4D Basics

[urchin]

Foremostly, thank you for the wonderful strain you've put on my brain-- I hope I don't blow out. Your chapters are clearly written and I've enjoyed the extremely helpful illustrations. The characters are fun too and greatly facilitate discussion. I've wanted to understand (conceptualize) the fourth spacial dimension ever since reading Flatland (which I hardly understood) during college. While I'm not quite there yet, having read most of this site I feel I'm starting to develop a solid gut feeling for how I would perceive interactions between the tetral world and the realmic world-- quite a breakthrough where I'm concerned. I have lots of questions, I'm sure I'll have more. I'll try to think them through as much as possible before breaking down and asking.

Let me start with this one:
How does Fred know if any given circle is from his own world or from the realmic world? Could he always test by pushing (ie-- when he pushes the circle, if the circle moves relative to his environment then it's "in" his world; if his environment moves but the circle remains stationary, it's from the realmic world)? Depending on the way this is answered, can you safely say that all impinging objects from a higher dimensional world are "fixed" or "attached" to that higher world (consequently making them immobile)?

[Watters]

Well just using some basic relitivity.........if fred push the circle and it moves or if the world around it moves then he can't tell the diference.......neither can any one wathcing this action........the only way it mgiht work is if he was pusing it clsoe to the speed of light it would mean and there was a clock in it and a clock out side of it......that way you could tell what actual was movin by the difference in times.

[Keiji]

No, either the circle moves or it refuses to move.

[PWrong]

Hmm. If Emily were to push a spherinder through Bob's house, Bob would see a sphere hanging in front of him. But the Earth is travelling around the sun at a high speed, so Bob's house is moving as well. To Bob, it would probably look like the sphere was moving incredibly fast in the opposite direction, and it would probably knock his house down.

[RQ]

That is if the sphere was stronger than the house.

[pat]

Hmm. If Emily were to push a spherinder through Bob's house, Bob would see a sphere hanging in front of him. But the Earth is travelling around the sun at a high speed, so Bob's house is moving as well.

Is there a reason to believe that Emily is not also orbitting the Sun?

[Keiji]

Emily's planet would orbit a star. Not the Sun - the Sun is a 3 dimensional star. A 4D planet would have to orbit around a 4D star.

[PWrong]

Anyway, my point is that 3D objects only have a velocity relative to other 3D objects. It's impossible to have an immobile object, because the whole universe could be moving in any direction, at any speed, and we wouldn't notice.

The only way a 4D universe could interact with a lower one is if the 4D world is somehow connected to the 3D universe. Imagine Fred builds a magical square, that somehow extends out towards us, and turns into a cube, so Fred's world looks a bit like a pop-up book. Now, when the square moves, the whole cube moves. Everyone's happy

[pat]

Emily's planet would orbit a star. Not the Sun - the Sun is a 3 dimensional star. A 4D planet would have to orbit around a 4D star.

Maybe our sun is a 4D star and we can only see a single slice of it. Regardless, from the point of view of gravitational attraction, the orbitted item need only be a point. There's no need for it to be 4D.

[Keiji]

Emily's planet would orbit a star. Not the Sun - the Sun is a 3 dimensional star. A 4D planet would have to orbit around a 4D star.

Maybe our sun is a 4D star and we can only see a single slice of it.

Yes, that's possible.

Regardless, from the point of view of gravitational attraction, the orbitted item need only be a point. There's no need for it to be 4D.

No - in a 4-dimensional world the Sun would have a bounding tesseract (what else can I call it?) of something by something by something by zero. The sun's volume is therefore zero in a 4-d world. If volume is zero, density will be infinity which means that the Sun would turn into a black hole. So, the Sun cannot exist in a 4-d world.

Wait - for that matter, no 3-d object would be able to exist in a 4-d world.

[elpenmaster]

bobxp:
if our sun existed in a 4d world, it would have zero 4-d volumxe. however, it would also have zero 4-d masss

if you take a square for example: it has zero 3-d area. however, it is an infinitly thin slice of a cube. it therefore has the mass of a cube divided by infinity. since the mass of a cube is finite, and a finite number divided by infinity is zero, the 3-d mass of a cube will be zero. since its volume is zero and its mass is zero, its density will be greater than zero and less than infinity, which equals a finite number

so the density of our sun in a 4d world would be finite, and thus not neccessarrilly a black hole

[RQ]

Light has 0 mass, yet it has pressure, think about that?

[RQ]

PWrong, a higher dimensional universe cannot interact with a lower dimensional one period.

[PWrong]

Well thanks for telling us now . This whole topic is about interaction between dimensions.

Btw, a square doesn't have 0 volume. It doesn't have a volume at all. You can't do a calculation with a measurement that doesn't exist. Anyway, you two should know better than to use infinity to win an argument.

[elpenmaster]

since when is having zero volume different than having no volume at all?

a square has zero volume, and a tetracube has infinite

the topic of infinity was discussed in that one thread that is five pages long
:wink:

[Keiji]

bobxp:
if our sun existed in a 4d world, it would have zero 4-d volumxe. however, it would also have zero 4-d masss

Volume is the amount of physical space an object takes up. Mass is the number of protons/neutrons in the object. So, a 3D object would still have mass in 4D.

Light has 0 mass, yet it has pressure, think about that?

Light has no mass, because it is made of photons. Photons can still have energy, like electrons.

[pat]

a square has zero volume, and a tetracube has infinite

Okay.. just one more time, I'm going to disagree with this notion.... after that... y'all are on your own.

The tetracube does not have infinite volume. The question of how much volume a tetracube has is ill-posed. How much area does your head have? The question is incomplete. Better questions are how much surface area does your head have? What is the cross-sectional area of your head if sliced longitudinally through your nose? What is the area of your head enclosed in the parallelogram with vertices where your ear lobes meet your jaw and where your tear ducts meet the corners of your eyes?

[Keiji]

lol.

A square has zero 3-d volume, just like any n-d shape has zero (n+1)-d volume, because to calculate that volume you are multiplying by zero, the thickness of its plane.

A tesseract has infinite 3-d volume, just like any n-d shape has infinite (n-1)-d volume, because to convert from 4-d to 3-d volume for a 4-d shape you must multiply by infinity.

Anything multiplied by zero is zero, anything multiplied by infinity is infinity. The only special case is that zero multiplied by infinity is one.

[Rybo]

since when is having zero volume different than having no volume at all?
a square has zero volume, and a tetracube has infinite
the topic of infinity was discussed in that one thread that is five pages long
:wink:

http://www.rwgrayprojects.com/synergetics/plates/figs/plate31.html

Elpen and all, here above is link to a graphic of a zero-volume tetrahedron that maintains its four triangular planes ergo it inherently defines the cubo-octahdron(a.k.a. Vector Equlibrium) composed of four hexagonal planes with additional 12 triangular flaps/wings extending into an octahedral space.

I hope the link works cause Im not sure where I was suppose to place tag(s).

Rybo

[jensr2000]

Anything multiplied by zero is zero, anything multiplied by infinity is infinity. The only special case is that zero multiplied by infinity is one.

Maybe not that important, but zero multiplied by infinity is indeterminate, not necessarily one.

[Keiji]

Ahem: http://tetraspace.alkaline.org/forum/vi ... yx0=1#1674

[PWrong]

We've had this argument in nearly every topic thread. With extra dimensions, the infinity argument doesn't matter anyway. Can't we just interpret the argument as a contradiction, which means we got something else wrong? In this case, we weren't even talking about a 3D sun in 4D, we're talking about a 4D sun, but we can only see a slice of it. The Presumably space is wrapped around the 4D sun, so that the fourth dimension doesn't exist anywhere except in the sun.


A 3D object can't physically exist in 4D unless it's composed of 4D atoms. There's a simple proof for this:
Assume the contrary, a 3D object does exist in 4D and is made of 3D atoms.
The 4D volume of the object is either 0 or undefined.
It's impossible to have 0 volume or undefined voume, so we have a contradiction.
Therefore, we cannot have an n-D object in n+1 dimensions, problem solved!

Any attempt to get a different result than this will probably include about twelve more contradictions and another huge argument.

[Keiji]

Like I said, any 3d object in a 4d space will have infinite density in 4d but not in 3d.

[PWrong]

You can easily say that, but if you try to do calculations for an object with infinite density, you'll still get a contradiction somewhere.

Infinity is nature's way of telling you that you've made a mistake.

[Geosphere]

Infinity is nature's way of telling you that you've made a mistake.

Not nature's - mathemetician's.

[Keiji]

You can easily say that, but if you try to do calculations for an object with infinite density, you'll still get a contradiction somewhere.

not neccesarily

Infinity is nature's way of telling you that you've made a mistake.

Not nature's - mathemetician's.

lol.

[Rybo]

Infinity is nature's way of telling you that you've made a mistake.

Not nature's - mathemetician's.

Gesopshere, Where does physical Universe practice infinity? E.g please and thank you for any evidence, circumstantial or otherwise, you may add.

Humans are nature mathemecticians. We can have a concept of infinity but since it is not a number-- i.e. it is enumerable -- it is beyond mathematics and ergo beyond numeration.

I forget the diffrrence but i think ive read there are tranendental numebers and irrational numbers. Infinity is beyond must be beyond eithere those, if they are indeed numbers.

Rybo

[Geosphere]

Gesopshere, Where does physical Universe practice infinity?

No where I know of. That's why I was saying it is not Nature's rule.

[PWrong]

We expect nature to be mathematically consistent. To be mathematically consistent, you have to eliminate infinities. That's why infinity doesn't exist in nature.

Bob, how can you calculate something with infinite density?

finite mass/ zero 4D volume = infinite density.
infinite density * zero 4D volume = zero mass

Here's one more example. This is what happens when you take infinity literally.

Take two separate 2D objects in 3 dimensions. Place one on top of the other. Because the objects have no height, they can be placed arbitrarily close to one another.

gravitational force = Gm1m2/r^3
As r approaches 0, force approaches infinity
We now have two bodies with a finite mass applying an infinite force on each other
F=ma
So the bodies are also accelerating at infinity ms^-2
1. Where are they accelerating? They have nowhere to go.
2. Where is the infinite energy coming from to do this, and what's stopping it from destroying the universe afterwards?
3. The two objects could just as easily be considered as a single object. Therefore the same thing will happen with a single object.
4. Since it's only a single 2D object anyway, the 3rd dimension doesn't have to physically exist. It will destroy the universe even if it doesn't exist.
5. The same can be applied to our universe. We don't even need a fourth dimension. Logically, we should all be dead already.


Now isn't that conclusion enough to make you realise there must be a mistake somewhere? I don't care what it is, there's probably hundreds of mistakes. The first mistake is putting infinity there in the first place.

All we have to do is make the 2D object 1 atom thick, or 1 Planck Length thick, and then there's no contradiction. Why can't we just do that instead of playing with zero and infinity?

Sorry this is all so long. It'll probably cause even more arguments. I'd rather talk about that slice of a 4D sun idea myself.