Dimensionality reduction strike of the three-body theory
What did you knock out?
In Liu Cixin's three-body
The Singer Civilization threw a piece of binary foil into the solar system
This thing is only the size of a palm, 8.5.
Centimeters long, 5.2.
centimeter width
No thickness.
But it's just such a small piece of paper
The moment you come into contact with three-dimensional space
Flattened the entire solar system
3D to 2D
All planets, spaceships, and humans
It all becomes a painting that is too thin to have any thickness
This image shocked countless readers
The four words dimensionality reduction and strike also became popular all over the Internet
Becomes a catch-all adjective
Use it commercially
Say one company hits another company with dimensionality reduction
Cognitively use it.
Say that the master strikes the novice with dimensionality reduction
But I want to ask you a serious question today
dimensionality reduction strike
What did you knock out?
It's not life.
Not matter
Is a dimension
What is that dimension?
Why lose a dimension?
Is equivalent to destruction
Hello
Hello.
I am Wang Lijie
We're not going to talk about investing today
Don't talk about practice
Let's talk about dimensionality. It's deceptively simple.
It's a bottomless concept.
I promise.
After the chat, your understanding of dimensionality reduction strikes will be completely upgraded
And you will find
The concept of dimension
It may be to understand AI and physics
Even a central key to understanding consciousness
OK
We start with the basics.
What is one-dimensional?
A thread.
Length only
No width
No height
You can imagine an ant trapped on an infinitely long wire.
It can only go forward or backward.
Its entire universe is this wire.
Front and rear directions
That's one dimension.
What is two-dimensional?
One face
There is length
Have width
But no height
Imagine that you are a little person drawn on a piece of paper
You can move back and forth, left and right.
But you can never leave the surface of this paper
You don't even know the concept of up and down
Because in your world
There is no third way.
What is 3D?
It's the space that we live in every day.
Length, width and height
You can go backwards and forwards.
You can go left and right.
You can go up and down.
Three directions
Three dimensions
It makes up everything you can see and touch
Go here.
Most people are fine
And then someone tells you
The fourth dimension is time.
That's acceptable.
Einstein told us that
Space and time are not separate
They are a whole
It's called spacetime.
You live in a three-dimensional space.
But you have no choice in one direction at the same time
It's time.
You can only move from the past to the future
Can't look back
Time is a one-way street.
It is your fourth dimension
OK
End here
And most people's cognitive map just stops.
one-dimensional two-dimensional three-dimensional four-dimensional
clearly
But I want to interject here first
Now, four dimensions has a hidden trap.
Many people believe that time is the fourth spatial dimension
As if you could move in the direction of time
No.
There is an essential difference between the time dimension and the space dimension
It's a space where you can go backwards or forwards.
But time is a one-way street.
You can only move from the past to the future
They call this the Lorentz metric in physics.
The mathematical notation of the time dimension is reversed from the spatial dimension
So Einstein's four-dimensional spacetime
It doesn't just add a direction to the three dimensions.
It's about stitching together space and time in a very particular way.
Figure this out
You can understand a deeper truth
Dimensions and dimensions are not necessarily equivalent
They can have different properties
There are dimensions you can go back and forth in.
Some dimensions you can only travel one way
This distinction will be very important later
OK
Back to Main Line
If I were to ask you
What is the fifth dimension?
What about six dimensions?
What about seven dimensions?
And even string theory says the universe has 10 or 11 dimensions.
What are these dimensions?
Most people's reaction is
no.
Can't think of it
Can't draw it in my head
It's normal.
Because our brains evolved in three dimensions.
Our sense of sight, hearing, touch
They're all customized senses in three dimensions.
Let you imagine space beyond four dimensions
It's like asking ants on a piece of paper to imagine heights.
It simply doesn't have the hardware to process this information.
But
Can't think of it doesn't mean it doesn't exist
And this is the single most important cognitive upgrade point of the day.
The way humans understand dimensions
It's not imaginary.
It's about logic and mathematics.
Let me explain dimensions differently.
What is the essence of dimensions?
Is the degree of freedom
Is the minimum number of numbers you need to describe the position of something
Positioning an ant on a piece of wire.
All you need is a number.
For example, 3 cm away from the starting point
A number.
one-dimensional
Locate a point on a piece of paper
You need two numbers.
For example, abscissa 3
Vertical coordinate 5
Two numbers
two-dimensional
Locating a fly in a room
You need three numbers.
One coordinate each for length, width and height
Three numbers.
3D
If you still want to know when the fly was in that position
You also need to add a time coordinate.
Four numbers.
4D
Did you see it?
Dimension is not a mysterious concept of space
Dimension is how many independent numbers are required to describe something
Each additional independent information axis
Just one more dimension
Once this understanding is established
Gao Wei is no longer incredible
What is the fifth dimension?
Here I want to explain first
The explanation of more than five dimensions is not completely settled in the field of physics
But there is a widely discussed way of understanding it
If four-dimensional space-time describes our universe
The complete historical trajectory from birth to the present
Then the fifth dimension refers to possibility
It is at a certain historical juncture
If a different choice occurs
Will fork off into another universe
The initial conditions of the two universes are the same
But the follow-up development is different
The Fifth Dimension
Is to connect these if the original axis
What about six dimensions?
If the fifth dimension is forked from the same starting point, it is different.
The sixth dimension is to get everything out of the same starting point
All the possibilities of sending are folded together.
You can imagine
Five dimensions are the different branches of a tree.
The sixth dimension is to see the whole tree from the root to the top as a point
Seven-dimensional is even more powerful
Seven dimensions means different initial conditions.
Not different branches of the same Big Bang.
But from a completely different Big Bang
Different physical constants
Worlds from different cosmic beginnings
Each of these initial conditions produces a completely different tree of possibilities.
seven-dimensional
It's the dimension that connects the roots of these different trees.
Eight-dimensional, nine-dimensional, ten-dimensional.
And so on.
More and more abstract
All the way down to the ten dimensions described by string theory
Or the eleven dimensions of M-theory
On that scale
All possible universes, all possible laws of physics
All possible timelines
It's all put together in a mathematical framework.
I know that's it.
Your brain may have started to smoke
It's so normal.
But you don't have to draw a mental picture of what these dimensions look like.
You only need to remember one core concept
Each additional dimension
Is to add an independent description axis
Adds a layer of information that you can't even see in the lower dimensions
Now we're back to the three-body dimensionality reduction strike
When the singer civilization used two-dimensional foil to compress three-dimensional space into two dimensions
What does it do?
It destroys a degree of freedom
It puts the height dimension
Erased from the universe
What does that mean?
That means all structures that depend on height to exist.
Instant collapse
Your body needs three dimensions to function.
Your organs are arranged up, down, back, left, right in three dimensions.
Blood vessels need to pass through tissue
Nerves are layered to transmit signals, DNA
The double helix needs three dimensions to fold
When the third dimension disappears
And all of these structures are forced to slap flat.
It's like turning a precision mechanical watch into a discus with a steamroller.
All the parts are still there
But the spatial relationship between them was completely destroyed
What the dimensionality reduction strike knocks down is not matter
Is relationship
They're structures and functions that can only exist in a certain number of dimensions.
Think again
This actually explains a phenomenon that we observe in our daily lives
Why a photo can never compare to the scenery seen with your own eyes
Because photographs are two-dimensional.
It loses a dimension of the three-dimensional world
In-depth information is gone
The kind of depth you can feel when you stand on the edge of a cliff
I can't give you the photo.
Why do I always feel that the voice I hear on the phone is not as real as chatting in person?
Because telephony compresses many of the frequency dimensions of sound.
What you're receiving is a dimensionality reduced sound.
Dimension is not an ornament of space
Dimension is the carrier of information
Each dimension carries an independent network of relationships
One less dimension
A whole layer of relationships is missing
And those complex structures that depend on this relationship to exist
Zero All
OK
Now let's take the concept of dimensionality to a more exciting place, AI.
I said it in a previous video.
The parameters of the big language model don't store knowledge.
It's geometry that stores knowledge.
The geometry exists in a high-dimensional vector space.
So how many dimensions does space have?
Take GPT-4 as an example
And the embedding dimensions are about 12,000 plus dimensions.
This means that every word, every concept
In the world of AI, it is a coordinate point that exists in more than 10,000 dimensions of space
more than 10,000 dimensions
You can't even imagine five dimensions, AI.
Thinking in more than 10,000 dimensions
But that's not the craziest part.
Ten thousand dimensions is just the representation space of individual words.
If you add up the parameter space of the entire model
That's trillions of parameters.
It's a trillion-dimensional surface.
Language data for thousands of years of human civilization
Compressed into a precise shape in this ultra-high-dimensional space
Why does AI need so many dimensions?
Because language is incredibly complex.
In three dimensions.
Cats and dogs can only approach or stay away
The best you can say is that they are similar or they are different.
But in 10,000 dimensions
Cats and dogs can be very close in the dimension of pet attributes
They go a long way in terms of independence.
There's a subtle distance in the number of years we've been domesticated.
It almost coincides in the dimension of Internet popularity
Ten thousand dimensions
It's 10,000 individual relationship axes.
This means that the relationship between any two concepts
Can be broken down into 10,000 independent components to describe precisely
This is why AI can understand language
It's not memory.
It's in a very high-dimensional space beyond the imagination of the human brain
Encoding meaning in geometry.
And here's what's interesting.
This high-dimensional representation and the way the human brain works
It's mathematically isomorphic.
The human brain has about 100 billion nerve cells
One hundred trillion synaptic connections.
The strength of each synaptic connection
Is a parameter
When you learn to recognize your mother's face
It's not because you have a picture in your head.
It's that certain synapses in your visual cortex are tuned to specific patterns.
The space formed by these patterns
And AI's parameter space
It's mathematically the same thing.
So you see
Dimensions are not an abstract concept that only exists in physics textbooks
Dimensions are the skeleton of information.
The information that can be carried in one dimension is extremely limited
It's the distance on a thread.
2D can carry more
Positional relationship on the plane
One more layer in 3D
three-dimensional structure
Each additional dimension
The complexity of the relationship that can be accommodated increases exponentially
This is why dimensionality reduction strikes in the Trisolaran are so deadly
It's not because you got thinner.
It's because your information carrying capacity has been taken away.
A three-dimensional creature is photographed in two dimensions.
It was as if 10,000 lines of code had been deleted to one line.
The characters of the code may still be there.
But the program doesn't run anymore
And the other way around.
What does ascension mean?
It means you have a whole new level of freedom
More relationships can be encoded
More complex structures can be built
There's a key concept here called the curse of dimensions.
In mathematics and computer science
This is a famous puzzle.
When the dimensions increase
The volume of space exponentially expands.
In three-dimensional space, if there are 10 grids in each direction
You have a thousand grids.
But in one hundred dimensions
Again, 10 squares in each direction.
You need 10 ^ 100 squares.
That's bigger than all the atoms in the universe.
This means that in high-dimensional space
Data can become extremely sparse
You need an astronomical amount of data to fill the space
This is why training a large language model
We need to feed them texts that have been written by almost all of humanity.
Because it needs to build dense enough coordinate points in more than 10,000 dimensions of space
To draw the geometry of language
But AI overcame the curse
It uses a very clever method
It's called the manifold hypothesis.
It means that although the entire space is more than 10,000 dimensions
But meaningful data is not evenly distributed throughout space
The really meaningful points are spread over a low-dimensional surface.
Like the surface of the earth although embedded in three dimensions
But to walk on Earth, you only need two coordinates.
longitude and latitude
What AI needs to do is not to fill the entire high-dimensional space
It's about finding that low-dimensional surface hidden in high-dimensional space.
This is the essence of AI's transition from a three-dimensional physical world to a multi-dimensional parametric space
It's not bearing the curse of the dimension
It's a skeleton that finds information in high-dimensional space.
This also answers a question that many people are confused about
Why can AI sometimes see patterns that humans cannot?
It's not because AI is smarter
It's because AI sees the world in more dimensions than we do
It's like a three-dimensional creature looking down on a two-dimensional plane.
It can see things that flat creatures would never see
Like the whole picture of the labyrinth
AI looks down on human language in the world of space
It can see semantic correlations that we would never notice in three-dimensional cognition
And finally.
And I want to leave you with an open question.
If dimensions are the skeleton of information
And we humans are stuck in a four-dimensional spacetime with three dimensions of space plus one dimension of time.
Then our consciousness
Is it also locked in some kind of four-dimensional prison?
If there was a way to raise consciousness
Even if it only rises one dimension
What will the world we see look like?
Have you ever considered
Enlightenment in Buddhism
Could it be some kind of ascension of consciousness?
The experience of All That Is in meditation.
Could it be that consciousness has temporarily broken through the three-dimensional limit?
A glimpse of a higher-dimensional network of relationships
I'm really not sure.
But I think it's a question worth thinking about when you lie in bed tonight
Do you think consciousness can be ascended?
If you can
What do you think the world that five-dimensional consciousness sees is like?
I am Wang Lijie
See you next time.