The Arbitrariness Inversion in Science
Or, why the foundations of physics isn’t the home of the non-arbitrary universals you were hoping for
When we are young, the hierarchy of knowledge looks firmer the lower you go.
At the bottom sits fundamental physics: austere, mathematical, universal. Surely these — whatever they are — must be pure necessity, the place where every “why” finally terminates in an equation that could not have been otherwise. That apparent inevitability is what lured generations of us into physics and mathematics.
At the top sprawl biology, psychology, sociology, politics, art, culture—domains that feel capricious, culture-bound, historically contingent. Geometric illusions? Obviously just a quirk. Political ideologies? Obviously just human noise. Empathy, fashion, music—surely these are the arbitrary froth on the surface of reality.
Both intuitions are spectacularly wrong.
Climb the tower and you discover that almost everything we labelled “arbitrary” is in fact highly structured—often mathematically forced—once the lower layers are fixed, and often completely insulated from the lower levels altogether.
Biology is not a grab-bag of accidents; it is geometry, information theory, and game theory playing themselves out under thermodynamic and selective constraints.
We see geometric optical illusions because any nervous system with processing delays must predict the near future to perceive the present accurately; the specific distortions we experience follow from the statistics of how we typically move forward through the world, with essentially no wiggle room.
Forward-facing eyes, long assumed a predator’s tool for stereopsis, actually evolved for “X-ray vision” through leafy clutter, with eye separation precisely tuned to typical leaf sizes in forest niches—again, a tight geometric optimization.
Emotional expressions, far from whimsical signals, serve as the primal negotiation language indispensable for social species, enabling subtle, involuntary cues for reputation-building, trust-signaling, and cooperative exchanges, all emergent from evolutionary game theory.
Change the biochemistry or the environment and the tree branches differently within the hierarchy of knowledge, but it branches along mathematically sharp channels, not randomly.
Even the squishiest human universals turn out to be convergence zones. Any species facing scarcity, individual self-interest, and the cognitive cost of central planning will rediscover the same tension between coordinated allocation and decentralised markets: socialism vs capitalism. The trade-offs are not anthropocentric; they are theorems in multi-agent systems.
Now descend to the supposedly solid foundation—the Standard Model, quantum field theory, and whatever lies beneath—and the atmosphere abruptly changes.
Here the free parameters bloom like weeds:
19 (or 26 counting θQCD) independent numbers in the core Lagrangian alone
13 Yukawa couplings that set fermion masses across nine orders of magnitude
mixing angles and CP-violating phases measured to many digits yet theoretically unexplained
three gauge couplings, a strong CP angle smaller than 10⁻¹⁰, a cosmological constant 120 orders of magnitude smaller than naive expectation
exactly three generations of fermions—an empirical fact from the Z boson width, not a derived necessity
a Higgs sector tuned so that atoms can exist at all
gravity weaker than the other forces by 38–40 orders of magnitude, with no mechanism in sight
String theory and other candidates for unification do not eliminate the arbitrariness; they merely push it one level deeper and multiply it. Ten or eleven dimensions, six or seven of them compactified on a manifold of particular size, shape, and topology chosen from a landscape of 10⁵⁰⁰ or more possibilities—that is not simplicity; it is a cosmic lottery ticket.
The great inversion is now in full view.
The domain we expected to deliver uniqueness and necessity turns out to be the most baroque and underived layer of all. The “fundamental” constants and symmetries look less like eternal Platonic truths than like frozen historical accidents—parameters someone (or something) simply wrote down from an immense catalogue of mathematical possibilities.
Meanwhile, the higher levels we dismissed as contingent and parochial keep revealing deep structural inevitabilities that any sufficiently complex system anywhere in the universe is forced to reinvent.
The true universals do not live at the bottom, where we first went looking for them. They emerge only after the long climb upward, in the rich, layered consequences that complexity is compelled to discover.
Perhaps the cosmos hides its deepest necessities not in the Planck-scale substrate, but in the theorems that survive the journey to minded creatures gazing back at the night sky.