Dear Verna,
Pardon me, but hoping on grace on a Sunday afternoon, I will breech the limit you requested in asking for replies from those who know a lot about perception, particularly along the lines of Arnold's or others' similar, interesting and useful, but still rather only visually oriented models. Hopefully you will get ample replies of the kind you seek from the knowledgeable respondents.
I don't know a lot about such visually oriented models but I rather ~see the terrain more in terms of the visual and other senses all being or reducing down to being in terms of an underlying, I guess my option is to call it a primary tactile sense.
In this alternate storyline, for instance, pardon my hunter-gatherer hypersensitivities, but if you set up an "observer focal point" (OFP) say, within one's gut, heart or head, and then if the wind comes toward the front heart-side of the body conveying a particular scent, or a distinctive noise, or even a pressure or other *feel*, if the sense or recognition is attractive or repulsive various optimal "lines" are clearly defined, actually, quite naturally, just in terms of minimizing energy use, or maximizing energy conservation.
Or, one hears a strange branch break unexpectedly which establishes a "line" and then one turns her gaze in that direction, along that line. So, consider lines of touch, lines of taste, lines of smell, lines of hearing, lines of sight. Touch, taste, smell and hearing all quite clearly involve some forms of tactile, molecular torquing. Similarly, with infrared (thermal) and, logically, other similar forms of electromagnetic sensing, perhaps in a manner similar to that in any of the various forms of analytical spectroscopy.
This structural-energetic recognition may all be managed, in my case at least, by my fearful and skittish little lizard brain (particularly for smell and taste), but hopefully, you and other readers can also notice some of the deeper origins and significances, of such invisible lines of force between objects -- self-centered though most of them may be.
In this, I will label it, deeper, more analog and tactile -- far less abstract intellectual-- level of organization such "lines of force" have quite real, integrated, energetic meanings and definitions. And considering this terrain, I suggest that even the so-called 3-D or volumetric framework is not robust enough to begin to accurately model our nested fields within nested fields existence and experience.
Granted, the Cartesian distances-in-three-directions abstractions provide us with an incredibly helpful initial approximation. However, as it also seems quite apparent from the content of your post that the 3-D, 2-D, 1-D countdown and liturgy, even after 370+ years of developments, STILL leaves us with extremely awkward and significant questions un-befitting of an actual rational scientific account or model.
If readers can tolerate it, consider that Descartes' model dissociates or ignores important aspects of reality, particularly energy, and allocates aspects of consciousness (particularly subjectivity -- also a form of energy) in similarly unhelpful and inaccurate ways.
If we can face the ~3-D..1-D anomaly squarely, calling it what it is: an excessively gross over-simplification -- a fatal flaw in the initial scientific paradigm; then it's possible we can subsequently sift through some other options and adopt or shift over to one of the improved enfolding structural-energetic trial theories, thereby gaining a reduction in error and and confusion, with some increase in paradigmatic accuracy.
In an age where 4-D space-time relativity has been in vogue for three generations and higher dimensional mathematical expressions and string theories models the nested standard model and various nested fields, in part with compactified or invisible, curved dimensions, off-hand it looks like a no-brainer that we all would be eager to turn away from 3-D..1-D debates and, as a matter of simple (reptilian) intellectual honesty, to minimally migrate to and embrace a nested, four-dimensional structural-energetic approximation, even as a transitional improvement for the lower elementary educational grade students.
I also expect that some of the ~modern answers regarding the longstanding 1-D zero-infinity conundra are also firmly pegged to and relate to the so-called compactified or inwardly curved (nested) higher mathematical dimensions in energetic field models. But, again, the gap to that understanding is rather humongous along the traditional abstract mathematical line. To begin to close the gap, to put this knowledge in the hands of grade school or high school students or to convey the developing news to others in the global science education classroom, one might hazard the guess that that effort would likely involve playing with something other than stacks of cubic wooden blocks and then also becoming a bit anxious later on about the associated and resulting 3-D..1-D ambiguities and anomalies.
If there is grace enough, excellent questions, Verna. As you might say on that side of the pond, with gusto and great *feeling*: Spot on!
Best regards,
Ralph Frost
http://magtet.com
Imagine consciousness as a single internal analog language forged in ordered water forming during respiration, in concert with experience.
En-Joy!
--- In jcs-online@yahoogroups.com, "Verna Muitt"
>
> Jo, and Harwood,
>
> Jo says:
> "To me an infinite number of points laid next to each other in the
> same direction would be a point because points have no length. If you allow
> points to have even the tiniest lengthness they are not points." and "So
> maybe a point is a case of immediate difference in all directions. Wherever
> you go from it you are in a different situation - NOT point. Then a line is
> a case of sameness in one set of opposite directions and immediate
> difference in all others, unless it has ends, in which case at the end there
> is only sameness in one direction. The line is only this set of relations,
> it is nothing 'in itself'. Points can be 'on' it but are not part of it."
>
> This is a beautifully expressed statement of just why points must be
> non-dimensional, lines one-dimensional (length), and planes two-dimensional
> (length and width), and goes much further than that as well, though this
> will come out better as the discussion continues (I hope).
>
> I have already replied to Harwood in a different thread, but to recap and
> perhaps fill in a little more:
>
> Someone pointed out to me a long time ago that 3-dimensions indicated
> volume, say a sphere, which when divided (as in losing a dimension) gave a
> plane of two dimensions, which when divided gave a line of one-dimension,
> which when divided gave a point with no dimension. From this argument,
> perhaps one could concede that perception addresses a volumetric space
> (only?), and thus things of fewer dimensions are simply incapable of (full)
> normal perception. We never actually see a one dimensional line, since we
> have to draw it (in the external world) using a three-dimensional object
> (chalk, charcoal, paint, stylus) on another three-dimensional object
> (blackboard, paper, canvas, clay). These are truly 're-presentations' made
> simply to re-present something in our mind (product of our mental
> processing) in such a way that it can come back to us via our 'normal'
> 'analytic/synthetic' mode of thinking/perceiving. Of course, we must take
> great care not to conflate the 3-D re-presentation with the initial 1-D or
> 2-D mental object.
>
> Thus the 3-D, _drawn_ 'line' _is_ substantial, and can be divided, but the
> divisions (into segments, per Harwood's note) can only be pointed to by
> non-dimensional points (otherwise they would disturb/interfere with the
> physical nature of the line per se). The 1-D line cannot consist of
> points only, as this would mean an addition of an infinite number of
> non-dimensional things, which equals 'nothing', or zero -- though note that
> this latter is achieved by means of an 'infinite' number, and so we have the
> paradox that both infinity and zero are involved in the description of the
> line (and points and planes perhaps, too?). In the country mapped below 3-D
> space there be dragons, it seems ......
>
> I would like to ask those who know a lot about the actual perceptual
> processes themselves to indicate if they can just which processes are most
> likely to bring about the 'sense' of this 1-D 'lineness', which is surely
> _part_ of the way we proceed to the full perception. That the 3-D effect
> lies in something connected with Arnold Trehub's retinoid space seems
> obvious, so we are looking for a process which precedes and contributes to
> the synthesis of Arnold's model, aren't we? Would Jo's model of the input
> from the environment of the dentritic endpoints fit the bill?
> Maybe I'm just way off beam, but it's worth a thought, and it just may be a
> trigger for an utterly different and much more satisfying notion ......
>
> Verna.
>
>
> -----Original Message-----
>
> From: Edwards, Jo
> Sent: Tuesday, March 05, 2013 9:58 AM
> To:
> Subject: [jcs-online] Lines
>
> Maybe this week Dale Purves is the answer to everything. He is talking at
> the Institute of Philosophy in London on Thursday. He says all sorts of
> interesting things about lines and colours. I bought 'Why We See What We Do'
> and I think it is very good value because I often go back to it. I had
> rather lost track of the line thread but Harwood raises some interesting
> issues.
>
> Euclid says a line is breadthless length, or that it lies evenly with the
> points on it. That sounds OK but I note Proofwiki says it could also be
> thought of as a 'continuous succession of points'. I am not happy with that.
>
> To me an infinite number of points laid next to each other in the same
> direction would be a point because points have no length. If you allow
> points to have even the tiniest lengthness they are not points.
>
> So maybe a point is a case of immediate difference in all directions.
> Wherever you go from it you are in a different situation - NOT point. Then a
> line is a case of sameness in one set of opposite directions and immediate
> difference in all others, unless it has ends, in which case at the end there
> is only sameness in one direction. The line is only this set of relations,
> it is nothing 'in itself'. Points can be 'on' it but are not part of it.
>
> It is maybe interesting that lines tend to be defined in a two dimensional
> context. The definition in 3 spatial dimensions seems to stay the same but
> for the 4 dimensions of reality maybe it needs sameness in time. But that
> seems arbitrary. Presumably this reflects the fact that 'line' is a real
> idea about a non-real abstraction?
>
> Jo
>
>
>
> On 4 Mar 2013, at 16:30, HARWOOD FISHER wrote:
>
> > Verna:
> >
> > Here is what puzzles me, if there is to be a 'model' that transacts
> > between the physiological data and the subjective experiences:
> >
> > Can you image a line that has no beginning or ending point; yet is
> > straight? Can you conceive such a line?
> > If the answer is yes to either, then the matter of the point is separate
> > from the issue of a subjective �sense� of a line.*
> > Alternatively, it suggests that different levels or orders of
> > representation are in some sense �independent� of the physiological
> > (neurological) patterns�or at least
> > independent from our capacities to represent those phenomena and/or
> > structures.
> >
> > *If one does take this 'infinite line' to be a matter of the inclusion of
> > infinite points, one is simply working by division to create segments.
> > So, if this 'imaging' is a 'superimposition' of points (or divisions);
> > then it avoids the capacity to �image� or �conceive� the line-ness;
> > straightness; and continuousness. No?
> >
> > Harwood
> > On Mar 1, 2013, at 10:06 AM, Verna Muitt wrote:
>
>
>
> ------------------------------------
>
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