/sci/ - Science & Math

[Anonymous No.6143460]

The tesseract -
I don't see the concept of four dimensions in this object. I see still a three dimensional object with a lot of claim that it is four dimensional because a three dimensional object is within a still, three dimensional object.

Opinions?

[Anonymous No.6143468]

>>6143460

That is a 2D representation of a 3D model designed to approximate the behaviour of a 4D object.

[Anonymous No.6143471]

>>6143460
What you see is the shadow of a 4d cube.
Think of a cube, it's angles are 90 degrees. However if you draw it(takes the 3d to 2d) these angles are not 90 degrees anymore.

The same goes for a tesseract, i 4d all of the angles are 90 degrees, however to show it in 3d, these angles can't be 90 degrees.

[Anonymous No.6143472]

>>6143468
I get that but explain to me where the behavior of the tesseract is 4D?

[Anonymous No.6143470]

>>6143468

/thread

[Anonymous No.6143473]

>>6143460
Such a 3D object would be the "shadow" of a 4D object.

[Anonymous No.6143475]

Maybe this will help the conceptualization

[Anonymous No.6143474]

>>6143460

You're looking at a 4D object projected onto a 3D surface projected onto a 2D surface.

Just as a 3D image is warped by projecting it onto your retinas, a 4D image is warped even more.

Does anyone have the rotating tesseract?

[Anonymous No.6143476]

>>6143474
there

[Anonymous No.6143482]

>>6143475

one of my favourite images ever.

so where are the 3D 'faces' of the tesseract'?

I gather the inner cube is one, and the outer surface. Are those trapezoidal objects between the outer edges and the inner cube also 3D faces?

[Anonymous No.6143484]

>>6143472

It has the right number of vertices and the right connections between them. You just have to imagine that all the angles are 90 degrees.

[Anonymous No.6143483]

>>6143460
>Opinions?
There are no opinions.

It is a projected shadow of a 4d object to 3d, and because it is on your screen it is further projected to 2d.

This is the only way it can be shown because in 4 space it is possible to have 4 lines be orthogonal to each other, you can't do thy here.

Look up a program called magic cube 4d to get an idea of its rotational behavior.

[Anonymous No.6143487]

>>6143476
A 3D object within a 3D object is a 3D object.
The shadow of a fourth dimensional object sounds like a hope more than literal scenario.
It's more of anything as an illusion than the 4th dimension in my opinion

[Anonymous No.6143489]

>>6143476

OP, when you rotate a cube, you see one face of the cube appear to grow, reach full size as it passes directly in front of you, then shrink.

The same thing is happening here, except each 'face' is an entire cube coming into your field of view.

[Anonymous No.6143491]

>>6143482
>Are those trapezoidal objects between the outer edges and the inner cube also 3D faces?
Yes, they are also actually cubes and are distorted in the projection.

Try drawing a cube on paper. From certain angles the faces of the cube you have drawn will appear as rhombuses, it is pretty much the same idea.

[Anonymous No.6143493]

>>6143484
That makes sense, but still it seems more of an idea than true logic.
I can see all 90 degree angles and I understand the concept of 2 Dimensions by screen, 3 dimensions etc and 1 dimension.
I don't understand why people are believing this to be a 4th dimension though (the shadow of a fourth dimensional object) that does not seem correct to me. It seems more like everyone is believing it just to have something to believe in.

[Anonymous No.6143494]

>>6143487
You clearly have done nothing in higher dimensional geometries. Stop talking.

[Anonymous No.6143497]

>>6143493
>It seems more like everyone is believing it just to have something to believe in.

[Anonymous No.6143503]

>>6143493
The transformations of a 4 dimensional object should be easy enough to figure out and presumably the tesseract transforms correctly as a projection [as the GIF is probably doing]. Thus, it satisfies all the criteria of being the projection of the 4D object mathematically.

[Anonymous No.6143501]

>>6143493
It's not about believing it is real or some nonsense like that. It's more about beauty of math. Try looking into some math in descrete structures for defining objects like this, or possibly the math in linear algebra for things like this.

[Anonymous No.6143502]

>>6143494
A dimension is experienced, not understand through logic. You may be able to explain the first second and third dimensions through the concept of lines but to imagine the fourth dimension through the same concept of lines is stupid.
Higher dimensional geometry, maybe if you believe in bull shit.

Meditation in my opinion is the closest you will get to the fourth dimension.

[Anonymous No.6143506]

>>6143502
>A dimension is experienced, not understand through logic.

>Higher dimensional geometry, maybe if you believe in bull shit.

>Meditation in my opinion is the closest you will get to the fourth dimension.

laugingwhores.jpg

[Anonymous No.6143508]

>>6143503
I want anyone to show me the math behind this object.

[Anonymous No.6143505]

>>6143502
>Meditation in my opinion is the closest you will get to the fourth dimension.
/sci/ everyone

[Anonymous No.6143513]

>>6143502
>A dimension is experienced
Lrn2dimension

[Anonymous No.6143515]

>>6143502
>A dimension is experienced
True. I currently experience a new dimension of stupidity.

[Anonymous No.6143522]

So, so far. I have - "this is a shadow of something that I can't explain to you." from every last one of you.
Great math guys!

"A cube inside of a cube is a shadow of the fourth dimension. no if ands or buts."

Sounds dumb to me.

[Anonymous No.6143528]

>>6143522
>>6143508
I'll drop the math on you when my classes are done.

[Anonymous No.6143541]

>>6143522
You are probably too dumb to get the math.

[Anonymous No.6143547]

>>6143508
<span class="math">\{{(x_1,x_2,x_3,x_4) \in \mathbb R^4 \,:\, -1 \leq x_i \leq 1 }\}[/spoiler]
It is topologically a 3-sphere.

[Anonymous No.6143550]

>>6143508
It follows the BC4 point group which we know the operations and structure of. Any object which obeys this point group is analgous to either a 4D cube or a 4D regular octahedron as it transforms as those objects should under all group operations.

[Anonymous No.6143551]

http://www.youtube.com/watch?v=AzL091mZQ-E

[Anonymous No.6143554]

>>6143497
If you're still around, try playing this game, you'll notice that you can still move along the normal six directions, but you'll also have another two that are best described as "in" and "out". The rooms that you're in are all tesseracts.
http://www.abovetopsecret.com/forum/thread741312/pg1

[Anonymous No.6143563]

>>6143547
copies from wikipedia does not explain the math.

[Anonymous No.6143566]

>>6143563
Actually it explains allot if you are literate in math.

[Anonymous No.6143569]

I have watched videos, read all of wikipedia, and I have even drawn the cube and tesseract to get more of an idea.
I would really like to understand why the tesseract is viewed as projection of a fourth dimensional object.

I see it.. i do.. but I simply do not agree with it.

A cube is drawn as a projection onto a 2d surface and the angles are distorted because of this.

A tesseract is shown as a 3d object, where the 3d object is drawn onto a 2d surface, where angles are distorted.

Even as a 3D tesseract, the angles are distorted.

Imagining the concept of the fourth dimensional version of this object still shows that if at best this concept is the concept of an illusion.

Trying not to argue with people, just have a decent conversation.

I see a lot of people go to class or drained college, have someone tell them how it is and when you finally understand the 'concept', everyone goes 'oooh I get it'

It's easy to get.. but in a sense this fourth dimension essence is along the same concept of a three dimensional existence.

Or.. looking into the idea that all angles in the fourth dimension would be 90 degrees, to deter from the distortion of angles due to projection into the third dimension.

It seems nothing more than a complex idea for a third dimensional object.

Maybe a better explanation would help me understand this concept.

[Anonymous No.6143573]

>>6143566
explain the math to me without quoting wikipedia.
I want you to explain it to me like you're explaining it to a child.

[Anonymous No.6143579]

>>6143569
>but I simply do not agree with it
Maybe you should say "I don't understand it yet."

>>6143573
I'm not the guy that posted the Wikipedia math. But if you want to know more on this subject I suggest you buy a book on linear algebra and a book on modeling descrete geometric structures and read them if you want a better understanding of this topic. As /sci/ has already done a good job of "explaining the subject like one would for a child".

Buying the books and reading them yourself is much easier than having me explain it, as I do not want to have to teach you the basics of these topics which you clearly have no to little experience in, as that would take to long. And that's probably why no one else here has given you the math for it, because you would probably have more difficulty reading it than you would the laymans explanations provided in this thread.

[Anonymous No.6143584]

>>6143573
>I want you to explain it to me like you're explaining it to a child.

lol /sci/

[Anonymous No.6143585]

>>6143573
>give me a free online remedial course in Math
mmmno

[Anonymous No.6143588]

I'm bready sure that 4 dimensions just means the space has 4 basis vectors. Phaggut.

[Anonymous No.6143591]

>>6143579
explain to me the fifth dimension then.
A cube inside of a cube inside of a cube?

HAHAHAHA math

I can teach someone how to astral project or how to program because of pure interest yet no one can explain even a small idea behind the tesseract?
Other than 'just imagine' or 'math'

"I won't explain it to you because I can't - by the way, grab a book"

"we all get it, we just can't explain it"

"grab 3 or 4 novels because I can't explain it to you in a thread - the math is just TOO complex.. oh.. but i get it! it's so simple!"

a lot of "lol's" and "ooh you don't know math"

shit answers is what I see.

This is the world wide web and not one website or video can sum an answer other than "it just is"

Yeah right. The tesseract is the dumbest shit i've heard in my entire life.

[Anonymous No.6143599]

What is a circle inside of a circle in the fourth dimension?

[Anonymous No.6143602]

>>6143584
If you can't explain a scientific concept to a child, at least in basic terms, you are not a good scientist and do not have full mastery of that subject.

[Anonymous No.6143605]

>>6143460
http://youtu.be/UnURElCzGc0?t=5m35s

[Anonymous No.6143608]

A line is a 0D point extended along the first dimension (x axis).
A square is a 1D line extended along the second dimension (y axis)
A cube is a 2D square extended along the third dimension (z axis)
A tesseract is a 3D cube extended along the fourth dimension (w axis)

[Anonymous No.6143609]

>>6143591
yes. it's easy. pick up a fucking book and get your head out of your ass.

[Anonymous No.6143611]

http://www.geom.uiuc.edu/~banchoff/Flatland/

you're welcome OP

[Anonymous No.6143613]

>>6143573
I'm not the guy who posted this, but it's not a difficult concept.
Say that we have a set that contains all ordered 4-tuplets whose values are all real numbers (like (x,y,z,w)). We'll call this set R^4.
Now, R^4 has a distance function (d(n)), so that a number n in R^4 can be assigned a value on the real line (R), d(n)=x where x is in R.
I want all real numbers that satisfy d(n)<1 or d(n)=1.
That type of set in analysis and topology is usually called a sphere. In topology, we call a circle a 1-sphere (in R^2), and a circle a 2-sphere (in R^3), so the object I just described is a 3-sphere (in R^4).

It doesn't really have a lot to do with projective geometry, so I'm not sure why it was brought up in the discussion.

[Anonymous No.6143627]

>>6143613
>It doesn't really have a lot to do with projective geometry, so I'm not sure why it was brought up in the discussion.

It does if you want to represent it in a lower dimension, like drawing a cube onto a piece of paper. Different views of the cube (i.e different perspectives) are connected by projectivities.

[Anonymous No.6143629]

>>6143609
meow meow meow meow meow
idiot who can't explain shit

[Anonymous No.6143630]

>>6143591
>A cube inside of a cube inside of a cube?
Nobody thinks that in this thread except for yourself.

[Anonymous No.6143648]

Explain to me where exactly the fourth dimension is taking place.

A two dimensional object exists within a three dimensional universe.

A two dimensional object would be invisible and not exist without the third dimension (depth)

Without depth, it is not there.

A sheet of paper even has depth, hence why we can see it.

A true two dimensional object would not have depth, and we would not be able to see it and explaining it is like trying to explain the fourth dimension.

Though two dimensions exist beyond the first dimension, still in a sense they would not exist without the third dimension.

Though the third dimension may exist within the fourth dimension, it would be like telling a fourth dimensional being about the third dimension, and them drawing the basic concept of the third dimension onto our three dimensional universe = their form of paper.

Where in the third dimension we can make an impression since there is depth, would the fourth dimension be able to make an impression onto the third dimension because of its depth?

Because the second dimension is theoretically x and y only, without depth therefore it does not exist on an atomic level, the fourth dimension is being explained nothing further than a three dimensional object that exists on a higher dimension with fixed angles.

The concept still exists as solid mass being portrayed in some way.

The third dimension only exists because the first and second dimensions exist.

Therefore the fourth dimension could only exist because the third dimension exists.

Therefore, being as the third dimension takes in the properties of the first and second dimensions.. so would the fourth dimension take in the properties of the third dimension.

The first and second dimensions are only thought examples. Same as the fourth dimension. -to continue

[Anonymous No.6143654]

>>6143602

It has already been explained to you in basic terms, you are just too retarded to understand it.

[Anonymous No.6143658]

>>6143648

The first and second dimension technically not existing without the third dimension are same examples as the fourth dimension not existing without the third. Whereas previously I stated these in opposite context.

When the first and second dimensions are technically not shapes.. whereas a sheet of paper is a shape but a sheet of paper is not a two dimensional object for it has depth.

Therefore a one and two dimensional object are only theorized.. same as the fourth.
So being as they are not shapes.. what makes you theorize that the fourth dimension is some shape?

Another question, would all higher dimensional beings fly?

And the main question.. does the fourth dimension have any impact on the third dimension, as technically, three dimensional objects move through two and one dimensional space at a constant rate.

That would mean that fourth dimensional objects move through two dimensional space at all times, which means that we would experience this event.

Being as time is not an object or nothing close to a tesseract.. what event do we experience that is showing us a peak of the fourth dimension?

I see nothing.
and I see only theory here.

Even the planck is theorized through math, where as space may continue infinitely through subatomic size and through mass size.

[Anonymous No.6143660]

[Anonymous No.6143674]

>>6143658
To sum it up.
Dimension 1: does not exist alone.
Dimension 2: does not exist without the third dimension.
Dimension 3: exists only with the help of dimensions 1 and 2.
Dimension 4 does not mean that it holds matter that relates to three dimensional space for technically the third dimension may seem non existent to fourth dimensional beings (probably not likely, but we don't know)

You are all explaining the fourth dimension by means of 'just imagine' or 'math that does not explain the fourth dimension, it only explains the concept of 'just imagine'.

A dimension seems to me way more complex than an idea which can be pulled from 3 dimensional objects due to lines and simple math.

The math only explains an idea. It does not yet explain the fourth dimension.

A dimension is something that is experienced, not seen.

I mentioned meditation previously in this thread, which is a word I hate to use but it does relate.

Infinite space in a non dimensional soul = an experience.
Inside of your yourself while outside of yourself in one moment = an experience = the next dimension.

[Anonymous No.6143679]

>>6143674
Further adding:
Perceptions are not experienced from outside, they are experienced within.

The concept of viewing an object is not you looking onto that object and seeing it but instead the imagery is travelling by means of light, which reflects into ones vision which is ultimately received within your mind.

If a third dimension is only perceived inside instead of outside, then the fourth dimension must be perceived inside instead of outside = a mental step.

Common sense explains things better than science or math, which has a constant change or improvement rate.

[Anonymous No.6143696]

>>6143460
Dumbass, it's what we think the *shadow* of a 4D object would look like.

[Anonymous No.6143698]

>>6143674
>The math only explains an idea. It does not yet explain the fourth dimension.

>A dimension is something that is experienced, not seen.

Such dumb. Is amaze.

[Anonymous No.6143699]

>>6143696
You stupid idiot. "What you THINK"
Get over yourself. A shadow.

[Anonymous No.6143703]

>>6143493
it looks 3d because you can't draw a 4d object

[Anonymous No.6143704]

>>6143698
All remarks. No real knowledge other than hearsay.

If the god damned shadow of these fourth dimensional objects were three dimensional, we would be seeing them all over the place.. such as seeing a fucking tesseract every other day.

Instead.. planets and matter.
Is all mass in this three dimensional universe the shadow of the fourth dimension???

Ridiculous and stupid.
Learn to think for yourself and come up with new ideas than copy idiots with old news like hawkins you fucking hipsters.

[Anonymous No.6143706]

>>6143699
Oh, I'm the idiot here?

What does the shadow of a 3D object appear as?
>A 2D object

So what would the shadow of a 4D object look like to us, then?
>A 3D cross-section

..so, how about you go fuck yourself, kid?

[Anonymous No.6143711]

>>6143704
Also since this three dimensional existence EXISTS within the fourth dimension and fifth and so on,are stars three dimensional projections of fourth dimensional objects?

Is all matter and space a projection of a fourth dimensional bigger picture??

If so.. then is time a projection and all concepts of metaphysics??

I'm sure if there were a fourth dimension, it'd be little more complex than the dumb and simple concept of a tesseract.

I'll repeat, i get the stupid idea.. still... it's stupid. It's still relating the concept of the fourth dimension to a third dimensional mind set.

[Anonymous No.6143715]

>>6143706
Kid? Ooooh nice one if I was a kid.
I would've thought someone as intelligent as you could've come up with something smarter to say.

Yes you are the idiot.

[Anonymous No.6143723]

>>6143715
Well anyone so stupid as to not understand the subject matter is either an ignorant child or or retarded, so it doesn't matter what I call you, you have no defense because you're just plain ignorant. Now be a good boy and go fuck yourself.

[Anonymous No.6143724]

>>6143711
>I'll repeat, i get the stupid idea.. still... it's stupid.

It's not stupid.

[Anonymous No.6143730]

>>6143723
I understand your dumb concept, you can't understand anything more intelligent. Way to use the same lines faggot.
Why don't you go shove a tesseract up your ass

[Anonymous No.6143737]

>>6143711
>relating the concept of the fourth dimension to a third dimensional mind set.

So are you complaining about the geometry or the measurement?

[Anonymous No.6143754]

OP your assuming that the explanation and the concept are both faulty before questioning your own understanding is a pretty arrogant and tiresome way to go about gaining knowledge

[Anonymous No.6143773]

>>6143460
>>6143472
>>6143482

http://www.youtube.com/watch?v=UnURElCzGc0

Carl Sagan's got this shit. Watch and be enlightened, not by some phony God's blessing but yadda yadda.

[None !!BJiYgff8zf2 No.6143786]

>>6143611

Flatland is shit.

[Anonymous No.6143824]

>>6143704
Nobody thinks these objects actually exist.
They are purely mathematical; they exist in 4D Euclidean space. We do not live in such a space.
>>6143711
The fourth dimension in physics is time, and it does not behave the same way as the 4D space in which tesseracts live.
>i get the stupid idea.. still... it's stupid.
What makes it stupid? Mathematicians study things that they find interesting, and these objects are interesting to enough people for them to be studied in depth. Just look at the Wikipedia pages for all these shapes! Often topologists want to study high-dimensional spaces, and representing them as things like the tesseract makes it easier to do so, because they are made up of a finite number of flat chunks, unlike a smooth (curved) space. Look at simplicial (co)homology. Here topological spaces are made up of simplices, which are like the tesseract, but the triangular version i.e line, triangle, tetrahedron, 4-simplex, 5-simplex, instead of line, square, cube, tesseract, penteract.
Beyond purely mathematical interest, higher-dimensional objects are used in physics all the time. Usually these will be smooth, rather than made of flat chunks like the tesseract. Spacetime in General Relativity is a 4D Lorentzian manifold. Is this also stupid? The symmetries of quantum field theories are also smooth manifolds (Lie groups). The Strong Nuclear force comes form an 8-dimensional object, which is why there are 8 gluons. Despite these objects being curved and smooth, they can be studied by their root systems, which look like tesseracts, simplices and other high-dimensional polytopes. The Lie group <span class="math">F_4[/spoiler] has a root system whose root vectors are the vertices of this 4D polytope, the 24-cell.
Go to http://upload.wikimedia.org/wikipedia/commons/f/f4/24-cell.gif to see this shape rotating (file is too large to upload here). Notice how this clip is just a more complicated version of the tesseract rotating.

[Anonymous No.6143829]

>>6143706
So what does 4th dimensional light look like? How does it behave?

[Anonymous No.6144219]

The boundary of <span class="math">[0,1]^n.[/spoiler] Deep.

[Anonymous No.6144286]

Wtf is a dimension anyway?
I see dimension as something we can measure but more than that i don't know what it really is.

[Anonymous No.6144317]

I always explain to retards that time can be viewed as a fourth dimension. Not a spatial one but one could imagine a "tesseract" as a cube that has a "length" of a unit of time. The "volume" would be x3t.

Like I said just as an analogue. Not to imply a time dimension is a spatial one. Just this nigger goes on about "duh furth duhmention"-nigga you are in a four dimensional world, don't forget time.

[Anonymous No.6144324]

>>6144317
To continue, like retard was saying true 2D objects don't exist in the real world, Ill say true 3D objects don't exist. A real 3D object would have no coordinate in the "time" direction.

Like a R^3 is a subset of R^4. But an object in R^3 can't exist in R^4. Its like implying that a 3D object can exist in our 4D world.

[Anonymous No.6144344]

5-cell > 8-cell

[Anonymous No.6144367]

>>6143754
/thread

[Anonymous No.6144405]

>>6144286
It's the minimum number of coordinates needed to verify the location of any point within that dimension.

x=1 dimension, like a point on a line
x,y=2 dimensions like a point on a square
x,y,z=3 dimensions like a point within a cube.

[Anonymous No.6144412]

>>6143754
this.

[Anonymous No.6144418]

>>6144324
Membranes and strings.

[Anonymous No.6144419]

>>6143824

If a mathematical discovery induces change, chances are that a purely rational man will find it utterly stupid.

The rational man continues to believe it stupid, and the irrational mathematician accomplishes things that the pure logician cannot.

This is why math is 'hard'. It's a very daunting mixture of rigor, logic, and playing pretend on various levels to describe the patterns of nature.

[Anonymous No.6144430]

>>6144317
No you retard, a tesseract is an object in 4d space. There's a difference between the 4th spacial dimension and the temporal dimension that is commonly referred to as the fourth dimension. They're completely different things.

[Anonymous No.6144507]

So by creating a teserect shadow model in rl does that mean we actually create a teserect in the 4d

[Anonymous No.6144511]

>>6144507
Like...when carl sagan holds up an actuall model of the teserect...he says its just a shadow...but by creating a shadow did an actuall teserect appear in the 4th dimension

[Anonymous No.6144512]

>>6144507
So by drawing a car on the sidewalk in chalk does that mean we actually create a car in the 3d

[Anonymous No.6144521]

>>6144512
Yeah but drawings arnt shadows...if a 4d shadow is an actual object in 3d...and you create that object...

[Anonymous No.6144535]

>>6144521
No one means shadow as in the thing the sun casts, shadow here means a representation of a higher dimensional object through lower dimensions. In other words a cube 2d shadow is a square, a squares 1d shadow is a line etc

[Anonymous No.6144539]

>>6144521
Are you saying we can create a duck based on only having seen shadow-puppets of them?

[Anonymous No.6144552]

>>6144521
>you create that object
Exactly how would a 3d being create a 4d object

[Anonymous No.6144551]

>>6144535
I'm gonna need something stronger than weed for this

[Anonymous No.6144553]

>>6144539
>>6144512
are you guys fucking idiots?
there's a fundamental difference between a shape and an actual object.

[Anonymous No.6144554]

>>6144553
A shape is an object, you realise?

[Anonymous No.6144557]

>>6144553
I think thats the point >>6144539
was trying to make

[Anonymous No.6144559]

>>6144554
but it doesn't have to be a physical object

[Anonymous No.6144571]

>>6144559
Are you trying to semantically outmanoeuvre us?

[Anonymous No.6144575]

>>6144571
No.
Creating a shape isn't like creating a duck or car.
Is it really that hard to see?

[Anonymous No.6144581]

>>6144552
Create the shadow...something with a shadow must exist...my brain hurts

[Anonymous No.6144582]

>>6144553
So much autism. how did you not get that they're trying to explain just that.

[Anonymous No.6144587]

>>6144581
The shadow is just a metaphor you idiot.

[Anonymous No.6144591]

>>6144582
>mfw a chalk drawing isn't a car

[Anonymous No.6144590]

>>6143460
You stupid spic, what you are seeing is a three dimensional "slice" of a 4th-dimensional object passing through our world. Clearly this is all beyond you so don't try to grasp it. There is a website called reddit full of people like you, you might want to post stuff there instead.

[Anonymous No.6144593]

>>6144587
An You're a fuckin dick...I'm jus tryin to have fun thinking about shit...

[Anonymous No.6144637]

>>6144593
Tesseracts are fun, you just need to study it more to fully understand the concept

[Anonymous No.6144645]

>>6144593
>fun
Why start a mission that can never succeed?

[Anonymous No.6144662]

>>6143613
Your original set describing the 3-sphere is slightly off. It should be that {x: d(x,0) <= 1} where x=(x1,x2,x3,x4), where d is any metric on R4.

[Anonymous No.6144670]

>>6144645
For fun...ass

[Anonymous No.6144673]

>>6144670
tautology has never brought success. Stop thinking of 'happiness' as the ultimate good.

[Anonymous No.6144675]

>>6144673
Having happiness and having fun are different

[Anonymous No.6144676]

>>6144675
Happiness is the product of fun. Fun is performed with the intention of gaining happiness.

[Anonymous No.6144699]

Just think of the tesseract as the unit ball in R^4 with respect to the supremum norm. Not that hard to grasp, n00b.

[Anonymous No.6144714]

>>6144317

The Minkowski metric of 4-D spacetime is completely different that the 4-D Euclidean metric, you colossal retard.

[Anonymous No.6144815]

>>6144419
Okay.

[Anonymous No.6144817]

>>6144662
That is what he said.
>I want all real numbers that satisfy d(n)<1 or d(n)=1.

[Anonymous No.6145264]

>>6144817
AN I SAID EAT MY BALLS FAGGOT

[Anonymous No.6145325]

>>6143460
A cube is basically made up of points (x,y,z) with |x| = |y| = |z| = 1, and lines between the ones which are closest together, i.e., which differ in only one place (e.g., (1,1,1) is connected to (-1,1,1) but not to (-1,-1,1)). In the 3d case, there are eight such points, and each point is connected to three other points. In 4d, it's easy to see that the same definition but with 4-tuples instead of 3-tuples gives sixteen points, each of which is connected to four other points. Hence the object in your picture is topologically the same as the frame of a 4-cube.

[Anonymous No.6145335]

Is there a retard in this thread who thinks that when mathematicians talk about 4D space they mean something real?

It's a construct of mathematics. A virtual space. Like how you can construct non-euclidean geometries. You can do rigorous mathematical calculations with them, regardless of whether or not they correspond to the real world.

You could, for instance, create a computer simulation of a world with as many dimensions as you want, since computers do such things mathematically and projective geometry can render anything into 2D images eventually.

No one is claiming that a fourth dimension like width, height and depth exists 'in reality'. Except string theorists.

[Anonymous No.6145352]

>>6145335
>implying our universe is euclidean

[Anonymous No.6145382]

>>6144817
Sorry, I meant the typeset stuff that's been quoted as "copied from wikipedia" was wrong (only valid for the metric induced by the l1 norm, not in general)

[Anonymous No.6145727]

>>6145352

> Not realizing our space is locally Euclidean.

A real manifold is by definition locally homeomorphic to a Euclidean space.

[Anonymous No.6145750]

>>6145727
yeah. and SR asserts that our 4d space is Lorentzian.

[Anonymous No.6145774]

>>6145750

It's still locally homeomorphic to R^4. It's a manifold.

[Anonymous No.6146280]

>>6144590
Obviously you're an idiot

[Anonymous No.6146502]

>>6143474
This is my first time in /sci/ and you've melted my brain.

[Anonymous No.6146689]

http://hypersolid.milosz.ca/

Dunno if anyone posted this but its an applet of a tesseract which you can rotate by its 6 planes. It shows that you cant see all of the shape from the same point of view, kind of like how a shadow is a 2d version of a 3d thing.

[Anonymous No.6146922]

>>6143547
>>6143613
That isn't a three sphere, it's homeomorphic to a 4-disc. The three sphere is
<span class="math">
\{(x,y,z,w)\in\Bbb{R}^4\mid x^2 + y^2 + z^2 + w^2 = 1\}
[/spoiler]

[Anonymous No.6146925]

>>6146922
fuck you sci
<span class="math">\{(x,y,z,w)\in\mathbb{R}^4\mid x^2 + y^2 + z^2 + w^2 = 1\}[/spoiler]

[Anonymous No.6146972]

so can all basic shapes be defined as the angle at which the sides connect to the other sides?
Such as anything from a square to a hyperract of whatever number of dimensions you want can be defined as "90 degrees at X dimensions?" and so on with triangles and octagons and such?

[Anonymous No.6147653]

>>6145727
Locally euclidean =/= euclidean.
Otherwise differential topologists would lead very boring lives.

[Anonymous No.6147658]

>>6143460
It's just the 3D shadow of the tesseract.

[Anonymous No.6150149]

>>6143460
>I don't see the concept of four dimensions in this object.

>3 dimensional space is a product of overzealous mathematicians

[Anonymous No.6150153]

>>6150149
>3 dimensional space is a product of overzealous mathematicians

Well, shit... I meant that to be "Greater Than" as opposed to greentext... let me try that again.

Greater than three dimensional space is a product of overzealous mathematicians.

It's amazing what you can do when your academic study isn't constrained by pesky things like reality.