Why do organisms all choose the same geometric structure?
Minimal surfaces provide the answer.
The shimmering blue light on a butterfly's wings
is not pigment.
If you scrape off the scales and look,
the layer underneath is transparent.
So where does that color come from?
The answer is:
Inside the scales of its wings,
the butterfly has built a nano-scale 3D labyrinth.
When light enters this labyrinth,
it refracts and interferes repeatedly against the walls.
Only specific wavelengths are selectively amplified.
The blue isn't painted on;
it is built through architecture.
But that's not what truly shocked me.
What shocked me is that
the geometry of this nano-labyrinth built by the butterfly
and the way certain mitochondrial inner membranes fold in your eyes
are actually the same mathematical structure.
And this mathematical structure
was derived in 1970 by a mathematician at NASA
using nothing but pen and paper.
Hello,
everyone,
I'm Wang Lijie.
Recently, a viewer who studies biological membranes left me a message.
She mentioned a phenomenon that got me so excited I couldn't sit still.
She said her research subject is the "cubic membrane,"
where the internal membrane of a cell folds into a special
three-dimensional periodic surface.
But what really made my skin crawl is that
this structure doesn't just appear in one species.
It's in butterfly wings,
in the eyes of tree shrews,
in the cells of amoebas,
and even green algae spontaneously generate it under UV stress.
A question immediately came to mind:
Why would organisms separated by hundreds of millions of years of evolution
coincidentally choose the exact same geometric shape?
Is it passed down through genes?
Impossible.
Their last common ancestor diverged over a billion years ago.
Is this just a coincidence,
or are laws of physics secretly giving orders to all life?
We've previously discussed the "Creator's design preferences."
If there is a designer behind this world,
she seems to have an obsessive preference for specific mathematical structures:
spirals, fractals, the golden ratio.
From galactic arms to seashell patterns,
these patterns emerge repeatedly from macro to micro scales.
Today, we're going to push the lens even deeper,
into the internal membrane systems of cells.
You will find that
the Creator's geometric preference is more than a decorative coincidence in the macro world;
it actually permeates the lowest-level operating system of life.
Alright,
let's first get to know this mathematical structure.
In 1967,
a mathematician named Alan Schoen joined NASA's
Electronics Research Center
as the head of the Office of Geometric Applications.
He was studying a pure mathematical problem at the time:
What kind of surface can extend infinitely in 3D space,
repeat periodically,
and have a mean curvature of zero at every point on the surface?
What does "zero mean curvature" mean?
Think of it this way:
Imagine a soap film stretched across a wire loop.
The soap film automatically finds a shape.
That shape is the state of minimum surface tension.
A soap film is a minimal surface.
It's not an artificially designed shape;
it's the least-energy answer automatically found by physical forces.
What Schoen was looking for
was how this least-energy answer would look
when extended infinitely in 3D space.
He spent three years
making precise plastic models using injection molding
and using early computer graphics for verification.
Finally, in a 1970 NASA technical report,
he published an unprecedented surface
named the gyroid.
What does a gyroid look like?
Imagine an infinite, curved membrane
that divides 3D space into two intertwined
but never-touching labyrinthine channels.
This membrane contains no straight lines
and possesses no planar symmetries.
It is so elegant it can stand on its own without support,
because mechanical balance is perfect at every point.
In simpler terms,
the gyroid is the most relaxed posture
a curved membrane can find in 3D space.
Just as water flows downhill,
membranes naturally curve toward the gyroid state.
Interestingly,
when Schoen published this structure,
he only proved its mathematical properties;
he didn't prove it was embedded,
meaning it wouldn't intersect with itself.
This proof wasn't completed by two German mathematicians until 1996.
A pure mathematical conjecture
took 26 years to be rigorously proven.
However, nature didn't need to wait for proof;
butterflies have been using it for hundreds of millions of years.
What mathematicians spent 26 years proving,
cell membranes found instantly
through thermodynamic intuition.
Keep that in mind,
and let's return to biology.
In 2008,
a study in the Journal of the Royal Society Interface confirmed
that the internal structure of many butterfly wing scales
precisely matches the gyroid mathematical model.
Note that
it's not just a rough resemblance;
it's an exact match.
Researchers used small-angle X-ray scattering to measure
the lattice parameters of these structures,
finding they highly coincided with mathematical predictions.
So how do these structures form?
This is the best part.
During the development of butterfly scales,
the smooth endoplasmic reticulum membranes spontaneously fold
into the gyroid shape.
There's no gene saying,
"Please fold into a gyroid."
Genes merely provide the lipid composition and protein environment;
then, under these physical conditions,
the membrane automatically finds the lowest-energy folding state.
Then, cells undergo apoptosis,
and chitin is deposited,
permanently freezing this living geometry into a solid photonic crystal.
When light enters this periodic structure,
Bragg diffraction occurs,
and only specific wavelengths are selectively reflected.
This is the source of those incredible metallic blues
and emerald greens on butterfly wings.
Butterflies never studied optics,
nor do they even know what color is.
But the membranes within their cells,
guided by thermodynamics,
automatically build photonic crystals that engineers
still struggle to replicate perfectly today.
A 2017 paper in Science Advances further pointed out
that the gyroid structure in butterfly wings
is a time-frozen snapshot of inner membrane development.
In other words,
the colors you see on a butterfly wing
are actually the membrane morphology of a cell at the moment of its death,
preserved forever.
The image itself is poetic enough:
a living cell, in its final moments,
folds itself into a mathematically perfect shape,
congealing in that posture
to become that flash of blue you see in the sunlight.
By the way,
human materials scientists have been trying to replicate
these photonic crystals found in butterflies.
Because its optical properties are exceptional;
it produces high-purity structural color without any pigments.
But so far,
replicating the gyroid structure precisely at the nanoscale remains
a massive engineering challenge.
What butterflies achieve with a self-assembling biochemical process,
humans cannot duplicate perfectly even with cutting-edge nanofabrication.
Alright,
so much for butterflies.
Now let's look at an even more shocking example:
the treeshrew,
a small mammal living in the tropical forests of Southeast Asia.
Resembling a squirrel,
it's actually more closely related to humans than you might think;
it is a close relative of primates.
In 1997,
German scientists studying the retina of treeshrews discovered
unusually large mitochondria in the inner segments of their cone cells.
Ordinary mitochondria are about 0.5 to 1 micrometer in diameter,
but these mitochondria in the treeshrew
reach diameters of 6 to 8 micrometers—
nearly ten times larger.
Even more puzzling is their internal membrane structure.
The cristae of normal mitochondria are lamellar,
stacked layer by layer like pages in a book.
But the cristae in these giant mitochondria
fold into an 8 to 12-layer gyroid cubic membrane array,
the same mathematical structure found in butterfly wings.
What does this do?
A 3D simulation study published in the Journal of Membrane Science
in 2023 revealed the answer.
This multi-layered gyroid arrangement can simultaneously perform
three optical functions.
First,
it acts as a multifocal lens.
Like a miniature zoom lens,
it focuses different wavelengths of light onto different focal planes.
Second,
it serves as an angle-independent interference filter,
selectively blocking ultraviolet light
to protect photopigments from UV radiation damage.
Third,
it forms a waveguide photonic crystal,
guiding light precisely to the location of the photopigment molecules.
Think about what this means.
What is the role of mitochondria in our textbooks?
The powerhouse of the cell,
responsible for synthesizing ATP to provide energy.
But in treeshrew cone cells,
the mitochondria simultaneously become a precision optical lens system.
One organelle
is generating energy
while also processing optical signals.
This dual-purpose design
doesn't rely on extra parts,
but simply on folding the inner membrane into a specific mathematical shape.
Pause for a moment and think:
if someone told you
that your radiator was also a high-resolution microscope,
you'd find it unbelievable, right?
Yet, that's exactly what the treeshrew's mitochondria are doing.
And the only secret to this miracle
is folding its inner membrane into a gyroid shape.
Same material,
same chemical composition—
only the geometry changes,
and the function gains a whole new dimension.
This is the power of geometry;
shape itself is information.
The treeshrew didn't invent this shape,
just as the butterfly didn't invent its own.
It's physical constraints;
once the lipid composition and protein environment are set,
they are automatically guided to the same destination.
Now, here's something even more incredible:
Amoebas,
single-celled protozoa.
Under stressful conditions,
such as nutrient deprivation or osmotic shock,
their internal membrane systems also spontaneously reorganize into
a gyroid cubic membrane.
The green alga Spirogyra does the same under UV stress.
This research was published in the journal Protoplasma in 2017.
Now, let's look at the list of organisms.
Butterflies are in the phylum Arthropoda.
Tree shrews are in the class Mammalia.
Amoebas are in the kingdom Protista.
Green algae like Spirogyra are in the kingdom Plantae.
These four cover almost every major category of eukaryotic life.
Their last common ancestor lived
at least 1.5 billion years ago.
Despite facing completely different functional demands—
creating color, focusing light, stabilizing membranes, resisting UV damage—
they all eventually converged on the same geometry.
This isn't a story of a single gene being passed down for 1.5 billion years.
This is the laws of physics themselves making the choice.
I want to stop here for a moment.
Please close your eyes for three seconds and consider this:
If you were a thin membrane
required to maximize your surface area in 3D space,
while making the stress perfectly uniform at every point,
and minimizing the energy cost of your existence in the universe,
the only answer you could find is the gyroid.
Not because someone chose it for you,
but because except for it,
no other shape can satisfy all three conditions at once.
This is the essence of what's called the Creator’s preference.
It's not the aesthetic choice of a supernatural being,
but the structural constraints of the laws of physics.
It doesn't need to be encoded in any gene.
It only requires membranes to exist, 3D space to exist,
and the conservation of energy to exist.
It inevitably emerges.
Water flowing downhill doesn't need to be programmed.
A membrane curving into a gyroid doesn't need to be programmed either.
But there's one final layer to the story,
and this layer involves you and me.
Recent research has found that
gyroid cubic membranes are rich in a
special type of lipid molecule
called plasmalogens.
Plasmalogens have a vinyl ether bond in their chemical structure.
This bond is extremely special.
When free radicals attack the cell membrane,
plasmalogens sacrifice their vinyl ether bond first to neutralize them,
protecting other functional lipids from oxidative damage.
It's like a guard who proactively takes a bullet for a teammate.
A 2025 review published in the FASEB journal,
Advances in Biology, pointed out that
plasmalogen levels drop significantly in Alzheimer's patients,
and the decline correlates with the severity of cognitive impairment.
Supplementing plasmalogens can reduce gamma-secretase activity,
the key enzyme catalyzing the synthesis of beta-amyloid.
Tracing data spanning several years from the
Rush University Memory and Aging Project shows that
older adults with higher plasma plasmalogen levels
have a significantly lower risk of dementia.
Do you see the logical chain here?
The gyroid minimal surface provides the most stable
intramembrane habitat for plasmalogens.
Because the surface curvature energy is lowest,
the membrane stress distribution is most uniform,
and the lipid molecules are most "comfortable."
In turn, plasmalogens use their
antioxidant capacity to protect the gyroid membrane from
disruption by free radicals.
The structure stabilizes the molecules;
the molecules protect the structure.
It's a two-way positive feedback loop.
But what happens when this loop is broken?
With aging,
the ability to synthesize plasmalogens gradually declines.
The membrane's antioxidant defense line collapses,
the gyroid structure degenerates and fails,
more lipids are oxidized,
and more structures are destroyed.
Once this negative feedback spiral starts, it's hard to reverse.
Our brains may not fail because of a single genetic mutation,
but because of the slow collapse of a geometric structure.
It's not that the software glitched;
It's the hardware's physical form that can't be maintained.
This perspective has redefined my understanding of aging.
We usually think of aging as a chemical phenomenon:
Gene expressions change,
proteins misfold,
and free radicals accumulate.
But if we dig one layer deeper,
the container for these chemical events
is the geometric structure of the membrane.
The shape of the container determines if the chemistry inside functions normally.
When the container's shape degrades from the highly stable gyroid,
a minimal surface, into a common, disordered structure,
the chemistry inside the container falls into chaos.
So perhaps the essence of aging
is geometric degeneration;
the physical form collapses first,
and chemical function follows suit.
Alright.
Let's tie together today's clues.
In 1970,
a mathematician working at NASA
derived a theoretical surface on paper.
Over fifty years later,
biologists found this same structure in butterfly wings, tree shrew eyes,
amoeba cells, and green algae chloroplasts.
And then,
medical researchers discovered
that a lipid molecule housed within this structure
might be the brain's key defense against aging and neurodegeneration.
A mathematician's pen tip, a butterfly's wing,
and the collapsing brain of an Alzheimer's patient—
the distance between them
is only the thickness of a minimal surface.
But the core question today isn't about these specific applications.
I want to leave this question to you:
Why is a mathematical shape derived purely from energy minimization
exactly the master key for life to solve optical,
structural, and biochemical puzzles?
Is it that the universe's mathematical foundation is perfectly suited for life,
or can life only exist upon such a mathematical foundation?
These two statements sound like the same thing,
but they point to completely different ideas.
The former implies the universe existed first,
and life was a later arrival that adapted.
The latter implies
perhaps this mathematical structure is itself a necessary condition for life,
just like water and carbon,
except we haven't written it into the textbooks yet.
What do you think?
Which view do you lean toward?
I'm really curious about your thoughts.
I'm Wang Lijie.
See you next time.