D w i

[AntonioLao]

Direction without inertia or direction without magnitude is as real as magnitude without direction. But having one attribute does not imply having the other. The former is called a null vector. The latter is called an absolute scalar. The generalization of scalars and vectors became known as tensor analysis. Consequently, the attribute of directions became synonymous with the idea of linear transformations and directions lose their physical important.

On the other hand, the introduction of 1D complex imaginary numbers into a form of mathematical analysis allowed Hamilton, in the middle of the 1800s, to search for their 3D representations. Subsequently, he invented the algebra of quaternions. Unfortunately, quaternions formed an abstract non-commutative ring under the binary operation of multiplication. Fortunately, restoring commutativity is done simply by using the algebra of 2 by 2 Hadamard matrices, without zero elements. Furthermore, these matrices are ideal representations for all 2-value elements of plus unity and minus unity. Therefore, 2 by 2 Hadamard matrices form a special type of abstract ring structure under the binary operations of addition and multiplication preserving both associativity and commutativity but no property of multiplicative inverses hence no identity matrix. The generalization of n by n symmetric Hadamard matrices provides a unique multi-dimensional operation of multi-ordered addition. This property can be used to define the physical quantization of electric charges as well as color charges. On the other hand, the quantization of inertia or mass can be realized by the binary operation of matrix multiplication of the same matrix order. However, in idealized mathematics, only the former property (charge quantization by addition) is dependent on direction without magnitude while the latter (mass quantization by multiplication) is dependent on magnitude without direction. A good physical example of direction without magnitude is a magnetic monopole and for a magnitude without direction is a scalar Higgs boson. Sadly, in a theory of quantized spacetime both cannot exist.

[mkirkpatrick]

Consciousness would be a candidate for dwi would it not?




regards michael.

[AntonioLao]

Absolute consciousness would be the prime immovable and therefore it is a magnitude without direction. Informally, direction implies motion or potential of motion. In TQS, its is a local infinitesimal motion (LIM) as 8 directional invariance.