Saturday, December 24, 2011

Nested tetrahedron

--- In, "RLG" wrote:
> Just a note on coordinate systems, probably unrelated to
> consciousness, but should be made clear for readers of this forum.
> Ralph wrote:
> > Alternatively, consider that we ARE taught XYZ-cubic coordination
> > and
> > visualization as a "first-language". That's our bias .    But then
> > we
> > encounter the new-found awareness that ALL of our transactions are
> > engaged, naturally, in this tetrahedrally coordinated dance.   And,
> > the tetrahedral dance does fit INSIDE the cubic framework, even, in
> > fact, naturally expressing multiple-states in the process.

>[RLG]: Rectilinear coordinate systems are just one popular and common system.
> Standard mathematics has an infinite number of such systems; spherical
> coordinates, polar coordinates, and so forth.  It should be really
> easy to have a linear transformation from the usual rectilinear
> coordinates to a coordinate system with axes in alignment with the
> tetrahedron shape.  That is all part of standard mathematics.
> However, such a change is no big deal and sheds no light on
> consciousness.
> R

[ref] Yes, equivalent frameworks are an important point. Given, for instance, the actual way consciousness works, how is it that they even arise or are recognized?   Or, put a slightly different  way, given the many inter-transformative equivalent representations, there ought to one or a few coordinations or configurations that do, in fact, instantiate more often within nature.   If previously unseen, discovery of such a more frequent natural configuration could certainly be enlightening on some features of natural consciousness.

Additionally, one of the perspectives I hold is that 100% of all abstract math symbols and expressions are artifacts of human consciousness. So, there is obviously SOME kind of important connections between the primary symbols and expressions -- the relationships -- within the fabric of human consciousness and with the secondary symbols and expressions people  cast to form terms and expressions of their abstract maths.  

I stress abstract math as an artifact of human consciousness, in part because I've observed that dogs, horses, cats, and cows that I have lived with and depended upon at various times, survive and function quite well and have superior senses and abilities, yet all without any dependence on or need for fiddling with any abstract maths.

Moreover, as described in my prior post,  having had the opportunity to study a small amount of organic and biochemistry, I have come to appreciate that a huge fraction of diverse molecular coordinations throughout the biosphere persist and function in the so-called sp3-bond hybridization.  That arrangement generally places four collections of "matter and charge", most often  at the four vertices of a tetrahedron.  (See: for  some molecular schematics mostly taken from Morrison and Boyd's "Organic Chemistry".)

This means that all of the molecules of water in the world's oceans, rivers and streams, and clouds,  as well as the water that makes up more than 60-70 percent of each person's being, are all in this one tetrahedral configuration. The same generally holds for all organic carbon (and nitrogen-ammonia) -- as our fats, sugars and proteins -- making up living systems.  As well the silicates making up the mantle and crust of Earth and terrestrial type planets, exist in the same tetrahedral configuration.

So, a large fraction of the volume and mass of the Earth, plus our own physical selves exist within tetrahedral coordination and patterns. As well, in our own  respiration reaction, some number of carbonaceous tetrahedral units are dissipated  as 10^20 (tetrahedral) water molecules are being formed each second.  

Thus nature sings a loud and joyous sp3 (tetrahedral) refrain.

As you point out, standard abstract mathematics as developed so far, basically building up from the XYZ Cartesian model of the 1640's,  does indeed have several seemingly equivalent and/or inter-related  coordinate frameworks. And our dominant scientific paradigm, the one that doesn't yet have much coverage for consciousness  does maintain the perspectives you express. Indeed, getting to a different scientific paradigm which does improve integration would, of course, involve making one or more discoveries and changes or shifts  related to some of these coordinating features and issues.

Another point, more related to efficiency in direct visualization rather than apparently equality of computed numerical measures arises when thinking about the significance of order.  Physicists may say it as "initial conditions are important", or "outcomes often are determined by initial conditions".  I am proposing that learning tetrahedral coordination FIRST leads to a different and improved, naturally more organic way of thinking, rather than, as has been most students' experience since the 1600's, embedding the XYZ-cubic coordination system first.

Again, the short demonstration of this, rather than start with a point and a line and the number line,   is to flip through the five ways to align four rod magnets along the radii of a tetrahedron and then note the look and feel symmetry of this one general handheld multiple-state model with the similar five possible charge or electronegativity patterns of the sp3-hybridized molecular arrangements.   One pattern begets five  states differing in increments of one-half spin. These five states model the patterns making up the molecular states of essentially all life and  much of our world.

Then, to shed some light on the un-sub-conscious, one can use the n2s2 magnetic tetrahedron unit and showing that there are six (or twelve) ways to orient it within or relative to an enfolding field (equivalent to beginning with the tetrahedron, then ADDING the XYZ-cubic framework).   Then the visualization shifts from the ~six states of the n2s2 magnetic tetrahedron, to the analogous ~six possible orientations of each water molecule forming during steps in our respiration reaction.   In under 20 lines of text,  that gets learners to an appreciation for and perhaps some physical intuition of the 6^n internal structural coding that is always running concurrent with all of our moods and experiences.  Since initial conditions influence outcomes, repeating vibrations in the environment obviously would form or select out repeating patterns in the chains of water molecules being formed during respiration. Thus, beginning with tetrahedron, learners would quickly experience and acquire an appreciation of at least one way living and breathing also results in having a somewhat functional internal associative  representation of our surroundings.  

Since the structurally coded packets of water molecules formed during respiration would subsequently influence protein-formation and folding, the same internal analog language can also be observed as having direct active connections with motility and, through protein-folding, ALL human expression and communication. So, the impression is of a deeply integrated associative/relational process.

Yes, certainly many would  probably say one counter-claim may be in favor of the total wad of abstract math that you referred to earlier and heading to quantum mechanics.   That is,  certainly the option is to start in with the Cartesian split, the point, line and number line and embed the XYZ-cubic framework FIRST, and then build outward  through the various layers and logics to also arrive at some appreciation and some distribution of physical intuition to students of reality as resting upon multiple-states.

As you said and I agree, going that route generates a lot of equivalent frameworks (which would also be characteristic of  a multiple-state system) but doesn't or hasn't yet seemed to lead to ANY clearly functional description or accommodation for "consciousness". (other than the one I am presently .-)

So, again, different initial states lead to different sets of outcomes and involve different levels of effort.    It will be interesting to discover how such  alternatives pan out.

Imagine facing the global classroom...

Best regards and Merry Christmas,

Joy, to the world
Heaven and nature sing.