importance of ring

[AntonioLao]

The advantage of ring over group as defined in mathematics for studying abstract patterns of symmetry is the extra mathematical operation. While the operation of multiplication is usually sufficient for defining group symmetry, ring symmetry requires both operations of addition and multiplication. In this sense, ring symmetry can describe both the charge and mass properties of matter and energy. It describes the charge properties by the operation of addition and the mass properties by the operation of multiplication while the other properties of intrinsic spin are inherent in its topology. These things which can be added or multiplied are the newly defined supersymmetric mathematical structures of singular symmetric Hadamard matrices. They are supersymmetric mainly because both local and global properties of internal and space-time symmetries are combined together. The resulting supersymmetry can describe the squares of energy as quantum vacuum fluctuations of zero-point energies of space-time charges.

Consequently, using a doubly linked ring superstructure its abstract geometry can be associated to the Hopf-Möbius topology of any given physical dimension. Nonetheless, the symmetry of this superstructure is easily demonstrated using merely one or two physical dimensions of space-time for both compact and noncompact structures. The compact structures describe one dimensional space-time quantization while the noncompact cyclic structures describe the two dimensional space-time continuums. The logical outcomes of these two distinctive domains of abstract description give a more plausible explanation why some elementary particles have zero masses and why the quantum of mass is almost impossible to define physically but easily define theoretically using abstract mathematics and without invoking the existence of spin zero scalar Higgs bosons.

[mkirkpatrick]

A ring to can be the opening made to accomodate the
formation of a vortex? A ring of truth to it!





regards michael.

[AntonioLao]

The ring of consciousness around the physical universe is topologically equivalent to the one-sided surface of Hopf-Mobius band. Moreover, there must exist mathematical relationships with the magic matrix of any order. Magic matrices have elements that corresponds to the numbers inside magic squares of any size. See the upcoming thread on magic matrix.

[mkirkpatrick]

The ring of consciousness around the physical universe is topologically equivalent to the one-sided surface of Hopf-Mobius band. Moreover, there must exist mathematical relationships with the magic matrix of any order. Magic matrices have elements that corresponds to the numbers inside magic squares of any size. See the upcoming thread on magic matrix.

Thanks for the explanation,will look out for new thread.



regards michael.

[AntonioLao]

A unidirectional Hopf-Mobius band is not necessarily topologically equivalent to another unidirectional Hopf-Mobius band. But taking three bands simultaneously, two of these must necessarily topologically equivalent.

[mkirkpatrick]

A unidirectional Hopf-Mobius band is not necessarily topologically equivalent to another unidirectional Hopf-Mobius band. But taking three bands simultaneously, two of these must necessarily topologically equivalent.

Yes that sounds about right.



regards michael.

[AntonioLao]

The conjecture is that the number of opposite direction of Hopf-Mobius bands must be equal in order to preserve perfect symmetry.