In conventional mathematics, a distinction is made between two kinds of countable numbers: real and imaginary. Each type comes in two mirror-opposite forms, identified as positive and negative.
1. Rules for Real and Imaginary Numbers
- Positive and Negative Forms:
Positive and negative numbers of the same kind sum to zero, treating their difference as “nothing,” which is uncountable. - Multiplication Rules:
Real and imaginary numbers follow specific multiplication rules. These rules align with the truth tables for the logic gates XOR and XNOR.
- Imaginary Numbers:
An imaginary number is defined as the square root of -1. For example:- The square of an imaginary number outputs -1.
- Hence, the sum of the square of the imaginary number (-1) and the square of the real number (1) equals zero.
2. Chiralkine Counting: A Symmetric Alternative
Chiralkine counting is also a dual system, like real and imaginary numbers. However, it introduces key differences:
- No Equations: Chiralkine counting avoids equations, preventing the reduction of distinctions to a singular “nothing.”
- Symmetry: Unlike the conventional real and imaginary system, chiralkine counting treats relationships symmetrically.
3. Quaternions and Chiralkine Counting
Quaternions, invented by Hamilton, expand the concept of imaginary numbers:
- Quaternions consist of three imaginary numbers (i, j, k) and one real number (1).
- Each imaginary number is itself a square root of -1.
- Multiplication rules for quaternions are non-commutative, meaning the order of multiplication affects the product’s sign.
Comparison with Chiralkine Counting:
- Order and Symmetry:
- Chiralkine counting numbers (a, b, c) are ordered similarly to i, j, k in quaternions.
- However, chiralkine counting maintains symmetry, unlike quaternions, which derive asymmetry from their reliance on equations.
- Real and Imaginary Numbers:
- In quaternions, there is a fixed distinction between the real and imaginary components.
- Chiralkine counting dissolves this distinction, replacing it with a fully symmetric structure.
4. Connections to Molecules and Particles
Quaternions have deep connections to chiral tetrahedral molecules and spinors. These relationships are explored in the paper “Chiral Tetrahedrons as Unitary Quaternions: Molecules and Particles Under the Same Standard” by Cappozziello and Lattanzi.
This paper was pivotal in shaping the development of chiralkine counting. It demonstrates how quaternions describe symmetry in molecules and fundamental particles. Meeting the authors in Italy was a key step in uncovering the deeper symmetries that chiralkine counting brings to light.
5. Beyond Conventional Distinctions
In chiralkine counting:
- Numbers do not reduce to uncountable “nothings” as in the conventional system.
- The process avoids privileging one kind of number over another, ensuring symmetry at every step.
- The counting cycle is non-commutative, like quaternion multiplication, but fully symmetrical.
(Acknowledgement: Chat GPT drafted this text based on a text provided)