The 4th Dimension

To clarify: The 4th dimension is not time. It would be silly if it was ^_^
Time is merely a byproduct of space itself. Dimensions are all strictly spatial.


Anyhow...on to the more mind-boggling things!

Each dimension is at a 90 degree angle of all previous dimensions.

Yes, the 4th dimension is at a right angle to all our other 3 measly dimensions.

Besides, the 4th dimension is pretty darn cool, for a lot of reasons, like, well, for instance, umm,,, more spaaaaace!!
[Insert Space Core Meme]


Okay, I really got to be serious ^_^;

So who can tell me what is the next number in this sequence:
∞, 5, 6, 3, __

What's this you say? "'Tis be impossible!"? Bah! The next number is 3! (And the one after that is 3, and the one after that is also 3, and the one after that is yet again 3...)

"But how?" as you call out in confusion.

These are the number of regular polys in different dimensions starting at the 2nd. And if you remember, there are 5 Platonic Solids, as seen in the above sequence! But what's this? The 4th dimension has another regular poly? Yes it does in fact! It's the hyperdiamond! :3 Sadly, all dimensions beyond the 4th are boring and only have 3 regular polys :<

2D:

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3D:

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Tetrahedron

Hexahedron

Octahedron

Dodecahedron

Icosahedron

4D:

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Pentatope, Hypertetrahedron, 5-Cell

Tesseract, Hypercube, Hyperhexahedron, 8-Cell

Hyperoctahedron, 16-Cell

Hyperdiamond, 24-Cell

Hyperdodecahedron, 120-Cell

Hypericosahedron, 600-Cell

Just in case you missed the hyperdiamonds:

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BEHOLD, THE HYPERDIAMOND

Next, we can dedicate this section towards our ever-beloved (Second, cats being first! ^w^ ) hypercube!

Here's a comparison between a spinning cube and a spinning hypercube:

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And a comparison between the folding of cubes and hypercubes:

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And finally, a comparison between various rotations on a cube, and the same set of rotations on a hypercube:

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But before we depart from the hypercube, here's a link to a nifty web thingamajig that allows you to view stuff in different dimensions! And stuff!


Another interesting thing, is that we would be unable to hide from a 4th dimensional monstrosity! D:
It would see us wherever we go, like as if we were a flat blueprint to it. It can see inside anything, and even sees our organs! It'll be able to easily reach in and do something nasty, like poke our pancreas!

Further interestingly so, all things 3rd dimensional would be really, really sharp to said creature X3
We could just slice through them like a mathematically perfect 2nd dimensional knife through a 3rd dimensional stick of butter!


But despite the undeniably awesome aspects of the 4th dimension, it has it's own downsides...

First, knots are impossible to tie in the 4th dimension. They will always untie themselves. As such, one can only expect the velcro cult to be thriving in the 4th dimension.

Another rather annoying aspect, is that elliptical planetary orbits are impossible, only perfectly circular orbits can stay in orbit. This is because gravity falls off way to fast as you move away, and becomes to strong too quickly as you come closer. As such, this makes elliptical orbits impossible.


Finally, here are some reading material if you'd like to know more! There's quite a bit more stuff I could've mentioned, but oh well!
Link #1
Link #2

 

I always imagined 4D space as an array of 3D space. That's how you would store it in code, anyway.

And the GIFs just mess with my mind! I'll need to do some reading before I can understand it.

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I also would like to point out that you put "link #1" twice at the end.

 

*mind literally implodes*
see I always knew there was n-dimensional space, I just didn't know what that meant - like what do those other dimensions add, etc.

 

I always imagined 4D space as an array of 3D space. That's how you would store it in code, anyway.

And the GIFs just mess with my mind! I'll need to do some reading before I can understand it.

Spoiler

I also would like to point out that you put "link #1" twice at the end.

Yeah, it can really do quite the number on our brains ^_^;
The supplementary reading material will help a lot with attempting to understand the 4th dimension

And the incorrect link number has been fixed!

 

Oh my... what is this.
It nearly starts to hurt my brain, as I try to understand this, but I can't.

 

Who's ready for another round of the 4th dimension? ;3


Let's start with something more tangible and less brain-racking:

Can you think of a 3rd dimensional shape, that when cut in half, still remains as a single piece?

...okay, maybe this will still hurt your brain a bit >.<

Or how about a 3rd dimensional shape with only one side and edge?

Still nothing? Well, it's called the Möbius strip!

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It's simply a strip of paper making a loop, but a single twist was made before conjoining it.

Now, try making one at home and try to cut it lengthwise. If for some obscure reason your are lacking in scissors, paper and glue, (Or {hopefully not} because you're lazy) you can see what happens here:

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And I'm not mentioning Möbius strips just because they can make mathematically superior bagel with a higher surface area for cream cheese; Möbius strips will be an important part for understanding what I'll be talking about soon.

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The thing about Möbius strips is that (Technically, at least) they are a 2nd dimensional object that has to project to the 3rd dimension to be possible.

But I can already hear you saying, "That doesn't make sense!" Well, to a *cough* Cubelander *cough* it doesn't.

For a moment you gotta think like a Flatlander. Here's an ordinary square. Nothing special, nothing not 2nd dimensional. Just a square. Not a cube, not a hypercube, not even a hypersquare. It's a square.

And here we've got this monstrosity that crosses into itself!

Sorry, my 2nd dimensional Möbius strip drawing skills suck ^_^;

How can be? Normally! It projects into the 3rd dimension so that it doesn't cross itself.

But what happens if you conjoin 2 separate Möbius strips together? Well, you get something called the Klein bottle:

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Sorry, I had to ^_^;;

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Cross section to help visualize:

It has only one surface, but as you notice, it crosses into itself.

By now your brain gears should be grinding and should come to a conclusion.
[Jeopardy Theme Song plays]

Got it? Yes? No? Well, because of the limits of this article of whether you figured it out yourself or gave up, here it is anyways!

It has to project into the 4th dimension so that it doesn't cross itself. Simple.

And finally, there are a total of 4 different Klein bottles. It all depends on the chirality (Handedness; i.e. left-handed, right-handed) of the Möbius strips you combine. When you combine 2 Möbius strips of the same chirality, you get the Klein bottle. But when you combine 2 Möbius strips of the opposite chirality, you get the Klein bagel .

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*Not to be confused with a Mobius strip bagel*

Cross section to help visualize:

 

why did i read this? #regretsfordays.... actually really interesting to think about. Thanks!

 

why did i read this? #regretsfordays.... actually really interesting to think about. Thanks!

Yep! No problem! ^_^

Just remember, this is only the beginning!

 

This all seems (relatively) like a child's interpretation of 4D space because it only deals with simple shapes. This might make sense in videogames where everything is 3d shapes made of polygons, but reality is much more complex. I would prefer that this be described at a molecular level. At the moment this seems like little more than a concept. Like someone trying to figure out how a second person shooter would work. Also the appearance should be defined by how light is reflected off a 4D object before that light reaches our eyes. Again, I think what you have shown is incredibly simplistic. If a 4th dimension of space actually existed then everything would be 4D, it would simply be a matter of dimensional perception.

 

This all seems (relatively) like a child's interpretation of 4D space because it only deals with simple shapes. This might make sense in videogames where everything is 3d shapes made of polygons, but reality is much more complex. I would prefer that this be described at a molecular level. At the moment this seems like little more than a concept. Like someone trying to figure out how a second person shooter would work..

The 4th dimensions gives us another direction to move into, and with this new direction, the interactions of everything changes. I've only delved into basic geometry for now, but if you'd like to satiate your curiosity in regards to the molecular and beyond I'll be supplying links: (These topics will be covered irregardless over time; others can wait for a fancy post, or jump the gun and read it)

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http://www.askamathematician.com/2012/05/q-what-would-life-be-like-in-higher-dimensions/

Also the appearance should be defined by how light is reflected off a 4D object before that light reaches our eyes.

That...wouldn't work for us Cubelanders. The below link will explain that.

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http://eusebeia.dyndns.org/4d/vis/01-intro#Is_it_possible_to_visualize_4D

Again, I think what you have shown is incredibly simplistic. If a 4th dimension of space actually existed then everything would be 4D, it would simply be a matter of dimensional perception.

As much as that may make sense, well, that's not how it seems our universe works exactly. This TEDx event should explain why so.

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As much as that may make sense, well, that's not how it seems our universe works exactly. This TEDx event should explain why so.

Actually that kinda proves my point. As the man said, according to string theory we have 9 spacial dimensions in which quanta can move in, yet we can only perceive 3 of those dimensions. Also his theories seem to go in entirely different directions to yours.

My point being that extra spacial dimensions would apply to everything universally. If a fourth spacial dimension exists then you are already a 4D entity, regardless of if you can perceive it or not.

 

Actually that kinda proves my point. As the man said, according to string theory we have 9 spacial dimensions in which quanta can move in, yet we can only perceive 3 of those dimensions. Also his theories seem to go in entirely different directions to yours.

My point being that extra spacial dimensions would apply to everything universally. If a fourth spacial dimension exists then you are already a 4D entity, regardless of if you can perceive it or not.

The thing is, I wasn't discussing any theories of whether our universe is 3rd dimensional, 4th dimensional, or even 11th dimensional; nor do I have any theory to share. I was only sharing the interesting quirks of the 4th dimension.

String theory says that strings/quanta vibrate in those other dimensions, but said other dimensions are really minuscule so that only equally tiny things like strings/quanta would be able to vibrate into them, we as Cubelanders are substantially larger and subsequently we are still constrained to 3 dimensions.

Oh and also, we don't perceive in 3 dimensions. We perceive only 2, but we infer the 3rd through lighting, parallax, and past experiences.

 

So essentially, 4D objects have space within their space?

So you could say that a 4D object is bigger on the inside than it is on the outside?

(INSERT DOCTOR WHO JOKE HERE)

 

So essentially, 4D objects have space within their space?

So you could say that a 4D object is bigger on the inside than it is on the outside?

(INSERT DOCTOR WHO JOKE HERE)

...umm, sorta? Just not exactly. Let me put it this way:

4D objects have surface volume encompassing their content just like 3D objects have surface area encompassing their volume. (And just like 2D objects have surface length encompassing their area)

As such, any n-dimensional object will be bigger on the inside than the outside.

 

So essentially, 4D objects have space within their space?

so meta

 

Oh and also, we don't perceive in 3 dimensions. We perceive only 2, but we infer the 3rd through lighting, parallax, and past experiences.

If you are going to discount lighting then we really don't perceive any dimension. If you have ever gone skiing in a white out you would understand that all 3 dimensions are inferred. Human beings are incapable of seeing space in the truest sense. Yet using light we are able to grasp spacial awareness in 3 dimensions with an success rate of well over 90%. Perception isn't about what you see, but rather about what you "perceive". I would advise you to look up that word in a dictionary.

String theory says that strings/quanta vibrate in those other dimensions, but said other dimensions are really minuscule so that only equally tiny things like strings/quanta would be able to vibrate into them, we as Cubelanders are substantially larger and subsequently we are still constrained to 3 dimensions.

We are little more than advanced colonies of conjoined single-celled organisms. Size should make no difference here.

 

This may not be about the fourth dimension, but here's Dimension 7

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I wasn't lying

 

If you are going to discount lighting then we really don't perceive any dimension. If you have ever gone skiing in a white out you would understand that all 3 dimensions are inferred. Human beings are incapable of seeing space in the truest sense. Yet using light we are able to grasp spacial awareness in 3 dimensions with an success rate of well over 90%. Perception isn't about what you see, but rather about what you "perceive". I would advise you to look up that word in a dictionary.

I never discounted anything. And also, please take note that I am using "perceived" and "inferred" in a technical sense. When you look with your eyes, you only see a flat 2 dimensional image; you're perceiving only 2 dimensions. From that image we process the parallax and lighting combined with past experiences with 3D to infer the 3rd dimension. Regardless if there is a white-out or not, you still perceive 2 dimensions, but because of lack of visual information, you cannot infer the 3rd.

We are little more than advanced colonies of single-celled organisms. Size should make no difference here.

Try comparing humans or even singular cells with strings/quanta in this nifty site: http://htwins.net/scale2/
(Hint, strings/quanta are really tiny)

 

please take note that I am using "perceived" and "inferred" in a technical sense.

As I said, you are not. You really aren't. What you see and what you perceive are fundamentally different.

When you look with your eyes, you only see a flat 2 dimensional image; you're perceiving only 2 dimensions.

That is sight, not perception. And as I said, that is seeing light, not space.

Regardless if there is a white-out or not, you still perceive 2 dimensions, but because of lack of visual information, you cannot infer the 3rd.

Wrong. In a white out (a real white out) you cannot perceive the width, height or depth of anything around you. As I said before, Humans cannot see space, they see light reflected off of objects (colour) and use it to infer space.

Try comparing humans or even singular cells with strings/quanta in this nifty site: http://htwins.net/scale2/
(Hint, strings/quanta are really tiny)

"The energy of an electron bound to an atom is quantized, which results in the stability of atoms, and hence of matter in general."

https://en.wikipedia.org/wiki/Quantum

As I said, it would apply universally.

 

As I said, you are not. You really aren't. What you see and what you perceive are fundamentally different.

That is sight, not perception. And as I said, that is seeing light, not space.

Wrong. In a white out (a real white out) you cannot perceive the width, height or depth of anything around you. As I said before, Humans cannot see space, they see light reflected off of objects (colour) and use it to infer space.

Even though we are 3D beings who live in a 3D world, our eyes actually only see in 2D. Our retina has only a 2D surface area with which it can detect light coming into our eye. What our eye sees is in fact not 3D, but a 2D projection of the 3D world we are looking at.

In spite of this, we are quite able to grasp the concept of 3D. Our mind is quite facile at reconstructing a 3D model of the world around us from the 2D images seen by our retina. It does this by using indirect information in the 2D images such as light and shade, parallax, and previous experience. Even though our retina doesn't actually see 3D depth, we instinctively infer it. We have a very good intuitive grasp of what 3D is, to the point that we are normally quite unconscious of the fact we're only seeing in 2D.

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"The energy of an electron bound to an atom is quantized, which results in the stability of atoms, and hence of matter in general."

https://en.wikipedia.org/wiki/Quantum

As I said, it would apply universally.

Quantized means that there is a discrete unit of measurement in different types of measurements. And unless I'm missing some excerpt, nothing mentions that dimensions would apply universally to everything.

I can tie my shoe, Earth still orbits the sun elliptically, and Magnesium isn't a Noble Gas. Seems like the 3rd dimension to me. But none of those matter (Darn puns >.< ) because atoms would (A bit unsure) become a soup of nuclei and electrons in dimensions beyond the 3rd, so we know for sure atoms are also 3rd dimensional. Strings/quanta are simply just different.

If you have ever read String theory, those extra dimensions are so to say 'rolled up into some very tiny but nonetheless interesting space of their own', hence why we are constrained to 3 dimensions.