An answer to Mikhail Gromov - 1/4 Generation, Transformation, Transmission, Memorization, Storage and (...)

An answer to Mikhail Gromov - 1/4 Generation, Transformation, Transmission, Memorization, Storage and (...)
7.4.2026, Institut des Hautes Etudes Scientifiques (IHES)

At the beginning* of the video (with deactivated comments) Mikhail Gromov asks for a principle for the Triplet or 21 proteins code of biology.

I want to answer on this question: 

1. Triplet to 21 proteins relation via Fibonacci numbers:
Triplet - 3 - F(4) and L(2)
21 proteins - 21 - F(8)
Both are Fibonacci numbers.

The same holds for four bases to a triple code.

2. Four bases to Triplet relation via Lucas numbers:
Four bases - 4 - L(3)
Trilet - 3 - L(2) and F(4)
Both are Lucas numbers.

3. Relation 1. and 2.:
L(2) = 3 and F(4) = 3 link both relations.

q.e.d.

Conclusion: The correspondence may appear arbitrary from a biochemical standpoint, but the underlying counts (4, 3, 21) suggest the genetic code is constrained by the same recursive symmetries [F(n), L(n)] found in phyllotaxis and other biological scaling laws, suggesting a structural rather than accidental origin.

Consecutive hypothesis: Fibonacci numbers and Lucas numbers are associatd by 5^1/2 and functions of the Golden Ratio Phi; thus I introduce the hypothesis that Fibonacci numbers, Lucas number, 5^1/2 and functions of the Golden Ratio Phi are principles in biology and nature.

The first Fibonacci numbers and Lucas numbers:

• Fibonacci F(n
  

  $$
  ): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
• Lucas L(n
  

  $$
  ): 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ...

References:

Wolfram Mathematica
Wikipedia
etc. 
and
Mikhail Gromov - 1/4 Generation, Transformation, Transmission, Memorization, Storage and (...)https://youtu.be/8h2S4XtcCLQ?si=Wnh1EXUkFd9WPUYt, https://youtu.be/8h2S4XtcCLQ?si=Wnh1EXUkFd9WPUYt
and
Geier Stefan et al. on ResearchGate, e.g.  @ResearchGate: https://www.researchgate.net/publication/399883837_FIBONACCI_and_LUCAS_Numbers_in_Animal_Body_Plans_and_GEIER's_Equations_Revisiting_John_J_WILLE's_Morphogenesis_Claims_Part_1?utm_source=twitter&rgutm_meta1=eHNsLTloS1NzVHZrTmJidlNiMXpwSTdBVmVTaVZFUE9lT3pyT3RPanB2UVZ0WSttbVFGaDhJU25ENkJQN3ZzcUVjSWJEZEc3OUZ6ajUyZlM5ZmtuQURybjFtUT0%3D  @ResearchGate: https://www.researchgate.net/publication/399883837_FIBONACCI_and_LUCAS_Numbers_in_Animal_Body_Plans_and_GEIER's_Equations_Revisiting_John_J_WILLE's_Morphogenesis_Claims_Part_1?utm_source=twitter&rgutm_meta1=eHNsLTloS1NzVHZrTmJidlNiMXpwSTdBVmVTaVZFUE9lT3pyT3RPanB2UVZ0WSttbVFGaDhJU25ENkJQN3ZzcUVjSWJEZEc3OUZ6ajUyZlM5ZmtuQURybjFtUT0%3D

*[00:16:20]: Mikhail Gromov uses these terms while discussing the "completely arbitrary correspondence between triplet of bases and amino acids" in the context of biological translation and the genetic code. (Here we show that the correspondence between triplet of bases and amino acids is not completely arbitrary as it fits to Fibonacci numbers and Lucas numbers.)