From: ghesmiz@brahms.udel.edu (Michael Macchione)
Newsgroups: alt.fan.piers-anthony
Subject: Re: mode & dimensions
Date: 7 Nov 92 00:32:35 GMT
Distribution: usa
Organization: University of Delaware

Scott C Stoness wrote

[stuff deleted]

-Just a short question on the need for a seven-dimensional universe for the
-anchor worlds to be different from one another.  I think you mean 3 dimen-
-sional anchor universes.  If a given universe consisting of three spatial
-dimensions can be specified by a time co-ordinate and an n-dimensional 
-universe vector, then for five anchors we need four dimensions to express
-the universe if it is to be equidistant from the other anchor universes
-(is this not the same number of dimensions needed for no three of the anchor
-universes to be collinear).  Thus, we have 3 spatial dimensions, three 
-universe dimensions, and a time dimension, for a total of seven dimensions.

No, if one draws a pentagon(in two dimensions) then no three points are
collinear.  Four is needed to make them equidistant.

-However, in the books (I have only read Mode, is this correct in the second
-book as well), any slice of the mode is still orthogonal to the time basis
-axis.  If the characters travel for three months, and eventually arrive back
-at their spatial and universal starting point, has three months not elapsed
-for the people at home?  If this is the case, then eight dimensions would 
-be needed, three of space, four of universe, and one of time, since the flow
-of time is unaffected in the mode.  If this is not the case, then seven
-dimensions would suffice.

-I don't recall any time distortions, but it has been a long time since I
-read the book, so please inform me if I am incorrect.

I believe you are correct.  In Fractal Mode, a world is revisited (since
you haven't read it I won't say which one), and if I remember correctly
the time elapsed in the world is the same as the time elapsed for the mode
travelers.


From: bosticj@CS.ORST.EDU (Jason Bostick)

-I hate to tell you guys this...But if you read the first book carefully
-enough you see that the virtual mode is more of a pentigonal shift through
-time.

-				A
-			B                C    	   
-			      D      E  

-When an anchor is broken...The string connecting them flies until it catches 
-another anchor person and then relocks.  With this in mind  it is possable 
-to travel between two worlds without going through the same two twice. if
-one of the two anchors was different.  it would change the direction you
-entered in.

The thing is though, when discussing things in more than two or three
dimensions, what does pentagonal mean.  If you mean a literal pentagon, as
drawn, then eliminating an anchor and replacing it would be difficult
since four points of the pentagon would be drawn correctly and the fifth
would have to be out of place unless we distort the shape of the universe.
That's why I think that the shape of the virtual mode is that of a 5-cell
(that's the name of the 4-dimensional shape made by 5 equidistant points).
If one removes one of the corners of a 5-cell then one can still find a
fifth point that is equidistant from the other 4. (Try thinking of
removing one corner from an equilateral triangle.  you can still find a
different point opposite the first corner that is equidistant from the
other two points)

Have a day,

Mike macchione aka ghesmiz
Newsgroups: alt.fan.furry