Through observation and reflection, we can divide the mental process of deepening understanding from accepting knowledge to the highest level of “enlightenment” into four stages: knowledge, understanding, consciousness, and enlightenment. The overall cognitive function is continuous and monotonically increasing, but there exists a quantum leap stage between accumulation and consciousness. Following axiomatic thinking, the definitions of these four terms must first be clarified.
First Level: Knowledge#
Simply put, knowledge is correct information stored in the mind. In other words, all correct information stored in the mind is called knowledge, making knowledge a very broad term. “Correct” information fundamentally means information that corresponds to reality, although it may not yet be verifiable—this is merely theoretical.
Knowledge can come from objective experience (including personal experiences) or from mental reasoning and generation. The structure of knowledge is complex with many levels.
Second Level: Understanding#
Here “understanding” is used as a noun, representing understood knowledge, also called living knowledge. For a piece of information (i.e., knowledge), if more related information is obtained, an information network or system centered on that information is formed. At this point, that information is called understood information, or understood knowledge, or living knowledge.
Of course, understanding of knowledge also has degrees. In fact, there’s no absolute boundary between basic knowledge and fully understood knowledge—it’s a continuous, ascending process of distribution. A prominent feature of knowledge understanding is the degree of systematization of knowledge.
Regardless, both basic and understood knowledge are merely stored as external knowledge and cannot yet be called one’s own knowledge. They may still be “forgotten” (understood knowledge being “forgotten” actually means sinking from memory’s cerebral cortex into the depths of the mind). However, these forgotten parts don’t truly disappear—they continue to exist as nourishment for the next stage.
Third Level: Consciousness#
After understood knowledge accumulates to a certain stage, an internal leap or sublimation may occur, manifesting as “rumination” and awakening of existing understood knowledge—a self-rediscovery of existing knowledge, called conscious knowledge.
Conscious knowledge has several major characteristics:
This knowledge, having been rediscovered by oneself, has become internal information, to the point where one no longer remembers its source, feeling as if it’s knowledge one has always possessed;
Conscious knowledge can be applied effortlessly, meaning it can be spontaneously and consciously used in unconscious, natural states following thought, without requiring conscious driving;
Conscious knowledge no longer involves issues of forgetting, memory, and recall. Conscious knowledge seems to exist not in the cerebral cortex but below it, forming fixed structures. Compared to non-sublimated knowledge, the storage state of conscious knowledge can be likened to data in computer memory—memory information can be directly accessed, while external storage information must go through memory (equivalent to conscious driving) before use.
Fourth Level: Enlightenment#
Enlightenment can also be called awakening, realization, insight, or synthesis. It goes deeper than consciousness, manifesting not only as “rediscovery” of knowledge but also involving deeper discovery sensations. This “discovery sensation” means that what enlightenment produces isn’t necessarily substantial inventive or creative thought, but rather a form of cognition with emotional and psychological coloring, a passion that can often only be experienced but not completely “expressed”—the so-called “can be understood but not spoken.” Using a Buddhist term, this state is called “prajna.” Because it carries internal emotionality and isn’t ordinary information, “the Tao that can be spoken is not the eternal Tao”—once expressed in language, this enlightenment becomes ordinary information, at most rising to understood information through explanation. Therefore, lectures, reports, and similar activities can at most facilitate the occurrence of consciousness or enlightenment, but cannot directly impart enlightenment like ordinary information transfer.
In summary, enlightenment is the advanced stage of consciousness. It has no clear boundary with consciousness but is a continuously distributed higher stage. It’s comprehensive knowledge that has sunk deeper into the depths of the mind (no longer single knowledge or simple knowledge sets, but their integrated embodiment, like sediment at the ocean floor—belonging to new “mineral deposits”). What is “enlightened” and what is “conscious” are both “memory” knowledge, truly belonging to oneself. Enlightenment is a thinking tool, a methodology. It’s the most essential part of knowledge, a highly concentrated and generalized embodiment of laws. It’s the product of integrating all the knowledge you possess. If understanding systematizes knowledge within a discipline, then enlightenment connects and analogizes knowledge between disciplines, providing mutual validation and reference. In ancient times, mathematics, physics, and philosophy were once unified, and we can broaden this further to include art. Through enlightenment, scattered and mixed knowledge fragments from different disciplines are combined into an organic whole.
A person’s consciousness and enlightenment “abilities” are latent within themselves. They can only accept inspiration, induction, stimulation, and development from external factors, but cannot be transferred, transcribed, or copied. On the other hand, the “background” for developing consciousness and enlightenment also lies within oneself—the long-term accumulation of knowledge.
Finally, enlightenment and inspiration are not the same thing. Inspiration can manifest as creation and invention of new things, appearing as point-in-time flashes, unpredictable and declining with age. Enlightenment mainly manifests as deeper, more abstract sublimation of existing knowledge, with expectability. We can only say it approaches inspirational creation, but isn’t yet inspirational creation.
Therefore, learning can only acquire general information (general knowledge). With good teachers and books as guides, at most it can rise to understood knowledge. In other words, all that learning can acquire is external information. A person’s consciousness, enlightenment, and other advanced knowledge cannot be directly obtained through learning. This is precisely what’s meant by “The master leads you to the door; cultivation depends on the individual.” Learning knowledge can only lay the foundation for consciousness and enlightenment, but only through the quantitative change of learning accumulation can the qualitative change of consciousness and enlightenment occur. This is the fundamental relationship between learning and wisdom (where wisdom is primarily manifested through consciousness and enlightenment abilities).
Those who possess enlightenment, or who have entered the enlightenment period, achieve vastly different levels of understanding in the same learning process. “Reviewing the old to know the new” exemplifies this principle. There’s a clear example: mathematicians throughout history have left countless heartfelt words about mathematics that today’s students find amazing. These are their insights and inner voices about mathematics, which should touch our soul’s keyboard repeatedly, causing tremors and resonances. But without entering the enlightenment period, one might treat them as ordinary information or knowledge, even mistakenly thinking these mathematical masters are showing off or advertising for mathematics. Such misunderstandings are common, but there’s no need to clarify them. Once you reach that realm, you’ll naturally understand. If you don’t learn to that level, explanations won’t help you understand.
Only those with enlightenment can easily be induced to produce enlightenment. Enlightenment is a mineral deposit everyone possesses, but different people have different depths (spiritual aptitude), and even the same person has different depths at different ages. Generally speaking, undergraduate level is the earliest starting point for the enlightenment period, while doctoral level is the optimal stage for enlightenment. But different people will certainly vary.
Generally speaking, during elementary and middle school learning, human memory is at its strongest, but this stage belongs purely to memorizing ordinary knowledge, purely in the category of rote learning. Entering high school and undergraduate levels, our rote memory ability declines, but comprehension ability greatly improves. During this stage, we’re mainly busy with knowledge storage and understanding—the most active period for comprehension-based memory. Some gifted people might begin developing enlightenment seeds during this period. Eventually, through continued learning, another more important learning characteristic (thinking characteristic) gradually strengthens—entering the “enlightenment period.” At this time, they naturally and unnaturally “ruminate” on already familiar knowledge, producing new feelings and deep-level consciousness. The characteristic is: once knowledge enters enlightenment thinking, it naturally becomes one’s own, while knowledge that hasn’t reached the enlightenment level gradually gets forgotten over time.
This might sound mystical, but that’s how it is. I, lacking talent, was fortunate enough to achieve enlightenment in my sophomore year. I’m deeply grateful for the rich accumulation from birth to middle school, and deeply regret squandering time from high school to freshman year.
Although enlightenment cannot be expressed in words, I still hope to share some small insights from learning. Though I know that once spoken, these can only become understood knowledge.
In Mathematics:
Understanding how the entire mathematical edifice is built with the bricks of sets, grasping the concept of mapping. Understanding the most basic relationship—order relations. Experiencing concepts of various spaces and dimensions.
In All Natural Science Disciplines:
Experiencing unity of opposites (the essence of motion and rest). Experiencing the concept of order (entropy, directionality). Experiencing the universality of causality (mathematical order relations extended in logic). Experiencing the principle of least action (a concrete manifestation of order thinking).
In Programming:
This is actually similar to mathematics—mastering the essence of mapping makes programming seem so simple. The core thought and function of all programs: transforming given input through a series of mapping transformations into required output. Secondary level includes: divide-and-conquer thinking (a concretization of least action).
Good articles provide resonance and inspiration from the deepest levels of the soul. Thanks to “Mathematics and Its Understanding”—most text here derives directly or indirectly from this book.
This article commemorates a leap in cognitive level.
Thanks to Teacher Chen Zhiyuan for his inspiration and teachings in my academic journey.