Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!nrl-cmf!ukma!rutgers!att!alberta!ubc-cs!fornax!zeke
From: zeke@fornax.UUCP (Zeke Hoskin)
Newsgroups: comp.lang.apl
Subject: Re: Visualization of arrays
Summary: Yes, we *use* N-dim arrays
Message-ID: <869@fornax.UUCP>
Date: 6 Feb 89 17:14:40 GMT
References: <121@infbsgr.infbs>
Lines: 32

In article <121@infbsgr.infbs>, hafer@infbs (Udo Hafermann) writes:
> Arrays of higher rank do not have any natural arrangement in space; 
> (As an aside, does anyone *use* 4-dimensional arrays at all?
   How do we use them? Let me count the ways....
(1) as intermediates in operations involving lower-rank arrays.
(2) as a natural way of representing data with more than three
   "coordinates", for instance a table of profit vs time, place,
    material, personnel cost, and tax classification.
(3) In modelling real-world physics problems where there are indeed
    more than three space-like dimensions. (This is over and above
    lots of trad scientific treatments of things like the slope of
    the temperature-pressure plane w.r.t five or six concentrations
    all treated as (admittedly not independent) cooordinates)

   As for how to visualize higher-rank arrays: I wish I could help
you here.  If you played a lot of 4-dimensional chess, or even
4-D tictactoe, eventually some of the painstaking gruntwork that
is associated with the "left brain" would create some kind of
association in the "right brain" where people make stupid mistakes,
know things that aren't so, and have dazzling insights.  

    Other things that might help: learn tensor theory (after, not
as I stupidly did before, the appropriate matrix algebra); fool
around with quaternions; do some topology; figure out the 
the properties of a space where one of the dimensions has negative
squares, so Pythagoras' Theorem becomes (H*2) = (A*2)-B*2, and then
wander around trying to deduce Special Relativity from them. Tradition
has it that it is useful to have a friend follow you around while you
are doing this, to stop you from walking into open manholes.
-- 
What makes one step a giant leap|Zeke Hoskin/SFU VLSI group,Burnaby,BC,Canada
Is all the steps before         | ...!ubc-cs!sfu_fornax!zeke