ckiit wrote: ↑Sun Mar 22, 2020 3:33 pm
Thus posited: symmetrically about the 4x4 matrix sits a single
transcendental axes of '4' composed of 2x2 null binaries:
all+/-not denoted {alpha/omega} and
causation+/-cessation denoted {beg/end}, each pair being a conjugate binary (+/-),
the
transcendental nature of which owing to the axes being wholly
space- and/or time-invariant,
thus must rest in/of and/or as '1' as well as
being '4' (if indeed both transcendental and universal).
This must be true because no non-transcendental axes can ever be used to transcend a displaced body(s)
beyond
the limitation/boundary of the axes itself. Because this axes transcends beyond space and time, it must follow that all
caused bodies contains this axes intrinsic to their own composition. In other words: all displaced bodies have local to them,
as part of their own constituency, a transcending axes
immutably concerning unity at
all times from
all places.
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This is the mathematical basis for mass/gravity (i.e. a "2D rotational base"), from which all matter (geometric form) is
derived as a series of recursive "shells" building outwards in counterspace (inwards in space): A/B and C/D (count of 4 ratios/motions) are each 2D rotations -- a pair of SOLID ROTATIONS (a pair of rotating
photons -- double, double magnetic rotation) except here D is unity -- and form the axes of '4' in
One. The goal is to be
unified; take my hand, be my Brother. The only way is One.
The datum for {A, B, C, D} is the NRS -- unity...
motion -- as these are
scalar magnitudes (in actuality each 2D as there is a
space aspect and a
time aspect),
the transcendental nature of which owing to the axes being wholly space- AND time-invariant. (Fixed it for us.
)
Before we start debating D is *not* a
cross ratio, I beg to differ: (1/1) × (1/1) = (1/1)
A/B & C/D comprise the '2x2 null binaries' (+/-) as
roots of
no coordinate dimension to be evolved
into coordinate dimension (raise power thru 'exponation' -- the integration process previously described for 1D→2D projection into
equivalent space/time):
[1] all+/-not denoted {alpha/omega} as represented by
inverses ALL (+1 or ∞ when observed from counterspace) -AND/OR- NOT (±π -- the
metaphysical,
ethereal "rotational base" --
nothing or '0' when observed from space), and
[2] causation+/-cessation denoted {beg/end} as represented by
conjugate motion in TSR & motion in STR -AND/OR-
conjugate motion in TR & motion in SR -- the totality of motion that seek the boundaries of {+1 ↔ -1} in space and {↔π↔π↔} in time... maximum of 2 displacement units in either "direction" (exclusive or: the first as
speed, the second as
energy)...
bperet wrote: ↑Wed Jan 01, 2020 3:11 pm
user737 wrote: ↑Wed Dec 04, 2019 12:09 pm
Are we certain speed of progression = speed of light? If not, this is another DOF.
It would not be another DOF, as the existing 15 degrees cover the motion of the photon (as birotation).
The speed of the progression is fixed, which is the unity in the 16th position of a 4x4 matrix.
Take it away, Bruce:
bperet wrote: ↑Sat Feb 28, 2009 12:42 pm
Row vector is a temporal "absolute location", formed by the intersection of three planes.
Column vector is a spatial "absolute location", formed by the coordinates of a point.
A,B,C are the three, scalar dimensions of motion.
The "r" values are the rotations/shifts for the respective dimensions (sine component). The cosine component is multipled across the two adjacent, scalar dimensions. For example, rotation about Z includes a cosine component to A and B.
tx,ty,tz are translations. The "S" translations are the linear, spatial translation we are familiar with. The "T" translations are the temporal "translation", which we would view as a phase angle of the turn (unbounded angle).
Ct is Clock time. Notice that it is REAL, not imaginary (temporal), thus making clock time
appear as though it was a "4th dimension" to space. It is actually a scale factor to space.
Cs is Clock space, an imaginary component that scales temporal vectors, and acts as a 4th dimension to time.
The inherent symmetry (of reciprocity) is immediately apparent and
cannot be denied.
bperet wrote: ↑Wed Feb 25, 2009 3:12 pm
Where absolute locations in space (row) and time (column) are linked to the compound, scalar speeds (4x4 matrix). ALL numbers are complex quantities, not integers.
I wish there was a strikethrough font available on the board for just this reason: swap ‘row’ and ‘column’ in Bruce’s comment above as he later flipped convention (from whence this quote has come) in providing for the final matrix transform form seen at the top of this post.
Also, Bruce, you said ‘ALL’ (emphasis
not mine) and I do not see that
necessarily true (I am being very deliberate with my word choice here) for unity datum: 1 + 0
w. This means there
must be other transforms for those others combinations of speed regions besides what we use here for TR ↔ ST/TSR. Talk to me, Goose.
Location in
space as represented by a Homogeneous coordinate (HC) column, with the 4
th coordinate being
clock time (scale factor for spatial location), and contain only the
real (linear) aspect of the complex quantity:
| X +
i0, Y +
j0, Z +
j0, 1=C
t |
Location in
time as represented by a Quaternion row, with the 4
th coordinate being
clock space (scale factor for temporal location), and contain only the
imaginary (rotational) aspect of the complex quantity:
| 1=C
s, 0 +
iZ, 0 +
jY, 0 +
kX | *
*note: must read read row backwards (right-to-left) to transcribe proper ordering per existing convention
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The 4x4 matrix includes a single transcendental axis (diagonal -- top left to bottom right) which comprises A, B, C, D (where D = 1 + 0
w) as shown. A, B, C are the 3 scalar dimensions of motion and are each measured as an
invariant (unchanging) cross ratio from unity:
bperet wrote: ↑Wed Feb 25, 2009 3:12 pm
The 4x4 matrix contains the various speeds of the three, scalar dimensions along the diagonal, with transforms for rotation (turn) and shift (translation) multiplied in, as complex quantities. One interesting result is that
spatial location is altered by temporal location, and vice versa, and that no single scalar dimension is directly represented in the system, as Larson claimed, but it is the
net motion of all three dimensions that is represented. (Not a problem most of the time, since two of the dimensions are usually at unity--identity--and have no effect).
ns/
nt x (1/1) =
nt/
ns IS the cross ratio (with respect to UNITY) and forms the basis for what
is a dimension:
user737 wrote: ↑Mon Apr 06, 2020 11:33 am
No dimension (no cross ratio!): point ↔ radius
D at 1 + 0
w (complex) provides for UNITY datum (1, ±π) within the larger framework of 4×4=16 elements and serves at least two purposes: (1) necessary to transform
Projective (parallelism not conserved) →
Affine (parallelism conserved) where the ideal plane at infinity is introduced to create the concept of
parallelism, and (2) establishes the
universal datum reference as outward motion at the "speed of light" (+1).
Projective invariants include
incidence and
cross ratio only; Affine introduces an additional invariant property,
parallelism as all parallel lines now meet at an ideal "point" at infinity. Differing sets of parallel lines meet at differing "points" on the 'plane at infinity' and the collection of "points" at the plane at infinity are labeled the ideal 'line at infinity'. We call this perspective.
The projection of the real
aspect (Φ-based) of the motion → equivalent
space, and can be directly observed/measured as anything with a net spatial displacement (some particles per "point" particle perspective, all atoms).
The projection of the imaginary
aspect (π
2-based) of the motion → equivalent
time, and can be indirectly observed/measured as a 1D "force" vector -- a scalar push/pull + 1D scalar bi-rotation (spin = torque), a
complex expression. All "forces" are temporal motion (motion in time) and includes the wave
perspective of some particles and all "force fields".
Seems not only do we not observe the NRS, nor do we observe space or time. We
manifest equivalent space and
equivalent time.