what is dharma-realm dependent origination
fractal geometry gives the answer
in nineteen eighty
a mathematician typed a formula into a computer
z equals z squared plus c
five symbols
one line of code
he pressed enter
a shape appeared on the screen
he zoomed in on that shape
he doubled the zoom
new details emerged along the boundary
he zoomed in ten times
hidden in those details were smaller copies of the same shape
a hundred times a thousand times a million times
there was never any end
at every level of magnification
the structure of the whole kept repeating
this mathematician was named Mandelbrot
this shape was later named the Mandelbrot set
using the simplest rule humans know
it generated an infinitely complex universe
Mandelbrot was not a pure academic
he was born into a Jewish family in Warsaw Poland
in nineteen thirty-six his family moved to France
and there he lived through all of world war two
as a boy he taught himself under his uncle who was a mathematician
he later joined IBM Research
in that era
he was one of the few mathematicians who could visualize with a computer
while others worked out formulas on paper
he looked at shapes on a screen
this habit changed the direction of mathematics
because there are some things
whose shape you could never compute in a lifetime
but the moment you draw them
the answer jumps right in front of you
hello
everyone
I'm Wang Lijie
thirteen hundred years ago
Fazang the third patriarch of the Huayan school stood before Empress Wu
trying to explain something he could not put into words
he said
within a single mote of dust
the entire dharma realm is contained
not reflected
not represented
but contained
every part
is the whole
this is not poetry
this is the central teaching of the Huayan school
called dharma-realm dependent origination
let me first explain these four characters
dharma realm
is the totality of all existence in Buddhist thought
you can simply take it as the whole universe and everything that happens in it
dependent origination
means that all things arise depending on conditions
nothing can exist on its own
dharma-realm dependent origination joins these two ideas together
and says
not only do all things depend on each other
but the structure of mutual dependence in each part
and the structure of mutual dependence of the whole universe
are exactly the same
this is not ordinary dependent origination
this is the dependent origination of dependent origination
it is the structure itself replicating at every scale
last episode we talked about Indra's net
every jewel on that vast net reflects all the other jewels
physics tells us through the holographic principle
that information in three-dimensional space really can be encoded on a two-dimensional boundary
the part can reconstruct the information of the whole
but what I want to say today is
reflecting and containing are not the same thing
reflection is a shadow
containing is the substance itself
Indra's net describes a projection relationship
dharma-realm dependent origination goes further every part's very existence
is already the whole
this claim sounds like pure metaphysics
until the second half of the twentieth century
when mathematicians discovered fractal geometry
before Mandelbrot
there was an earlier example
in nineteen oh four
the Swedish mathematician Koch drew a snowflake curve
the method is simple
take a straight line
replace the middle third with two sides of an equilateral triangle
then repeat the same operation on every new segment
again and again
repeating infinitely
and in the end you get a perfect snowflake
this snowflake has an unsettling property
the area it encloses is finite
but the length of its boundary is infinite
a shape you can hold
yet with a boundary you can never finish walking
classical geometry has no way to handle something like this
more than sixty years later
Mandelbrot took the Koch snowflake and a whole family of similar monster curves
and unified them into one framework
in nineteen sixty-seven
he published a famous paper in the journal Science
titled
how long is the coast of Britain
the answer is
it depends on how long a ruler you measure with
the shorter the ruler
the longer the coastline
because at every smaller scale
new bends and jagged edges appear
you can never finish measuring
because mathematically the detail is infinite
this blew up the foundations of classical measurement
we had always assumed nature's boundaries were smooth curves
but it turns out they are rough
and that roughness looks the same at every scale
within the bends of a coastline hide smaller bends
and within those smaller bends are even smaller ones
seen at ten thousand times magnification
and seen at normal scale
the statistical patterns are exactly the same
Mandelbrot gave this kind of structure a name
he called it a fractal
the core feature of a fractal is one word
self-similarity
in other words
the part and the whole share the same structure
he found that fractals are not a mathematician's fantasy
but nature's default design
and not just one design among many
it is the most efficient design
nature uses fractals to solve an engineering problem
how to pack infinite surface area into finite space
your lungs do something extremely elegant
they branch the bronchi like tree limbs about twenty-three times
and the branching ratio at each level is almost identical
this fractal structure takes the fist-sized space in your chest
and unfolds it into nearly a hundred square meters of gas exchange area
your vascular system follows the same logic
from the aorta to the capillaries
the fractal structure lets a heart of less than one liter
deliver blood precisely to tens of trillions of cells throughout the body
a tree's trunk splits into large branches
large branches split into smaller ones
smaller branches split into twigs
break off a small branch
and its branching shape looks like a shrunken version of the whole tree
a river system
from the main channel of a great river to the tiniest stream
in aerial photos and satellite panoramas
the branching pattern is almost identical
the discharge path of lightning and the neural network of your cerebral cortex
actually follow the same fractal pattern
even your heartbeat is fractal
a healthy heart rate does not beat evenly like a clock
but has tiny irregular fluctuations at every time scale
cardiologists have found
the closer a heartbeat gets to perfect regularity
the more dangerous it becomes
because it means the heart has lost its ability to adapt across scales
fractals
in a sense
are the mathematical signature of life itself
this is no coincidence
nature uses the same recursive algorithm
to build from the smallest scale all the way up to the largest
this is called scale invariance
whether you zoom out or zoom in
the pattern you see is the same
now let's look back at what Fazang said
a single mote of dust contains the entire dharma realm
if we translate it with fractal mathematics
it means
the structural information of the whole
is encoded in the recursive rule of every part
you don't need to see the whole forest
to understand the logic of the forest
the fractal veins of a single leaf
already tell you the growth algorithm of the whole tree
the branching structure of one tree
and the river system of an entire rainforest
are mathematically isomorphic
Buddhism says all of this in four characters
one is all
but fractals give a more precise formulation
it doesn't say one equals all
but that the one and the all share the same generating rule
the Mandelbrot set is the most extreme proof of this
the tiniest bud on its boundary when magnified
matches the shape of the whole set exactly
not approximately
not similar
but exactly identical
because they are the same formula
z equals z squared plus c
producing outputs under different initial conditions
this is exactly what dharma-realm dependent origination means
the Huayan school has a core concept called the unobstructed interpenetration of all phenomena
it is not saying there is some mysterious resonance or connection between things
but rather
the reason all things look different
is only because you observe them at different scales
look at another scale
and the same structure of the dharma realm
appears intact in every phenomenon
a flower and a galaxy
run on the same dependent origination
how is this different from Indra's net
the core of Indra's net is the holographic principle
information is encoded on the boundary
the part can reconstruct the information of the whole
this is a projection relationship
the core of dharma-realm dependent origination is the fractal
the part itself runs the same rule as the whole
this is not projection
it is generation
here's an analogy
one says
your shadow contains all the information about you
the other says
in every cell of your body
runs the exact same genetic code as your entire body
holography is equivalence of information
fractals are equivalence of rules
Indra's net lets you know
that you and the universe share the same data
dharma-realm dependent origination lets you know
that you and the universe share the same source code
you can verify this on yourself
next time you see the silhouette of a big tree
break off its smallest branch
and hold it up to the light
the branching structure of that twig is almost identical to the whole tree
this is the most direct physical evidence of one is all
not a metaphor
not poetry
but an exact correspondence in mathematical structure
in nineteen eighty-two Mandelbrot published his most important book
titled The Fractal Geometry of Nature
in the opening he wrote a line
that has since been quoted countless times
he said
clouds are not spheres
mountains are not cones
coastlines are not circles
bark is not smooth
and lightning does not travel in a straight line
all of Euclidean geometry spent twenty-three hundred years
describing only the things humans made themselves
straight lines circles squares cubes
these shapes barely exist in nature
real nature
never thinks in straight lines
it uses recursion
a single rule running itself
layer within layer
until it generates the whole world
what's interesting is
thirteen hundred years ago Fazang had no computer
no fractal mathematics
but he used an extremely simple physical device
on the four walls four corners ceiling and floor of a room
he mounted mirrors everywhere
placed a Buddha statue and a torch in the center
and let Empress Wu see infinite nesting with her own eyes
every mirror reflected all the other mirrors
mirrors within mirrors
images within images
recursion layer upon layer
endless and without limit
this was the closest thing to a visualization of fractal recursion he could find
today if you open any fractal rendering software
enter that five-symbol formula
and keep zooming in
what you see and the dharma-realm dependent origination Fazang described
are structurally identical
infinite detail
eternal self-similarity
the part is the whole
what does this mean
it means that the claim Fazang made thirteen hundred years ago
that a single mote of dust reveals the vast universe
is no longer a crazy declaration in mathematical terms
it is a precise description of recursive structure
of course
I need to say this clearly
this is a structural isomorphism
not an equals sign
fractal geometry is a mathematical tool
with precise definitions and a rigorous system of proof
dharma-realm dependent origination is a framework for philosophy and practice
pointing toward insight into existence itself
their domains and standards of evidence are completely different
but it is precisely this structural convergence reached along entirely different paths of knowing
that makes you feel something here deserves to be taken seriously
an insight someone reached through inner contemplation thirteen hundred years ago
and a shape that emerged on a computer screen in nineteen eighty
point to the same conclusion
this universe is not made of things
it is made of rules
and that rule
is simple enough to write in just five symbols
Mandelbrot died in twenty ten
at the age of eighty-five
in an interview during his life he said something
that stayed with me
he said
all I have done my whole life is tell people
roughness is not a flaw
roughness is the true grammar of nature
smoothness is a human simplification
roughness is the truth
this echoes dharma-realm dependent origination in a remarkable way
one of the core insights of Buddhism is
our discriminating mind simplifies the world
we draw boundaries
separating you and me inside and outside big and small
but dharma-realm dependent origination says
the boundaries you draw do not exist
every layer is the whole
every scale is the complete dharma realm
you don't need to reach the edge of the universe to understand it
the place where you stand right now
is already everything
if the complexity of the universe really comes from a rule recursing on itself
then the question of who you are
may need to be asked again
you are not a part inside the universe
you are the universe running in full at your scale
the rule that generates galaxies
is generating your thoughts right now
think about it
every decision you make shapes your next decision
every emotional reaction you have adjusts
the threshold of your next emotional reaction
your psychological patterns are recursive
your habits are self-similar
the mistake you made in a relationship ten years ago
and the one you made today
seen up close
are strikingly identical in structure
Buddhism calls this samsara
it calls this the perfuming of seeds
fractal mathematics calls it
iteration
the output of the same formula at different points in time
and spiritual practice
is perhaps rewriting one parameter in that formula
even if you change it just a little
after countless iterations
the resulting shape becomes entirely different
what do you think
do you think nature's self-similarity is a coincidence
or some deeper structure speaking
I'm Wang Lijie
see you next time