The genetic code is constructed in ordered chains of bases selected from four different kinds:
- Adenine (A)
- Thymine (T)
- Guanine (G)
- Cytosine (C)
Three ordered bases (a codon) code for one specific amino acid and/or a start or stop signal in the synthesis of a protein.
However, DNA’s structure contains an additional layer of symmetry:
- Each base pairs exclusively with one of the other three bases, called its complement:
- A pairs with T.
- G pairs with C.
If the four bases are considered as relational, not absolute objects, then the DNA code reveals an elegant structure of symmetry and opposition:
The four “what it is” components and the four “what it is not” components defining each base form two mirror-opposite chiral tetrahedrons, embedded within a cube.
These mirror-opposite chiral tetrahedrons are relational objects. Each is not the other. They correspond with the relational symmetry of Order 4. The relationship can be seen by looking at opposed cube faces such that one is viewed from the front and the other from the back as reflected in a mirror. This conserves the sense (clockwise or anticlockwise) of the order of the bases as between front and back faces.
To grasp this concept intuitively, look at the diagram below showing how the three primary additive and subtractive colours can arise from the symmetry of Order 4.
The symmetry of Order 4 constrains the number of ways in which four objects can be ordered in rings to six. These correspond with the different possible orderings of the letters A, G, T and C in the faces of the cube. Each face functions as a relational codon. This is just how three bases code for an amino acid.
Different codons in the genetic code define more than six amino acids, so evolution (recursive distinctioning) has so far not brought the code into full simple convergence with the symmetry of Order 4. However, the fingerprint of Order 4 is there to see.
So where do codons (three ordered bases) come from in the symmetry of Order 4? The symmetry of Order 4 constrains what appears to four oppositional pairs of basis to function as three pairs (a triplet) and one pair (a singlet) which functions as a logic mirror to separate the pair members). The identities of the members of the four oppositional pairs (a, A, g, G, c, C and t, T) merge functionally into three pairs.
Look at the cube again as a Necker cube to see the controlling logic. What appears to be the last of four ordered objects coding a cube face and generated by the controlling logic is actually related to the first object as not to is. There is duplication, which comes fundamentally from the way in which logic is controlled by chirality. Colour arises inherently from respecting mirror symmetry as the rules for the truth tables for the logic gates exclusive or (XOR) and not exclusive or (XNOR) are applied recursively.
What appears to be a mirror pair of quaternions a,b,c,d generated simply by using XOR and XNOR symmetrically to draw a distinction between what is and what is not a countable object is actually a mirror pair of strings of six ordered objects, two of which are hidden. These mirror pairs of strings simply slide along through the cycle each time a counting step is performed. These are the codons.
Replacing the letters in the table with their colours, this looks like:
The symmetry inherent in Order 4 compresses the system coded in four relational objects (the bases A, G, C and T and their complements) down to three, just as it compresses mathematical and logic systems coded in four relational objects (the input pairs of 00, 11, 10 and 10 and their complements that generate outputs). It is not that one of the four relational objects disappears, but all four relational objects behave as three. Hence a codon such as aBc in a chiralkine cycle behaves as a codon for an amino acid, for example, AUG.