Blog

Weber’s Law of Just Noticeable Differences can help us understand our perceptions of changes in force against an opponent when practicing Taijiquan (太極拳). Weber’s Law applies to most types of perception, like the perception of different light intensity or duration or wavelength (color), loudness or length or pitch of sounds, and even psychological perceptions like differences in costs for products or services.

In Taijiquan, the major sense that we are training is touch. Pressure on our skin is detected with our mechanoreceptors. There are other skin sensors that can detect an opponent, including thermoreceptors (detecting heat) and hair follicle receptors (detecting movements of our hairs), but the role that these play in most Taijiquan practice is probably negligible.

Proprioception – the sensing of the strength of effort of neighboring parts of one’s body being used in movement – is also very relevant to sensing the interactions with an opponent in Taijiquan. Mechanoreception and proprioception together is much more sensitive (about seven fold) than mechanoreception alone. But since Weber’s Law should apply to both mechanoreception and proprioception, I will only use mechanoreception, which is easier to illustrate, in this article’s examples.

Weber’s Law essentially states that our ability to sense changes (differences in magnitude) in force (pressure) is proportional to the magnitude of the initial stimulus. Thus, the greater the initial force, the greater a change must be in order to be able to perceive that change; using less pressure (practicing softer) would allow practitioners to sense changes in pressure sooner.

The ability to sense changes in pressure would yield a linear relationship, due to having a constant ratio, which can be plotted as shown in the accompanying graph. The formula would be ∆P/P = k, where ∆P is the minimal detectable change in pressure at pressure level P, and k is the constant. The constant k is, for ease of illustration, arbitrarily set as equal to 0.1 for the blue line in this example, and is 0.15 for the red line (representing someone less sensitive to pressure changes than the person represented by the blue line). [Note that, for an average human, k = 0.14 when measuring pressure on the skin without movement, and k = 0.02 (or 2%) for lifted weights – which includes both mechanoreception and proprioception.]

For this graph, a practitioner (blue) that can sense no less than a 10g pressure change when the initial pressure is 100g, would need a change of 0.1kg when the initial pressure is 1kg, or a 0.2kg difference when the initial pressure is 2kg, etc. The less sensitive participant (red line) would only notice a detectable difference in pressure when there is a 15g change if starting at 100g, 0.15kg change when starting at 1kg, 0.3kg change when starting at 2kg, etc.

For relative comparisons, a golf ball weighs about 45g (0.045 on the X axis of the graph), a baseball weighs about 150g (0.15 on the graph) and a women’s shot put weighs about 4kg (4 on the graph).

Weber’s Law does not always hold for extremes of stimulation, like near the limit of a practitioner’s ability to sense pressure (values close to zero on the graph), or near the maximum that their receptors can sense. If there is no pressure, then the mechanoreceptors will be unable to sense anything, but in order to affect an opponent, some force must be present, so this limitation is unlikely to affect our understanding regarding Taijiquan training.

Weber’s Law indicates that practicing Taijiquan softly would allow the sensing of changes in pressure sooner (i.e., smaller pressure changes) than when practicing more forcefully. This applies to both practitioners indicated in the above graph. But it also indicates that the more sensitive participant will be more sensitive over all the levels of force at which the two practice.

If practitioners are focusing on training for improved sensitivity, then they may benefit from practicing softly. The softer one practices, the less change needed before practitioners can feel that change.

Note that Newton’s Third Law of Motion states, in general, that for every action, there is an equal and opposite reaction. This law means that one practitioner will have the same amount of pressure at the point(s) of contact as the other participant. One practitioner cannot be softer at the point of contact than the other person. One practitioner could try to lessen the mutual (net) force by easing up, or they could try to increase the force by trying to applying heavier pressure, but whatever level one participant is at, it is the same for the other participant.

[See: http://resource-bank.nzip.org.nz/draft-under-construction/mechanics/newtons-third-law-misconception-2/]

Although the amount of force two practitioners have at the point of contact must be the same, one participant could be using less effort to produce that level of force. Effort is related to efficiency, in structure, breathing, even mental anxiety, etc. I suspect that many people incorrectly use the term “force,” when they actually mean “effort.” We want Taijiquan to be as effortless as possible. We seek to feel calm and “comfortable” while practicing.

Continue to page 2…

I wasn’t a particularly nervous child. I just never seemed to fit in.

I’m not telling you this because I want your sympathy either. I’m telling you because this is the first step on a journey to understand how Tàijíquán changed my life.

I know that most kids are socially awkward, but I was particularly so. I was not athletic. I liked science, but was poor in math because of undiagnosed dyslexia—which meant I wasn’t good in math or science either. I was good at art, but that’s not enough to make you popular, so I was quite the target for being made fun of by my classmates. I was put down by my teachers, and had very few friends.

To complicate matters in 5^th grade I began—along with the rest of my family—suffering from Chronic Fatigue Syndrome (CFS). At the time, very little was known about CFS, and so the school administration and teachers were skeptical to say the least. They said that my brother, sister, and me were faking it. My parents fought tooth and nail against that accusation, even hiring a lawyer and threatening legal action. At that point the school district came back with the statement that we were suffering from a psychosomatic illness and that we needed to be treated by psychiatrists.

My parents took my brother, sister, and me to a psychiatrist who sent the school a written affidavit attesting to the fact that we were, in fact, truly sick and needed medical care, not a school district full of administrators without a medical degree trying to give us a diagnosis.

The school’s response to this was that my siblings and I were kicked out. We were told that since we were sick and nobody knew what was wrong with us, we were a risk to the other students and could not attend.

From the middle of 5^th grade to the beginning of 8^th, we were home schooled. I missed out on a lot of socialization because of that, and became even more awkward. By high school, my sense of isolation, depression about how poorly I fit in was so bad that every morning before school I had an anxiety attack.

Because nothing in my life was normal, I had no way of measuring what was right and what wasn’t. I aware enough to realize that anxiety attacks might be a medical condition. Since I didn’t realize my experience wasn’t normal, I said nothing and suffered in silence.

By the time I was ready for college, my CFS was in remission, and I was feeling pretty good. I also reconnected with something I truly enjoyed before I became sick: martial arts. Before being isolated from my fellow students, my mother put me in several summer programs involving a local Taekwondo school.

I enjoyed learning to kick and punch, and I didn’t even mind the calisthenics, but felt that what I was learning was spiritually bereft. During that time, all the martial arts movies were filled with a spiritual, quasi-religious tone that never entered the stuff I was learning. Instead of words of wisdom and fatherly advice, my Taekwondo teacher gave speeches about self-discipline, and hard work.

So when I wanted to reconnect with the martial arts, I felt I needed something different, and moved away from the Korean art I’d been studying and began a search for something with a more spiritual bent. After trying several other styles, but feeling like they weren’t the right fit for me, I was ready to give up. A friend of mine at the time suggested that I try Tàijí, so I looked in the phone directory and discovered the Houston Institute of Martial Arts and Medicine.

I started that week, and was immediately pleased to discover that my teacher talked about the importance of breath and the psychological and spiritual benefits of Tàijíquán. From that moment on, I was hooked.

I began my lessons with Jeff Bolt and the same week I started studying with Madam Wang Jurong as well. Within a year, my anxiety went away, my emotions became more balanced, and I felt more confident and calm. By my second year of Tàijíquán study, I was calm enough to enter my first competition. I took gold in the beginners division, and my teacher told me that next time I competed, that I’d have to do it as an advanced student.

I didn’t write this to say that Tàijí is a magical panacea that will cure everyone of every problem they’ve ever had. I’m not even saying that everyone should be doing Tàijíquán. On the contrary, I don’t think it’s for everyone. Some people don’t have a personality suited to learning things like Tàijíquán.

However, I am saying that the mindfulness training from my Tàijí practice helped me deal with anxiety that I would probably have probably needed medication to control. The breath work and spiritual benefits of my training were what I needed to help me get back on track socially, psychologically, and physically.

I am also saying that if it benefited me in this way, there’s a chance that it will help others also. Maybe you should share this story with someone who might profit from some lessons.