By 苏剑林 | January 28, 2018
The Colorful World of Jin Yong
In the works of Jin Yong (and indeed many martial arts novels), martial arts can be divided into three types: The first type is raw, solid power, such as Hong Qigong's "Eighteen Subduing Dragon Palms" or Jiumozhi's "Dragon-Elephant Wisdom Skill." Their main characteristic is fierce strength. For example:
Qiao Feng's Twenty-Eight Subduing Dragon Palms were passed down by the previous beggar clan leader, Wang Jiantong. However, Qiao Feng was born with extraordinary talent and was blessed in the realm of martial arts. His Twenty-Eight Subduing Dragon Palms were like a crushing dry weed, invincible and even more powerful than Clan Leader Wang's. Seeing the opponent pushing with both palms, Qiao Feng felt that if he resisted with a single palm and fought to a draw, he might seem to have a slight advantage, which would be disrespectful. Thus, he also struck out with both palms. In his left and right palms, the force used was still "three parts external, seven parts internal," keeping most of the strength in reserve.
——From "Demi-Gods and Semi-Devils," Century Revised Edition
The second type focuses on feints. This means that if you cannot be stronger than your opponent, you win by deceiving them. An example is the "Withered Cherry Blossom Divine Sword Palm" of Peach Blossom Island:
This palm technique was created by Huang Yaoshi while watching the falling cherry blossoms on Peach Blossom Island. The moves change unpredictably, and there is an emphasis on the beauty of the posture. As she moved her arms, palm shadows appeared from all directions—sometimes five feints and one real, sometimes eight feints and one real. It was like a wild wind rising in a peach forest, with ten thousand flowers falling at once. It was elegant, as if she were dancing. However, because her cultivation was shallow and she was hesitant to cause harm, she could not strike with the sharpness of a sword. Guo Jing was dazzled and could not maintain his defense. Before he knew it, "pa pa pa pa," he was hit four times on his left and right shoulders, chest, and back. Huang Rong had used no force, so Guo Jing felt no pain.
——From "The Legend of the Condor Heroes," Century Revised Edition
The third type focuses on technique. It does not seek mere raw power, nor does it rely solely on feints. Instead, it emphasizes using force exactly where it is needed to achieve the effect of "overcoming hardness with softness" or "deflecting a thousand pounds with four ounces." Clearly, the representative of this style is Tai Chi. Additionally, the Dog Beating Stick Technique, the Great Heaven-Earth Shift, and the martial arts of the Quanzhen Sect and the Ancient Tomb Sect also contain this principle. For example:
In a moment of crisis, Yang Guo used a Quanzhen Sect sword move, which yielded surprisingly good results. He followed up with the "White Rainbow Traversing the Sky" move, striking the wheel with a horizontal rotation of his sword. The wheel was heavy while the sword was light; a horizontal strike should have been ineffective. However, this rotation was perfectly timed, aligning with the martial principle of "deflecting a thousand pounds with four ounces." The direction of the iron wheel was diverted, and it flew back toward the National Master's head.
——From "The Return of the Condor Heroes," Century Revised Edition
The saying "deflecting a thousand pounds with four ounces" (Si Liang Bo Qian Jin) has appeared in many literary works. Many readers likely believe that this is just an exaggeration used in novels and is impossible in reality. Others might think that ancient "martial arts" have simply been lost but actually existed. Here, we will analyze the possibility of this feat from the perspective of physics, providing an alternative example of how a science student reads Jin Yong.
Physics
In fact, the basic principle of "deflecting a thousand pounds with four ounces" is not to meet force with force ("hard-on-hard"). The so-called avoidance of "hard-on-hard" means that your applied force should be perpendicular to the incoming force so that, theoretically, you do not receive the impact of the incoming force. Of course, this is not enough. For a basic analysis, we can simplify the problem as follows:
A massive object is in uniform linear motion (a great force heading towards us). Then, at a certain moment, it begins to be subjected to a force of constant magnitude (the force we can apply), and this force is kept perpendicular to the object's instantaneous velocity. Find the trajectory of the object (to see if we can avoid this attack).
We can simplify further by assuming the motion is in a plane for ease of analysis. The key to the analysis lies in describing "the force direction being perpendicular to the velocity direction." We know that for describing angular relationships, complex numbers are most suitable. We can assume a complex function $z \equiv z(t)$ to describe the trajectory. Letting the constant force magnitude be $f$, we can write the equation of motion as:
\[m\ddot{z}=f\frac{\dot{z}}{|\dot{z}|}e^{i\pi/2}\]
To solve this equation, first let $\dot{z}=re^{i\theta}$. Then we have:
\[m\frac{d}{dt}(re^{i\theta})=fe^{i(\theta+\pi/2)}\]
Expanding this, we get:
\[m\dot{r}e^{i\theta}+mir\dot{\theta}e^{i\theta}=fe^{i(\theta+\pi/2)}\]
The magic of complex numbers is that we can now divide both sides by $e^{i\theta}$:
\[m\dot{r}+mir\dot{\theta}=fe^{i\pi/2}\]
According to the principle that real and imaginary parts must be equal:
\begin{aligned}
&m\dot{r}=0 \\
&mr\dot{\theta}=f
\end{aligned}
It is clear that:
\[r \equiv v_0,\quad \theta=\theta_0+\frac{f}{mv_0}t\]
Note that $re^{i\theta}$ describes $\dot{z}$, which is the velocity. Therefore, the above equation tells us that the magnitude of the velocity is constant, and the direction of the velocity changes at a constant rate. This is "uniform circular motion"! Of course, this result could be obtained without solving differential equations, but the general analysis process is provided here so that interested readers can apply it to analyze more complex processes.
By rotating the coordinate axes, from
\[\dot{z}=v_0\exp \left(i\theta_0 + i\frac{ft}{mv_0}\right)\]
integration yields:
\[z(t)=z_0 + \frac{mv_0^2 e^{i\theta_0}}{if}\left[\exp\left(i\frac{ft}{mv_0}\right)-1\right]\]
Since the punch direction is "attacking" us, we can take $\theta_0=\pi$, giving:
\[z(t)=z_0 + \frac{imv_0^2}{f}\left[\exp\left(i\frac{ft}{mv_0}\right)-1\right]\]
Breaking it down into components:
\begin{aligned}
x =& x_0 - \frac{mv_0^2}{f}\sin\left(\theta_0 + \frac{ft}{mv_0}\right)\\
y =& y_0 + \frac{mv_0^2}{f}\left[\cos\left(\theta_0 + \frac{ft}{mv_0}\right)-1\right]
\end{aligned}
Actual Application
Since the resulting trajectory is uniform circular motion—a circle!—it is not difficult to understand this passage from "The Heaven Sword and Dragon Saber":
Zhang Wuji’s wooden sword drew circles in the midst of the cold light. Every move was executed in an arc and retracted in an arc. There was no trace of hesitation in his heart; he moved the sword with intent. Every time the wooden sword made a move, it was as if it released a fine silk thread that wrapped around the Heaven Sword. The silk threads accumulated more and more, seemingly forming a mass of cotton, enveloping the Heaven Sword within.
...
Zhang Wuji continued to draw circles with his sword. Except for Zhang Sanfeng, no one could tell whether each move was offensive or defensive. This Tai Chi sword technique consisted merely of circles—large and small, forward and backward, slanted and straight. If one were to count the moves, one could say there was only one move, yet this move was infinitely varied and inexhaustible.
————From "The Heaven Sword and Dragon Saber," Century Revised Edition
Therefore, from a physics perspective, we know that the secret of Tai Chi is to draw circles along the direction of the incoming force—this is the "sticking" (粘) technique—and to maintain a perpendicular force. Clearly, Tai Chi is very technical. Some readers might wonder: if Zhang Wuji had not learned the Nine Yang Manual and lacked deep internal strength, would it still be possible to "deflect a thousand pounds"?
Let's look at a more rigorous example with data from "Is 'Deflecting a Thousand Pounds with Four Ounces' Possible? — A Physics Analysis of 'Deflecting a Thousand Pounds with Four Ounces'":
Using the person being attacked (the Tai Chi practitioner) as the origin, let's assume the arm weight $m=6\text{kg}$ and the punching speed $v_0=7\text{m/s}$. Let $(x_0,y_0)=( 0.5\text{m},0)$; 0.5 meters is roughly where we begin to exert force on the opponent. We then have:
\begin{aligned}
x =&\, 0.5 - \frac{294}{f}\sin\left(\frac{ft}{42}\right)\\
y =&\, \frac{294}{f}\left[\cos\left(\frac{ft}{42}\right)-1\right]
\end{aligned}
When the opponent's punch (would have) hit us, $x=0$, so:
\[\sin\left(\frac{ft}{42}\right)=\frac{f}{588}\]
leading to:
\[y = \frac{294}{f}\left[\sqrt{1-\left(\frac{f}{588}\right)^2}-1\right]\]
If the width of the body is $d_{min}$, we need at least $y > d_{min}$. Given this is a transcendental equation, we can solve it numerically.
(The image described here is the function plot between y and f, where the horizontal axis is f in Newtons and the vertical axis is y in meters.)
If we want to avoid an attack to the head, we might consider $d_{min}=0.1\text{m}$. From the graph, this requires $f \approx 250\text{N}$. What does this force represent? According to the analysis in the linked article, the punching power of an ordinary martial artist is roughly in this range! If we want to avoid a body attack, we might consider $d_{min}=0.25\text{m}$, which requires $f \approx 500\text{N}$! This likely already exceeds the punching power of an ordinary martial artist.
Of course, this is a very mechanical analysis. In reality, we can also dodge flexibly; we wouldn't just push. It's like the line from the movie "Tai Chi 0": "One grab, one lead, one hook, one pierce; hitting me until I'm flying all over the place." But this analysis is sufficient to show that relying solely on "deflecting," "deflecting a thousand pounds with four ounces" (where four ounces $\approx$ 0.125kg $\approx$ 1.25N) is impossible.
Conclusion
It seems Tai Chi is a better match for the Nine Yang Manual. Without the foundation of the Nine Yang Manual, it is probably difficult to use Tai Chi in combat. The insight from the "Great Heaven-Earth Shift" seems more profound:
The first one or two levels of the Great Heaven-Earth Shift are similar to the method of "deflecting a thousand pounds with four ounces." However, at higher levels, it becomes "deflecting four ounces with a thousand pounds"—using a vast internal force of nearly a thousand pounds to deflect the small force of the opponent. It seems like "using a heavy ox-cleaver to kill a chicken," but it is precisely because an "ox-cleaver" is used that killing the chicken becomes effortless.
————From "The Heaven Sword and Dragon Saber," Century Revised Edition
What if one already has the power of the Nine Yang Manual? Readers might be confused: if the Nine Yang Manual is already powerful enough to defeat enemies, why go through the trouble of practicing Tai Chi? It appears that the specialty of Tai Chi is not to save energy, but to reduce damage to oneself. Imagine two fists colliding hard-on-hard—what a painful realization that would be! By avoiding the brunt of the force and using Tai Chi's circular pushing method, the damage to oneself is minimized.
(Actually, I know nothing about boxing or martial arts. The above is purely for entertainment and dinner conversation. I hope it brings a smile to the readers~).