[Blindmath] psychology statistical diagrams

Tue Oct 26 10:52:07 UTC 2010

Hi, yes thanks - Kennedy is the figure/ground guy (I believe)
who is blind and draws amazing perspective diagrams of objects.

I think on the reading of the advice so far this is a "degrees
of freedom" thing?  My attempt to embed a surface into 3D and
then "project" the result to produce lines in such a way that
they gave depth cue was bound to fail (but it took 2 days to
convince myself ...).  What if, instead of a surface, it was
a sphere.  I suspect because it is a convex object with all
potential surface normals "pointing outwards", it would be more
amenable to successful representation - it becomes a coherent
object, the space it occupies cannot be shown occupied by
anything else.  Thus most space preserving projections:
perspective, orthogonal you name it? should reserve that space
in all views - and provide figure/ground separation if
presented correctly, and be amenable to representation tactually
(is that the right word?).  I suspected this is what Kennedy
was been getting at, in the only paper by him I've read ...
(And many apologies, if I've miss-represented his work)

The "haptics" people may have a way to do this.  A "haptic
model" of solid 3D objects can be generated, then wearing
"haptic gloves" you feel the object (the boundary surface,
or figure/ground, if you will).  You can also use "haptic pens"
that allow you to touch the sphere.  From perception of lots
of such sampling, the sphere emerges in the mind. (Costs? mmmm)

The "haptic model" and the "convex surface model" essentially
"image synthesis" or "computer graphics", often comes from
a "scene graph" - a formal textual description of objects
in some space, and their movement through that space.
Each solid object has a surface representation, for graphics
display and haptic representation purposes.
"Solidity" emerges and is "tactile" because each object
is positioned relative to the observer, who occupies the
same "haptic space" and can interact with the objects.
If there are 6 degrees of freedom to the observer (using
gloves, pens, whatever) then those can be used to perceive
that 3D world.  This is not possible with 2D projections
(I'd surmise) which remove at least 3.5 degrees of sensing
freedom.
The best one could hope to do, using David Marr's conjecture,
would be to get 2.5D (e.g. the Tiger examples below that have
x, y, and 8 dot heights - Marr surmised "colour") which is
what conventional bubble-paper, and Braille dot diagrams can
achieve successfully I guess.

But all this is far removed from maths, and Braille, sorry.

Regards - Bernard Diaz.

Sarah Jevnikar wrote:
> Here's a link to his c.v, detailing all his work and providing contact info.
> http://www.utsc.utoronto.ca/~kennedy/cv.html
> 
> -----Original Message-----
> From: blindmath-bounces at nfbnet.org [mailto:blindmath-bounces at nfbnet.org] On
> Behalf Of Christine Szostak
> Sent: October 25, 2010 7:42 PM
> To: Blind Math list for those interested in mathematics
> Subject: Re: [Blindmath] psychology statistical diagrams
> 
> Check out John Kennedy, I think he is Professor of Psychology at U. Toronto,
> 
> He studies drawing and total blindness and I think he has done some work 
> with 3-D though I could be wrong on my memory.
> many thanks,
> Christine
> 
> 
> Christine M. Szostak
> Doctoral Candidate
> Language Perception Laboratory
> Department of Psychology, Cognitive Area
> The Ohio State University
> Columbus, Ohio
> szostak.1 at osu.edu
> ----- Original Message ----- 
> From: "Larry Wayland" <larry.wayland at arkansas.gov>
> To: "Blind Math list for those interested in mathematics" 
> <blindmath at nfbnet.org>
> Sent: Monday, October 25, 2010 4:28 PM
> Subject: Re: [Blindmath] psychology statistical diagrams
> 
> 
>> I agree with Lloyd on this.  I do not think there is anyway a three 
>> dimensional representation can be adequately done using a Braille drawing. 
>> Indicating three dimensions on a two dimension plane is done by using 
>> optical allusions.  You can't do that tactually.  The lines are all there 
>> but they just will not look three dimensional.
>> Larry
>>
>>
>> Larry Wayland
>> -----Original Message-----
>> From: blindmath-bounces at nfbnet.org [mailto:blindmath-bounces at nfbnet.org] 
>> On Behalf Of Rasmussen, Lloyd
>> Sent: Monday, October 25, 2010 2:15 PM
>> To: Blind Math list for those interested in mathematics
>> Subject: Re: [Blindmath] psychology statistical diagrams
>>
>> As a totally blind electronics engineer who got his bachelor's degree in 
>> the 1960's, I think that getting an understanding of three-dimensional 
>> concepts from two-dimensional drawings has severe limitations.  Is this an
> 
>> isometric or perspective projection?  From what distance is the "object" 
>> being viewed?
>>
>> Talk to the people in the math department who study topology.  Do they 
>> ever make solid models of the shapes they are describing algebraically? 
>> Note that the solution to the problem of everting a sphere (turning it 
>> inside out) was first proposed by a French blind mathematician.  He 
>> visualized what sighted people were unable to visualize.
>>
>> Talk to people in mechanical engineering or industrial design departments 
>> about stereolithography or 3D printing, where numerically controlled 
>> machines are used to create solid models (quite expensively and slowly).
>>
>> Going these routes will not get you all the drawings your textbooks use, 
>> but they should get you enough information and examples so that you 
>> understand the concepts, in some cases more correctly than sighted 
>> students will from the limited viewpoint of paper and blackboards.
>>
>> Lloyd Rasmussen, Senior Project Engineer
>> National Library Service for the Blind and Physically Handicapped
>> Library of Congress   202-707-0535
>> http://www.loc.gov/nls
>> The preceding opinions are my own and do not necessarily reflect those of 
>> the Library of Congress, NLS.
>>
>>
>>
>> -----Original Message-----
>> From: blindmath-bounces at nfbnet.org [mailto:blindmath-bounces at nfbnet.org] 
>> On Behalf Of Bernard M Diaz
>> Sent: Monday, October 25, 2010 2:00 PM
>> To: Rasmussen, Lloyd; Blind Math list for those interested in mathematics
>> Subject: Re: [Blindmath] psychology statistical diagrams
>>
>> Hi,
>>
>> I've experience of generating only one diagram that NEEDED 3D - a plane 
>> embedded in 3D; that is a "surface"; and yes used the Tiger system.  It 
>> took about 2 days playing to get a not too successful result, which we did
> 
>> not use in the end!
>>
>> I'm clearly not very good at this sort of thing, it needs an artistic (I 
>> think that's the best word) flourish which I guess I don't have.  And I 
>> guess, my knowledge of 3D use is limited too ...
>> I'm sorry I've not looked at economic stuff, trends, and time series 
>> stuff - which I suspect could all benefit from the 3D aspect you suggest. 
>> I suspect, for each, it would be useful to know the approach chosen - if 
>> anyone attempts to do (or has done it) please do share your findings.
>>
>> Simple "images" (essentially phtographic stuff rendered into "tonal 
>> pictures") e.g. most of the Tiger examples I've looked at: flowers parts, 
>> coloured country diagrams, digestive systems, most maps - all work well. 
>> Where there is an attempt to get tonal representation to mimic depth 
>> cueing - what I've done suggests: a) its hard, and b) not too successful 
>> at getting over what is intended.  But, as I say, perhaps I'm not thinking
> 
>> about this in the correct way - and would appreciate pointers.
>>
>> A final note.  Many staff use Powerpoint. Where a diagram is involved I 
>> suggest that they copy the "slide" then edit that to remove all but the 
>> diagram.  Enlarge that so that it fuses correctly ("touchably" .... is 
>> that the correct word? This also involves thinking about any colour coding
> 
>> used) and provide in the "notes" section for that slide a textual 
>> description of the diagram using the language guideline mentioned before. 
>> Then, those slides are "hidden" with a note that they are for 
>> "accessibility purposes".  The idea is that the student (or teacher) can 
>> fuse the diagram (slide object); Jaws the notes section (notes object) 
>> while "touching" the fused version, and have Jaws read any text on the 
>> slide proper as well.
>> ...
>>
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