From: ziert@beloit.edu (Tom Zier)
Subject: PHIL: VR and VISUAL FORMS (reply to John Costella)
Originator: hlab@stein.u.washington.edu
Organization: University of Washington
Date: Wed, 18 Nov 1992 23:41:34 GMT


Let me first thank John Costella for reading, and interpreting for
physicists, my submission to the group. It is not specifically tailored to
the ongoing discussion, but considering the time constraints which we all
work under I'm sure the group will understand. 

I believe that the interdisciplinary character of this group is unique, and
an important asset to retain given the impact that this field will have on
our society in the coming decades; otherwise I wouldn't be wading through
all of the technical postings, etc., which are very difficult going for me.
An example may be the Gallilean Anti-Aliasing posting which is still
challenging me.

John is quite right that I have used some physics terms freely; 

> 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.

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

>    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.

These terms are used freely, but with some caution learned through heated
debates as well; however I feel that the constructs presented by
relativistic theory are necessary to my work, and they are important
landmarks in the development of modern scientific expectations as well.

> 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.

please;

> 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 criticizing
> 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.

Quite correct on all of the above counts, including the sixties part. I
guess I'm caught in a time warp. I don't mean to grasp at ANY alternative
though, what I would like to do is offer a substantially improved framework
for one specific mode of perceptual referencing which has gone unexplored as
yet.

> 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.

I have used these models and terms, as stated earlier, with some hesitation.
Lacking any other language (and or model) to explain the topological
configurations suggested in my work I have ventured into these disciplines
to build a bridge across disciplinary boundaries.

> 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.
> 

Quite correct, my error, and to my benefit that you pointed this out;
however


> 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.

I would like to point out for the physicists who begin to feel quite smug at
this point that within the mathematical heritage of ancient Greece Euclid
suddenly created these distinct categories of space, time, and body
(distinct from one another) with no acknowledgment whatsoever that he had
transformed the ancient traditions. Again, I am not asking you to fold space
and time into rate, rather, I would like to acknowledge the pre-Euclidean
characteristics (represented in statements concerning the sensible realm by
'aweful' figures such as Parmenides, to quote Plato) which are consistent
with an embodied visual form . 

(See 'The Invention of Space' by FM Cornford; lectures in honor of Gilbert
Murray)

> 
> 
> 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.

Please feel free to barf, I am not offended at my naivet, and I hope you
aren't either; these efforts at communication across disciplinary boundaries
are sometimes very gut-wrenching.

> 
> 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 covariance is precisely what I mean to convey, and they are not well
attended to in the modern or classic theories of visual forms. In
contemporary visual theory we have been content with a rather antiquated
Gallilean framework in which the arbitrary framework (undone, rebuilt?, by
Albert) are still substantially in place.

> 
> 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.

As a matter of appropriate use,  Albert borrowed a perceptually based model
to found his physics arguments on; ie the tram or gondola perceptual models.
These models, which John uses in his GAA paper, are equally valuable in both
physical and perceptual models; but recognition of this has been slow to
occur. I am willing to risk the criticisms of the physics, and perceptual
psychology, communities in bringing this long overlooked asset into view.
These mathematically founded models of theoretical physics can be very
helpful in perceptual psychology's recognition of an embodied visual form. 

The most valuable part of my effort here, as I see it, is to provide a
philosophical framework for such an adaptation as well as the
neuro-anatomical correlations which will make the transformation more
meaningful and acceptable.

> 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.

Here is a very important point, and contribution to the argument by John,
that I did not fully explain. I don't intend to use a gravitational
'mechanism' in explaining the form of a binocular visual field, rather, I
intend to borrow a descriptive technique long accepted in the study of
physics. The descriptive technique in physics itself, as mentioned above,
grew out of a perceptual 'thought experiment' (in the tradition of
Leonardo), which I believe may be appropriate to both physics and perceptual
matters equally.

We tend to be drawn toward things of interest in the visual field, and place
what is commonly called the fovea of our vision upon that feature which most
interests us. This is not a gravity well, which would be appropriate in
physics as related to inertial frames etc., but descriptively these formal
structures of perception are similar in character to the notion of an
inertial frame. Each of us, as we move through our environment focuses at a
given distance according to our rate. These distances of focus change
according to our changing rate of movement and mass; in a truck of a given
mass our focus is further from us due to the unique inertia, compared for
instance to a bicycle with less mass. 

In a shared environment (virtual or not) these individual frames of
reference, or focus, must be accounted for if we hope to establish a
meaningful ecology; not only must they be accounted for, they must be
created and represented in a descriptively appropriate manner such as the
binocular field projection.

> 
> 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 :).

I haven't bagged Geometry per se, but feel that where it performs a
disservice it ought to be reformed.

> 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!

In this case the affine transformations were clearly misused, and that is
demonstrably so. Just as Euclid's projective techniques are inadequate to
perspectival problems, so are LaGournerie's techniques inappropriate to any
sort of perspective other than parallel arrangements. DEMONSTRATIONS UPON
REQUEST; in my studio only (until I can deliver images of a sufficient
quality to the archives of virtu-l).

Mathematics are not discarded by myself, but current techniques are simply
inadequate to the task. Anyone want to have a go at it?

> 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.

Let's leave Descartes demon out of this, please.

> 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.

The assumption (in particular) that I wish to question is still in place,
found in post-Euclidean Geometry, and not necessarily appropriate to
sensible descriptions of visual experience; the dimensional factoring
through which Euclid created his cognitive or rational spacial reckonings.
This is clearly evidenced by the insistence of all physicists and
mathematicians who claim that we cannot 'fold' time and space into rate. 

> 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.

I very much welcome the preceding discourse, and invite heated debate, as I
refine my position accordingly. Just think; I got taken to school and I
didn't even have to pay tuition.

---------------------------------------

FURTHER COMMENTS WHICH WILL HELP ALL WHO HAVE READ THIS ONGOING DISCUSSION
TO APPRECIATE THE UTILITY OF THE SUGGESTED FORM BEYOND 'ARTISTIC' INTERESTS
OF VIRTU-L GROUP MEMBERS / SUBSCRIBERS.

The binocular field projection is designed such that it clarifies, helps to
distinguish, the roles of 3 known neural visual pathways. We are commonly
concerned with only color and external structures of visual phenomena in
todays representations. I mean by 'external structures of visual phenomena'
to say that we attend to the scale of other things, thier position in the
external world, and thier motion through that space. Thus we represent
essentially a minkowski model of space in contemporary visual forms; even
when perceived in a stereoscopic mode. 

Let me suggest on the basis of my own work that the third neural network is
dedicated to perceiving our own body's location of residence, perceived in
the parvo-interblob-palestripe network (Livingstone, Scientific American),
and it functions according to principles best approached (or schematized)
thru the Gaussian spacial models and the inertial frames of Albert's
gravitic relativity. A tenuous example of this implied relationship to
gravity itself is contained in the tram discussion of John Costellas GAA
paper, where he points out that our perceptual adjustments to changing rates
depend upon gravity for an appropriate response. (Though this is not the
sort of argument or example which I can depend on for making a meaningful
behavioral claim.) Models which support my topological expectations are
based on macro-anatomical functions. 

I am not suggesting that we discard either of the current modes (color, or
stereopsis), but rather embrace the third mode of representation (binocular
field projections) in a manner that would enhance the illusion of immersion
in our current visual representations. Here, then, is the reason that TECHS
and CODE-WRITERS should be interested (even participating) in this ongoing
discussion. If we can represent a more replete visual form which contains
cues for rate of movement by the perceiver's body; then, as John Costella
points out in his GAA paper, we may be able to lower the refresh rate of
video frames and/or the resolution of displays because the illusion itself
will be more convincing fundamentally. Its the old question about whether
you want to be information rich (frontend) or computationally heavy in your
processing environment.

The perceptual psychology crowd will certainly become interested in the long
term, since the explanations of phenomena such as those touched on by S.
Rushton in the example of his vertigo box are more refined (elegant) when
couched in terms of the binocular field, but for now they remain
understandably skeptical due to lack of experimental proof which will
require extensive resources not yet available to me. (You may have noticed
the difficulty encountered explaning associated VR-PSYCH effects;
stereoscopy and optic flow do not ADEQUATELY specify these embodied
phenomena.)

I intend to support this discussion further by posting a portion of my
manuscript with the appropriate images to virtu-l archives as soon as I can.
For now; I ought to shut up and listen.

-------------------------------------------------------------
t. zier                                                        
ziert@beloit.edu
-------------------------------------------------------------

Disclaimer?     He's a harmless fool.
Newsgroups: sci.virtual-worlds