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Why do organisms all choose the same geometric structure?

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Minimal surfaces provide the answer.

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The shimmering blue light on a butterfly's wings

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is not pigment.

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If you scrape off the scales and look,

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the layer underneath is transparent.

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So where does that color come from?

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The answer is:

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Inside the scales of its wings,

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the butterfly has built a nano-scale 3D labyrinth.

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When light enters this labyrinth,

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it refracts and interferes repeatedly against the walls.

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Only specific wavelengths are selectively amplified.

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The blue isn't painted on;

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it is built through architecture.

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But that's not what truly shocked me.

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What shocked me is that

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the geometry of this nano-labyrinth built by the butterfly

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and the way certain mitochondrial inner membranes fold in your eyes

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are actually the same mathematical structure.

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And this mathematical structure

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was derived in 1970 by a mathematician at NASA

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using nothing but pen and paper.

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Hello,

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everyone,

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I'm Wang Lijie.

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Recently, a viewer who studies biological membranes left me a message.

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She mentioned a phenomenon that got me so excited I couldn't sit still.

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She said her research subject is the "cubic membrane,"

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where the internal membrane of a cell folds into a special

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three-dimensional periodic surface.

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But what really made my skin crawl is that

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this structure doesn't just appear in one species.

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It's in butterfly wings,

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in the eyes of tree shrews,

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in the cells of amoebas,

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and even green algae spontaneously generate it under UV stress.

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A question immediately came to mind:

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Why would organisms separated by hundreds of millions of years of evolution

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coincidentally choose the exact same geometric shape?

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Is it passed down through genes?

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Impossible.

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Their last common ancestor diverged over a billion years ago.

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Is this just a coincidence,

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or are laws of physics secretly giving orders to all life?

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We've previously discussed the "Creator's design preferences."

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If there is a designer behind this world,

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she seems to have an obsessive preference for specific mathematical structures:

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spirals, fractals, the golden ratio.

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From galactic arms to seashell patterns,

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these patterns emerge repeatedly from macro to micro scales.

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Today, we're going to push the lens even deeper,

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into the internal membrane systems of cells.

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You will find that

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the Creator's geometric preference is more than a decorative coincidence in the macro world;

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it actually permeates the lowest-level operating system of life.

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Alright,

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let's first get to know this mathematical structure.

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In 1967,

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a mathematician named Alan Schoen joined NASA's

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Electronics Research Center

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as the head of the Office of Geometric Applications.

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He was studying a pure mathematical problem at the time:

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What kind of surface can extend infinitely in 3D space,

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repeat periodically,

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and have a mean curvature of zero at every point on the surface?

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What does "zero mean curvature" mean?

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Think of it this way:

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Imagine a soap film stretched across a wire loop.

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The soap film automatically finds a shape.

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That shape is the state of minimum surface tension.

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A soap film is a minimal surface.

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It's not an artificially designed shape;

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it's the least-energy answer automatically found by physical forces.

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What Schoen was looking for

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was how this least-energy answer would look

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when extended infinitely in 3D space.

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He spent three years

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making precise plastic models using injection molding

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and using early computer graphics for verification.

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Finally, in a 1970 NASA technical report,

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he published an unprecedented surface

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named the gyroid.

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What does a gyroid look like?

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Imagine an infinite, curved membrane

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that divides 3D space into two intertwined

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but never-touching labyrinthine channels.

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This membrane contains no straight lines

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and possesses no planar symmetries.

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It is so elegant it can stand on its own without support,

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because mechanical balance is perfect at every point.

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In simpler terms,

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the gyroid is the most relaxed posture

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a curved membrane can find in 3D space.

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Just as water flows downhill,

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membranes naturally curve toward the gyroid state.

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Interestingly,

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when Schoen published this structure,

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he only proved its mathematical properties;

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he didn't prove it was embedded,

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meaning it wouldn't intersect with itself.

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This proof wasn't completed by two German mathematicians until 1996.

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A pure mathematical conjecture

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took 26 years to be rigorously proven.

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However, nature didn't need to wait for proof;

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butterflies have been using it for hundreds of millions of years.

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What mathematicians spent 26 years proving,

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cell membranes found instantly

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through thermodynamic intuition.

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Keep that in mind,

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and let's return to biology.

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In 2008,

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a study in the Journal of the Royal Society Interface confirmed

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that the internal structure of many butterfly wing scales

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precisely matches the gyroid mathematical model.

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Note that

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it's not just a rough resemblance;

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it's an exact match.

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Researchers used small-angle X-ray scattering to measure

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the lattice parameters of these structures,

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finding they highly coincided with mathematical predictions.

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So how do these structures form?

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This is the best part.

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During the development of butterfly scales,

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the smooth endoplasmic reticulum membranes spontaneously fold

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into the gyroid shape.

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There's no gene saying,

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"Please fold into a gyroid."

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Genes merely provide the lipid composition and protein environment;

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then, under these physical conditions,

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the membrane automatically finds the lowest-energy folding state.

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Then, cells undergo apoptosis,

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and chitin is deposited,

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permanently freezing this living geometry into a solid photonic crystal.

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When light enters this periodic structure,

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Bragg diffraction occurs,

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and only specific wavelengths are selectively reflected.

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This is the source of those incredible metallic blues

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and emerald greens on butterfly wings.

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Butterflies never studied optics,

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nor do they even know what color is.

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But the membranes within their cells,

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guided by thermodynamics,

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automatically build photonic crystals that engineers

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still struggle to replicate perfectly today.

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A 2017 paper in Science Advances further pointed out

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that the gyroid structure in butterfly wings

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is a time-frozen snapshot of inner membrane development.

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In other words,

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the colors you see on a butterfly wing

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are actually the membrane morphology of a cell at the moment of its death,

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preserved forever.

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The image itself is poetic enough:

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a living cell, in its final moments,

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folds itself into a mathematically perfect shape,

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congealing in that posture

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to become that flash of blue you see in the sunlight.

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By the way,

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human materials scientists have been trying to replicate

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these photonic crystals found in butterflies.

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Because its optical properties are exceptional;

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it produces high-purity structural color without any pigments.

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But so far,

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replicating the gyroid structure precisely at the nanoscale remains

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a massive engineering challenge.

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What butterflies achieve with a self-assembling biochemical process,

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humans cannot duplicate perfectly even with cutting-edge nanofabrication.

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Alright,

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so much for butterflies.

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Now let's look at an even more shocking example:

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the treeshrew,

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a small mammal living in the tropical forests of Southeast Asia.

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Resembling a squirrel,

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it's actually more closely related to humans than you might think;

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it is a close relative of primates.

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In 1997,

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German scientists studying the retina of treeshrews discovered

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unusually large mitochondria in the inner segments of their cone cells.

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Ordinary mitochondria are about 0.5 to 1 micrometer in diameter,

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but these mitochondria in the treeshrew

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reach diameters of 6 to 8 micrometers—

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nearly ten times larger.

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Even more puzzling is their internal membrane structure.

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The cristae of normal mitochondria are lamellar,

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stacked layer by layer like pages in a book.

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But the cristae in these giant mitochondria

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fold into an 8 to 12-layer gyroid cubic membrane array,

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the same mathematical structure found in butterfly wings.

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What does this do?

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A 3D simulation study published in the Journal of Membrane Science

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in 2023 revealed the answer.

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This multi-layered gyroid arrangement can simultaneously perform

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three optical functions.

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First,

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it acts as a multifocal lens.

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Like a miniature zoom lens,

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it focuses different wavelengths of light onto different focal planes.

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Second,

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it serves as an angle-independent interference filter,

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selectively blocking ultraviolet light

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to protect photopigments from UV radiation damage.

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Third,

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it forms a waveguide photonic crystal,

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guiding light precisely to the location of the photopigment molecules.

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Think about what this means.

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What is the role of mitochondria in our textbooks?

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The powerhouse of the cell,

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responsible for synthesizing ATP to provide energy.

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But in treeshrew cone cells,

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the mitochondria simultaneously become a precision optical lens system.

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One organelle

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is generating energy

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while also processing optical signals.

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This dual-purpose design

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doesn't rely on extra parts,

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but simply on folding the inner membrane into a specific mathematical shape.

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Pause for a moment and think:

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if someone told you

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that your radiator was also a high-resolution microscope,

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you'd find it unbelievable, right?

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Yet, that's exactly what the treeshrew's mitochondria are doing.

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And the only secret to this miracle

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is folding its inner membrane into a gyroid shape.

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Same material,

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same chemical composition—

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only the geometry changes,

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and the function gains a whole new dimension.

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This is the power of geometry;

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shape itself is information.

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The treeshrew didn't invent this shape,

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just as the butterfly didn't invent its own.

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It's physical constraints;

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once the lipid composition and protein environment are set,

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they are automatically guided to the same destination.

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Now, here's something even more incredible:

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Amoebas,

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single-celled protozoa.

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Under stressful conditions,

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such as nutrient deprivation or osmotic shock,

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their internal membrane systems also spontaneously reorganize into

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a gyroid cubic membrane.

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The green alga Spirogyra does the same under UV stress.

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This research was published in the journal Protoplasma in 2017.

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Now, let's look at the list of organisms.

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Butterflies are in the phylum Arthropoda.

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Tree shrews are in the class Mammalia.

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Amoebas are in the kingdom Protista.

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Green algae like Spirogyra are in the kingdom Plantae.

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These four cover almost every major category of eukaryotic life.

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Their last common ancestor lived

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at least 1.5 billion years ago.

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Despite facing completely different functional demands—

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creating color, focusing light, stabilizing membranes, resisting UV damage—

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they all eventually converged on the same geometry.

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This isn't a story of a single gene being passed down for 1.5 billion years.

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This is the laws of physics themselves making the choice.

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I want to stop here for a moment.

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Please close your eyes for three seconds and consider this:

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If you were a thin membrane

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required to maximize your surface area in 3D space,

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while making the stress perfectly uniform at every point,

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and minimizing the energy cost of your existence in the universe,

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the only answer you could find is the gyroid.

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Not because someone chose it for you,

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but because except for it,

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no other shape can satisfy all three conditions at once.

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This is the essence of what's called the Creator’s preference.

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It's not the aesthetic choice of a supernatural being,

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but the structural constraints of the laws of physics.

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It doesn't need to be encoded in any gene.

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It only requires membranes to exist, 3D space to exist,

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and the conservation of energy to exist.

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It inevitably emerges.

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Water flowing downhill doesn't need to be programmed.

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A membrane curving into a gyroid doesn't need to be programmed either.

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But there's one final layer to the story,

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and this layer involves you and me.

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Recent research has found that

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gyroid cubic membranes are rich in a

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special type of lipid molecule

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called plasmalogens.

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Plasmalogens have a vinyl ether bond in their chemical structure.

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This bond is extremely special.

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When free radicals attack the cell membrane,

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plasmalogens sacrifice their vinyl ether bond first to neutralize them,

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protecting other functional lipids from oxidative damage.

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It's like a guard who proactively takes a bullet for a teammate.

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A 2025 review published in the FASEB journal,

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Advances in Biology, pointed out that

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plasmalogen levels drop significantly in Alzheimer's patients,

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and the decline correlates with the severity of cognitive impairment.

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Supplementing plasmalogens can reduce gamma-secretase activity,

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the key enzyme catalyzing the synthesis of beta-amyloid.

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Tracing data spanning several years from the

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Rush University Memory and Aging Project shows that

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older adults with higher plasma plasmalogen levels

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have a significantly lower risk of dementia.

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Do you see the logical chain here?

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The gyroid minimal surface provides the most stable

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intramembrane habitat for plasmalogens.

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Because the surface curvature energy is lowest,

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the membrane stress distribution is most uniform,

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and the lipid molecules are most "comfortable."

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In turn, plasmalogens use their

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antioxidant capacity to protect the gyroid membrane from

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disruption by free radicals.

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The structure stabilizes the molecules;

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the molecules protect the structure.

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It's a two-way positive feedback loop.

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But what happens when this loop is broken?

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With aging,

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the ability to synthesize plasmalogens gradually declines.

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The membrane's antioxidant defense line collapses,

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the gyroid structure degenerates and fails,

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more lipids are oxidized,

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and more structures are destroyed.

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Once this negative feedback spiral starts, it's hard to reverse.

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Our brains may not fail because of a single genetic mutation,

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but because of the slow collapse of a geometric structure.

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It's not that the software glitched;

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It's the hardware's physical form that can't be maintained.

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This perspective has redefined my understanding of aging.

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We usually think of aging as a chemical phenomenon:

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Gene expressions change,

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proteins misfold,

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and free radicals accumulate.

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But if we dig one layer deeper,

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the container for these chemical events

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is the geometric structure of the membrane.

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The shape of the container determines if the chemistry inside functions normally.

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When the container's shape degrades from the highly stable gyroid,

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a minimal surface, into a common, disordered structure,

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the chemistry inside the container falls into chaos.

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So perhaps the essence of aging

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is geometric degeneration;

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the physical form collapses first,

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and chemical function follows suit.

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Alright.

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Let's tie together today's clues.

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In 1970,

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a mathematician working at NASA

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derived a theoretical surface on paper.

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Over fifty years later,

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biologists found this same structure in butterfly wings, tree shrew eyes,

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amoeba cells, and green algae chloroplasts.

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And then,

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medical researchers discovered

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that a lipid molecule housed within this structure

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00:14:37,429 --> 00:14:41,269
might be the brain's key defense against aging and neurodegeneration.

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A mathematician's pen tip, a butterfly's wing,

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and the collapsing brain of an Alzheimer's patient—

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the distance between them

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is only the thickness of a minimal surface.

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But the core question today isn't about these specific applications.

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I want to leave this question to you:

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Why is a mathematical shape derived purely from energy minimization

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exactly the master key for life to solve optical,

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structural, and biochemical puzzles?

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Is it that the universe's mathematical foundation is perfectly suited for life,

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or can life only exist upon such a mathematical foundation?

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These two statements sound like the same thing,

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but they point to completely different ideas.

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The former implies the universe existed first,

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and life was a later arrival that adapted.

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The latter implies

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perhaps this mathematical structure is itself a necessary condition for life,

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just like water and carbon,

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except we haven't written it into the textbooks yet.

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What do you think?

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Which view do you lean toward?

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I'm really curious about your thoughts.

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I'm Wang Lijie.

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See you next time.