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Casual Musings

Does the Meaning Outside the Formula Matter?

数学

A long time ago I began to feel confused about many things, and after becoming confused I never thought to reflect, so I just continued in confusion—never imagining that this would become a tremendous obstacle.

At first it started with some mathematical problems: if equations make solving things obviously easy, why invent so many strange ways of thinking? Isn’t it better to just use equation-style thinking?

Sunzi Suanjing: Now there are pheasants and rabbits in a cage; there are thirty-five heads and ninety-four feet in all. How many pheasants and rabbits are there?

This is a problem primary school students can solve today, and the answer is relatively simple.

One way of thinking is this: thirty-five is the total number of heads. Suppose they are all chickens—then there should be only seventy feet. The extra twenty-four feet must belong to the rabbits, and since we have already counted two feet for each earlier, the twenty-four feet divided by two gives twelve rabbits.

If rewritten as equations, it goes like this: x + y = 35 , 2x + 4y = 94

Solving simultaneously: 2*(35−y) + 4*y = 94  => 2*35 − 2y + 4y = 94 =>  2y = 94 − 2*35

 Actually this is the mathematical meaning described above, but if one uses equations, one can skip a step of cognitive transformation, and each step of the equation can be expanded into a real-world meaning—though some are solvable and some are obscure.

So a problem arises: is the meaning accompanying each step of thinking important, or is it more important to focus only on the core mathematical calculation?

Workers in a light-bulb factory are paid according to points. Each qualified bulb earns 4 points; each defective bulb not only earns no points but also deducts 15 points. One worker produced 1,000 bulbs and earned 3,525 points. How many of the bulbs were defective?

The positive side is 4 points and the negative side is 15 points; the solution is the same. If all 1,000 bulbs were positive, that would be 4,000 points—but clearly that is 475 points more than 3,525. Because each was scored 4 points earlier, here it is equivalent to deducting 19 points; so 475 divided by 19 equals 25 defective.

But this problem can in fact ignore the content and simply set up equations: 4x − 15y = 3425, x + y = 1000, then x and y can easily be found, yielding the result directly. That is to say, the equation method is like cracking open the shell, and in this way one obtains the answer directly.

Reality thus appears quite cold—it simply does not care how you package things on the outside; as long as the internal structure satisfies certain characteristics, it belongs to that structure and fixed methods can be used to obtain the result, while any other packaging outside the formula is meaningless.

This shows the objectivity of reality: no matter how you try to imagine them obeying your thoughts, it is useless—they will not act as you wish. And according to Murphy’s Law, bad things will always happen—so they will always fail to act as you wish.

To make everything controllable, one must do something—but does doing something violate the way of non-action (wuwei)? Anyone with a bit of brain would absolutely not believe the popular explanations of non-action.

The Daodejing says: “The Dao is forever nameless, plain and simple. Though small, nothing in the world can master it. If princes and kings can guard it, the ten thousand things will submit of themselves. Heaven and earth unite and send down sweet dew, which the people measure not yet distributes evenly of itself.”

All things submit of themselves; heaven and earth unite and send down sweet dew, and without needing to command the people they will spontaneously interact fairly. Yet the precondition for all this is “able to guard it.” Since it is “guarding,” how can it be non-action? The opening already said: “These two emerge from the same source but are named differently.” So action and non-action actually emerge from the same place—not in action, not in non-action, but in the place where action and non-action emerge together.

Therefore the Wenshi Zhenjing says: “The sage governs things with the mind, and gathers the mind with nature; then the mind is one with creation and transformation, and even the Five Phases cannot bind it.”

Yet one must not assume that because of non-action, action is the same as non-action, because they are still different—the only sameness is that they emerge from the same source. Hence it is said: “Do not, because the sage acts tirelessly, say the Dao is accomplished through diligence; do not, because the sage clings unyieldingly, say the Dao is attained through holding fast. When the sage acts, it is like shooting an arrow—acting because of the other, not acting on my own. When the sage holds fast, it is like grasping an arrow—holding because of the other, not holding on my own.” People in the world always take the sage as a model, but sometimes they only learn the sage’s outer form and not the inner substance. When the sage acts, it is like an ordinary person drawing a bow to shoot—an ordinary person actively pulls the arrow to shoot, but the sage drawing the bow responds because of the other, not doing it actively on his own.

If understood this way and one looks back at many cases in history, an interesting thing will be found: many case studies in Yi divination seem to have detailed explanations, but here one explanation, there another, with no complete and systematic account throughout. This shows that behind them there must be another system of inference logic, and this logic is the truly important part—everything else is various elaborations deduced outside these core logics.

The so-called “ten thousand changes never leave their essence” means exactly this: like mastering an equation, one can transform and rearrange the operational symbols in a thousand ways, and at each step one can construct an “interpretable” real-world meaning—but such real-world meaning is actually unimportant; the most important is still the core result, and everything else is merely decoration added on the basis of the determined result.

Written by Master Sanfu on October 23, 2015. Please credit the source if you share.

Translation Notice: This English version was translated with AI assistance. Specialized, historical, religious, or culturally sensitive terms may contain nuances, inaccuracies, or debatable wording. In case of ambiguity or discrepancy, the original Chinese text shall prevail.