In the two-body dynamics of Argentine tango, the leader does not generate force; he only schedules it: what he offers is a set of feasible directions, not a single trajectory. The follower appears passive, but is in fact continuously choosing a point within the range that the points of contact allow. The magnitude of the force scarcely determines success or failure; the number and placement of the contact points determine where this pair of dancers can go.
Replace the pair of dancers with a natal chart, and the same shape surfaces. The chart supplies feasible directions, the annual and luck cycles supply external disturbances, and the person is always choosing a point between the two. The only difference is that the dancers can see the contact points, while a person cannot see his own state equation.
I. Knowing Fate: Identification, Not Verdict
The term "knowing fate" is easily read as foreknowledge. In cybernetics, the job it corresponds to is called system identification: first determine what the plant is, then determine what can be observed from the plant.
Ou Yue splits knowing fate into two things. The first is the overall structure of the natal chart, which belongs to the method of principle; the second is the correlation between chart features and real-world events, which belongs to the method of image. The former is structural identification, the latter observation-model identification. Do neither, and the subsequent "using" and "making" have no ground to stand on.
The object of structural identification is the state. Take the male chart of the Ren-wu year, Yi-si month, Wu-zi day, Wu-wu hour: Wu earth as day master, Si fire as the month command, fire and earth travelling together, Si being the Lu of Wu and Wu being Emperor Prosperity; on the water side, Ren is rooted through Zi water at Emperor Prosperity, but Zi water meets two Wu clashes and its root qi is damaged; Yi wood has no root in the branches and must further rely on the constrained Ren water to generate it. The fire-earth side keeps loading, and lacks an outlet.
Wording must be precise. What I said is "lacks an outlet", not "is bad". Once structural description and value judgment are mixed together, the model is immediately void.
Written as equations, the state is the inner-layer distribution of the five phases' strength, the input is the acquired, operable behaviour and environment, the disturbance is the annual and luck cycles, and the observation is real-world events:
x_{k+1}=f(x_k,u_k,w_k),\qquad y_k\sim p(y\mid x_k)Two modelling choices must be stated clearly. First, the observation is not written as a function but as a conditional distribution. The same chart feature may correspond to different events, or the mapping may fail; one-to-many is the norm, and writing it as a function would smooth that away. Second, w_k is an exogenous disturbance, not an input. The annual and luck cycles obey no one's scheduling; using them as a control variable is the most common class of error in controllability analysis.
【Figure: a natal chart split into an inner-layer and an outer-layer block diagram, the inner layer being a distribution of a set of state variables, the outer layer a scatter of the event space, the two joined by a noisy arrow.】
The other half, the method of image, is modelling the observation. The stem-and-branch image categories provide a coarse mapping from symbols to events—Jia wood being "crooked and straight", for instance, corresponds to a class of things that grow upward; relational mapping provides structured channels, the palaces governing distance and precedence, the Ten Gods governing generating and overcoming relations. Only the two together barely amount to an observation equation.
And an observation equation always carries noise. Whether p(y\mid x) is wide or narrow directly determines how much can be done later. The real output of knowing fate is not a conclusion but the width of a distribution.
II. Controllability: First Ask Whether, Then Ask How Hard
Controllability asks a very narrow question: does there exist a set of admissible inputs that carries the state from the current point into the target set? If it exists, the system is controllable; if it does not, no amount of force helps.
After linearization there is a clean criterion. If x_{k+1}=Ax_k+Bu_k, then controllability holds if and only if
\operatorname{rank}\big[\,B\ \ AB\ \ \cdots\ \ A^{n-1}B\,\big]=nIn the expression, each column of B is one input channel. Insufficient rank means that certain state directions simply have no channel to push them. Increasing the gain only saturates the existing channels; it will not conjure a new direction out of nothing.
Back to that case. The missing direction is Geng metal. Fire and earth have intake with no outlet, and a draining channel is needed; if Geng is exposed, Wu earth has a Food-and-Wound outlet for its refinement, Geng further generates Ren, Ren further generates Yi, and only then does the whole chart flow.
Where is Geng? Geng is stored within Si, but is not exposed in the stems. The handiest option is to take it from the annual and luck cycles. The problem is that the annual and luck cycles are not inputs. He is twenty-five now; what follows is Wu-shen and Ji-you, with metal only in the branches, which cannot drain Wu earth; Geng metal being exposed in the stem must wait until Geng-xu at age forty-six.
Twenty-one years. That is no longer the time scale of a control problem; it is a waiting problem.
Plainly: if the only Geng metal channel is supplied by w_k, then over a control horizon whose length is "the most youthful twenty years", the controllability of that direction is close to zero. Not difficult—uncontrollable. The term is underactuated: more state dimensions than independent input channels.
【Figure: a timeline from age twenty-five to age forty-six; the Geng metal channel is broken for the first twenty-one years and only connects at the right end.】
This judgment does not fall on good or bad. It is only a structural statement: given the available input set and the control horizon, the reachable set does not cover the target direction. Change the person, change the horizon, and the conclusion can be entirely opposite.
III. Using Fate: Choosing a Point Within the Reachable Set
The reachable set is the region into which the state can be brought, given the input set, the horizon and the disturbance sequence. What using fate does is seek a trajectory within that region:
\begin{aligned}\mathcal{R}_N(x_0;w)&=\Big\{\,x_N\ \Big|\ \exists\,u_{0:N-1}\in\mathcal{U}_{\mathrm{adm}},\ x_{k+1}=f(x_k,u_k,w_k)\,\Big\}\\ u^\star_{0:N-1}&=\arg\min_{u\in\mathcal{U}_{\mathrm{adm}}}\ \mathbb{E}\Big[\sum_{k=0}^{N-1}\ell(x_k,u_k)+g(x_N)\Big],\quad x_N\in\mathcal{R}_N\end{aligned}Both constraints are inside it. One is the admissible input set \mathcal{U}_{\mathrm{adm}}, which is the capability boundary; the other is that the terminal state must lie within the reachable set, which is the factual boundary. Cross either one and no solution exists; all you get is an optimum on paper.
This also explains why using fate insists on a certain "following along". Following along is not submission; it is choosing points along the direction in which the reachable set naturally extends, where the control cost is lowest. Choosing against it is not impossible, but requires a larger control effort; and control effort has an upper bound—once it saturates, the trajectory halts halfway.
The example of the Eating God generating wealth can be brought in here. The inclination is "exchanging output for resources"; that is only a direction, not a post. Writer, blogger, company employee are different landing points along this direction; product manager, programmer, operations are different facets within the same landing point.
But for coordinating posts such as civil servant, administrative position, project manager, the landing point lies to the rear flank of this direction. Not that one cannot go, but that it costs a continuing control effort, and that cost does not automatically shrink with time.
The degrees of freedom of using fate all lie inside the reachable set. What it changes is the choice of point, not the set itself. That is its boundary with making fate.
IV. Making Fate: Expanding the Reachable Set Itself
What making fate moves is the set. The reachable set is jointly determined by f, \mathcal{U}_{\mathrm{adm}} and the horizon; there are three ways to expand it: change the plant, change the input set, change the horizon.
The third way, plainly put, is waiting. As N grows, \mathcal{R}_N grows monotonically, and this always holds mathematically; the price is the years waited away themselves. Twenty-one years for one exposed Geng: this solution exists, it merely folds the horizon into itself. The original text did not take this road; it took the other two.
Ou Yue's making fate has two layers: changing the subject himself, as in fitness, health regimen, skin care, entertainment; and changing the surrounding environment, as in feng shui, geography, orientation, implements. In the language of control, the former tunes the plant parameters, the latter changes the boundary conditions. Both act on f, not on u.
Tuning parameters is slow, and has limits. A more effective step is to change the input set: add a column to B, obtaining B'=[\,B\ \ b_{\text{声}}\,], where b_{\text{声}} is the action direction of the newly added channel.
The point of adding a column is not to increase an existing force, but to make a previously unreachable direction reachable. The controllable subspace grows, and the reachable set grows with it. That is the structural position of the word "making".
Thus that piece of advice can be explained: go and train the strong mixed-voice high register.
Why Geng metal? The Book of Documents, "Great Plan": "metal is called following and reforming"; the Di Tian Sui: "Geng metal bears the killer aura, the most firm and vigorous"; Ren Tieqiao further explains Geng metal through autumn austerity. In image terms, Geng metal is austere and vigorous. The high register has high frequency and a high, strident sound, like a sickle swung from above downward—the direction matches.
Why the strong mixed voice? Chest voice strains in the high register, head voice is thin, and weak mixed voice is primarily control with insufficient power. Strong mixed voice can remain solid in the high register, even producing an explosive super-high note. The attribute of firmness and vigour requires a carrier that does not collapse.
The channel is not only one. The lung belongs to metal; the Su Wen, "Great Treatise on the Yin-Yang Image Correspondences", matches the lung with metal; voice training is qi training, and breath control acts directly on the lung and respiratory system—this is the reverse path from image back to the body itself. For Wu earth, Geng is the Eating God, and the Eating God is expression; in this chart the Food-and-Wound is not exposed, expression is pressed down, and singing is itself output. Three paths point in the same direction, and only then is this column added securely.
Behavioural intervention is where this apparatus lands. The subject has a gentle temperament; making him "have a killer aura" is harder than climbing to heaven; telling him "express more, output more" is equivalent to issuing another command to an already blocked channel—no gain.
An executable action is different: it bypasses the bottleneck of will. A person cannot change his character by an act of thought, but he can decide to go and train his voice today. Keep training, and the parameters slowly change, the channel slowly opens. The entry point of control is action, not resolve.
The second example is more blunt. Metal and water are too abundant, the branches are damp earth, a whole expanse of cold damp, and fire is needed to adjust the climate; yet the chart has no fire, and the two fire luck periods have also passed. The two pieces of advice given are to go to the snack street and eat snacks, and to go to the university town and look at young female students. Appetite and sexual desire—desire is heart fire. These two are not symbols; they are two inputs that can actually be pressed.
The original text lists the disaster layer separately; in the language of control, that belongs to trajectory replanning. Averting a calamity is trimming the feasible region: with a triple punishment in the spouse palace, press attention onto communication and cut off that most expensive mapping branch in advance. With the Chou-xu-wei triple punishment together with the Chou-wei clash, introduce Zi, and use the Zi-chou combination to lock the conflicting term—this is adding a coupling constraint that softens a hard conflict.
Meeting the calamity is more thorough. The energy of a single chart feature is limited and cannot map out everything in the event space; when one thing happens, the probability of another comes down. Since the total is conserved, choose the outlet with the lowest cost and let it discharge first. In the Nine-Bend Yellow River Formation, the twelve golden immortals had three flowers shaved away and five qi dissolved—their cultivation was gone, their lives preserved; in the Ten Absolute Formations, disciples were sent into the formations first and the higher immortals broke them afterwards—the sense of offering to the formation and standing in for the calamity is all here.
The real-world version is to become an internet troll in a year of the Wounding Officer meeting the Officer, getting muted and having posts deleted; when the day branch is punished, go and donate blood, or get grazed by a small electric scooter. All of them exchange a controllable small violation for an uncontrollable large one. In engineering this has a rather blunt name: controlled failure.
【Figure: a cluster of reachable sets on the phase plane, pushed open from the side into a fan shape by a newly added input direction; the old boundary dashed, the new boundary solid.】
Three stages in a closed loop, each minding one stretch. Knowing fate identifies the plant and the observation, and gives the width of that distribution; using fate seeks the optimal input within a given reachable set, and insists on following along; making fate changes the set itself, and insists on going against.
The three are not parallel steps; they are dependent. If identification is wrong, the optimal solution is meaningless; if the reachable set is not expanded, the optimum can only stop at the boundary.
One more thing must be said. The eight characters are a sampling of the spacetime energy information at the moment of birth, not the energy itself. A baby born at sunrise on the summer solstice carries the information of that day, but does not carry that day's total solar radiation. Information can take effect, but the effect must pass through the person's body and experience, and these are not especially sturdy. So "controllable" in this model never equals "arbitrary".
Controllability speaks of existence, the reachable set speaks of range, and optimal control speaks of trade-offs within the range. Together the three only make clear "what can be done"; they do not fix "what will happen".
Compiled by Qiushui Guanxiang Studio