          There is a very important and direct relationship between a time cycle and a physical spatial area.
The time cycle can be represented by a circle.
The surface area is commonly represented by a square.
The relationship between the square and the circle can thereby be interpreted to be a representation for the relationship between space and time.

Square ~ rib ~ line ~ space
Diagonal ~ circle ~ cycle ~ time

The relation between the square and the circle has been known in alchemy as the squaring of the circle.
How this relationship is significant can be seen in the Moorish architecture such as for the Alhambra.
There that has been found that the buildings have been created by using a very simple and specific ratio between the square and its diagonal.
The diagonal was traces with the compass to extend along the side of the square and then used as the basis for a rectangle with the width of the side of the square but the height of the length of the diameter of the initial square.

In this way the ratio was continued because the diagonal of the newly created rectangle was them traced out and up again to extend along the vertical side of the rectangle, and used as the height of next rectangle with the same width as the side of the original square.
In that way the architecture of the Moorish houses would have the width of the square the length of the diameter of the square, the length of the diameter of the rectangle created by the circle that diameter of that square, and again the length of the diameter of the rectangle which was created out of that next in the sequence.

If the length of the side of the square is called one them its diagonal has the length root two the length of the next square the heights of the next square would be the root three and the height of the next square would be root five.
In this way it is also possible to see a direct relationship of the Fibonacci series built into the creation of these Moorish houses.
Now it is possible to apply that same understanding as the relationship between space and time by understanding that that diagonal of the square (when it is being traced into a circle) is in fact part of a cycle.
That means that the very many values of roots of a number in physics can be equated to an understanding of the diagonal of the square which corresponds with that square.

The physical square then represents a spatial relationship.
The diagonal of that square then represents the basis of cyclic movement
which will trace out four squares side-by-side fitting in a circle (=cycle).

This makes is possible to simply reconsider the whole relationship of that of the  square and its diagonal, as a relationship between time and space.
The temporal interpretation of the cycle would be the base frequency associated with that square’s diagonal; in fact it would be the wavelength correspondence for the resonance of the vibration within the square.

From algebraic perspective this would amount to the determinant of the matrix which represents the notation/formulation of the square.
From a musical perspective this would mean the base frequency of the resonant wave which would fit in the square as defined by that geometry of space.

This puts a relationship between the Moorish architecture and the architecture of the masons building the mediaeval cathedrals.
One of the main characteristics of these cathedrals is their spatial volume and spatial geometry in fact specifies a specific combination of wavelength in the length and width of the Cathedral which in combination define the resonant frequency's determining the sound qualities of that Cathedral as a resonator.

That means that we can then understand the Cathedral as an acoustic resonator (compared this to a hologram amplification resonator) which is of a similar nature of that of any musical instrument.
For example, the violins built by Stradivarius are known to be excellent resonators for the vibrations of the cat-gut string, plucked by the horsehair violin bow.

By understanding that the musical instruments integrates the vibrations into a standing wave pattern around the Eigen-frequency of the instrument, then it will be clear that the actual shape-relationship of length and width and height of the instrument will determine what kind of frequencies can be amplified within that system.

This helps understand how specific shapes function as filters for acoustic resonance.
It also means of combinations of shapes, such as seen and in the creation of the cathedrals, were cube's on top of each other, combined with cube in the length direction to each other combined with cube's at lateral orientation with respect to each other, will determine the specific diameters of the wavelength of the sound which will be resonant on that specific construction.

That means that there is a direct relationship between the length of the side of the cube, the diagonal of any of the sides of the cube and the main diagonal through the centre of the cube.
Each of these frequencies will be resonant frequency determining the timebase for the wave propagation of the eigen-frequencies within that spatial structure.
That means that we can then consider any specific shape in nature as a construct or composition of spatial cubes in a very specific arrangement.

Combining this with the understanding of network calculus in algorithmic computation it is possible to approximate for example the shape of the violin built by Stradivarius and computes which wavelength patterns would be defined within that specific network nodal computer algorithmic calculation.
These calculations can be very complex, especially when there are relationships between square forms and circular forms; such as in musical instruments.

We need to compare the circular forms of the musical instruments (such as those found in the side of a violin), and relate them, correlate them, to the resonant shape forms such as presented for the geometry of the atom.
An atom is a standing wave form in which the wave bands are spheroidal.
That means that every next waveband is in fact a self-resonant frequency, for the specific geometric construct which will define the shape of the atom.

### Atomic Resonance

The so-called inter-orbital gaps in the atom are the wavebands in which the wave length is not an integral number but an integral number plus or minus ½, which means that in that wave band region the wave resonance will be destructive.
This is the characteristic for the organisation of the atom, as defined by the equations of deBroglie: at the wave band of an integer wavelength there will be wave resonance which means that there will be a defined resonant vibration in existence, while at the wave length N +/- ½ there will be a maximum wave potential but no wave resonance whatsoever.

### Cell Divisions

This understanding we can now apply to the structural organisation of cells in the living being.
We can use the matter model of the atom as a metaphor for this speroidal organisation of the cell.
We can use the juxtaposition of one cell next to the other as a geometric reference for spatial organisation of cells in a close packing or other packing formats as described in crystal analysis for atomic lattices.
We can then see that the wavelength in those spatial organisations will be defined by the same principles as has been described for for example the buildings of the Alhambra, the cathedrals built by the masons, and the musical instruments such as the violin built by Stradivarius.

In considering the wave propagations in the living body we are not just dealing with the geometric organisation of the cells in their specific lattice.
We are also dealing with the speed of propagation of sound in matter, which in living organisms is defined by the temperature/materials that have been produced by the living cell.
That means that we need to have a kind of computational algorithm of a similar kind of that is used in the computation of the relationship between the River and the bedding; interactive computation.
We need to see how the material substance will determine the speed of sound and propagation and thus the resonance organisation in phase and in space, but likewise we must correlate the frequencies that result from this to the resonant pattern as has been described for the spheroidal orbital atomic wavebands by which the materialisation of the physical body takes place.

That means that we have now a very fundamental and basic model to correlate the organisation of cells within the living body in terms of time and space.
We now have a very simple model to correlate the relationship between space and time, in the geometric representation of the square versus the circle.
We now also have a fundamental understanding of the role of the square root in the mathematics of physics, where we can see that we are dealing with the diameter of a spatial square (or a cube) and that we are thereby in fact correlating the organisation in space to the organisation in time (diameter=cycle).
This also ties in with the finding that the most fundamental formulations of physics such as F=m.a or I=O2.R or E=MC2, or all equations of a similar kind in which the squaring is essential to the description of the relationship between space, time, mass or energy.

We now have to understand this in a more fundamental manner because we are now also dealing with the musical phase relationships take place within that time space geometry and algebra.
That means that we now need to understand that the calculations that we are dealing with are not just spatial, they are not just temporal, and they are not just energy/frequency determined, but there are also of the nature of consciousness, intelligence, intent, which is the ability to invert information from the what takes place within the system to what takes place outside of the system.

We see that kind of information exchange from inside the system to outside of the system in the formulations by Bruce Lipton.
There are many others who have are addressed these characteristics of transfer of information/energy from outside of the body to inside of the body.
Hans von Reckeweg and James Oshman for example described how information respectively electricity, is propagated from the environment into the body.
Bruce Lipton describes a mechanism for the incorporation of information into the physical structure of the living self.

Therein the sensor protein functions as an antenna to capture frequency resonant waveforms outside of the cell to relate them to what happens inside of the cell.
The portal protein then makes it possible to respond to that information by opening or closing the surface of the cell by opening or closing a cell singularity, which is in fact the portal protein.
The correlation between the information and the action takes place in the linking protein within the living body cell.
The activity of the linking protein is then mirrored, transcribed, onto the DNA by the DNA mantle-protein.

These processes are all taking place in the domain of frequency.
All of our perceptions of our environment by our sensory system are all based on frequency patterns.
The only way to coherently understand the relationship between our environment and our body is in terms of vibrational frequency field coherence.
Which means that we must forego of the traditional interpretation of a sensory system composed of hearing, seeing, smelling, tasting, and so on, but instead we must regard the whole of the body as an information/energy frequency filter system.

It is in that relationship that we must find a way to describe the frequencies of the environment (as registered by sensory system) in relationship to the internal response of our living body.
This is where we can then understand our living body as a resonator to external frequencies of the environment, in the same way as a crystal will resonate and respond to the frequencies of its environment.
In this case we can understand that the whole body is able to not only resonate to those ambient frequencies, but also to change is internal physicalisation to correspond with those are phase frequencies transformations.
It means that we have to combine the understanding of physical crystaline packing systems in the relationship to the orbital resonance sphere dynamics which we know as atoms.

### HyperMandala

This is where we can make use of the understanding of Roberto Renout, as he formulated it in the concept of the hyperMandala.
The hyperMandala is based on the orbital frequencies of the planets revolving around the sun.
That means that these findings can be applied all equally to the orbital frequencies, in the deBroglie terms, for the atomic orbits.
Roberto Renout realised that a planetary system is in fact the superposition of cycles, and thus of frequencies, thus of time bases, which together form a coherent fabric.

### AtoMolecules

By the approach of the hyper Mandala of Roberto Renout it is possible to correlate the formation of atoms and molecules.
An atom is a concentric harmonic multiplex oscillation in space and in time.
A molecule is a concatenated, linear, juxtaposition of resonant radial frequencies.
In fact, the relationship between the two is defined in the Mach conic where the radial resonance and the lateral propagation of resonance can be combined in one formulation.

### Phase Space

Combining this view, with the shape of the Gothic cathedrals (see above), it is possible to understand the composition of resonant phase space dynamics.
A Gothic Cathedral will define a resonator within which ambient frequencies will organise and group themselves just as the Stradivarius violin will bring coherence to the sound of the vibrating strings.
It means that it is possible to then understand that within this stable, fixed, structural organisation of the Gothic Cathedral, there will be a preferential resonant wave field of defined in phase space only.
It is that precise understanding that we need to be able to elaborate a concept of MatheMusics and MuseMathics.

Because we need to see how the time dynamics within the living body are correlated with the spatial organisation of the living body.
Evidently, it is necessary also to understand that the phase dynamics is more important than the spatial organisation.
It means that we need to invert that understanding which we have described above in terms of their musical resonance within a large Cathedral.
Because within the living body we see that the organism dies as soon as the organisational phase dynamics of the electromagnetic fields exchanges in the body and the environment has stopped.

The difference between living being and a dead being is that precise information propagation within the organism.
This is not based on the physical characteristics of the organic object, as can be seen upon death.
Because when an organism dies in most cases the a(na)tomic structures and features are perfectly intact and are should be conceptually functional.
What however is missing is the information organisation orchestrating the electrochemical atomic interactions between the living cells and within the living cells.

### Information Fields

That means that we need to understand the living body in terms of an electro-magnetic radio-information field, which has its own organisational coherence dynamic.
It means that we can NOT interpret nor describe the living body as a physical entity or organism.
Instead we must describe the nature of being and the quality of life as the dynamic information organisation coherence.
Which means that we need to define the phase information organisation dynamics by themselves (phasics), which is precisely the essence of MatheMusics or MuseMathics.

That means that we now need to find a precise relationship between the phase field (process/time) dynamics outside of space (diagonal, ‘root’) to the resonant organisation of phase coherence which can than map onto the organisation of spatial structure (‘square’).
For this we can make use of the insights of Roberto Renout described as the hyperMandala above.
In fact, it is a generalisation of the principal described by deBroglie for spatial harmonic resonance organisation, such as found in planetary systems, in atoms, in molecules, and thus also living body cells.

### TimeBased GeoGebra

This is why be now need to see a relationship between algebra and geometry in the very simple relationship between the square and its diameter.
In this case the diameter is understood to be a tracing of a circle and has to be interpreted as formulated as such.
That means that every diameter (or every algebraic operator determined by a square and its root) will be the equivalent of a temporal based frequency notation.
Which means that all of the formulations which have the quality of a square or a root in algebraic systems are in fact counterparts of a temporal notation taking place in space.

### Squares (2) are squares, cubes (3) are cubes

That means that we need to look at all algebraic formulations in these terms.
That the simple variable such as X, Y, Z and so on would correspond to the side of the square
The squaring of that symbol would correspond to the implied diagonal of that square, as found in X squared, Y squared, Z squared, and so on.
Likewise the formulation of X cubed, Y cubed, Z cubed, and so on would again have the literal Association from the cubic organisation and the main diameter of that specific cube being the trace of the half-wavelength of the time-cycle orbit-frequency associated with that specific geometric form.

### Root = Timebase

This text has given a basic understanding of the way we can interprets the geometric and temporal relationship in terms of the algebraic formulations.
Therein it is clear that the squared forms and cubed forms of the functions are literally the transition from a planar to a higher dimensional organisation.
However now there is an implied notation that with the extension of that specific spatial form in its extended dimensional that is also the need to imply a defined duration in time.
Which means that the construct of the line, the square, the cube, and so on will always tie in with a required extended duration of that form in order to physically exist.

### Root = Rate

That means that we now have an implied time component in the spatial notations which science has traditionally given.
It also means that the traditional physical algebra which was interpreted to be valid outside of the domain of time is in fact implied in the domain of time as well, always.
This means that we can now look for a reduction or complexification of algebraic formulae in which the variables XYZ as measures of space, can be now correlated to XYZ-squared as correlated to time and likewise for XYZ-cubed as correlated for time with a deeper embedding of phasic/psychic organisation.

### Timing represented by Tiling

In separate text this correlation between the square and the circle will be extended and its application for the way the vitality of the cell is defined by this temporal embedding of oscillation.
We’ve already seen that frequency organisation is the essence of our sensory system and of our vital functions.
We can now correlate the spatial geometry with the temporal extensions and apply this to the organisation of the electromagnetic field.
Therein we will always need to correlate the electric wave with the magnetic wave but also with their counterpart of the radio wave and its ensuing information field.

### Frequency = Rhythm

This concludes this introduction to the understanding of the concept of the squaring of the circle.
In fact we have found that we are dealing with the relationship and the correlations between space and time.
We also found that we can now give a different interpretation for algebraic equations to suggest their implied temporal base phase frequency conditions in the so-called squares, or their roots.
And we can thereby apply the same understanding as we have seen for the architecture of the Alhambra, the mediaeval cathedrals, and the musical instruments, for the understanding of the importance of dynamic phase frequency coherence of organisation in the living being.       [Welcome] [Core Concepts] [Topics] [Participants] [Publications] [Research] [Projects]  