The Two Entropies: Why You Don’t Look Like William the Conqueror — And Why the Universe Still Remembers Its Beginning
People romanticise ancestry.
If you are the 26th great-grandchild of William the Conqueror, it feels inevitable that something of him must echo in your face or temperament. A founder should leave a trace.
That intuition is wrong.
And understanding why turns out to illuminate something much deeper—about what the universe can and cannot remember about its own beginning.
1. Genealogy Expands, Genetics Forgets
Genealogically, the past explodes.
Go back 30 generations and the number of ancestral slots exceeds the population that existed. Lineages fold back on themselves. By the late medieval period, ancestry is nearly universal within a population.
So yes—if you are European, you are almost certainly descended from William the Conqueror.
But genetically, that fact carries almost no weight.
Each generation:
- chromosomes recombine
- segments fragment
- only a random subset survives
After ~10–12 generations, most ancestors contribute no DNA.
By ~30 generations, the expected contribution from any specific ancestor is effectively zero. Even if tiny fragments persist, they are typically indistinguishable from background variation.
The system does not preserve lineage.
It preserves only what survives repeated fragmentation.
2. This Is Not “Entropy” in the Usual Sense
It is tempting to call this “genetic entropy,” but that risks confusion.
Nothing here resembles thermodynamic entropy in a strict sense. No heat flows, no microstates are counted.
What is increasing is something more specific:
the loss of information about particular ancestors.
Recombination is not disordering matter. It is erasing traceability.
After enough generations:
- ancestry becomes universal
- attribution becomes impossible
The past is still there—but no longer identifiable.
3. The Superficial Analogy to Cosmology
At first glance, the universe looks similar.
- it begins in a simple state
- complexity grows
- information about the beginning becomes inaccessible
This suggests a loose analogy:
recombination erases ancestry
entropy erases the past
But this is only a surface similarity.
The underlying processes are completely different:
- recombination destroys lineage information through mixing
- gravitational entropy increases through instability and clumping
They are not the same mechanism.
What they share is only this:
in both systems, detailed information about origins becomes unrecoverable.
That resemblance is real—but limited.
4. Penrose’s Claim: The Beginning Is the Anomaly
Roger Penrose’s point is not about forgetting.
It is about how strange the beginning was.
The early universe was:
- extraordinarily smooth
- almost perfectly uniform
- with negligible Weyl curvature
In a gravitational system, this is not typical.
Quite the opposite:
almost all possible mass distributions are highly irregular and clumped.
Smoothness corresponds to a severe restriction on gravitational degrees of freedom.
In phase-space terms, it occupies an extremely small region.
Penrose famously quantified this as something like:
- 1 in 10^(10^123)
This number should not be taken too literally. It depends on how one defines gravitational phase space and what counts as a possible configuration.
But its role is clear:
it signals that the initial condition is not just low entropy—it is extraordinarily non-generic.
5. The Real Contrast
Now the difference with ancestry becomes precise.
Ancestry
- starts simple because populations are small
- low information is trivial
- nothing about it is improbable
The Universe
- starts simple in a very specific geometric way
- low entropy is highly constrained
- the initial condition is deeply non-generic
So:
a single ancestor is expected
a perfectly smooth universe is not
The two kinds of “simple beginnings” are not comparable.
6. The Question the Piece Cannot Avoid
Saying the initial state is improbable is not an explanation.
It is a problem.
Different approaches attempt to address it:
- Inflation: tries to explain smoothness dynamically (Penrose argues it presupposes low entropy rather than explaining it)
- Anthropic reasoning: we observe such a universe because only such universes permit observers
- Conformal Cyclic Cosmology (Penrose): proposes that our low-entropy beginning is inherited from a previous aeon
None of these are universally accepted.
So the situation is this:
we can describe the specialness of the beginning far more precisely than we can explain it.
7. What Actually Survives
This is where the comparison with ancestry becomes useful again—but only if stated carefully.
In both systems, detailed origins are lost.
But something does survive.
Not content—constraints.
In genetics:
- you cannot recover a specific ancestor
- but you can recover statistical structure:
- linkage patterns
- allele distributions
- population history
In cosmology:
- you cannot recover “the Big Bang matter”
- but you can observe:
- large-scale homogeneity
- the cosmic microwave background
- the absence of primordial gravitational irregularity
What persists is not the past itself.
It is the shape of what was allowed to happen next.
8. Constraints, Not Memories
This is the deeper point.
Low-entropy initial conditions do not leave detailed records.
They leave restrictions.
- In genetics: constraints on what combinations can appear
- In cosmology: constraints on how structure can form
These constraints propagate forward.
They shape everything that follows.
So causality across entropy gradients works like this:
the past is not remembered
it is enforced
9. Conclusion
You do not resemble William the Conqueror because recombination erased any identifiable trace of him.
The universe, however, still reflects its beginning—not as a memory, but as a constraint.
And the crucial difference is this:
ancestry begins simply because it has no choice
the universe began simply in a way it almost certainly should not have
That is why one is forgettable—
and the other remains one of the deepest open questions in physics.
https://thinkinginstructure.substack.com/p/the-two-entropies-why-you-dont-look
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