Equitation science is an emerging discipline that combines learning theory, biomechanics and behaviour to examine the relevance and effectiveness of horse-training techniques. However, it does not seek to turn equitation into a science. It aims to develop scientific methods to study, measure and interpret interactions between horse and rider during equitation. This in turn leads to evidence-based training - your training will be vastly more effective when you base your methods on evidence of what actually works.
Horses are only ever required to do 4 things:
Go (start, quicken, lengthen)
Stop (slow down, stop, shorten, rein-back)
Even the most complex moves are just a combination of these basis elements. Any ridden problems will be routed in an issue with one or more of these basic elements and once the route of the problem has been identified, it can be fixed rather than simply being covered-up.
Horses with non-ridden problems such as poor loaders or horses that bite / are aggressive almost always have a problem with one or more of the basic elements. If you fix the 4 basic elements properly, the unwanted behaviour normally stops.
By applying Learning Theory to horse training, the International Society for Equitation Science has developed a series of training principles which can be applied to whatever training method to choose to use; whether it is classical dressage or 'natural horsemanship', double bridle or bitless, it doesn't matter - these principle still apply.
This 'shaping scale' is applied to each of the basic elements of forward, backwards, sideways and turn. 'Rhythm' basically means you ask once and the horse keeps doing that thing until you tell him to do something different. Rhythm in 'forward' means you don't have to keep kicking to keep the horse going, rhythm in 'backwards' (which is also slow down and stop) means you don't have to keep holding to stop the horse speeding up (see Training Principle 7 above). The point of this being a scale is that you can't expect Rhythm until you have Obedience and the is no point trying to work in a Contact until you have properly achieved Rhythm and Straightness. Training in each basic element may progress at different rates - just because your horse will go forward in a contact doesn't mean he will go sideways in a contact.
In the video below, Dr Andrew McLean talks about biomechanics and learning. There is a lot of his work available online but this video is a pretty good introduction to the subject and worth watching by anyone involved with horses as a rider, coach or judge.