Monday, 21 February 2011

10 spacial dimensions: what does that mean?

In my previous post I explained why we think there are multiple dimensions. In this post I want to clarify exactly what I mean by "dimensions" and to try to give you a way of visualising what that means in practical terms. The word "practical" is hardly appropriate when we are referring to states of being - of existence - that are literally out of this world, but bear with me.

Esoteric science and spiritual definitions of dimensions include "vibrations" or "planes of existence". For example in the the theosophical and taoist traditions, there are seven named planes: the Physical, Astral, Causal, Akashic, Mental, Messianic and Buddhaic planes. Those who subscribe to a belief in Pleiadian extra terrestrials have a 12 "dimensional" definition of consciousness (more info about this at the foot of this post).

I want to make it clear that the dimensions referred-to in string theory are not (necessarily) the same. In this blog, when I refer to the word "dimension" I am using it as defined by the science of mathematics, unless stated otherwise.

In mathematics the dimensions of a point are the minimum number of co-ordinates necessary to define the position of that point. For now, forget the idea of space-time and try to imagine a dimensionless domain in which there exists a single point. That point has no height, width, depth or any other dimension that can define its position. This is the "zeroth" dimension.

Now define another point, anywhere, and join it to the first by a line. We now have a one-dimensional object that has length but zero width. Another way of thinking about this 1D line is that it consists of an infinite number of points stacked side-by-side in the direction of the first dimension.

Now stack an infinite number of 1D lines side-by-side, parallel to one another. The shortest distance between any two of these lines would be at right angles to the line, measured in the direction of the second dimension. You can imagine that all these 1D lines when placed side by side, define a flat surface or a 2D plane. It has length and breadth but zero height.

Now stack an infinite number of 2D planes on top of one another. The shortest distance between any two of these planes would be at right angles to the plane, measured in the direction of the third dimension. You can imagine that all these planes when placed one on top of another, define a three dimensional domain, like the one that we live in which we call "space".

It is a requirement of each new dimension that it must be at right-angles to all of the other dimensions. In mathematics we use an expression to describe the idea of all the dimensions being at right angles to one another. We say they are "mutually orthogonal".

A diagonal line on the 2D plan can't be a new, third dimension in its own right because any point on that line can be defined entirely using 2D coordinates. Tilt that diagonal line upwards, above the 2D plane and you still haven't defined a new dimension because the line isn't at right angles to the plane. Only when the line is orthogonal to the plane is it possible to move along it - in the third dimension without changing your co-ordinates in the first or second dimensions.

I'm using imagery to help you visualise higher dimensions one at a time, but now we have arrived at our familiar 3D space how can we visualise the 4th spacial dimension? I'll let physicist Carl Sagan do that for you in the following videos.

Part 1

Part 2

We can't easily conceptualise what a 4th spacial dimension might look like, but if you've followed my reasoning so far, you will appreciate that the 4th dimension consists of an infinite number of 3D spaces stacked parallel to one another at right angles. Perhaps these might be thought of as parallel worlds?

Continuing the idea, the 5th dimension is an infinite number of parallel 4D realms stacked together orthogonally, the 6th dimension is an infinite number of parallel 5D realms stacked together orthogonally and so-on until we reach the 10th spacial dimension which is an infinite number of parallel 9D realms stacked orthogonally.

The stacking order of the dimensions is important because each higher dimension consists of an infinite number of realms of the next dimension down.

Supposing some or all of the extra dimensions of string theory are below the first dimension? In other words, could they be a subset of 3D space? This would mean that our 3D space might actually be the 8th, 9th and 10th dimensions. The following video describes the model developed by mathematicians Theodor Kaluza and Oskar Klein in which a 4th spacial dimension is described as "curled-up" within 3D space. To my way of thinking, if they are contained within our space then they are lower dimensions.

The Extra Spatial Dimensions of String Theory

We can only speculate about what the individual characteristics of each additional dimension are and how it adds meaning to the ones below. I subscribe to Rob Bryanton's visualisation as described in his book "Imagining the 10th Dimension". His video (shown below) has certainly reached the imagination of the public having scored nearly 1.5 million hits on YouTube.

Rob Bryanton: Imagining the 10th Dimension
Part 1

Part 2

If you are confused by the fact that M-Theory states there are 11 dimensions and Rob is describing a 10-dimensional model, then realise that 10 dimensions are sufficient to describe reality and to unify gravity and quantum mechanics and that the 11th dimension is the one that explains why there are many possible 10D models. Rob has produced a vlog to discuss this in more detail - "Aren't there really 11 dimensions?"

The order of the dimensions is not important to my view of reality - specifically the role consciousness plays in the universe - but exactly where time fits-in is one of those questions that has caused me a great deal of wonderment. In my next post "Is Time a Dimension?" I will discuss this in more detail.

From the perspective of THIS universe, I am "The REAL" Jeff Hall

More reading

Imagining other dimensions

David Roberts 12 Dimensions of Consciousness (Esoteric)


  1. Brilliant article Jeff. I’m looking forward to the next episode. In the meantime there is a very interesting article in the May edition of Scientific American on ‘Octonions’ and their use in String Theory.

  2. Thanks for your support David. I'm not sure if I can get hold of SA over here in England - do you know if it's published online?

  3. You can read some of their articles online - - but I will pass my paper copy on to you when I've read it.

  4. Thanks David. I've asked my newsagent if she can source a copy and she said she would "try her best" - which basically means she's not sure!

    Do you know my contact details? if not then email me through my profile page - click on my mugshot.

  5. I will scan the article as jpegs and e-mail them to you.

  6. Thanks David - you're a proper Gent!

  7. No sooner said than done! My friend David Godwin has scanned it and just emailed it to me!

  8. I've now had a look at the Scientific American article on Octonians and the gist of it says that there exists an elegant 8-dimensional mathematical device which when traced-out in time as a membrane adds three further dimensions matching the 11 of M-Theory.

    Because similar devices only exist in 1, 2, 4, or 8 dimensions, it is implied that octonians are a natural fit with nature and maybe String Theory is the latest fit that we've found.

    There is a precedent for this. I recall that the simple Fibonacci series crops up everywhere in Nature even though it was possibly originally just a device discovered by an (Indian?) mathematician.

  9. Yes your are wright and thanks for post a good topic . your post is

    top most in related post of Imagining the 10th Dimension.