Last night before bed, for no particular reason, I thought about Wolfgang Pauli and his obsession with the number 137 (see Wolfgang Pauli & the Weirdness of # 137).
This morning I woke up wondering if the weirdness of the fine-structure constant (α≈1/137) must express a relationship between atomic physics and living things such as man.
In other words, the seeming randomness of the value may be conceptualized as a feature of atomic physics that enabled life to come about, and should therefore be viewed as pertinent to the complex system of life. Another way of putting it is that if the number were any other value, we might not be here to observe it and marvel at its apparent quirkiness.
This morning I asked GROK the simple question: Are there numbers in molecular biology that correspond with numbers in atomic physics?
The following is the answer. I have highlighted what strike me as the key elements in black.
Yes. Molecular biology sits on chemistry, and chemistry is low-energy atomic physics, so many of its characteristic numbers are the atomic ones, rescaled by small numerical factors.
The two scales that set almost everything are the Bohr radius and the Rydberg energy. The Bohr radius is the size of the hydrogen atom. . . .
The matching energy is the Rydberg energy, Ry≈13.6 eV, the binding energy of the hydrogen atom. Covalent bond energies are a fraction of that, typically a few eV. . . .
The fine-structure constant α≈1/137 is what ties these scales together.
Nobel physicist Eric Cornell has put it this way: in the physics of atoms, molecules, chemistry, and biology, ratios of bigger things to smaller things tend to be powers of α\alphaα. Because α\alphaα is small, electromagnetism is weak enough for electrons to form extended atoms that can share electrons, and large enough for stable chemistry.
The story gets even weirder in a distinctly anthropological way when one considers that not one, but three Biblical patriarchs are said to have lived to the quirky age of 137.
Ishmael: The first son of Abraham and Hagar, whose lifespan is recorded in Genesis 25:17.
Levi: The third son of Jacob and Leah and the ancestor of the Levitical priestly tribe, whose age at death is noted in Exodus 6:16.
Amram: The father of Moses, Aaron, and Miriam, whose death at 137 is recorded in Exodus 6:20
This really struck Wolfgang Pauli, whose father had taken extraordinary steps—including changing his surname from Pascheles to Pauli—to conceal his Jewish family history. Pauli’s paternal great grandfather, Wolf Pascheles, was a seller of Jewish prayer books in Prague.
Pauli was further astonished to discover that in the Jewish mystical tradition of Kabbalah, every Hebrew letter corresponds to a number (a practice known as Gematria). The Hebrew word for Kabbalah (קבלה) adds up exactly to the numerical value of 137.
Pauli’s quest for understanding that took him back to the mystical literature of his ancestors strikes me as a perfect expression of T.S. Eliot’s famous lines:
We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.
Random fun fact: The Bible opens with "In the beginning...", and the word sum (a=1, z=26) of that phrase is 137.
137 is also the 33rd prime number. And 33 has its own host of significances.
Perhaps The Hitchhiker's Guide to the Gallaxy was right that the Answer to the Ultimate Question of Life, the Universe and Everything is a number, but it was 137 not 42?