# Movie: What is a dimension? In 3D...and 2D... and 1D

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## Comments

Archit Bajaj

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Jake Hayward

If we lived in a 1-dimensional universe that looked 3d, how could we travel

from one point to another in so many different ways? Wouldn't we be forced

to take one route because it's only a 1-dimensional line? Could someone

explain?

The only explanation I can currently think of, is that there are an

infinite amount of 1-dimensional dimensions to connect each point together

to give the illusion of a 3-dimensional universe. I'm going to spend

several weeks looking into this.

from one point to another in so many different ways? Wouldn't we be forced

to take one route because it's only a 1-dimensional line? Could someone

explain?

The only explanation I can currently think of, is that there are an

infinite amount of 1-dimensional dimensions to connect each point together

to give the illusion of a 3-dimensional universe. I'm going to spend

several weeks looking into this.

3snoW

Space filling curves aren't at all what you are saying. If you truly fill

space (be it 2-D or 3-D) using only a 1D line, then for any points A and B

in the curve, if you were to follow the line from A to B, you'd travel an

infinite distance. So, it's not like we could use only one coordinate that

would tell you the position in the line (and therefore in the space) you

are at, all the points are infinitely distant from one another so there is

no metric. You NEED more dimensions to fully describe the space.

What you CAN argue is that you can do an approximation of a space filling

curve. A 1-D line that does not pass through every point in space, but that

passes nearby every point in space. And by nearby i mean that the shortest

distance from any point in space to that line is always smaller than the

Planck's length. Then, you *could* argue that you can describe 3-D space

using only one coordinate, because any distance smaller than the Plank's

length doesn't make much sense, and therefore, as far as your calculations

are concerned, the line does pass through every point in space, and is

1-D.

space (be it 2-D or 3-D) using only a 1D line, then for any points A and B

in the curve, if you were to follow the line from A to B, you'd travel an

infinite distance. So, it's not like we could use only one coordinate that

would tell you the position in the line (and therefore in the space) you

are at, all the points are infinitely distant from one another so there is

no metric. You NEED more dimensions to fully describe the space.

What you CAN argue is that you can do an approximation of a space filling

curve. A 1-D line that does not pass through every point in space, but that

passes nearby every point in space. And by nearby i mean that the shortest

distance from any point in space to that line is always smaller than the

Planck's length. Then, you *could* argue that you can describe 3-D space

using only one coordinate, because any distance smaller than the Plank's

length doesn't make much sense, and therefore, as far as your calculations

are concerned, the line does pass through every point in space, and is

1-D.

TheMrFloorball

if we could define our world a 1D line, we have to pass the following point

on the line before reaching another point, we couldn't go directly there

on the line before reaching another point, we couldn't go directly there

Abe Dillon

What if there are dimensions we can't directly measure? Imagine you're on a

space craft that has rockets to move up and down and rockets to move left

and right, but no rockets to move forward and backward. You may be moving

forward at some speed, but you can't change our speed in that direction.

You can only measure the effects of moving in that direction (like noticing

that things moving slower than you, pass you by or that stars in front of

you seem more blue than stars behind you). Now imagine that nothing, not

even particles have a way to effect their forward/backward velocity. A gas

on your ship would spread out in a 2D disk.

This seems to me to be the case, because light doesn't move through time

and is the primary force carrying particle. Therefore, other particles

can't change each other's velocity through time if all their interactions

are mediated by photons.

Am I missing something? Is this an accurate interpretation?

space craft that has rockets to move up and down and rockets to move left

and right, but no rockets to move forward and backward. You may be moving

forward at some speed, but you can't change our speed in that direction.

You can only measure the effects of moving in that direction (like noticing

that things moving slower than you, pass you by or that stars in front of

you seem more blue than stars behind you). Now imagine that nothing, not

even particles have a way to effect their forward/backward velocity. A gas

on your ship would spread out in a 2D disk.

This seems to me to be the case, because light doesn't move through time

and is the primary force carrying particle. Therefore, other particles

can't change each other's velocity through time if all their interactions

are mediated by photons.

Am I missing something? Is this an accurate interpretation?

thesunandthestripes

Am i still the only one who has discovered how to actually see a tesseract

hahah

hahah

Jarred Mack

This video proposed a question but didn't answer it and proceeded to

introduce more questions.

introduce more questions.

martijn van weele

if you curl up a line it automatically becomes at least two-dimensional,

your argument is invalid.

your argument is invalid.

Tardi Grade X-tra

One direction is also known as 1D! Oh wait! 1D IS One direction! Are the 1D

guys scientist? How did they know that?

guys scientist? How did they know that?

Stefano Cipollone

You sound a bit unenthusiastic, hope everything is well.

Benjamín Marcolongo

What about the homotopy group's? In fact we know that 1D (R1), 2D (R2) and

3D (R3) are not topologically the same thing. For example the real line R

is not homeomorphic to the plane R2, the prove goes as follows: suppose

there were a homeomorphism h of R onto R2. Select some point x0 e R. The

restriction of h to R-(x0) would then carry it homeomorphically onto

R2-(h[x0]). However, R-(x0) is not connected, whereas R2-(h[x0]) certainly

is connected . Since connectedness is a topological property, this cannot

be and we have our contradiction. We can use a similar argumet between R2

and R3, R3 is simply connected and R2 is not.

Think now in a point electric charge "q" residing at the origin of some

intertial frame of reference. The electric field E satisfy the static,

source-free maxwell equations divE=0, curlE=0 (idem with B) in R3-(0,0,0) .

Because of the “simply connectedness” property of R3 we can guarantee the

existence of a scalar potencial function whose gradient is E and solve the

problem, therefore electromagnetism and this kind of phenomena tells us

information about the topology and dimension that could have the space.

3D (R3) are not topologically the same thing. For example the real line R

is not homeomorphic to the plane R2, the prove goes as follows: suppose

there were a homeomorphism h of R onto R2. Select some point x0 e R. The

restriction of h to R-(x0) would then carry it homeomorphically onto

R2-(h[x0]). However, R-(x0) is not connected, whereas R2-(h[x0]) certainly

is connected . Since connectedness is a topological property, this cannot

be and we have our contradiction. We can use a similar argumet between R2

and R3, R3 is simply connected and R2 is not.

Think now in a point electric charge "q" residing at the origin of some

intertial frame of reference. The electric field E satisfy the static,

source-free maxwell equations divE=0, curlE=0 (idem with B) in R3-(0,0,0) .

Because of the “simply connectedness” property of R3 we can guarantee the

existence of a scalar potencial function whose gradient is E and solve the

problem, therefore electromagnetism and this kind of phenomena tells us

information about the topology and dimension that could have the space.

Animiles

I want my room to be 11x3x3x5m. How would that look? If it is 11x3, then it

is flat.

Another thing, if the line is in all directions, then the line is 3d,

right?

is flat.

Another thing, if the line is in all directions, then the line is 3d,

right?

Andrew Luo

Make a video about the 4th dimension :)

Imad Gibbs

Could anyone explain what Henry means when he says "A square and its side

have the same number of points"?

have the same number of points"?

Hiker Wolfspaine

Yet for some reason the universe has 11 dimensions.

JinonTheChildish20Yearold™

"You just waisted 1:20 minutes of your life!" Sorry. I had to. XD

TOTASS1

Michael Bomsdorf

How do we know we live in 3 dimensions?

SparkySywer

If we lived in a 1d universe, the 1d universe couldn't curl up on itself.

Sarah Kettell

*What is a Dimension and Do We Actually Live in a 1D World?*

This is probably one of the most interesting and intelligent discussions

I've ever read in YouTube comments. The video itself is good enough, but

the comments make you think.

This is probably one of the most interesting and intelligent discussions

I've ever read in YouTube comments. The video itself is good enough, but

the comments make you think.

101jir

A curled up line: By Euclidian geometry, that is a contradiction in terms.

Thus, other geometries have to be used, yes. But its not just that simple.

A "curled up line" by itself will violate rules depending on which set you

use. I would assume that the system of dimensions was originally conceived

based on Euclidean geometry, so it could be considered a part of the

definition.

Thus, other geometries have to be used, yes. But its not just that simple.

A "curled up line" by itself will violate rules depending on which set you

use. I would assume that the system of dimensions was originally conceived

based on Euclidean geometry, so it could be considered a part of the

definition.

kamiab ayani

Plz make hour physics as well and explain in more detail as well . I love

ur channel

ur channel

Harrison Desa

-31

cuddlepartyatmyhouse

If it was one dimensional but curled like yarn. A thing would have to

travel all the way around the universe on that line until it ended up on

the line next to it. Therefore a photon would take many times the age of

the universe to move to an adjacent "tread".

travel all the way around the universe on that line until it ended up on

the line next to it. Therefore a photon would take many times the age of

the universe to move to an adjacent "tread".

Darwin Kim

is the music at the end backwards?

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