Leonard Susskind the theoretical physicist has this to say about orthonormal vectors
[A 3-vector is just a vector for 3 dimensional space. For 3 dimensional space, orthonormal can just be taken to mean at right angles.]
" Orthonormal Bases When working with ordinary 3-vectors, it is extremely useful to introduce a set of three mutually orthogonal unit vectors and use them as a basis to construct any vector. A simple example would be the unit 3-vectors that point along the x, y, and z axes. Each is of unit length and orthogonal to the others. If you tried to find a fourth vector orthogonal to these three, there wouldn’t be any—not in three dimensions anyway. However, if there were more dimensions of space, there would be more basis vectors.
The dimension of a space can be defined as the maximum number of mutually orthogonal vectors in that space. Obviously, there is nothing special about the particular axes x, y, and z. As long as the basis vectors are of unit length and are mutually orthogonal, they comprise an orthonormal basis."
So we have a concept of a set of directions that can fully describe a space, all other directions being able to be described using the basis vectors. The 2 dimensions of the plane being what we normally describe as the four directions. And then we could define the other dimension as up-down.
In 3 dimensions of space orthonormal means at right angles. The creation of a basis, or intitial decision on the 'directions' in experiment is usually chosen to make calculations easier, which would be driven by the nature of the experiment.
So it brings another question I think, why, if there are four directions that can form a basis for a space, is any set of four directions more important than any other?
The answer I believe perhaps lies more importantly in the intial creative impulse, which defines it, and after the fact, in what we were measuring and the way that we measure it in order to make sense of it, which would be a a function of its current state.
Last Edit: Jul 13, 2015 19:33:14 GMT 9.5 by Deleted
> So does space have a natural rectangular structure?
I think this has deep significance, and that a square or rectangle sheared into a lozenge or diamond does hold a key.
There is another way to define a direction of course, and that is with polar co-ordinates, "a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction." Polar coordinate system
That only works if you know where is the center of Existence. For most creatures that is unknown.
But if a natural grid exists then it can be referenced everywhere
I was thinking how a natural grid might be used as a refence for locations. Unless the grid is uniquely identifiable at each node or on a sensibly local scale then it would have to rely on other physical uniquely identifiable objects nearby to the grid as markers, distant stars for example might be sufficently fixed for the purpose, which might remove the need to even reference the grid in the first place.
Without knowing the very centre, any uniquely identifiable node could in effect become a point of origin to measure from. The grid being natural it would seem to make sense to use a co-ordinate system that matched the structure of the grid, but seeing as an origin would be defined to measure from, the choice of co-ordinate system would not be limited to cartesian. Effectively the centre would become wherever you decided to measure from.
In the absence of a natural grid, the measurer would just have the challenge of finding some way of marking/locating a point in space which would remain unambiguously a marker for that location, and the co-ordinate system used would just be matter of preference or ease of calculation.
Last Edit: Jul 14, 2015 3:44:52 GMT 9.5 by Deleted
So what is the nature of a direction - in the spatial sense?
direction is a universal highway of ones will and intent imo now is the human able to follow the map is question ... in a spatial sense i believe there are 360 degrees of direction and also invisible angles or paths exist within these angles of direction
So does space have a natural rectangular structure?
I think the rectangular structure is the best form suited to house the energy's of direction... each right angle holds the form solid in essence with always one right angle being the cornerstone so to speak or where the energy streams in and out...most natural formations are smooth and circular with a sort of toroidal vortex motion for example rocks trees ....
<<<But if a natural grid exists then it can be referenced everywhere....
<<<<In the absence of a natural grid, the measurer would just have the challenge of finding some way of marking/locating a point in space which would remain unambiguously a marker for that location, and the co-ordinate system used would just be matter of preference or ease of calculation.
From my own studys natural grids and there center...could these be referenced as triangles in masonic areas here in the US there are about three in my immediate area and they are all located around areas of high energy fluctuation one of them houses a darker force as there is always car accidents in the 2 block radius and alot of lower activity bars funeral homes liquor stores butcher shops all within this triangle....there is also another triangle where there is more higher activity in this one is next to a hospital churches numerous places of worship parks...
Last Edit: Jul 14, 2015 18:11:00 GMT 9.5 by elijah
I suspect that not only is there are natural grid but there are cyclical flows on the grid. When I look at the pavement in a local lodge the flows seem to reverse several times an hour.
I wholeheartedly go along with the concept of a natural grid. I think it is also true of heavenly bodies themselves. The earth itself has a grid with energy flows horizontally and vertically. It might be reasonable to think that the same applies to the solar system as likewise the cosmos.
Distant peaks emerge....clear as day. The hermit's lantern turns to guide the way. Hermit's Way - F. J. Rogers
