The Conjugate Entangled Manifold of Space–Time Induced by the Law of Unity of Contradiction

. The emergence of the contradiction between two different objects u and v is attributed to a mechanism that their opposite position information is transmitted and is meeting at a contradiction point. To describe this mechanism, the paper constructed the Conjugate-Entangled Coordinate (CEC) System in which the invariances of the contradiction points can perform certain transformations, such as the phase switching of time and space, the scale transformation of the measurement unit, and the invariances of the contradiction point position transfers as the relative velocity ratio information of the two opposite objects changes. This CEC system was constructed by synthesizing the time-space coordinate and the space-me coordinate. It allows the Inner Product induced by the invariance of contradiction point changes from 0 to 1 as the relative velocity ratio information of the two opposite objects changes. This induces not only an integral for all contradiction points in interval [0 𝑥 ,1 𝑥 ] but also a Conjugate-Entangled Manifold, in which the invariance of Inner Product under the transformation and rotating of coordinate system can be represented.


Introduction
According to Formal logic and Mathematical logic, there is no contradiction among the most basic laws of the world.On the contrary, dialectical logic believes that the world is full of contradictions, and regards "unity of opposites, mutual change between quality and quantity and negation of negation" as " The basic law of universal application".
Can the law of non-contradiction and the law of contradiction be reconciled?How to reconcile?These questions has long broken through the scope of philosophy, epistemology and logic, and has become a basic subject that must be studied in almost all fields involving mathematics, physics, chemistry, biology, psychology, intelligence, thinking, as well as sociology, economics, political science, military science, etc.The core question about how contradictions arise is the entrance to the study of contradictions.
The source of contradiction between two oppositions  and ( ≠ ) has been attributed to whether there exist a non-zero distance (  ,   ) ≠ 0 or not?The contradiction of  and  is varying with time  has been conversed into the function of the distance (  ,   )(≠ 0) vary with time , () = ((  (),   ()).
In mathematics, the distance of   () and   () can be represented by complex number   (, ) and   (, ) in Complex Coordinate, respectively, and the distance (  ,   ) is defined as the root of inner product of a pair of vectors   (, ) and   (, ): (  (),   ()) = √  (, ) ⋅   (, ) .Since an inner product is not only a core concept throughout mathematics, physics and neural network, but also a polarization invariant quantity under coordinate translation, by it an Entangled Vector and Clifford Geometric Product can be induced too, as well as a category and a topos, such that Artificial Neural Network defined by Inner Product can be converted into computing of tensor follow.
The emergence of the contradiction between two different objects u and v is attributed to a mechanism that their opposite position information is transmitted and is meeting at a contradiction point.To describe this mechanism, the paper constructed the a coordinate system in which the invariances of the contradiction points can perform certain transformations, such as the phase switching of time and space, the scale transformation of the measurement unit, and the invariances of the contradiction point position transfers from 0 to 1 as the relative velocity ratio information of the two opposite objects changes.
It is shown that the time-space (or spatial-time) complex coordinate system can be obtained by shifting of the time (or space) axis to  = − , in which the mechanism of contradiction emerging and meeting at the contradiction point can be expressed as a function of the position component of a pair of conjugate complex numbers vary with time component (or on contrary) and meeting at the contradiction pointas, and by the transformation of plane-polar coordinates, even to expressed as a wave function.
It is also shown that, by a synthesizing of the time-space coordinate and the spaceme coordinate, a Conjugate-Entangled Coordinate System can be constructed, in which the Inner Product induced by the invariance of contradiction point transfer as the relative velocity ratio information of the two opposite objects changes from 0 to 1.This induces not only an integral for all contradiction points in interval [0  , 1  ], but also a Conjugate-Entangled Manifold, in which the invariance of Inner Product under the transformation and rotating of coordinate system can be represented.It is known that inner product is a key concept across philosophy, mathematics and physics, and artificial neural networks, and can be defined by inner product.However, we propose that a qualitative mapping can be induced by inner product too such that a qualitative grid computer can be proposed in this way.

The Conjugate Coordinate System for Contradiction Point
The mechanism of the emerging of the contradiction between two objects  and , which are separated by a unit distance, is attributed to that the location information of  and  is transmitted to each other at unit velocities ̇() and ̇(), respectively, from time  = 0  , and meets at the midpoint of the line connecting 与 in a half of unit time
(2.14)+(2.15) ) .Similarly, the triangle )  ( 1  2 ,0  ) can be constructed by the product of the integration ∫ ̇ Since there is a right hand spiral can be produced by the pair of triangles, by which a Clifford Geometric Product can be induced too.In adding, because ∆  = 1  − 0  as the measurement unit of time is very arbitrary, this is mean that there is not only the invariances of the Contradiction Point under the scale transformation of unit, but also an Entanglement between the pair of triangles, by which the opposite and unifying of contradiction between the  and  can be represented, can be induced.
It is need special to be point out that the scale of unit |∆  | = |1  − 0  | is reduced by right spiral, but is expanded by left spiral, in the extreme, the entanglement between a pair of triangles could be changed to be the quantum entanglement, but the expanding of they could be conversed in to relative expanding.
Since Artificial Neural Unit is defined as a Inner Product, and an Attribute Grid Computer Based Qualitative Mapping, such that a Qualitative Grid Computer based

2 )
is the increment of the differential   from  = 0  to  =

Fig. 2
Fig.2 Two Triangles Constructed by the product of the integration and