Interesting, I haven't had a chance to look too in depth at Waser's model yet but it seems similar to a model that Zi Hua Weng uses in his papers.Not sure if its the same model but he uses it to demonstrate several interesting results such as the fact that gravitational mass is altered in the presence of strong magnetic fields. https://www.researchgate.net/profile/Zi_Hua_Weng

He uses octonions (perhaps the same as biquaternions?), modelling gravity as a quaternion orthogonal to Maxwell's quaternion for the EM field. He shows that the gravitational mass is the inertial mass plus small terms that become relevant at large EM field strengths https://www.researchgate.net/publicatio ... tic_fields

Assuming the biquaternion is just another name for an octonion, it sounds like he is using the same or a very similar model as Waser.

## Speed of the Progression of the Natural Reference System

### Dual Quaternion not the same as Octonion

Bi-qauternion is *not* just another name for octonion as it uses the same unit vectors (namelyAssuming the biquaternion is just another name for an octonion, it sounds like he is using the same or a very similar model as Waser.

*i*,

*j*, and

*k*) utilized in quaternion calculus and not

*e*

_{1},

*e*

_{2},

*e*

_{3},

*e*

_{4},

*e*

_{5},

*e*

_{6}, and

*e*

_{7}.

Bi-qauternion or dual quaternion is a Complex quaterion

*q*hat =

*d*+ ε

*r*where

*d*and

*r*are quaternions.

More: https://en.wikipedia.org/wiki/Dual_quaternion

Let's not forget the Epsilon function: ε

^{2}= 0; ε ≠ 0

as we're working with DUAL quaternions: https://en.wikipedia.org/wiki/Dual_number

Dual quaternions are isomorphic to the Clifford algebra elements

*i*,

*j,*ε with

*i*

^{2}=

*j*

^{2}= -1 and ε

^{2}= 0. Recall: ε also cannot be 0 or we're back to single quaternion.

Define

*k*=

*i.j*and ε =

*k*, then the relations defining the dual quaternions becomes a self-defining closed set.

I abstract this in my mind as two double-rotating systems (r1/r2, r/3/r4) or one hyper-rotation (R1/R2) forming a hyper-volume which is 4D (one dimension for each of the angular displacements in time). These 4 dimensions (r1, r2, r3, r4) are

*inverse speeds*, angular displacements in time, and are measured in counterspacial

*turn*and is angular-based (as opposed to linear-based).

Turn IS the

*reciprocal*of time (

*frequency*) -- cycles per second instead of

*seconds per cycle*-- which within the unit space boundary (time region) is an

*inverse*speed (

*energy*).

Those four dimensions (of

*equivalent space*) would then be

*i*,

_{1}*j*,

_{1}*i*, and

_{2}*j*

_{2}*k*

_{x}is no longer an independent variable as it is defined as

*k*

_{x}=

*i*and furthermore ε =

_{x}.j_{x}*k*and ε

^{2}= 0 and ε ≠ 0

This means

*k*must be 'at infinity' (as zero is out by definition and the square of any non-zero number is not a solution). Interestingly enough this also seems to imply that infinity squared is zero. I bet this is the case

*geometrically*speaking where the

*separation*between two infinities is always the same: none.

Would this then make

*k*, the 1-dimensional spatial "electric"... the REAL, a

*net*strain caused by the dual projection of

*i*/

_{1}*j*and

_{1}*i*/

_{2}*j*?

_{2}Depending on which element you may choose to equate with unity an inherent bias is created. For instance, setting det(A,B;C,D) = 0 where D = 1 + 0w using 4-vector notion in matrix form for doing transformations... that "1" is the same "1" that goes into the assumption of the plane at infinity creating the concept of parallel at the Affine strata.

As we see here from Bruce:

Pressure can be interpreted as force per area: t/s...only the net magnitude of speed can be transmitted across it (no orientation). In RS, that is limited to thepressureof linear motion. In RS2, it is acomplex quantity, composed of the linear (real) and the rate of spin (imaginary). That means that anything we measure that is on the other side of a unit boundary will be observed as a complex quantity--not the actual structure that is there. (emphasis mine)

^{2}per s

^{2}or t/s

^{4}in this sector (time-space) and s/t

^{4}in the conjugate space-time sector.

We can also define gravity/mass as the shear (cross-product) of material and cosmic pressures:

s

^{3}/t

^{3}= t/s

^{4}× s/t

^{4}

Second, the dual quaternions are isomorphic to the even part of the Clifford algebra:

*e*

^{2}

_{1},

*e*

^{2}

_{2},

*e*

^{2}

_{3}= -1

*e*

^{2}

_{4}= 0

i.e. there is a connection to octonions but dual quaternion have some distinct properties of their own.

I suspect similar as to to how the geometric rules of interaction play out as differences in modes of combinations of motions, the algebra will play a similar role in how we recognize the subtle distinctions inherent in the differences of say treating a system as a dual quaternion vice an octonion.

In this case I would say

*dual*quaternion is appropriate if we're dealing with

*inanimate*structures such as atoms where there is both a material and cosmic influence (what exists in space must also exist in time). These motions are mutually stable together but they are not

*one*and hence they are not living.

However octonions ARE

*life*and must be treated as a

*single*system, rather than a combining of two systems, as this is what defines life where one and one come together not to form two but to again create one whole; a

*single*compound motion which involves all of the time/space sectors: local body (

*time-space*) made up of material atoms (

*time region*) and non-local mind (

*space-time*) made up of cosmic c-atoms (

*space region*).

Infinite Rider on the Big Dogma