The link between between many extent physical theories and the recirpocal system of theories

is harmonics. Harmonics occures through out the universe fom the atomic to the astronomical scale

and surfaces in various theories and experiments. Such a henomeneon needs to be accounted for any

Theory of everything oincluding RS and RS2.

The harmonic series is the reciprocal of the counting number series and through my work on the bi-radial matrix

a direct analgy can be made. The reciprocal relation between time and space (as exdpressed geometrically

in the bi-radial matrix) is directly analogous to the reciprocal relation between the counting numbers and the harmonic series.

Larson to my knowledge did not make this precise connection and once realized expands the range of RS2 to account for all

phenomenon relating to harmonics.

The "lines of force" observed by Faraday and any one experimenting with magnets and iron filings are an expression of motion

bothg according to Larson and according to the bi-radial matrix where each angular increment represents a "quantum" of time and each

linear increment along the time axis represent a "quantum of space. The line segments makng ujp the "lines of force" are actually a graph of the space time

relationship (motion) that is typically expressed in orthagonal graphs. These field lines when rotated around the cental "D" axis (see diagrams) forms a

fundamental form the torus or toroid. The harmonic (or near harmonic) structure is indicated in the geometry of the matrix.

It has been my goal since the 22nd anual ISIS convention to show the precise geometric expression of the RS and show the reciprocal relation between space

and time has a direct numerical expression relating directly relating to the recirpcol relationship betrwen the counting numbers and the harmonic series.

I have updated the bi-radial matrix web site with more details than can be shown here: www.bi-radialmatrixintro.com

It includes a scaling mchanism, a derivation of both attractgion and repulsion fields from first principles, a derivation of a bi-readial inverse square law,

and a derivation of the harmonic series ferom the underlying structure. There is a blog section to open forum. Thanks for your attention. RK

## Reciprocity and Harmonics

- Djchrismac
**Posts:**145**Joined:**Fri Nov 08, 2013 7:14 pm

### I learned something today...

Hi Russell,

Thanks very much for sharing your work, i've read through it and although i'm no mathmetician I followed everything and it's a very good way to visualize space/time and some of the other RS concepts, thoroughly enjoyable.

This actually makes two things stand out for me personally, one is my love of Spirograph when I was very young and the other was when I took Salvia Divinorum as one of the effects you get with that is a very pronounced "lines going off into infinity" visualisation just like when you extend the geometric analogy between the two gravitational fields to give you the two sets of angles, rays and the resulting set of vertices which create the bi-radial matrix.

A few other things which stood out are from your Visual Gallery, images 1 and 2 are pretty much a musical waveform and some of the others are almost like a grid that's been put "over space/time". Image 3 also reminds me of the Flammarion image and how time/space is visualised in this picture:

This is also a pretty good clue as to what you are doing when you take the "Seer's sage", peeking through to the other side of the space/time coin.

Last of all you almost get a holographic effect from image 5 in your gallery.

Overall I have found this very usual to help me see how the structure of space/time can be built up from the fundamentals and how it relates to so many other things and it will help me to understand some of the other RS papers.

Cheers!

Thanks very much for sharing your work, i've read through it and although i'm no mathmetician I followed everything and it's a very good way to visualize space/time and some of the other RS concepts, thoroughly enjoyable.

This actually makes two things stand out for me personally, one is my love of Spirograph when I was very young and the other was when I took Salvia Divinorum as one of the effects you get with that is a very pronounced "lines going off into infinity" visualisation just like when you extend the geometric analogy between the two gravitational fields to give you the two sets of angles, rays and the resulting set of vertices which create the bi-radial matrix.

A few other things which stood out are from your Visual Gallery, images 1 and 2 are pretty much a musical waveform and some of the others are almost like a grid that's been put "over space/time". Image 3 also reminds me of the Flammarion image and how time/space is visualised in this picture:

This is also a pretty good clue as to what you are doing when you take the "Seer's sage", peeking through to the other side of the space/time coin.

Last of all you almost get a holographic effect from image 5 in your gallery.

Overall I have found this very usual to help me see how the structure of space/time can be built up from the fundamentals and how it relates to so many other things and it will help me to understand some of the other RS papers.

Cheers!