The V9 group.
There are 2 video playlists that describe this group. I will only post the initial video here, but both playlists should be studied compared and contrasted.
[VIDEO=http://www.youtube.com/watch?v=7pvuTZ5u6Kg&feature=youtube_gdata_player width=620 height=375][/VIDEO]
And Norman’s more general “mathematical” or consensus treatment:
[VIDEO=http://www.youtube.com/watch?v=jJx68l29U6s&feature=youtube_gdata_player width=620 height=375][/VIDEO]
Now when the idea of a group structure on a topological form is mentioned it is a form of rhetoric. A topological space is usually a Form on which a metric is imposed. This literally means the observer decides to apply some form as a Metron to fractalise that space/ form. So the form is fractured, turned into a fractal, made into a multiple form based on the Metron, factorised, conjugated by the Metron within the space . All these rhetorics underlying ultimately what is meant by measuring a space.
Because of the fashionable rhetoric of referring to a set , it becomes necessary to specify what kind of set, and a topological space is a general specification that a set has a metric and a group or ring algebra associated ith that metric.
I particularly like this presentation because it ties in nicely with Grassmanns generalised notion of a combinatorial process for synthesis of a resultant. In this case a point on the circle. Grassmann gave a simple product rule for 2 points, that was the straight line that joined them. This is in fact not a closed rule, strictly speaking because it flips out of a set of points to a line, that is it goes from a point algebra to a lineal one. However, this is why Grassmanns analytical and synthetically method is so powerful. Without his structural inconsistency we would never be able to construct a model of “reality” consisting of collections of distinguished points. These non closed definitions of combinatorial processes allow us to define and study the combinatorial structure of sets which include other sets at a different level of “interpretation”.
These levels of interpretation are surprising because they exhibit the same formal structure whatever level is chosen! This means that analogous thinking has this formal basis to which it can be compared. It also means that a solution at one level may provide a solution at another level, and contrariwise a question at one level may be a valid question at another level.
Hermann apprehended this analogous superstructure, and I recognise it as a characteristic of a fractally generated structure. Thus Grassmanns analytical and synthetically method is highly fractal : recursive and iterative.
It is also nice to see a direct and cross application of the parallel line being the bais of a combinatorial process of synthesis on a circular decomposition of the plane!
It is extremely important to realise that when Norman says this applies to all comics, this means our formal models of gravity and electromagnetism, strong and weak nuclear pressures can be decomposed into all these analogous forms.
The V9 group is therefore only one of many decompositions of the circle that can describe our formal mathematical structures. Norman gives 3 examples and the V9 group is a fourth, but there are many others. 9 has a special numerical place in Bahai philosophy and metaphysics. The 8 has a special place in Vedic philosophical and metaphysical wisdom. But as you can see, these are really anchor points in a more general spaciometric description of our formal models of ” reality”.
It is important to note, that this means reality is more complex than our formal models!