What orientation would other dimensions be to ours?

You are mistaking dimensions for alternate realities.
Dimensions are things like the 3 spatial dimensions and the time dimension plus the 7 extra dimensions in M-theory (In which our universe, a 4 dimensional brane is floating around in the 11 dimensional hyperverse, next to other branes. A collision between those branes is thought to have possibly caused the Big Bang.).

You are using comparison factor of different dimensions as orientation- because thats how we define 1st, 2nd and 3rd dimension. A line, a plane and a solid. It all begins with a point assumed to have no dimensions. However, that is so because we are 3D beings. So we think in terms of 3D with ease. We use the coordinate system and the mutually perpendicular x, y and z axes. But thats all we can do easily and obviously.

But when we try to imagine higher dimensions, this system of ours of orienting axes and plotting points starts to seem incomplete. We cannot plot more that 3 dimensions in such way. So what do we do? We combine the first three dimensions as a point (which can be assumed to be dimensionless and represent it in higher three dimensions). Thus, we can have another 3-dimensional system with 4th, 5th and 6th dimensions. And it goes on for however long we wish to.

So basically, the orientation factor is only within a 3-dimensional system. Between any two distinct 3-dimensional systems, the comparison factor is that of size. So, the higher dimensions are simply much much larger dimensions in which our 3d world is nothing but a dot. Similarly, there can be lower dimensions too. These lower dimensions must have a finite but very small size in our perspective and so we group them together as a dot- the zero dimension from which we construct our 3 dimensions.

I would like to add that quantum physicists say that the ‘other’ dimensions are curled up in a very tiny space and so we cannot see them. Alternatively, they could also be expanded vastly such that we cannot perceive them. In any case, we cannot experience these ‘other’ dimensions because of our size

I like to think of each dimension perpendicular to the prior one. It’s not correct, but it’s the easiest way for me to visualize it.

I imaging other dimensions as a direction or property that does not fit or map into the others For example Y direction is only a point on the X. The Z direction is only a point on the X-Y plane Time does not map in XYZ. In my imagination temperature is another dimension So is Electromagnetic field intensity. While they do not map into our conventional 4 dimensions they do have a Zero boundary. I picture the other world existing in the negative side of that boundary.

I am like @Rarebear. The 4th dimension is perpendicular to all previous dimensions. As @ragingloli pointed out, you are equating realities with dimensions. Dimensions are measurable, realities are not,

All of the above ways of imagining or measuring or contemplating a 4th or higher dimension are correct, because all will fit a mathematical model.

@zenvelo @Rarebear The axes indicating the first three dimensions are mutually perpendicular.
Where can we accommodate a distinct 4th axis that is perpendicular to all the previous three axes? Any attempt to draw a perpendicular will only fall within the three dimensions.

Or is drawing perpendicular to the dimensions and drawing perpendicular to the axes different?

@krrazypassions We can’t construct a 4th dimension perpendicular to all three of our present dimension, so I can’t tell you how it would work. I live in a 3 dimensional world.

It’s like the book Flatland: people in a 2 dimensional wold cannot describe 3 dimensional world.

“Perpendicular” is sometimes expressed mathematically as “orthogonal”, a more general term for a property of various relationships.

I don’t believe it’s possible for humans to visualize 4 or more spatial dimensions without either projecting onto 3 dimensions or implicitly invoking time as a 4th dimension. I don’t think even Einstein himself could do that.

Orthogonal is the operative term here, meaning that a measure in that dimension can’t be expressed in terms of the other dimensions. Perpendicular implies 90 degree angles and such, which only applies to the spatial dimensions.

One could say 3D movies are 4 dimensional images

@krrazypassions visualize the 4th dimension as forward and backward in time.

In a nutshell, that a plumber could grasp, if we were in flatland and we could not comprehend above or below the paper, or the 4th dimension is through time, etc. where are the other dimensions? We are embedded in the other dimensions, they embedded in us? And since no one has found a way to get to these other dimensions how can scientist be sure there are not 15, 23, or even 58 different dimensions?

String theories of physics require at least 11 dimension, some as many as 26. The usual explanation (hand-waving dodge?) is that we only seem to live in 4-dimensional space-time because the other spatial dimensions are compactified or “rolled up” to a very small size (Planck scale) relative to ordinary matter. Imagine a very wide, short rectangle. Now imagine that its height shrinks to a small fraction of a proton’s diameter. It’s still a 2-dimensional rectangle in theory, but what’s observed is a 1-dimensional line segment. This is (they say) analogous to how a spatial dimension may be “hidden” from view by compactification. A lot of top theorists buy into this, though it’s hardly a satisfying explanation…

Funny thing is Brian Greene, fairly well known physicist, and a team of physicists are working on trying to prove if there is in fact a multiverse. So hopefully we’ll be around when they get their answer and tell us for sure.

I would like to mention two people:

Rob Bryanton of the Imagining the Tenth Dimension project…. See this video
(watch with annotations off if you are not familiar with this already.. if you find it interesting use the annotations for navigating to other topics he explains with deeper explanation)
It explains his theory about dimensions in short- its quite an interesting one- the most interesting for me personally being that like time is the fourth dimension, the set of choices we have at a particular time is the fifth dimension

Nassim Haramein of the Resonance Project Foundation See his video lectures on google video
He has expounded a lot of radical ideas about the nature of the universe- He uses fractals as the structure of our universe- says that atom was the smallest unit, then we put in some more money to build better instruments and discovered protons, electrons and neutrons. Then we put in a lot more money and came up with quarks and other subatomic particles. The truth is, he says, that as we make more and more powerful particle accelerators, we will find smaller and smaller particles. We should not be looking at the structure of matter- its infinite like the fractals- rather we should be studying the dynamic nature of the energy which is the true absolute component of matter. He goes on to say that a proton is like a black hole-which has a very strong gravity and very small size- and so the strong nuclear force is nothing but gravity. There are only two forces- gravity that contracts the universe and electromagnetic force that radiates outwards and expands the universe.

These are radical ideas, so there will be a lot of critics, especially in the mainstream- but we seem to be facing several dead ends- dark matter, dark energy, Higg’s Boson and so on- and we need to give a chance to those thinking out of the box. Who knows, perhaps these alternate theories could explain things better.

By the way, a very good book to sort of visualize alternate dimensions is Flatland.