Also, because it is in essence merely a geometric convergence of optimum simplicity, it also applies equally to all information outside
our sensory and cognitive TIWs. So for example if we tap out a four-beat with one hand, and an eight-beat with the other, this can be regarded as a 'temporal octave'. The same applies for a 3/6 beat or any time signature based on factors of two of a given fundamental. In fact if we take this argumet to it's conclusion we can make a rather bold statement:
This principle of the convergence of simplicity states that all information we will ever process in any and all domains can be regarded as temporal and spectral modulation of factor-two symmetries. While the maximum complexity of information in a signal may appear divergent or psuedo-random, conversely the maximum simplicity is absolute and finite. Therefore a factor of two frequency relationship is both the simplest type of harmonic interval, and also the simplest type of rhythm. All other harmonic and rhythmic relationships can be regarded in terms of finite complexity relative to this optimum simplicity.
Therefore all music, all language
, all sensory perception and eveything we will ever know, think or feel can be described as modulation of factor-two symmetries. As it turns out, the Standard Model of physics is no exception...
I've made some simple geometric analysis re. cellular assemblies and the likey links between this symmetry and the underlying neurology - the main premise being that temporal and spectral factors of two pertain to connective and impulse rate equilibria, and utlimately cortical lateralisation and why we 'chunk' everything into groups of seven, though i won't go into that here.
Of course there's other ways of descibing this equivalency domain - powers of two, log base of two, it's also the most prominet overtone/undertone of the harmonic series, and doubtless other goemetric progressions. What has stunned me though is that it apears to describe all
information. There's several salient examples here:
The first periodic table, proposed by John Alexander Newlands, was discovered on the back of this apparent "law of octaves". Newlands found there are seven groups of chemical characteristics, and that these repeat every eighth grouping - IOW there is a functional and/or qualitative octave equivalency intrinsic to all matter! http://en.wikipedia.org:80/wiki/John_Alexander_Reina_Newlands
The quark electric charges in QCD are also defined by modulation of factor of two symmetries - 2/3 and 1/3. Likewise if we take halfspin as the minimum (or fundamental) unit of angular momentum then there's one octave of AM between each fermion and boson.
Therefore it seems all information everywhere, at a most fundamental level, can be described in terms of informational complexity in relation to the same convergent thermogeometric equilibria.
And so ever since i've discovered this i've been wondering; to what extent are the laws of physics - and everything else we know - a projection of how we ourselves process information?
Does the universe work the way we think, or do we work the way the universe thinks? I've written this up in a denser format here
if anyone's interested.