At 01:39 pm 18-10-04 -0400, you wrote:
>Hi Horace.
>
>you write:
>>Something looks a bit magical about 4 dimensions with the all-4-spins-alike
>>combinations getting a special treatment, though there is no apparent
>>physical justification.
>
>Yes, I was hoping four would suffice. It's interesting to me that
>adding more dimensions drives the number closer to .5, 

<snip>

It seems to me, Keith, that you have put your finger on it.

The real world is multi-multi-dimensional.  See:-

http://www.journaloftheoretics.com/Articles/5-3/commentary5-3a.pdf

     ==============================================
     "...If we return to more primitive methods of 
     measuring time and length we will appreciate 
     that the notion that time and space are simple 
     entities or simple concepts is illusory. They 
     are as complex as the world they describe. 
     Likewise the notion that time and space are 
     one and three-dimensional respectively is also 
     illusory. The dimensionality of any concept 
     or physical entity is merely a reflection of 
     the hierarchical level from which we are 
     viewing it. Space has as many or as few 
     dimensions as we wish to give it, and so 
     has time.
     ==============================================

The sooner we adopt finite arithmetics for Cartesian dimensions,
the sooner we will be able to nest spaces within spaces within
spaces and recognise the true relationship between time and
space.  8-)

Cheers 

Grimer     

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