From: jpc@tauon.ph.unimelb.edu.au (John Costella)
Newsgroups: sci.virtual-worlds
Subject: Re: PSYCH and VISUAL FORMS in VR
Date: 17 Nov 92 01:39:25 GMT
Article-I.D.: u.1992Nov16.100941.11570
Organization: University of Washington
Originator: hlab@stein.u.washington.edu



Many will have noted Thomas Zier's posted Introduction to his upcoming
paper; some may be wondering just what it all means. Since my name is
used in vain <grin> in his note,

   and the visual field formulations of VR (Costella) which are central 
   to the topic of this work. 

and many physics/mathematics terms are used quite freely throughout the 
posting; for example,

   it includes a discussion of particular distinctions, as well as 
   similarities, between pre-Euclidean and post-Euclidean spacial 
   reckonings.

   (By the way; both of these boundary functions are essential 
   characteristics of metric spaces in the theoretical operations 
   of mathematical constructs also.)

   are an artifact of relativistic mechanics, and as such, they support 

   we have conscientiously represented a unified field of dimensional 
   values because space, time, and body are incorporated into a single 
   expression of rate.

   I will use theories of general relativity, first touched on during

   General relativity offers a standard language and the most appropriate 
   topological models in mathematical or physical terms for a description 
   of the binocular field structure, and the inertial frames of general 
   relativity prove to be similar in many respects to a plane of projection 
   necessary for creating two dimensional images from the binocular field.

   The phenomenon has been named the 'differential rotation effect' by a 
   perceptual psychologist who performed observational experiments on this 
   topic. And that work will be reviewed here -- as will be a rebuttal 
   founded on the mathematics of affine transformations by LaGournerie. 

   in that the differential rotation effect phenomenon is clearly the 
   result of very complex relativistic dynamics within the binocular 
   visual field which are processed through an essentially unexplored 
   neural network dedicated specifically to local effects.

then perhaps I will be permitted to express the opinions of one who
has a background largely of physics, mathematics, engineering and
computers, for the benefit of others in a similar position, who may
be wondering about the use of these terms.

The first warning that one is swimming in unfamiliar water is Thomas's 
use of the spelling "spacial", which to science-type people is usually 
"spatial", although both spellings have equally distinguished histories.
A scientist should therefore tread carefully before criticising  
anything in the posting, unless one has a firm grasp of all of the
fields that the author touches on.

Another of Thomas's terms to watch (for a scientist) is "sensible". 
In this country, at least, this term is now generally thought to mean 
"not silly" or "not idiotic". However, I think that Thomas means 
the term in the original sense of the word, namely, perceivable by
the senses; thus, I hope that his comment

   In this nearness based (or sensible) type of survey the spaces we 
   perceive, the time in which we perceive it, and the body which 
   
will not cause misguided flames to be thrown. This is particularly
a problem when it follows, as it does, what is (to my mind) a badly
worn path of "these things are Western, let's grasp any alternative",
which I thought went out with the sixties; I think Thomas's ideas
will stand up without this crutch.

Given these caveats, though, Thomas does (as the earlier clippings show)
use a number of terms and phrases which, at least on the fact of it,
appear to be in the realm of a physicist. To do so, and post the results
to a newgroup prefixed by "sci.", opens the author to criticism if
the science is not up to scratch. The reason I say this is that the
(introduction to) his paper seems to otherwise be more interested in
the art, philosophy and psychology of visual perception; these topics 
are of great interest to many, but---for philosophy particularly---are 
not quite subject to the same "rules of the game" as the hard sciences. 

My concern is that some of the scientific terms that Thomas uses are
there to simply add some sort of credence to the ideas; I fear that,
at least in their understood mathematical or physical senses, they are
being abused. I do not believe that this is necessary: the days that
the hard sciences were considered "good", and the soft sciences, and
philosophy, "not so good", are surely long gone: each has its place.

Having said that, I would like to point out what I feel to be abused
or, at least, ill-fitting scientific terms in Thomas's Introduction to 
the paper. I feel that the bulk of the paper will be of immense to
some workers in VR, and of general interest to many others, but (given
the scientific backgrounds of many of the field) may be dismissed out
of hand if scientific terms are perceived to be thrown about reckelessly
(even if this is not, in fact, the case). I list my comments as follows:

Relativistic mechanics
----------------------
   How? Temporal notations found in the Cubist visual form are an 
   artifact of relativistic mechanics, and as such, they support an 
   
Hmm. "Relativistic mechanics" has a well-defined meaning today: the   
(specially) relativistic mechanics of Einstein's 1905 work. I would
be very suprised to find the speed of light entering into the
Cubist visual form (but I may be proved wrong :).

Perhaps prefixed by the adjective "Galilean", we might imagine 
Galilean Relativity instead of Einsteinian. The adjective "temporal"
(i.e. with respect to time) then suggests we have a Galilean 
transformation coming into play. I think, though, that some further
elaboration would be needed to make this convincing.


Space, time and rate
--------------------
   And the evidence of these complex relationships within this sensible 
   spacial reckoning prompts me to suggest that we have conscientiously 
   represented a unified field of dimensional values because space, time, 
   and body are incorporated into a single expression of rate.

This sounds like gobbledegook to a physicist. At least for the scientific
meaning for the term "rate", you cannot fold spacetime up into it. I am
not sure what is being meant here, but words are being used that will
confuse a scientist.


General relativity
------------------
   I will use theories of general relativity, first touched on during
   discussions of Cubist temporal notations, to illustrate some 
   essential relationships of the binocular field to the plane of 
   projection required when creating an image on two dimensional 
   surfaces. We often make common assumptions about these Euclidean 
   projective techniques, but in creating a projection of the binocular 
   field we must carefully examine our assumptions in order to preserve 
   the commitment to an embodied circumstance. General relativity offers 
   a standard language and the most appropriate topological models in 
   mathematical or physical terms for a description of the binocular
   field structure, and the inertial frames of general relativity prove 
   to be similar in many respects to a plane of projection necessary 
   for creating two dimensional images from the binocular field.

   [...] in that the differential rotation effect phenomenon is clearly 
   the result of very complex relativistic dynamics within the binocular 
   visual field which are processed through an essentially unexplored 
   neural network dedicated specifically to local effects.

A physicist must be allowed to barf upon reaching these paragraphs. One
might conceivably imagine that the term "general relativity" has an
artistic meaning completely distinct from its physics meaning; however,
mention of "inertial frames" and "local effects" makes this impossible.

There are three senses in which the term "general relativity" is used.
The first is as a synonym for "general relativistic covariance" or
"generally covariant"; to quote its incarnation by Albert:

   The general laws of nature are to be expressed by equations which
   hold good for all systems of coordinates, that is, are generally
   covariant with respect to any substitutions whatever (generally
   covariant).

This is saying something about the mathematics of the laws of physics; 
it does not talk about perception, as such, at all. The second use
of the term "general relativity" is the one that Albert would have most
liked: namely, a system of *mechanics* in which all the laws of Nature
a generally relativistically invariant.

The most *common* use of the term "General Relativity", however, is
to refer to the theory of *gravitation* that Einstein formulated.
It was the first generally relativistic theory (in the above sense),
but by no means the only one. I fail to see any connection between 
gravitation, though, and the topic of Thomas's paper.

I think that Thomas is simply saying that his results are presented
in the language of non-Euclidean geometry (as, indeed, Einstein's
gravitational theory, in its current classical form, still is).
However, having bagged geometry, both Euclidean and non-, I suppose he 
would be reticent to put it in those terms :).

If even this guess is off-track, then the use of the term "general 
relativity" is not even excusable.


Disproving mathematics without mathematics?
-------------------------------------------
   The phenomenon has been named the 'differential rotation effect' 
   by a perceptual psychologist who performed observational experiments 
   on this topic. And that work will be reviewed here -- as will be a 
   rebuttal founded on the mathematics of affine transformations by 
   LaGournerie. [...]

   To do that, methods consistent with properties of the sensible
   realm must be substituted for linear experimental techniques which are
   employed in the studies mentioned above, and the results of these new
   efforts compared to earlier findings. On the whole I find that sensible
   experimental methods clearly support some conclusions of earlier
   observational experiments; but these sensible experimental methods 
   just as clearly refute the mathematical predictions of LaGournerie 
   in more cases than not.

Err ... either the question is mathematically describable or not. If not,
then the affine transformations were misapplied; if so, then you cannot
disprove them by discarding a mathematical description of the world!

I am sure that, again, there will be a sensible discussion in the full
paper on this topic, but the above Introductory comments will tend
to magnify any cynical doubts that scientific readers may already harbour.


Euclidean assumptions
---------------------
   preventing us from running aground on sometimes well concealed 
   Euclidean assumptions or processes; specifically those assumptions 
   and processes which persist in what today is casually called
   non-Euclidean geometry.

This statement might be misinterpreted by a mathematician. Euclid's
*axioms* were well laid out; these axioms are modified in any
non-Euclidean geometry. They are not hidden. However, Thomas may be
referring to the common assumptions underlying what "geometry" actually
means: that space is smooth, not too weirdly connected, and so on.
You can change these ideas too; if you go too far, then a scientist
may not accept the thing you create as "geometry". But it may well be
a valuable construct.


Conclusion
----------
I think that Thomas's paper will be valuable to some in the field,
especially those intimately interested in the artistic side of VR.
However, I fear it may be opened to excessive flaming if some of
the mathematics and physics claims are not either modified, or
justified.


John Costella

----------------------------------------------------------------------------
John P. Costella              School of Physics, The University of Melbourne
jpc@tauon.ph.unimelb.edu.au         Tel: +61 3 543-7795, Fax: +61 3 347-4783
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John

----------------------------------------------------------------------------
John P. Costella              School of Physics, The University of Melbourne
jpc@tauon.ph.unimelb.edu.au         Tel: +61 3 543-7795, Fax: +61 3 347-4783
----------------------------------------------------------------------------