The 64 codons
The genetic code also has 64 = 2⁶
Change the base to bit encoding and watch the map reorder; tap a codon for the detail.
The 64 hexagrams and the 64 codons coincide in number (both are 4³ = 2⁶), and that allows them to be paired. But it is an isomorphism of combinatorial structure, not a biological fact nor a mystical affinity: there is no reason why a hexagram “is” an amino acid. This experiment shows it by demonstrating that the pairing depends on an arbitrary choice.
Each codon is three bases, and each base can be written with 2 bits: 3 × 2 = 6 bits, a hexagram. To pair them you must decide which pair of bits is each base, and there lies the trick: there are 4! = 24 possible assignments and none is canonical. Change the encoding and the whole mapping reorganizes. The correspondence is real as structure and arbitrary in the details.
the 64 hexagrams (Fu Xi order) → codon → amino acid, coloured by class. ■ = stop codon.
That same hexagram, depending on which of the 24 encodings you use, can land on 4 different amino acids. There is no “true” one: the choice is free.
Amino acid table: standard genetic code (NCBI, translation table 1).
The genetic code has 64 = 4^3 = 2^6 codons, like the hexagrams, but the correspondence is a combinatorial isomorphism, not a biological fact: it depends on one of the 24 base-to-bit encodings, none of them canonical.
Analogy with a disclaimer: the coincidence in number is real as form and arbitrary in the details; the standard code is cited in the experiment itself (NCBI), which is not part of this bibliography.
The types of claim and the full bibliography (APA) are in Foundations.