Chiralkine numbers provide a novel framework for computation, distinct from the conventional mathematical systems that rely on equations. These numbers prioritize symmetry by treating the two mutually exclusive sides of distinctions as mirror opposites, without privileging one over the other.
Chiralkine Numbers vs. Conventional Numbers
Conventional computation is based on five numbers:
- 0 (a singular zero), and
- The countable pairs: ±1 (real numbers) and ±i (imaginary numbers).
In contrast, chiralkine computation employs six countable numbers:
- A, b, C, a, B, c, arranged as three pairs: (A, a), (B, b), (C, c).
Key Differences:
- Symmetry vs. Asymmetry:
- Conventional computation switches between a singular zero and positive-negative pairs, treating the two sides of a relationship independently.
- Chiralkine computation proceeds in a cycle, coupling the sides of relationships to ensure they are treated symmetrically.
- Commutativity vs. Non-Commutativity:
- In conventional mathematics, operations are commutative: a·b = b·a.
- Chiralkine numbers introduce non-commutativity: a·B ≠ B·a.
Square Roots in Chiralkine Numbers
The concept of square roots provides a way to understand the differences between chiralkine and conventional numbers.
Conventional Square Roots:
In conventional mathematics, square roots arise from equations, and the process is commutative:
- The square root of a product a·b is independent of the order of multiplication:
√(a·b) = √(b·a) = ±c. - Reversing the operation by squaring ±c always yields the same result:
(+c)² = (-c)² = a·b = b·a.
For example, if a = +1 and b = -1, then:
- The square root of a·b is ±i.
Chiralkine Square Roots:
Chiralkine numbers, by contrast, do not rely on equations. Instead:
- The order of multiplication matters: √(a·B) ≠ √(B·a).
- In chiralkine terms:
- a is turned by B into c, and
- B is turned by a into C.
This non-commutative behavior reflects the cyclical nature of chiralkine computation and its resistance to reducing distinctions through equations.
Connections to Spinors
A useful analogy for chiralkine numbers is found in spinors, which are sometimes described as the square root of geometry. Spinors, like chiralkine numbers, exhibit non-commutative properties. However, spinors are still constructed using equations, while chiralkine numbers avoid equations entirely, preserving their symmetry.
Logic Gates and Symmetry
Both conventional and chiralkine numbers are founded on the same mirror-opposite logic gates:
- XOR and XNOR.
Conventional Numbers:
- Conventional systems privilege one logic gate over the other, leading to asymmetry and commutative operations.
Chiralkine Numbers:
- Chiralkine numbers treat XOR and XNOR symmetrically, ensuring that:
- All operations are non-commutative.
- Relationships between numbers evolve cyclically, coupling distinctions without reducing them to a singular zero.
Conclusion
Chiralkine numbers redefine computation by prioritizing symmetry and rejecting equations that privilege one side of a relationship. Their non-commutative nature introduces a dynamic, cyclical approach to computation, offering an alternative framework that aligns with natural systems of balance and opposition.
This revolutionary perspective challenges conventional mathematical principles while opening new possibilities for computation and understanding.
(Acknowledgement: text drafted by Chat GPT based on text provided to it).