The night was as dark as ink, like a vast piece of velvet tightly wrapping the entire city. This darkness was boundless, not a single glimmer of light could penetrate its curtain. Yet, at the city's highest point, an apartment emitted a faint glow, like a lonely star in the night sky.
The walls of this apartment were occupied by bookshelves and enormous display screens. The bookshelves were filled with all kinds of books, from ancient classics to the latest technological works, a dazzling array. The screens flickered with various charts and data, seeming to tell some mysterious story.
Yue'er sat curled up on a spacious sofa, her legs tucked under her. The sofa was submerged in books and draft papers, like a small mountain of knowledge. Her fingers unconsciously twirled a strand of fallen hair, but her gaze penetrated the apartment's floor-to-ceiling window, staring at the distant streets below where car lights flowed slowly like molten lava.
Those car lights shuttled through the darkness, like flowing rivers of light, sketching the blurred outlines of the city's streets. However, Yue'er's consciousness had long departed from this mundane scene. Her thoughts, like wild horses breaking free, galloped through another universe composed purely of abstract structures and logical relationships.
In that universe, there were no concrete objects or images, only countless lines and symbols intertwining and entangling, forming an intricate network. In Yue'er's mind, these lines and symbols constantly transformed and combined, forming various marvelous patterns and logical relations. She seemed to be in a mathematical maze, exploring its mysteries.
Before her hovered a massive light screen, like a boundless universe within which symbols flowed like waterfalls. These symbols were not ordinary code but mathematical poetry, weaving together in a unique way to form the language describing the deepest fabric of the universe.
Lately, she had been attempting to fuse non-commutative geometry with topological field theory—two seemingly unrelated theories—hoping to explain the extremely faint traces of fiber bundle structures that might have been left during the universe's early inflationary period. This was an immensely arduous task, requiring her to delve deeply into complex mathematical formulas and theories while facing loneliness and uncertainty.
Yet, despite the difficulties, she was deeply immersed in it. Every breakthrough and discovery filled her with unparalleled excitement, as if she were unraveling the universe's mysteries.
Just as she was fully absorbed in thinking about how to further advance this research, she suddenly sensed something amiss. Her fingers tapping on the virtual keyboard involuntarily paused, her gaze drawn to a subtle change on the light screen.
In one corner of the screen, a set of programs that had been running silently in the background suddenly popped up a faint alert. This alert was not an alarm but a "ripple"—an almost negligible statistical fluctuation deviating from the standard model.
Though tiny, this "ripple" held significant meaning for her. It might indicate the presence of some undiscovered anomalous fluctuations in the Cosmic Microwave Background (CMB) radiation, and these fluctuations could be related to the fiber bundle structure traces she was studying.
An ordinary person might simply dismiss this phenomenon as noise, but Yue'er was different. Born into a family of mathematicians, she possessed an extraordinary intuition for "patterns" and "anomalies." As she gazed at the waveform of that "ripple," a strange glimmer flashed in her eyes, as if it were not merely an ordinary fluctuation but contained a unique "elegance."
Yue'er straightened her posture, her previously somewhat lazy sitting position instantly becoming upright. A sharp light flickered in her eyes, as if to penetrate the waveform on the screen and reveal the secrets hidden within. Her hands moved like nimble butterflies, swiftly and precisely swiping across the light screen, expertly calling up deeper analytical tools.
"Interesting..." Yue'er murmured softly, her voice almost inaudible in the quiet room yet carrying an indescribable excitement. This tiny "ripple" had piqued her interest so intensely that she decided to explore it from the most fundamental tool—Fourier Analysis.
Anyone who has studied engineering mathematics or signal processing knows that Fourier transform is a powerful mathematical tool that decomposes a time-domain signal (such as a sound wave changing over time) into a series of sine waves with different frequencies and amplitudes. It's like a complex symphony being decomposed into pure tones of different instruments and pitches. Through Fourier transform, we can see the "main melody" and "harmonies" hidden within the signal, thus better understanding its essence.
Yue'er took a deep breath, focused her mind, and directed all her attention to that faint "ripple." Using her exceptional skills and experience, she performed an ultra-high-precision Fourier transform on this "ripple."
As she worked, the spectrum of the "ripple" gradually appeared on the light screen. This was an image with frequency on the horizontal axis and energy on the vertical axis, showing the energy distribution of the "ripple" across different frequencies.
Sure enough, as Yue'er had anticipated, apart from the ubiquitous noise background, an extremely faint spike appeared in a very specific high-frequency region. This spike was unusually harmonious and sharp, forming a stark contrast with the surrounding noise—clearly not a product of random noise.
However, Yue'er was not satisfied. She knew that while Fourier analysis excels at processing stationary signals, it might lose some important temporal information for non-stationary signals like this "ripple" that appear instantaneously.
When exactly did this spike appear? How long did it last? These questions were crucial for understanding the nature of the "ripple." Yue'er decided to delve deeper, not missing any possible clues.
Thus, she resolutely decided to introduce the powerful tool of wavelet analysis. If Fourier transform uses eternal, unchanging sine waves as a "ruler" to measure signals, then wavelet analysis employs a "microscope" that can zoom and move. This "intelligent microscope" not only clearly observes the frequency components of a signal but also precisely locates the time when those components occur.
After careful consideration, Yue'er selected several mother wavelet functions, then aimed this "smart microscope" at that segment of data, beginning a meticulous scan. Time passed minute by minute, Yue'er's tension growing as she stared intently at the screen, afraid of missing any important detail.
Finally, the results emerged. Yue'er couldn't help but gasp, holding her breath as she gazed at the wavelet coefficient map before her. The image clearly showed that the strange spike appeared within an extremely brief time window, lasting only milliseconds! Even more astonishing, under the wavelet scale, the waveform of this spike displayed a staggering self-similar structure—a nascent fractal!
A fractal? Found in the deepest background radiation of the universe? This discovery shocked Yue'er. She realized she might have touched upon an unprecedented scientific realm.
Her heartbeat slightly accelerated, as if an invisible force were gently plucking her heartstrings. This feeling was both unfamiliar and familiar, stirring doubt within her.
It didn't seem as straightforward as a natural product but more like something meticulously designed, deliberately arranged. Like a secret hidden deep within the folds of spacetime, revealed only at specific moments.
This "signature" seemed to be a unique piece of information, skillfully woven into the wrinkles of spacetime. It might be a hint, a guide, or perhaps the prelude to some significant event.
She quietly felt this accelerating heartbeat, trying to decipher its meaning. What did this "signature" truly signify? Was it connected to her destiny, or merely a coincidental occurrence?
Regardless, this mysterious "signature" had captured her attention, igniting her curiosity. She decided to follow this feeling, to explore this secret hidden deep within spacetime.
To validate this nearly crazy idea, she knew that relying solely on existing mathematical knowledge was far from enough; she needed stronger and more profound mathematical tools for support. Thus, without hesitation, she plunged into the study of differentiable manifolds.
Differentiable manifolds—this concept might seem somewhat unfamiliar to the general public, but in the mathematical realm, it is an extremely important concept. Simply put, a manifold is like a space that locally resembles the ordinary Euclidean space we're familiar with, but viewed as a whole, it may be curved, even possessing very complex topological structures.
Our universe can actually be seen as a four-dimensional spacetime manifold. This means that the three-dimensional space and time in our daily lives can be uniformly described as different dimensions on this manifold.
Yue'er's goal was to transform that brief "ripple" and its displayed fractal characteristics into a local vibration of a tiny "fiber bundle" on this enormous manifold through mathematical modeling. This task was undoubtedly formidable, as it required a deep understanding of differential manifold and fiber bundle theory and the skillful application of these theories to construct a reasonable model.
Fiber bundles—this is a mysterious mathematical concept, like a hidden code in the universe, revealing certain intrinsic degrees of freedom at each point in spacetime. Like a comb, its base represents spacetime, while each tooth is a "fiber" attached to that point; these "fibers" can be various possibilities in internal spaces like direction, phase, etc.
Electromagnetic fields, weak and strong nuclear force fields—these seemingly complex and elusive physical phenomena, from the perspective of fiber bundle theory, exhibit a concise and elegant description. Her thoughts raced like lightning; concepts that would daunt ordinary people—Chern-Simons theory, curvature forms, connections—flowed naturally from her fingertips like clouds and water, transforming into lines of elegant equations.
She immersed herself completely in this mathematical exploration, trying to solve this puzzle: What kind of "gauge field" and what kind of "excitation" could produce such a peculiar and brief vibrational pattern? It was like searching for an exit in a vast maze, each step requiring precise calculation and keen insight.
Just as she was fully engrossed, suddenly, her personal terminal glowed softly, as if a mysterious signal were summoning her. Curiously, she opened it and found an encrypted message. The sender was someone she never expected to contact her at this moment—Mozi.
Mozi—that person she had met at several top academic conferences—had left a deep impression on her. His eyes were sharp as an eagle's, seemingly capable of seeing through everything; and his expression, always tinged with a hint of disdain for existing theories, made him stand out even more. He was a quantitative trading expert with remarkable achievements in the financial field.
Yue'er looked at this brief and direct message, feeling a mix of confusion and surprise. The mentioned anomalies in financial time series and nonlinear dynamic characteristics were familiar territory to her, but their similarity to the mathematical model in her paper on stochastic resonance at cosmological scales three years ago struck her as unexpected.
She couldn't help but recall that paper—an important research achievement in her cosmological work. She had spent considerable time and effort explaining stochastic resonance phenomena in the universe through complex mathematical models. Now, Mozi was actually linking financial time series to her research—truly unimaginable.
Yue'er froze, her mind racing with various thoughts. Financial time series? Cosmological stochastic resonance? What connection could there possibly be between these two? She decided to reply to Mozi, to see what exactly he wanted to discuss.
Two seemingly unrelated fields, showing similar mathematical patterns?
She looked again at the "ripple" on the light screen, nearly drowned in the vast cosmic noise, then at Mozi's message.
A strange sensation seized her. It felt as if she were standing at the entrance of an infinitely vast maze, having just picked up two key fragments that seemed to come from different dimensions yet fit together perfectly.
Outside the window, the city remained bustling, traffic still flowing silently. But in Yue'er's mathematical universe, a brand-new movement—one that could all existing knowledge—had just sounded its first, faint yet clear note.
She took a deep breath, her fingers hovering over the reply interface. After a brief hesitation, she typed:
"Mr. Mozi, this is interesting. Coincidentally, I've also discovered some... perhaps not coincidental 'fluctuations' on my end. How about College Cafe tomorrow at 3 PM?"
Pressing send, she felt a long-lost shiver—a mix of immense curiosity and faint unease. It wasn't fear but the excitement of an explorer about to step into unknown territory.
Tonight was destined to be sleepless. Her battlefield wasn't in this visible world but in that world constructed of equations and symbols—a world that might be closer to reality. She needed to catch that "angel in the wave equation," to see what mysteries, or perhaps crises, it foretold.