Sunday 22 April 2012

The kolmogorov complexity of tai chi

Building on mathematical tai chi way of thinking previously discussed I wondered...What is the Kolmogorov Complexity of tai chi. I.e. how simply can it be described in a scientific sense? Kolmogorov Complexity might be the answer. It is an abstract construct used to describe the minimum amount of information required to represent a particular object/process/concept. For example the higher the number of different sub components that make up an object the higher its Kolmogorov Complexity will be.

Although there is currently no really good way to measure Kolmogorov Complexity except on simplified mathematical problems, I would consider this a good measure for scientifically assessing different people's tai chi. I would hypothesise that for a given tai chi form, there is a notionally "perfect" way of doing it that has the minimum Kolmogorov Complexity possible. In other words, this perfect form uses only a couple of simple building blocks and just rearranges them in every movement. It is completely flowing and smooth such that the trajectories are easily described mathematically etc. Anyone performing the form would have removed all superfluous movements and every instance would be a perfect embodiment of tai chi principles.

By contrast, when anyone demonstrates the same form they are going to be not quite as perfect. Where two postures should in fact be built upon the same building block the practitioner has not quite appreciated this, and so they are actually performed differently. This difference increases the Kolmogorov Complexity, because whereas in the perfect form I could just say both postures were X now have to say one is X and one is Y. Similarly if I don't quite move perfectly smoothly, the trajectories are more complicated to describe mathematically and so the Kolmogorov complexity increases.

How good a student is at tai chi can therefore be directly postulated in a scientific way, as a percentage error between the Kolmogorov Complexity of the student performing the form, and the notional theoretically perfect implementation of the form.

So how can you go about quantifying this "performance measure"? Well as I said above the mathematics of this still has a long way to come and would be exceptionally challenging. However the first step would be to be able to perfectly measure the movement. For a long time I have thought that motion capture technology could be used to achieve this and so was glad to see that recently a tai chi master has actually done so. Once we can capture the movements of different people we can use computers to analyse similarities and differences and in effect determine who is better (should we wish). [Of course it's not quite as simple as that as a less advanced student might deliberately simplify bit is of the form....]

At the end of the day however, to say how good individual practitioners are is not really what is important. What this would represent would be a way to test my hypothesis that the best tai chi is tai chi that has the lowest Kolmogorov Complexity. In otherwords good tai chi is simple tai chi. And good tai chi is self consistant tai chi. Perhaps in the further such mathematical metrics could also be used used to form the basis of a new wave of interactive tai chi learning systems.

Wednesday 18 April 2012

Structural engineering

If I were to choose the most optimal scientific discipline for a tai chi practitioner to come from, I would most likely choose structural engineering. Just like when building bridges and towers, structure is crucial in tai chi and understanding and manipulation of forces is the key essence.

As an analogy, when we are learning tai chi, it is human nature to focus on the hands and try to copy that. Just as if we imagine being tourists looking at Big Ben, we are naturally drawn to staring at the ornamental spires and turrets at the top. What is actually important in tai chi however is the connection with the ground, controlled primarily by correct foot placement. Our structural engineer when faced with big ben will therefore naturally be curious about the bottom of the tower, as they have been trained to understand that the foundations control the structure.

Everything we doing tai chi must come from the feet, as it is the only connection we have anything other than a potential opponent. When you are learning tai chi therefore, try to copy what your instructor's feet to the rest will follow.

Thursday 12 April 2012

Technique vs superpower

Where do these astounding abilities of tai chi and other martial art masters come from? Surely they are supernatural and fuelled by chi power. That can be the only explanation. Or not.

It seems to me there is a direct parallel here to Arthur C Clarke's famous phrase "any sufficiently advanced technology is indistinguishable from magic". What this means is that although something may appear supernatural to one person, it is in fact totally rational and explainable to another.

I believe martial arts, and internal martial arts like tai chi in particular, have an analogous property. So recasting the phrase we get "any sufficiently advanced technique is indistinguishable from superpower". Hence when a tai chi master throws people around alarmingly (and you can find many such videos), it does not conform to your expectations or understanding of technique. It appears that it must be a manifestation of this masters chi, or some other supernatural ability. If you were to train and dedicate yourself to the art for decades so as to learn the techniques, you will realise that there is no magic or secret. The Master simply has a level of competence and control over his own body, that "it defies belief".

His sufficiently advanced technique is indistinguishable from a superpower.

Sunday 8 April 2012

Star wars yoga

Is this robot yoga :-)

Original source here.

Wednesday 4 April 2012

Perception of weight distribution in tai chi stances

Tai chi weight distribution scales
In tai chi we make a significant conscious effort to control the distribution of our weight in postures and stances. This led me to wondering, that although we talk about having 70% of our weight on one leg (for example), how accurate and exact is this 70% figure? I intend to carry out some tests myself, but in the meantime I did a quick search for scientific literature on the subject and discovered this particularly relevant journal paper entitled "Perception of unilateral lower extremity weightbearing during bilateral upright stance".

The abstract of this paper is below, but in summary it seems that humans can judge the weight distribution to within a 7% error for asymmetrical stances [i.e. if you feel like it's 70% of you weight, it is likely somewhere between 65% and 75% of your weight]. It seems reasonable to assume that with tai chi training, this error margin is reduced, as it is a conscious, learned and developed skill say to a 3% accuracy [i.e. if you think it's 70% of you weight it is likely somewhere between 68% and 72% of your weight] - which is pretty accurate.

What this means is that this 70% figure is not just an arbitrary feeling that our teachers are talking about (as it would be if the average percentage error was high implying humans were bad at judging weight distribution, like say >20%), but a real scientific quantification of what we should be doing. Hence when we talk about moving 70% of our weight onto one leg, not only should this feel like 70% of weight is on that leg, but practically it should also be 70%. Hence it makes sense to play around with bathroom scales at home to actually measure how good your stances are and improve your perception of weight distribution for better control.

Abstract of "Perception of unilateral lower extremity weightbearing during bilateral upright stance"
"The primary purpose of this study was to describe the error in 61 healthy subjects' perceptions of weight-bearing at three target levels during bilateral upright stance. The secondary purpose was to describe the effects of age, sex, lower extremity dominance and target weightbearing level on the error in perceptions of weightbearing. Weightbearing was determined while subjects stood on digital scales. They adjusted their weight in an attempt to bear 25, 50, and 75% of their weight through a designated lower extremity. Three trials were allowed at each weightbearing target, and the results were averaged. Each subject's error in perception of weightbearing at each target level was determined by taking the absolute value of the target percent weightbearing minus the mean actual percent weightbearing. The mean errors at the 25, 50, and 75% targets were 7.3, 3.3, and 7.7%, respectively. The magnitude of the error was unrelated to age. An analysis of variance showed that error was not dependent on sex or whether the dominant lower extremity was used for making judgements. The error did differ between target levels. Clinicians cannot assume, based on the findings of this study, that individuals can accurately judge the percent weightbearing they are placing through one of their lower extremities during bilateral upright stance."
Note I disagree with the final sentence of this abstract, as I believe that this weight distribution perception is the key skill that tai chi practitioners are developing, and hence their ability to judge it is significantly better than the normal population. You can hypothesise an extrapolation of this fact from the numerous scientific studies demonstrating that there are benefits to doing tai chi for improving balance. I would argue that improving your balance is primarily driven by improving the accuracy of your weight distribution perception.