting good data with garbage data.

The first step taken by Jiang Lin was tiered data cleaning.

In the last column of that huge index table, he added a field name that determined the life or death of the samples.

[data_quality (Data Confidence Level)]

Class A samples: The literature must simultaneously clearly provide a clear basis for the Lundquist number calculation, an undisputed current sheet length, an ion inertial length based on actual measurements, a turbulence intensity estimate supported by spectral analysis, unambiguous system boundary conditions, and most importantly, the definition of the reconnection rate in the paper must be rigorously traceable in physical formulas, rather than just empirical values lacking definition in the text.

These conditions were perversely strict, and samples meeting them were as rare as phoenix feathers.

Out of more than 1800 scenarios, after reviews one by one by Jiang Lin like holding a magnifying glass, only a pathetic three hundred or so were left in the end.

Class B samples: Papers were allowed to have missing or ambiguous secondary parameters, but the missing parameters had to be able to be reverse-derived by Jiang Lin using basic plasma hydrodynamic equations from other physical quantities given in the paper, and the error limit band of this reverse derivation had to be clearly written in the table.

This type of sample was the mainstay of the academic world, with the largest quantity, and after sorting, there were about seven hundred plus.

Class C samples: Data was severely missing, and only rough estimations on the order of magnitude could be made.

For example, many observation papers grandly gave the observed reconnection rate, but completely failed to give the macroscopic length of the current sheet.

Or some experimental reports only provided a colored geometric schematic diagram without providing any characteristic scale ruler for peers to review and normalize.

These samples were kept by Jiang Lin in the index library as a reference, but were forbidden from entering the fitting calculation of core parameters.

Class D samples: Directly eliminated.

Reasons included: some reconnection rate definitions were completely out of dimension with other general papers and lacked comparability entirely, some had terribly explained experimental boundary conditions, and some had key parameters that could not be recovered.

There were also some early numerical papers that, limited by their era, did not explain artificial dissipation and mesh processing in enough detail to enter the same statistical caliber.

In the bitter winter of the thirtieth year, heavy snowflakes blocked the windows of the Stone House.

Beside the warm hearth, Jiang Lin finally began the moment of data visualization.

He decided for the first time to use only Class A samples to draw the chart.

The code ran, and the image was generated.

X-axis: The pride defined by him—the G-index value.

Y-axis: The measured dimensionless reconnection rates reported in those top papers.

When the blue scatter plot popped up on the black-background screen, the finger of Jiang Lin hovered over the mouse, staring at the screen for a very, very long time.

What appeared on the screen was not the kind of textbook-perfect narrow curve expected by him in dreams, capable of deterring the entire academic world as an absolute truth.

Nor was it a pretty straight line that could be described by a simple linear equation.

That was a cloud.

A very thick, scattered nebula of data points filled with observation errors from the Real World and huge variances brought by different system endowments.

But the eyes of Jiang Lin, piercing through this seemingly chaotic cloud layer, keenly captured the soul deep within it.

This cloud had an extremely clear macroscopic physical direction.

For samples with a large G, the scatter cloud as a whole rose sharply, the values of the reconnection rate were absolutely on the high side, and they burned wildly.

For samples with a small G, the scatter cloud clung tightly to the bottom like a pool of stagnant water, the reconnection rates were generally sluggish, and they dissipated slowly.

For samples with G approaching the critical interval, their reconnection rates seemed to be constrained by some mysterious force, densely squeezing between the narrow horizontal strip channel of 0.05 to 0.15 on the Y-axis.

This was definitely not a seamless mathematical proof.

Nor could it even be considered exclusive strong evidence; the variance was too large.

But this was indeed a statistical phase transition trend presented in a library of more than three hundred of the purest Class A human Physics samples.

Jiang Lin took a deep breath and did not rush to press the save button to keep this final chart.

He was going to continue applying pressure.

He switched out the code, replaced it with Class B samples containing more variance, and ran it again.

Because Class B samples were large in number and carried reverse-inference errors, the cloud layer on the chart instantly became thicker, the dispersion expanded sharply, and some unruly outlier points even drifted extremely far, as if mocking the fragility of the theory.

However, if you squinted your eyes and took two steps back, that overall diagonal Physics evolutionary direction of fast, medium, and slow, like a spine, still supported the center of the chart without breaking.

Immediately afterward, he fiercely overlapped and merged the Class A and Class B samples.

Over a thousand data points slammed onto the chart.

The trend remained rock-solid.

Finally, he took a deep breath and overlaid those reference-only Class C samples in dim gray at the very bottom layer.

The entire grand chart instantly became even messier.

Densely packed data points intertwined together, just like a chaotic nebula filled with interstellar dust in deep space, making one feel dizzy at a single glance.

Yet even under such extreme violent interference, the overall outline of that cloud was still not completely broken up.

It still stubbornly spanned the coordinate system, roughly along the same direction from small to large, from flat to sudden rise.

Time came to the early spring of the thirty-second year.

The Wasteland ushered in a new round of recovery.

In front of the workstation, Jiang Lin typed the final title for this ultimate nebula chart that had taken five years and gathered half a century of human wisdom and fallacies.

[G-index V0.1: trend only (Gated Index V0.1: Displaying Global Statistical Trends Only)]

Afterwards, below the judgment, he wrote down four self-explanations regarding the huge variance of the chart in a calm and objective tone.

First, the emergence of this tenacious trend very likely meant that the G-index, on the underlying algebraic topology, had indeed fortunately captured the cross-scale multi-channel phase transition gating effect in the plasma universe.

Second, the huge data dispersion in the chart inevitably stemmed from the complex parameter reverse-derivation theoretical error of Class B samples.

Third, the dispersion might also come from the inconsistent internal use of the dimensionless reconnection rate in fluid dynamic definitions by authors of different eras when writing papers.

Fourth, at the deepest possibility, this dispersion indicated that the current G-index V0.1 version had serious theoretical flaws; it omitted a key Physics channel sufficient to change local weights, especially [Channel VI: Multi-loop Collective Response Network], which had not yet found a mathematical way to be incorporated into the formula.

These four explanations prevented it from being directly falsified by huge data errors.

But these four explanations also announced that its current form was at best an oceanic map drawn by navigators in the early Age of Discovery based on experience and a broken compass.

Vague, crudely crafted, full of spine-chilling statistical noise, and even some islands were drawn crookedly.

But fortunately, the general direction it pointed to, the route leading to the new continent of Physics, was not completely wrong.

On the afternoon of September 17th in the thirty-second year.

The anniversary exactly five years after the definition of the G-parameter by him.

In the distance, the indicator lights of Observation Point A and B carrying the Wasteland environmental data were still tenaciously recording the passage of time.

Inside the Stone House, on the high-definition screen of the workstation, the chaotic scatter plot composed of blue and gray spots, gathering 1800 samples, was quietly resting there.

Jiang Lin leaned against the somewhat peeling computer chair, gazing deeply at the nebula framed between the X-axis and Y-axis on the screen.

Amidst the long gaze, he seemed to suddenly have an epiphany about some deeper scientific research destiny.

In the long years to come, he could no longer continue to expand the sample size of the index library like these past five years.

Even if the number of samples increased by another ten thousand, one hundred thousand, filling the entire chart airtight, it would never undergo a leap from quantitative change to qualitative change, nor could it extract and sublimate a chaotic cloud established on statistical probability into a pure mathematical theorem connected by strict equations.

Empirical trend fitting based on macroscopic data had reached the end of human cognition at this step.

If he truly desired deep down to know whether this self-crafted G-index had touched upon nature's unshakeable laws of Physics, he had to take a knife to it.

Strip it from the grand narrative and dismantle it into a geometric model free from any experimental noise interference.

The current G-index vainly attempted to contain six violent Physics channels simultaneously; its scope of application was too grand, its data sources were too dirty, and it bore too much of the wild engineering flavor of Outposts repairing wind turbines.

In that sanctuary of Physics called truth, what could truly be gripped tightly by emotionless mathematical logic and withstand hundreds of years of scrutiny was never some grand comprehensive model.

The gaze of Jiang Lin gradually locked onto one of those six channels.

The Plasmoid evolution channel.

Two-dimensional incompressible resistive MHD.

Long and thin current sheets with finite aspect ratios.

The energy method.

A priori estimates in Sobolev spaces.

The rigorous energy functional variational method.

As well as those analytical a priori estimates in Sobolev spaces hidden in high-dimensional topology.

Only by using these pure mathematical weapons to break through it at this narrowest point could the G-parameter be endowed with a true soul.

Jiang Lin moved his mouse and closed the scatter nebula chart that had cost him five years of hard work without any reluctance.

Open the research log.

[Thirty-second year archival summary]

[G-index V0.1 did show an undeniable strong statistical trend in the full-scale stratified sample database.]

[Phase conclusion: Its underlying phenomenological validity has not been falsified at present.]

[Restriction warning: The trend existing in such high-credibility samples is merely a statistical compromise, by no means a rigorous theoretical proof of first principles. It is currently still a non-universal crude tool, and it is strictly prohibited to blindly extrapolate it to unknown extreme parameter space, especially with relativistic effects.]

[Unresolved known landmines: The topological response of Channel VI is not included, critical thresholds lack analytical derivation, extreme parameter interval behavior is unknown, and the algebraic form of the turbulent term dealing with non-monotonicity lacks mathematical uniqueness.]

[Strategic next action, and the final action: Abandon global fitting. From the complex G-parameter system, extract only that narrowest door crack (the ideal current sheet tearing phase transition under resistive MHD conditions).]

[I will no longer use statistical data to support it.]

[I will use pure mathematics to prove it.]