Sunday, January 23, 2011

The Emperor's New Colthes -Part 2

Why is standard ski instruction completely wrong? Why are the instructions back to front? Why can practically no-one see this or deal with it? What is going on?

Meet Mr d'Alembert... (or if you prefer not to heat up too many neurons go directly to the end of the post)

Jean le Rond d'Alembert, born 1717, found abandoned on the doorstep of the church of "St Jean le Rond", was just 10 years old when Sir Issac Newton died. D'Alembert became a brilliant mathematician. He had pretensions however to be a physicist and believed that physics should be based on metaphysical principles and not experimental evidence. Newton in sharp contrast based his laws of motion on experimental evidence. D'Alembert was rather special though because it was he who introduced "string theory" to the world in 1747 and that is today's main topic of theoretical physics and he directly generated the foundations of electromagnetic and other field theories, special relativity, and quantum mechanics.

So what has d'Alembert got to do with us? More importantly, how did he manage to screw up so many skiers?

Engineers today still use d'Alembert's mathematics to number crunch their way through mechanics problems. D'Alembert's concepts are logical and rational but unfortunately do not describe reality. There are many tricks in mathematics that work very well using abstract concepts - such as "imaginary numbers" - but which are not present in reality. Newton's physics - which is based upon reality - is the correct version. Newton's second law describes how unbalanced forces cause the acceleration of an object. A bullet leaving a gun is accelerating and just has one unbalanced force (ignoring air resistance) against it. This subject is called "dynamics" and is the mechanics of "disequilibrium". D'Alembert saw this problem from a mathematician's perspective and was interested in making calculation easy. He simply removed the acceleration and replaced it with an equal and opposite fictitious force - balancing the real force. This removed the pesky accelerations and made calculation simple and accurate. This reduced the dynamics problem to a statics problem with balancing forces - however to clarify that it was not statics he called it "dynamic balance". "Dynamic balance" is of course a fiction - not a reality. In the real world we have accelerating objects that are out of balance. Unfortunately people in engineering tend to think that D'Alembert's principle is the same as Newton's second law - but it is not. It is just a mathematical trick - there is no such thing as “dynamic balance” in reality.

Medical texts and sports instruction continually refer to "dynamic balance" with an air of authority - but they never explain it. Dictionaries define the issue away in a purely circular manner also without explanation. They are all paying homage to the Emperor's new clothes. The King of engineering standing in front of me summed it up when he admitted that he didn't know what Newton's third law was. That's quite something from someone who claims to be the most famous engineer in the entire world. The self-proclaimed king of engineering also stated the entire universe is in equilibrium and that even if he fell over he was still in balance. He didn't know Newton because he worked with D'Alembert's mathematics all the time and believed that this is how physics worked in reality. I wouldn't have bothered but he was telling me that all my theory (Newton) was wrong and I had used this theory to work out my ski teaching exercises. He did at least acknowledge that the exercises worked! 

The issue becomes even further clouded because we also use the term "dynamic balancing" for correcting the rotational behaviour of a wheel or for stabilizing a movie camera. There's more sense in this application but in reality this is not about "dynamics". A stationary mass may be in perfect balance on a fulcrum, but due to asymmetrical shape it will not remain in balance when spinning. The spinning object will then wobble and counter-weights need to be added or subtracted from the system to remove this wobble and also keep the object in balance when not rotating. In mechanics however a rotating rigid object is actually a form of "statics" (Newton's first law). Send it into outer space and it will rotate forever because there is no unbalanced force accelerating it. Some people might think that we are applying "dynamic balancing" to skiing - but this is simply not relevant. Newton's second law, dynamics, is relevant to the skier. Newton's third law describes the complete system of both the skier and the ground - with opposite and equal forces acting upon each separate object - unbalancing both objects. The Earth is so big though that we don't notice it being accelerated by the skier.

People are unconsciously determined to cling on to anything that justifies the naive belief in "dynamic balance". It's not because they want to believe in "dynamic balance" - it's just that they need to praise the Emperor's new clothes because if they don't they will risk being considered stupid and incompetent - exactly as in the fable. D'Alembert was apparently an argumentative and stubborn man and probably thrived on intimidating those around him – in fact he designed the Emperor’s new clothes for himself. It was for this reason that he appears to have failed to understand the significance of the experimental nature of Newton's physics. It's a bit like how people use a GPS without thinking for themselves or worse, without looking out of the window. D’Alembert was lost in an abstract world of mathematics.

People don't consciously try to conform like this, but there is usually something else helping the situation along. The idea that we are in "balance" is seductively simple and until very recently there were massive gaps in science that meant we couldn't explain how complex systems worked at all. Newton's laws at one stage almost became a religion with mathematicians such as Laplace thinking that if you knew the initial position of every atom in the universe you could calculate the future trajectory of everything and literally see everything in the future - like a God. The first people to spot that there were serious problems here were artists and poets who were not attracted by the ugly industrial revolution resulting from Newtonian mechanics. William Blake famously referred to this as "Newton's death" and spotted the "infinity in a grain of sand" that would reveal the limitations of Newtonian mechanics and pre-empted the discovery of chaos theory. Basically when dealing with more than two objects Newtonian mechanics broke down. Calculating the trajectory of planets worked perfectly when only two were considered, but no one could calculate with three planets. Newtonian mechanics went on to become the basis for social sciences and even brought the invention of communism. Modern mathematician Ian Stewart said "If Newton couldn't predict the behaviour of three balls, how could he predict the behaviour of three people?" Chaos theory simply points out that you can never know the initial position of objects accurately enough to be sure of the eventual outcome in a complex system. Laplace was wrong. Chaos theory explains why every snowflake is different and why every skier is different. The upright human being is more than just an unpredictable personality - he is a perfect model of physical chaos theory - a classic "feedback driven disequilibrium system" - constantly and unpredictably out of balance and corrected by feedback. We remain stable as an outcome of this "out of control" control. Newton's laws still underpin the basic motions but the physical control comes from intelligence - not balance. It's still tempting to define all of this away as simply "dynamic balance" - but that doesn't just tell us nothing - it's categorically wrong.

What does all this this actually mean then for the skier or other athlete receiving instruction? Quite simply, the instructions become completely reversed. (In a nutshell: The skier's job (and mindset) is to fall over. The ski's job is to lift up.)

Snowplough based upon “balance”…
Press the outside ski to turn. Move the Centre of Mass over the outside foot. If you want to balance statically over a foot you do have to move the CM directly out over it. This “outside” ski is pointing downhill and rapidly becomes an accelerator – the skier goes out of control and many problems arise because the CM has moved away from the turn instead of going into it as would happen in any other activity.

Snowplough based upon “dynamics”…
Move the CM over the inside ski. The inside ski flattens slightly and can slip into a turn but act as an effective brake at the same time. The CM has moved towards the centre of the new turn – which is a future requirement for more dynamic parallel skiing. When the skis cross the fall line the outside ski takes over automatically with the geometry of the mountain dictating the pressure on the ski – the pressure is always on whichever ski is downhill of the skier and helps the skier to brake and remain in control while developing the appropriate movement pattern for dynamic skiing. The start of the turn is actually done on the lower ski on its uphill edge. Later this skill is simply transferred to the other ski (one ski/one leg) and the plough is rapidly dropped.

If instructors can’t even teach a snowplough intelligently then they have no hope of working out anything more advanced – and unfortunately this is precisely the case. So what impact does this have on the ski industry?  There are several classic repercussions. The commercial ski industry is like a fast food business. This business thinks that people want to learn but without any effort or challenge and for a certain category of people they are correct – just look at how busy McDonald’s is normally. The “quick fix” simplistic “balance and emotion” based instruction will not challenge anyone – and it will certainly not challenge the ski instructor to exercise any neurons. Unfortunately it doesn’t work and most people give up after the first holiday – some statistics show that this is the case for 90%. Many people struggle on for several years to try to get rid of the snowplough – usually to try to please their friends or partners – and some people due to natural selection and variation simply succeed in spite of all the nonsense. Self-taught people usually fare better because at least they are not being brainwashed into doing the exact opposite of what is required. I know because I was self-taught and never had a lesson until starting instructor training. I was perhaps naturally selected to some extent but I did have a strong background in ice skating – which is really what skiing is all about anyway – except on a slope. In general the instructors themselves just muddle on the best they can. Some instructors succeed through pure personality - trying their best to help people to enjoy their experience even if they don't make much of their skiing. Many instructors just find ways around the useless teaching methods and have a bag of tricks they can use to help overcome the more obvious limitations - but few if any can really explain what is going on. Some revert to brutal natural selection in race courses - where in the USA it is estimated that from a starting number of 10,000 a team of 8 successful skiers will eventually be formed. On the more cynical side there is a great number of instructors who come to detest their job. They end up just doing it for the money. Many get into it because they think that they will be able to ski a lot and end up frustrated when they don't get that opportunity. They can't get satisfaction from teaching because they are trained to teach nonsense and it goes absolutely nowhere. The suicide rate amongst ski instructors in the Alps is shocking.

Skiing is a constant challenge at every level and that’s what makes it amazing. “Balance and Emotion” just don’t do it - and "natural selection" just isn't good enough.

No comments:

Post a Comment