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Muoq Muon Zlielq Sien, Galq Hal Gluo Thlien
Gluoq Marh Kieh Hurnq, Thalh Thlan Vuon Vuonh
Dhuoq Lieq Kirn Glieh, Glur Yel Zlan Glieq
Guon Gielh Yenh Thlieq, Thien Thlan Lielq Glieq

In loneliness, ignorance, surrender, sentience— the dog, monkey, boar, ape—
Chases, reacts, abandons, confuses— and the beast whirls in winds and maddens.
In solitude, abstraction, suffering, sapience— the nautilus, squid, octopus, jellyfish—
Observes, ponders, responds, elucidates— and the sage infers in rhythms and wisens.

☰

Muoq yeq lieq mie, thirn zrq krq zar
Muon mienh bieh glanh, mluoh glarh thirn sar
Zlielq thlienh xlanh dhuoq, thirn klrn kuoq tar
Sien glurq luo murq, mie thielq lielq zlar

In loneliness, it is easily drawn to obsessions that cannot quench the heart.
In ignorance, it covers its face to avoid reflection as fog clouds the mind.
In surrender, the poisons of enmity are born as its heart sinks under bitter waves.
With sentience turbid like ink, its is lead astray without the illumination of credence.

☱

Galq vieh kiel banq, muoq nglrh valq dharh
Hal hlieh muonh dhuonq, muon lirn gluon thirh
Gluo ngurh nie vuoq, zlielq tuo thirn blar
Thlien mlien hienq thalh, yirq thienh nan tir

The dog barks seeking companionship, driven by directionless longing.
The monkey plays in reckless fashion, laughing in a forest of ignorance.
The boar lies wallowing in mud, despair painting over its heart.
The ape’s cries reveal the beast, its wild nature hard to tame.

☲

Gluoq liel valq thieq, glur kuon hlr slar
Marh mluo dhienh hienh, hlien mie han slar
Kieh thlieh lieq lanh, glrn mluo vaq tar
Hurnq luo vuon kieq, mluo thlrq kuon klar

It chases the current unceasingly, pursuing emptiness and noise.
It reacts without intent, a wandering ship that has lost its course.
It abandons the world for the billows, sinking with no escape.
It confuses like a rising wind, a disorderly and raging tide.

☳

Thalh thlie thieh mlieh, xlrq xlirnq valq mur
Thlan vuon hlie klan, thirn dhuonq luo bur
Vuon kuon zlrnh plurq, than zirnq thirn wur
Vuonh zluon slien lanh, luonh lan zlr gurq

The beast follows the four tastes, its desires never abating.
It whirls in winds and grows anxious, thoughts moving like waves.
The wild wind shakes the ego and kills the heart of hearts.
Madness, in its final throes, overflows, and instability results.

☴

Dhuoq mluonh thlan luon, dhurnq thlieh zien thiel
Lieq zienh thie xlie, han hluonh harq kiel
Kirn zirnq balq slrq, xlie blarh xlie yelq
Glieh slurn luo lien, hlan glar luoh liel

In solitude, gazing at mountain ranges, I withdraw from the world to cultivate.
In abstraction, my thoughts are clear as I navigate through a sea of fantasy.
In suffering, I spare no effort crossing mountains and fording rivers with failure as my only friend.
With sapience pure like a lotus, the mysteries are unveiled with the morning dew.

☵

Glur thlan dhuoq thienq, zienq zlarh lienh muoq
Yel mluoq klal lieq, thlrn sien tuolq thuoq
Zlan glan kuoq tan, mlrnh dhaq mluo thluoq
Glieq vuo glieh liel, zlarh mien thluoh wo

The nautilus spirals in solitude, its stillness refining its field of vision.
The squid dances in abstraction, diving deep to escape worldly affairs.
The octopus spreads across the shoals of suffering, its reach endless in inquiry.
The jellyfish floats in currents of sapience, illuminating depths and clearing imperfections.

☶

Guon thlieh mluo lrn, dhuoq tir thirn hien
Gielh lieq thieh harq, dhuonq xlie klrn xlien
Yenh kirn mlieh plieh, glieq mienh vuon sien
Thlieq luo hien nglielq, glieh xlirn zlrnh tien

I observe the world in impartiality as solitude tunes the heartstrings.
I ponder deeply and distantly, breaking free and forsaking worldly attachments.
I respond to suffering without retreat, confronting storms head-on.
I elucidate like a waxing crescent’s crescendo, sounds of sapience resonating through the skies.

☷

Thien zalh thieh xlirn, nglrq mlieh zirnq thliel
Thlan lielq xan nien, xlirnq zluonq pir liel
Lielq hlrn thlrq gar, zieq plarq turq mlielh
Glieq mlien nglielq yen, klie zrq kluon thliel

The sage plays the four tones, the melody never-ending and incomplete.
They infer in rhythms calm and content, endlessly turning, wandering adrift.
The rhythms follow an orderly ascent, each beat dispelling biases and faults.
Wisdom shines with the waxing of the moon, and when it wanes, refinement begins anew.

☯

Mlieh wo wur xlirn mlieh gr mlieh yeq
Zalh wo wur mlieh xlirn gr xlirn yeq
Sien wo wur glieh sien gr sien yeq
Lielq wo wur sien glieh gr glieh yeq

$$\displaylines{
\frac{d味_i}{dt} = 味_{i} − \frac{音_i}{味_i} \\ \\
\frac{d音_i}{dt} = 奏_i − \frac{味_i}{音_i} \\ \\
\frac{d情}{dt} = 情 − \frac{智}{情} \\ \\
\frac{d智}{dt} = 律 − \frac{情}{智}
}$$

$$\displaylines{
P(隨,味) \propto \prod_{i=1}^n \phi(味_i,隨_i)\phi(隨_i,味_{i+1}) \ where \ 味_5=味_1 \\
P(奏,音) \propto \prod_{i=1}^n \phi(奏_i,音_i)\phi(音_i,奏_{i+1}) \ where \ 奏_5=奏_1 \\
P(音,味) \propto \prod_{i=1}^n \phi(音_i,味_i)
}$$

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Overview: The Four Tones and the Four Tastes

Sapientism is one of the primary philosophies of the Thern, and the Gien Glieh (經智) or “Classic of Sapience” serves as its foundational text. It is founded on pivotal concepts referred to as 四音四味 (thieh xlirn thieh mlieh), or “the four tones and the four tastes.” This framework places significant emphasis on distinguishing sapience 智 (glieh) from sentience 情 (sien), advocating for the cultivation of the former and the restraint of the latter. Each tone and taste represents a fundamental attribute of sapience or sentience, associated with specific acts and emblematic animals, serving as metaphorical reminders of each attribute and act.

The term 音 (xlirn), translated as “tone,” symbolizes the orderly universe and self-realization achieved through a sapient mind’s application of logic and rationality. Conversely, 味 (mlieh), or “taste,” epitomizes the experience of the universe and self through a sentient mind, driven by emotions and impulses. While all beings naturally gravitate towards 味 “tastes,” the Thern believe that the pursuit of 音 “tones” are both a goal and a responsibility of the sapient mind, counteracting impulses associated with 味 “tastes.” The ideal being who fosters sapience while purging sentience is termed 仙 (thien) “sage,” whereas one who succumbs to sentience is labeled 獸 (thalh) “beast.”

The Four Tones:

1. 獨 (dhuoq) “solitude” emphasizes self-respect and rational autonomy, the shedding of social biases, and abstention from society and collective conformity. Its animal emblem is the nautilus (螺 glur).
2. 理 (lieq) “abstraction” champions intellectual curiosity and creativity, fostering the capacity to conceptualize and imagine alternative realities, built upon the foundation of 獨 “solitude.” Its animal emblem is the cuttlefish (魷 yel).
3. 勤 (kirn) “suffering” involves pragmatic problem-solving and acceptance of the inevitable challenges and failures that must be endured to constructively interact with the world, built upon the foundation of 理 “abstraction.” Its animal emblem is the octopus (鱆 zlan).
4. 智 (glieh) “sapience” is the culmination of these tones and the realization of their harmony, representing the attainment of wisdom. Its animal emblem is the jellyfish (蜇 glieq).

The Four Acts of Sapience:

1. 觀 (guon) “to observe” is the act to cultivate solitude. It involves removing oneself and striving for impartiality.
2. 究 (gielh) “to ponder” is the act to cultivate abstraction. It involves maintaining an open, curious, and creative mind.
3. 應 (yenh) “to respond” is the act to cultivate suffering. It involves willingness to experiment and strive.
4. 釋 (thlieq) “to elucidate” is the act to cultivate sapience. It involves using the knowledge gained from observing, pondering, and responding in order to refine oneself, ones understanding, and ones questions.

The cycle of tones is often referred to as 仙之侖 thien zie lurn or 侖仙 lurn thien “sequence of the sage” while its practice is referred to as 旋律 thlan lielq “rhythmic inference” or “rhythmic restraint”. The attainment of sapience is not viewed as something static, nor is the idealized concept of the sage viewed as something attainable. Instead, “rhythmic inference” is a neverending and repeating process of updating and improving ones sapience. This cycle is driven by the concept of 律 (or 率) lielq which can be understood both as ‘credence’ and ‘restraint’ or ‘sapient action’.

The Four Tastes:

1. 慕 (muoq) “loneliness” is the inclination to seek love and relationships and to conform. It arises from ones desire for affirmation and validation. Its animal emblem is the dog (狗 galq).
2. 蒙 (muon) “ignorance” is the inclination to seek comfort in materialism, the present, and accepting ones surroundings as truth. It arises from ones desire to indulge in personal biases and sensual pleasures, never questioning oneself or ones surroundings. 慕 “loneliness” unbridled naturally leads to 蒙 “ignorance.” Its animal emblem is the monkey (猴 hal).
3. 絕 (zlielq) “surrender” is the inclination to give up in the face of adversity. It arises from the desire to control the uncontrollable and to avoid the unavoidable, and instead of learning and adapting, one succumbs to anger, fear, and despair. 蒙 “ignorance” unmitigated naturally leads to 絕 “surrender.” Its animal emblem is the boar (豬 gluo).
4. 情 (sien) “sentience” is the culmination of the other tastes and refers to a state of being bounded to instinct and emotions, living in total ignorance and hedonism, an existence no different than that of a beast. Its animal emblem is the ape (猩 thlien).

The Four Acts of Sentience:

1. 逐 (gluoq) “to chase” is the actualization of 慕; it involves seeking relationships, community, and validation.
2. 冒 (marh) “to react” is the actualization of 蒙; it involves acting on impulse and living in the present.
3. 棄 (kieh) “to abandon” is the actualization of 絕; it involves giving up and giving in to destructive emotions.
4. 混 (hurnq) “to confuse” is the actualization of 情; it involves emotional instability and both mental and behavioral incoherence.

The cycle of tastes is commonly referred to as 獸之渦 thal zie xluo or 渦獸 xluo thal “vortex of the beast” while its actualization is referred to as 旋風 thlan vuon “erratic unrest”. 情 is viewed as something that is always present and ultimately unavoidable, but through the active application of rhythmic restraint, it is something that can be mitigated. The cycle of tastes is driven by the concept of 風 vuon which can be understood as both ‘bias’ and ‘instinct’.

Mathematical Models

To understand the models given in the classic, we can first outline each variable. First, we define the flavors (味) and tastes (音) and their respective actions (隨, 奏) as sets.

$$
\displaylines{
味 = \{慕,蒙,絕,情\} \\
隨 = \{逐,冒,棄,混\} \\
音 = \{獨,理,勤,智\} \\
奏 = \{觀,究,應,釋\}
}
$$

The first differential equation accordingly models the rate of change in a given taste. Here, 味 refers to the ones level of a taste, i.e. how much they are affected by an undesirable natural tendency; 味易 refers to the rate of change of this affectedness; and 音 refers to the level of the corresponding tone, i.e. how much of a desirable state one has achieved acting as the direct inverse of the undesirable tendency.

$$\begin{align}
\frac{d味_i}{dt} = 味_{i} − \frac{音_i}{味_i}
\end{align}$$

Accordingly, the rate of change of an undesirable natural tendency (d味_i/dt) is modeled as the current level of the natural tendency itself (味_i) minus the level of the corresponding desirable state achieved (音_i), moderated by the sum of ones current level of the natural tendency (味_i). In other words, the more 味​ one has, then the faster that 味 grows. This can be mitigated or even reversed by cultivating the corresponding 音; however, the effectiveness of cultivating 音 is moderated by the magnitude of 味​, meaning the higher ones 味, the more difficult it will be cultivate 音.

The second differential equation models the rate of change of a given tone. Here, an additional variable 奏 is introduced refering to an action or conscious effort for cultivating a corresponding tone.

$$\begin{align}
\frac{d音_i}{dt} = 奏_i − \frac{味_i}{音_i}
\end{align}$$

In this case, the rate of change of a desirable state (d音_i/dt) is modeled as the amount of effort taken to cultivate that sate (奏_i) minus the level of the corresponding undesirable tendency acting against it (味_i), moderated by the sum of ones current level of the desired state (音_i). In other words, the more 奏 one outputs to cultivate 音​, then the faster their 音 grows. This is mitigated by their corresponding level of 味, and if high enough, may even reverse their cultivation; however, the effect 味 on cultivation is likewise moderated by the magnitude of 音 achieved​, meaning the higher ones 音, the easier it will be to cultivate more 音.

The third and fourth differential equations are essentialy the same but refer to the net sum of ones sentience (情 = Σⁿ_i=1味_i) and sapience (智 = Σⁿ_i=1音_i) rather than a specific taste or tone. In other words, 情 refers to ones level of sentience, i.e. the net sum of their undesirable innate tendencies; 情易 (d情/dt) refers to the rate of change of ones level of sentience; 智 refers to ones level of sapience, i.e. the net sum of the desirable mental states cultivated; and 律 (Σⁿ_i=1奏_i) refers to restraint or rationality, i.e. the net sum of efforts and actions expended for cultivating desirable states. Accordingly, the third and fourth differential equations follow the same logic as the first and second equations.

$$\begin{align}
\frac{d情}{dt} = 情 − \frac{智}{情} \\ \\
\frac{d智}{dt} = 律 − \frac{情}{智}
\end{align}$$

In addition to the differential models, a probabilistic model in the form of an undirected graph is given detailing the dependencies of the various tastes and tones and their associated actions. This graph can be expressed as a set of joint distributions that factorize according to a set of potential functions, ϕ. Each factor ϕ defines a local dependency between variables. P(隨,味) details the process of the vortex of the beast and implies a dependency between a sentient action (隨_i) and its corresponding taste (味_i) as well as the subsequent taste (味_i+1), with a wrap around condition (味₅ = 味₁).

$$\displaylines{
P(隨,味) \propto \prod_{i=1}^n \phi(味_i,隨_i)\phi(隨_i,味_{i+1}) \ where \ 味_5=味_1
}$$

Similarly, P(奏,音) details the process of the sequence of the sage and implies a dependency between a tone (音_i) and its corresponding sapient action (奏_i) as well as the subsequent sapient action (奏_i+1), also with a wrap around condition (奏₅ = 奏₁).

$$\displaylines{
P(奏,音) \propto \prod_{i=1}^n \phi(奏_i,音_i)\phi(音_i,奏_{i+1}) \ where \ 奏_5=奏_1
}$$

Finally, P(音,味) details the relationship between these two processes and implies a simpler relationship where each tone and its corresponding taste are directly dependent.

$$\displaylines{
P(音,味) \propto \prod_{i=1}^n \phi(音_i,味_i)
}$$

In other words, the vortex of the beast relies on dependencies flowing from sentient state to action to state, while the sequence of the sage relies on dependencies flowing from sapient action to state to action. Furthermore, the states of the vortex (tastes) are inherently dependent on the states of the sequence (tones) and vice-versa.

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