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what is dharma-realm dependent origination

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fractal geometry gives the answer

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in nineteen eighty

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a mathematician typed a formula into a computer

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z equals z squared plus c

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five symbols

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one line of code

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he pressed enter

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a shape appeared on the screen

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he zoomed in on that shape

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he doubled the zoom

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new details emerged along the boundary

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he zoomed in ten times

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hidden in those details were smaller copies of the same shape

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a hundred times a thousand times a million times

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there was never any end

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at every level of magnification

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the structure of the whole kept repeating

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this mathematician was named Mandelbrot

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this shape was later named the Mandelbrot set

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using the simplest rule humans know

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it generated an infinitely complex universe

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Mandelbrot was not a pure academic

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he was born into a Jewish family in Warsaw Poland

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in nineteen thirty-six his family moved to France

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and there he lived through all of world war two

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as a boy he taught himself under his uncle who was a mathematician

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he later joined IBM Research

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in that era

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he was one of the few mathematicians who could visualize with a computer

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while others worked out formulas on paper

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he looked at shapes on a screen

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this habit changed the direction of mathematics

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because there are some things

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whose shape you could never compute in a lifetime

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but the moment you draw them

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the answer jumps right in front of you

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hello

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everyone

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I'm Wang Lijie

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thirteen hundred years ago

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Fazang the third patriarch of the Huayan school stood before Empress Wu

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trying to explain something he could not put into words

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he said

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within a single mote of dust

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the entire dharma realm is contained

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not reflected

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not represented

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but contained

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every part

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is the whole

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this is not poetry

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this is the central teaching of the Huayan school

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called dharma-realm dependent origination

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let me first explain these four characters

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dharma realm

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is the totality of all existence in Buddhist thought

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you can simply take it as the whole universe and everything that happens in it

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dependent origination

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means that all things arise depending on conditions

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nothing can exist on its own

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dharma-realm dependent origination joins these two ideas together

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and says

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not only do all things depend on each other

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but the structure of mutual dependence in each part

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and the structure of mutual dependence of the whole universe

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are exactly the same

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this is not ordinary dependent origination

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this is the dependent origination of dependent origination

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it is the structure itself replicating at every scale

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last episode we talked about Indra's net

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every jewel on that vast net reflects all the other jewels

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physics tells us through the holographic principle

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that information in three-dimensional space really can be encoded on a two-dimensional boundary

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the part can reconstruct the information of the whole

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but what I want to say today is

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reflecting and containing are not the same thing

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reflection is a shadow

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containing is the substance itself

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Indra's net describes a projection relationship

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dharma-realm dependent origination goes further every part's very existence

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is already the whole

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this claim sounds like pure metaphysics

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until the second half of the twentieth century

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when mathematicians discovered fractal geometry

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before Mandelbrot

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there was an earlier example

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in nineteen oh four

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the Swedish mathematician Koch drew a snowflake curve

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the method is simple

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take a straight line

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replace the middle third with two sides of an equilateral triangle

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then repeat the same operation on every new segment

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again and again

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repeating infinitely

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and in the end you get a perfect snowflake

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this snowflake has an unsettling property

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the area it encloses is finite

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but the length of its boundary is infinite

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a shape you can hold

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yet with a boundary you can never finish walking

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classical geometry has no way to handle something like this

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more than sixty years later

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Mandelbrot took the Koch snowflake and a whole family of similar monster curves

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and unified them into one framework

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in nineteen sixty-seven

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he published a famous paper in the journal Science

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titled

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how long is the coast of Britain

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the answer is

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it depends on how long a ruler you measure with

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the shorter the ruler

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the longer the coastline

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because at every smaller scale

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new bends and jagged edges appear

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you can never finish measuring

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because mathematically the detail is infinite

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this blew up the foundations of classical measurement

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we had always assumed nature's boundaries were smooth curves

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but it turns out they are rough

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and that roughness looks the same at every scale

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within the bends of a coastline hide smaller bends

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and within those smaller bends are even smaller ones

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seen at ten thousand times magnification

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and seen at normal scale

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the statistical patterns are exactly the same

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Mandelbrot gave this kind of structure a name

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he called it a fractal

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the core feature of a fractal is one word

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self-similarity

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in other words

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the part and the whole share the same structure

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he found that fractals are not a mathematician's fantasy

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but nature's default design

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and not just one design among many

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it is the most efficient design

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nature uses fractals to solve an engineering problem

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how to pack infinite surface area into finite space

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your lungs do something extremely elegant

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they branch the bronchi like tree limbs about twenty-three times

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and the branching ratio at each level is almost identical

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this fractal structure takes the fist-sized space in your chest

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and unfolds it into nearly a hundred square meters of gas exchange area

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your vascular system follows the same logic

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from the aorta to the capillaries

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the fractal structure lets a heart of less than one liter

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deliver blood precisely to tens of trillions of cells throughout the body

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a tree's trunk splits into large branches

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large branches split into smaller ones

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smaller branches split into twigs

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break off a small branch

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and its branching shape looks like a shrunken version of the whole tree

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a river system

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from the main channel of a great river to the tiniest stream

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in aerial photos and satellite panoramas

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the branching pattern is almost identical

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the discharge path of lightning and the neural network of your cerebral cortex

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actually follow the same fractal pattern

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even your heartbeat is fractal

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a healthy heart rate does not beat evenly like a clock

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but has tiny irregular fluctuations at every time scale

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cardiologists have found

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the closer a heartbeat gets to perfect regularity

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the more dangerous it becomes

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because it means the heart has lost its ability to adapt across scales

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fractals

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in a sense

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are the mathematical signature of life itself

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this is no coincidence

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nature uses the same recursive algorithm

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to build from the smallest scale all the way up to the largest

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this is called scale invariance

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whether you zoom out or zoom in

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the pattern you see is the same

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now let's look back at what Fazang said

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a single mote of dust contains the entire dharma realm

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if we translate it with fractal mathematics

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it means

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the structural information of the whole

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is encoded in the recursive rule of every part

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you don't need to see the whole forest

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to understand the logic of the forest

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the fractal veins of a single leaf

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already tell you the growth algorithm of the whole tree

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the branching structure of one tree

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and the river system of an entire rainforest

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are mathematically isomorphic

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Buddhism says all of this in four characters

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one is all

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but fractals give a more precise formulation

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it doesn't say one equals all

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but that the one and the all share the same generating rule

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the Mandelbrot set is the most extreme proof of this

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the tiniest bud on its boundary when magnified

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matches the shape of the whole set exactly

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not approximately

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not similar

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but exactly identical

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because they are the same formula

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z equals z squared plus c

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producing outputs under different initial conditions

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this is exactly what dharma-realm dependent origination means

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the Huayan school has a core concept called the unobstructed interpenetration of all phenomena

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it is not saying there is some mysterious resonance or connection between things

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but rather

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the reason all things look different

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is only because you observe them at different scales

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look at another scale

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and the same structure of the dharma realm

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appears intact in every phenomenon

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a flower and a galaxy

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run on the same dependent origination

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how is this different from Indra's net

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the core of Indra's net is the holographic principle

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information is encoded on the boundary

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the part can reconstruct the information of the whole

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this is a projection relationship

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the core of dharma-realm dependent origination is the fractal

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the part itself runs the same rule as the whole

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this is not projection

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it is generation

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here's an analogy

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one says

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your shadow contains all the information about you

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the other says

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in every cell of your body

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runs the exact same genetic code as your entire body

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holography is equivalence of information

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fractals are equivalence of rules

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Indra's net lets you know

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that you and the universe share the same data

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dharma-realm dependent origination lets you know

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that you and the universe share the same source code

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you can verify this on yourself

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next time you see the silhouette of a big tree

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break off its smallest branch

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and hold it up to the light

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the branching structure of that twig is almost identical to the whole tree

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this is the most direct physical evidence of one is all

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not a metaphor

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not poetry

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but an exact correspondence in mathematical structure

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in nineteen eighty-two Mandelbrot published his most important book

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titled The Fractal Geometry of Nature

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in the opening he wrote a line

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that has since been quoted countless times

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he said

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clouds are not spheres

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mountains are not cones

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coastlines are not circles

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bark is not smooth

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and lightning does not travel in a straight line

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all of Euclidean geometry spent twenty-three hundred years

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describing only the things humans made themselves

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straight lines circles squares cubes

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these shapes barely exist in nature

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real nature

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never thinks in straight lines

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it uses recursion

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a single rule running itself

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layer within layer

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until it generates the whole world

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what's interesting is

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thirteen hundred years ago Fazang had no computer

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no fractal mathematics

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but he used an extremely simple physical device

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on the four walls four corners ceiling and floor of a room

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he mounted mirrors everywhere

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placed a Buddha statue and a torch in the center

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and let Empress Wu see infinite nesting with her own eyes

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every mirror reflected all the other mirrors

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mirrors within mirrors

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images within images

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recursion layer upon layer

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endless and without limit

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this was the closest thing to a visualization of fractal recursion he could find

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today if you open any fractal rendering software

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enter that five-symbol formula

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and keep zooming in

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what you see and the dharma-realm dependent origination Fazang described

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are structurally identical

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infinite detail

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eternal self-similarity

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the part is the whole

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what does this mean

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it means that the claim Fazang made thirteen hundred years ago

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that a single mote of dust reveals the vast universe

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is no longer a crazy declaration in mathematical terms

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it is a precise description of recursive structure

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of course

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I need to say this clearly

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this is a structural isomorphism

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not an equals sign

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fractal geometry is a mathematical tool

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with precise definitions and a rigorous system of proof

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dharma-realm dependent origination is a framework for philosophy and practice

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pointing toward insight into existence itself

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their domains and standards of evidence are completely different

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but it is precisely this structural convergence reached along entirely different paths of knowing

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that makes you feel something here deserves to be taken seriously

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an insight someone reached through inner contemplation thirteen hundred years ago

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and a shape that emerged on a computer screen in nineteen eighty

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point to the same conclusion

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this universe is not made of things

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it is made of rules

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and that rule

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is simple enough to write in just five symbols

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Mandelbrot died in twenty ten

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at the age of eighty-five

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in an interview during his life he said something

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that stayed with me

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he said

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all I have done my whole life is tell people

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roughness is not a flaw

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roughness is the true grammar of nature

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smoothness is a human simplification

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roughness is the truth

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this echoes dharma-realm dependent origination in a remarkable way

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one of the core insights of Buddhism is

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our discriminating mind simplifies the world

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we draw boundaries

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separating you and me inside and outside big and small

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but dharma-realm dependent origination says

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the boundaries you draw do not exist

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every layer is the whole

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every scale is the complete dharma realm

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you don't need to reach the edge of the universe to understand it

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the place where you stand right now

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is already everything

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if the complexity of the universe really comes from a rule recursing on itself

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then the question of who you are

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may need to be asked again

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you are not a part inside the universe

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you are the universe running in full at your scale

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the rule that generates galaxies

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is generating your thoughts right now

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think about it

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every decision you make shapes your next decision

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every emotional reaction you have adjusts

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the threshold of your next emotional reaction

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your psychological patterns are recursive

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your habits are self-similar

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the mistake you made in a relationship ten years ago

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and the one you made today

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seen up close

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are strikingly identical in structure

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Buddhism calls this samsara

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it calls this the perfuming of seeds

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fractal mathematics calls it

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iteration

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the output of the same formula at different points in time

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and spiritual practice

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is perhaps rewriting one parameter in that formula

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even if you change it just a little

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after countless iterations

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the resulting shape becomes entirely different

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what do you think

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do you think nature's self-similarity is a coincidence

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or some deeper structure speaking

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I'm Wang Lijie

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see you next time