/sci/ - Science & Math

[Anonymous No.6979244]

Explain 4-dimensional space to me. It's literally just a 4th axis, right? How is that even possible?

[Anonymous No.6979251]

>>6979244
it isn't
these people have a time space delusion, it's a pathological concept.

[Anonymous No.6979275]

It's hypothetical. The concept of a forth dimension is useful for some math and physics concepts. It's like imaginary numbers; they don't actually exist, but it's useful to act as if they do for some calculations.

[Anonymous No.6979277]

>>6979244
The number of dimensions is just the number of coordinates needed to uniquely identify a point. For example, the set of pairs of points in the plane forms a 4-dimensional space, because specifying a pair of points in the plane requires 4 coordinates (two for each point). Likewise, the set of 100-tuples of points in a plane forms a 200-dimensional space.

It's only a troubling notion if you try to naively visualize it, which won't work because your visual cortex evolved under the constraints of a world with three spatial dimensions. But if you look at it mathematically, there's no problem at all — just add more coordinates.

[Anonymous No.6979284]

>>6979244
https://www.youtube.com/watch?v=eGguwYPC32I

[Anonymous No.6979288]

>>6979275
There's nothing any more "hypothetical" about complex numbers than about other kinds of numbers; they "exist" in the same sense that any numbers "exist". Can you show me the number four itself? No, because it's "just a concept" (a phase people often throw around as though it makes something less real) — all you can do is show me a collection of "four things", i.e., a physical model of the concept "four". Similarly, complex numbers arise naturally in certain physical models of the universe, but they aren't physical objects themselves.

[Anonymous No.6979291]

>>6979288
I can show you four rocks, and I can show you something with three dimensions. Can you show me √-2 rocks or a 4th dimensional object?

Sure, the abstract concept of numbers itself isn't real, but you can actually have a real number of thinks in life. You can not actually have an imaginary or negative number of things.

[Anonymous No.6979391]

>>6979284
I like this kid, he's cute.

[Anonymous No.6979398]

4 dimensional space is easy. Just imagine N-dimensional space and set N = 4.

[Anonymous No.6979402]

>>6979244
Regardless of how many dimensions actually exist, we can only perceive up to 3 dimensions so it is pointless to try to imagine a 4th dimension. Just do the math.

[Anonymous No.6979405]

>>6979402
I mean, just do the math and stop trying to imagine how it looks like.

[Anonymous No.6979414]

>>6979291
>Can you show me √-2 rocks
No, because <span class="math">\sqrt{-2}[/spoiler] isn't a cardinal number, so it doesn't represent the "size of a collection". Wrong type of number. (You can't show me <span class="math">\sqrt{2}[/spoiler] rocks or <span class="math">-1[/spoiler] rocks, either. Natural numbers are the only finite cardinal numbers.)

>or a 4th dimensional object?
Take any three-dimensional object and view it over an interval of time. (I can't show you a 4-dimensional object all at once because "show" suggests it's embedded in spacetime and "all at once" gives a 3-dimensional slice of spacetime, and you can't embed an object in a lower-dimensional space.)

Or, you could go with the example of "the configuration space of pairs of points in a plane", which is four-dimensional. But I'm not sure whether you'd count that as "showing" it to you, even though it's a pretty concrete object.

[Anonymous No.6979415]

>>6979291
The only confusion here arises from the fact that you're limiting the things that you consider valid representations of numbers.

You're right, I can't show you <span class="math">\sqrt{-2}[/spoiler] rocks. But I also can't show you <span class="math">\sqrt{2}[/spoiler] rocks.

I can, however, make a ball revolve in a circle of radius <span class="math">\sqrt{2}[/spoiler].

Okay, so we've expanded our definitions. If we're only considering quantities, then the only numbers that matter, according to you, are integers. But obviously that's not true. Real numbers are important. Why is that? Well, because they can represent a physical, observable quantity in a system (for example, the radius of a planet in orbit may be a real number and not necessarily an integer).

Okay, then. If we accept that the real numbers are meaningful, then it is only one step further to say "any number that can be used to represent an observable physical quantity is meaningful."

Complex (imaginary) numbers are the only reasonable way to represent probability amplitudes in quantum mechanics.

So they're meaningful.

"bait"

[Anonymous No.6979486]

>>6979398
Classic

[Anonymous No.6979488]

>>6979284
Maybe the first dimension is time.
0 dimension = point
1 dimension = line or a point traveling through time
2 dimension = plane or a line moving through time
3 dimension = cube or a plane traveling through time
4 dimension = hypercube or a cube traveling through time

If the universe is 3 dimensions with time, a fourth dimensional being would see the entire universe as a static object, everything that has happened and will happen as a single object. Having dimensions without time creates a static environment which is essentially 0 dimensional.

[Anonymous No.6979493]

>>6979244
It doesn't need to be a geometric dimension. It is just a way of modeling something numerically. I can might make a model that has 6 dimensions Each data point consisting of {x,y,z,time,color,temperature}

Then I can perform useful transformations on those data to understand the space.

[Anonymous No.6979502]

>>6979488
no dimension is "time", because time is just our consciousness perceiving a continuous lime of 3rd-dimensional points,
its the same way the 1st dimension is just a line of 0th dimensional points

[Anonymous No.6979562]

>>6979502
>continuous lime

[Anonymous No.6979601]

>>6979488
we are fourth dimensional beings because we utilize the 4th dimension in our movement and documentation

[Anonymous No.6979609]

>>6979277
>It's only a troubling notion if you try to naively visualize it, which won't work because your visual cortex evolved under the constraints of a world with three spatial dimensions. But if you look at it mathematically, there's no problem at all

mind blown

[Anonymous No.6979614]

It's just a theory, like evolution

[Anonymous No.6979620]

>>6979614
>no understanding of what a theory actually means
a theory is not a guess, its a malleable, confirmed equation

[Anonymous No.6979629]

I have a few questions related to this:

People throw the concept of space time around and make it seem like space and time are completely interchangeable. I have limited knowledge of relativity, but what I do know is that if you were to treat the relationship between two objects/events in space and time as a vector in 4 space, the absolute distance between these two events (sqrt(x^2+y^2+z^2+c^2t^2)) should be the same for all observers. So then, how far does this relationship between time and space go? What is the fundamental difference between space and time besides how our brain observes these dimensions? Entropy?

My second question is what would a universe with 2 temporal dimensions be like? What implications that have?

[Anonymous No.6979645]

>>6979629
>what would a universe with 2 temporal dimensions be like?
it would only be inhabited by line creatues, who move through the 2nd dimension to create the illusion of time.
the book Flatland has a nice representation of what a line society would be like

[Anonymous No.6979656]

>>6979562
Am I on 420chan?

[Anonymous No.6979670]

existence blows my mind and will blow until i die

[Anonymous No.6980416]

>>6979415
>But I also can't show you sqrt2 rocks.
actually you can. Just break off parts of the second rock so the total you show me is the right amount.

[Anonymous No.6980427]

>>6979601
Time is our perception of the fourth dimension.
We may reference it but we never actually encounter it. If we were fourth dimensional, we could see our entire bodies' insides.

[Anonymous No.6980499]

Dimensions are just variables.
No, you cant imagine 4D space. You aren't wired to do so.
Time can be thinked of as a dimension but it is very different from a spatial one.

[Anonymous No.6980524]

>>6979502

Time dilation suggests otherwise

[Anonymous No.6980535]

why is a hypercube a 4th dimensional object?

[Anonymous No.6980705]

>>6980427

4th space dimension =/= time.

in 2d, there can still be time, and it would not be the 3rd space dimension.

Someone explain to me why so many people are so confused about this.
I mean, 6980427 might be trolling, who cares. But a LOT of people actually can't distinguish between these two concepts.
NO idea why.

on topic:
you can't really imagine a 4th, but you can extrapolate from a jump from 2nd to 3rd dimension and apply that to jump from 3rd to 4th dimension.
Like if a 3D ball goes through a plane or if you imagine it going through a piece of paper, on paper it would look like a circle appearing out of nowhere.
So, for a 4D "ball" going through 3D space, it would look like a dot appearing out of nowhere, growing, then shrinking again out of existance.

Note that it has shit-all to do with calling time a space-dimension.

[Anonymous No.6980798]

How is believing in the 4th dimension any different that believing in god?

>It's hypothetical. The concept of a forth dimension is useful for some math and physics concepts. It's like imaginary numbers; they don't actually exist, but it's useful to act as if they do for some calculations.

>Belief in god is hypothetical. The concept of a god is useful for some unanswered questions that can never be answered.

[Anonymous No.6980801]

>>6980535
It's not, it's the hypothetical 'shadow' of one

Here, Carl Sagan explains it very simply:
https://www.youtube.com/watch?v=UnURElCzGc0

[Anonymous No.6980809]

>This thread.
How can you people congregate so readily and vomit your turd words so readily?

Carl sagan did a good explination, google that.

[Anonymous No.6980973]

>>6980535
because each side is a cube on a hypercube.
each side cannot be a cube in the 3rd dimension

[Anonymous No.6981037]

>>6979391
Yeah, and what a hot, deep voice for a smooth young boi like him.

[Anonymous No.6981463]

>>6979244
Yeah, it's another axis. You can't understand it. Your brain isn't made to.
4d to you would be what 3d would be to a 2d being.
Just think of it that way, that's the only way you can..

[Anonymous No.6982181]

>>6979244
>>6981463
go read flat land

[Anonymous No.6982186]

You've heard of an ordered pair with three members? Well, it's an ordered pair with four members. That's all. And there's some neat geometry shit you can do with it. I don't see how it's not possible.

[Anonymous No.6982189]

>>6982181
The Planiverse is better.

[Anonymous No.6982244]

>>6980524
gravity distorts space, distortion of space implies distortion of movement, of processes, occurring within that space (at least, relative to the stuff that is happening outside that space).

[Sceak No.6982380]

>>6979244

Time is sometimes regarded as a fourth dimension. I'm going to re-use someone else's introduction of the four-point coordinate system, and demonstrate how you can truly identify a particle in a dynamic system.

Say, (45,75,0,January 1st, 1980 00:00:00.00000). That space is maybe occupied by an atom of nitrogen at that time, whereas an atom of oxygen will occupy it at a later time.

If you really care about physical dimensions, a four-dimensional physical space would be a lot like ours, except it would have four dimensions and we'd look weird to four-dimensional beings (like if a drawing was to exist and move around in our space, it could, but it'd lack depth). Four dimensions in a three dimensional plane would probably morph, like the tesseract, except it would take no time for it to morph. The tesseract, if it were to exist in our world and we were to see it morph, would be a five-dimensional object.

I understand this might be complex and hard to understand, but it's sometimes complex and hard to understand that this might be complex and hard to understand.

[Anonymous No.6982386]

>>6979244
It doesn't exist.

[Anonymous No.6982445]

>implying we aren't just a tiny piece of an infinite-dimensional omnistructure and that 4-D isn't babbyshit to the everdimensional beings of complexity so vast that our dimensional universe isn't even as notable to them as a single photons movement is to us and that it doesn't take like 5 trillion dimensions for them to even figure out where a single negativenumberparticle is in their dick is at any given ultrahypersecond

[Anonymous No.6982455]

>>6981037
>implying he didn't use a voice changer

[Anonymous No.6982625]

An entire THREAD full of people who have NO IDEA what a cartesian product is.