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Someone commented “… as you can see, the multidimensional ideas have been thoroughly explored before, and found unworkable,” and pointed me to the article “On the dimensionality of spacetime” by Max Tegmark.
On many points I seem to agree with Tegmark, judging by “The Mathematical Universe”, where he argues that out physical world is an abstract mathematical structure.
Tegmark analyses the characteristics of partial differential equations with n space + m time dimensions. His very clever anthropic* argument states that all higher dimensional combinations of n+m result in universes that are unpredictable. Any observer with a consciousness similar to ours, i.e. characterised by a linear sequence of thoughts, would require the ability to extrapolate from memories and to make predictions about the future.
* “Anthropic” means that if all the the universes exist but in all but one there is no life to experience them, then us observers would forcibly find ourselves in that one.
Firstly I’d like to point out that in my theory we don’t have flat n+m dimensions but a hierarchical structure and that the world can be approximated in the lowest dimensionality that exhibits space and time properties, which is 3 space and 3 time dimensions. According to Tegmark’s paper this should result in an unpredictable world . If I understand it correctly then the problem with that reasoning is that it assumes a traversal at an arbitrary angle through the time dimensions. In my theory the subjective path that observers take through the time dimensions is down the path of the steepest complexity gradient. (The chapters under the heading “Multi-dimensional time” in the menu on the right explain this in detail.)
To paraphrase this part of my theory, a traversal too far off the line of steepest complexity gradient would not allow observers to make sense of cause and effect. We should remember that the mathematical patterns that exhibit these complexity gradients are made by a simple generating function, and that any partial differential equations that describe the behaviour are emergent effects.
In the function that generates a structure with 3 space dimensions (x,y,z) and 3 time dimensions (tx, ty, tz) the pairs (x,tx), (y,ty) and (z,tz) are interchangeable (the interchangeability of the space dimensions is consistent with our experience of the world). The steepest complexity gradient (for stationary patterns) is therefore the diagonal between tx,ty,tz as shown by the red arrow t in this diagram:
There is only one diagonal that passes exactly through the origin, but if we allow some sideways drift then far far away from the origin we have lots of these red time lines that are to all intents and purposes parallel.
I have made an intuitive argument with a lot of hand waving that we experience time as one dimensional as macroscopic observers, while at the microscopic level the effects of neighbouring time lines becomes important.
Max Tegmark’s paper provides a much more scientific explanation as to why a consciousness with the ability to make predictions cannot travel across time-lines or through multiple time dimensions simultaneously. In my opinion his argument supports rather than contradicts my thesis.