Abstract or Concrete
Shelley Walsh
I see that my post about The Gift of Dyslexia started quite a thread. I hope
you all enjoyed that. It also started in interesting discussion I have been
having with Eldon about a great variety of subjects. One idea it got me
thinking about is this.
I am a very mild dyslexic--if dyslexic at all, but I think I am--and it seemed
when reading about dyslexia from Ron's book that in some ways I felt like I
thought in a similar way, but in others I felt absolutely diametrically
opposite, like a kind of antidyslexic, and indeed this is also consistent with
some of my recent dealings with severe dyslexics where it seems that we both
feel we are more on the same wavelength with nondyslexics that with eachother.
After I thought about this more what I realized that the difference seems to
be is that they are much more concrete that most people and I am much more
abstract that most people. When I thought about it further it seemed that
there may be a pattern here. It seems that the other mild dyslexics that I
know are also very abstract in their thinking. So what I am now curious to
hear about is has anyone else noticed this pattern, and if so do you have any
idea of why it might be so? I have a few ideas and Eldon seems to have some
too, but I don't want to prejudice you, and I'm not even sure if it is true,
so I would like to first hear about what the rest of you think about the
matter.
--
Shelley Walsh
Milton, Cambridgeshire, England
She...@shells.demon.co.uk
http://www.shells.demon.co.uk
Shelley's MathHelp
http://www.shells.demon.co.uk/softdev.html
EldonB123
>there may be a pattern here. It seems that the other mild dyslexics that I
>know are also very abstract in their thinking. So what I am now curious to
>hear about is has anyone else noticed this pattern, and if so do you have any
>idea of why it might be so? I have a few ideas and Eldon seems to have some
>too, but I don't want to prejudice you, and I'm not even sure if it is true,
>so I would like to first hear about what the rest of you think about the
>matter.
>--
both just going to wait to hear what the rest of you think. I think neither of
us would mind sharing our discussions so far, but for now we're going to pick
your agile and active brains ;-)~
--Eldon
Frank
^ I am a very mild dyslexic--if dyslexic at all, but I think I am--and it
seemed
^ when reading about dyslexia from Ron's book that in some ways I felt like I
^ thought in a similar way, but in others I felt absolutely diametrically
^ opposite...
^ It seems that the other mild dyslexics that I
^ know are also very abstract in their thinking.
I am assuming that abstract thinking is creative thinking.
In my psychology class this last quarter there was a girl who I thought was
dyslexic. She is very creative (music, art), ambidextrous, easily distracted,
frequently stares into the distance while talking, thinks a lot, etc, but
after talking with her for several weeks I was unable to find any real
evidence of dyslexia.
This got me thinking more about the hemispherical differences in the brain. I
think it might be that there is a spectrum of abilities running from purely
left-hemisphere to purely right-hemisphere, and that most people have their
dominant abilities in one or the other. When someone is very strong in
left-hemisphere abilities they are thought of socially, and perhaps
incorrectly, as very intelligent. If this same person is weak in
right-hemisphere abilities they are merely thought of as "not creative."
Someone who is very strong in right-hemisphere abilities with no apparent
left-hemisphere weaknesses is merely thought of as creative. This leaves the
person who is strong in right-hemisphere abilities but weak in left-hemisphere
abilities, this person is thought of as dyslexic.
The above is just supposition.
I think we should come up with a label for people in the second category
(above), those who are strong-left and weak-right. How about dysvisia (bad
vision) or dysarsia (bad art) (Latin from
<http://humanum.arts.cuhk.edu.hk/Lexis/Latin/>).
Frank
Shelley Walsh
> I am assuming that abstract thinking is creative thinking.
No, I don't think that is a correct assumption at all in general and
especially in the case at hand. Perhaps eventually I need to clarify further
what I mean by abstract and concrete, but for now I'll get by with using these
terms someone loosely. But to my mind there is nothing to say that a concrete
thinking person cannot be creative, nor that an abstract thinking person
cannot be creative, but they are creative in very different ways. What I
associate with concrete is grounded, practical, down to earth, good at
hands-on, good at dealing with--at possibly creating with as well--that which
you can accessed with the 5 senses--but on the negative side, not so good at
going beyond them. There are plenty of people who are creative in this way,
earth mothers, sensual, live for the present. I am struggling to put this in
positive a way as I can considering that I don't posess that style. To me such
people strike me as more artistic than creative, but really they are merely
creative in a different way, maybe creative with things but not with ideas.
That's probably not true either, but their ideas tend to be grounded and
practical pertaining to things they have tangible experience with, not up in
the clouds or based on the conjectural or the extrapolated. People who I have
met who are that way--and Davis appears to be one of them--seem to, contrary
to my way of thinking associate abstract and concrete in exactly the opposite
way you just did. I tend to think your way too, but after thinking about it a
bit I could see the other way too. Abstract thinking involves such things as
symbolism. Sybolism-->words-->verbal thinking-->linear thinking. And yet this
is false, because symbolism doesn't necessarly imply linear thinking, and
linear thinking doesn't imply a lack of creativity either. Certainly verbal
thinking doesn't imply that because otherwise no novels would be written. I
also suspect that your equation of right hemisphere with creativity and left
hemisphere with what is usually regarded as intelligence is not quite
anatomically sound.
So, I repeat, no, the assumption you are making is not at all is a fair one.
jip
>
> I tend to think your way too, but after thinking
> about it a bit I could see the other way too.
> Abstract thinking involves such things
> as symbolism.
> Sybolism-->words-->verbal thinking-->linear thinking.
> And yet this is false, because symbolism doesn't necessarly
> imply linear thinking, and linear thinking doesn't imply
> a lack of creativity either. Certainly verbal thinking
> doesn't imply that because otherwise
> no novels would be written.
>
There's a very wide gap between symbolism and words.
Verbal thinking is a linear way of thinking because
the characters, words and sentences must stay in
chronological order to keep their meaning clear.
You use flash backs and things like that, but this
is also done in a orderly way (like a new chapter or
paragraph in a book).
It's difficult (or impossible) to process different types
of verbal information. Listening to two persons talking at once,
reading while talking to someone else, etc. In verbal thinking
it is also infinitely difficult to think of more conversations
at once.
When you use symbols while thinking about abstract problems
you can make your problem more concrete. With a little imagination
you can create all kinds of surrealistic realities where your
abstract problems turn into concrete ones. Some people prefer
to build their surrealistic worlds out of parts of
realistic examples. Others use mathematical notations,
formulas and graphs.
I prefer to make use of a multi-perceptible type of
symbolism (very visual). Because this is a multi-dimensional
way of thinking instead of a linear one, it makes it easier
to 'look' at a problem from different 'points of views'
at the same time. But it's difficult to translate it into
a linear model again, which is nessesary for communication.
jip
--
WARNING: Because I am dyslexic, spelling errors may occur in my
writing. I hope this doesn't annoy you, but if it does
you can always mail me the correction.
°
° °
http://jip.mypage.org/ |_o_/
http://www.dse.nl/balans/ ¥
mailto:ji...@geocities.com #
------------------------------------------------\\--------------------
EldonB123
Thomas G. West (author of In the Mind's Eye) at this URL:
http://www.ldonline.org/first_person/west.html
Eldo...@aol.com
Shelley Walsh
>
> Shelley Walsh wrote:
> >
> > I tend to think your way too, but after thinking
> > about it a bit I could see the other way too.
> > Abstract thinking involves such things
> > as symbolism.
> > Sybolism-->words-->verbal thinking-->linear thinking.
> > And yet this is false, because symbolism doesn't necessarly
> > imply linear thinking, and linear thinking doesn't imply
> > a lack of creativity either. Certainly verbal thinking
> > doesn't imply that because otherwise
> > no novels would be written.
> >
>
> There's a very wide gap between symbolism and words.
Yes, I realize that. Do realize that I was playing the devil's advocate sort
of here. This would not have been my way of thinking. It is somewhat tricky to
try to empathize with a mentality that is as foreign to me as this is, but
this seems to be roughly the way some people would see it. And I think I have
met people who would see it sort of that way, and I think Davis seems to think
sort of that way too. He is a sculptor and associates nonlinear thinking with
the concrete and the physical, because perhaps his nonlinear thinking is
concrete. My natural tendency is to make exactly the opposite associatian
perhaps because my nonlinear thinking is abstract, and associate concrete with
linear and abstract with nonlinear, but with a bit of stretch of the
imagination I can kind of see his side. In fact, although I don't profess to
be enough of an expert on neuroanotomy to make a statement like this with any
authority, my intuition kind of suspects--how's that for qualification--that
abstract thinking can't really exists without some input from the left
hemisphere, and a really strong right hemisphere orientation would indeed be
VERY concrete. From what you have written it sounds like you make the same
association that I do, but not everyone does.
Realize also that I don't intend the arrows as literal implications, but only
as rough associations along kind of the lines that it makes sense for the most
extreme of nonverbal thinkers to have trouble with any kind of symbols. And
indeed I have had the experience of having dyslexic algebra students who did
not seem to have the ability of working with symbols even to understand what
it meant to use a variable to represent a number. You on the other hand from
what you have written appear to be not at all that way. You appear from what
you have written to be reasonably comfortable with the abstract, so the
appropriate question relevant to this thread seems to be, how would you rate
your dyslexia? Clearly it can't be too bad, because you've managed to read and
respond to my message. Another possibly relevant question for you: Were words
that you couldn't associate a picture with like 'the' and 'a' ever a major
reading problem for you?
I just looked it up and read it. I'm not so sure about the connection to this
thread. Maybe I am missing something.
One thing is clear to me, though. I sure can identify with West's experiences
and thinking style a lot better than what I was reading from Davis. Now that
is a dyslexic that I feel on the same wavelength with. I had just about
exactly the same kinds of aptitudes as he did in school. He even had trouble
with the same kinds of sports as I did. It was totally uncanny reading that. I
was certainly much less extreme at least in the academic things in that I was
never at the bottom of my class in anything, but I was very mediocre and those
'easy' things that you learn in elementary school and didn't excel at anything
until I got to university. I suspect if I had lived someplace like Germany
where you have to qualify for gymasium at an early age based on the idea that
if you aren't really good at the 'easy' things you couldn't possibly have a
chance at handling the difficult university subjects, I would have had quite a
hard time making it. In fact actually this isn't totally theoretical, come to
think of it I knew someone like that when I was in Germany. She wasn't
admitted into the university because she didn't get a good enough grade in
dictation, and the whole business really horified me. Fortunately we were
never made to do dictation in school, because that I would have failed.
I would guess him to be fairly abstract. He was good at philosophy. Well, he's
certainly more dyslexic than I am, but he did learn to read on his own somehow.
EldonB123
>thread. Maybe I am missing something.
>
be assuming there's something in this short article that is just touched on,
because I am pretty familiar with West's work.
>One thing is clear to me, though. I sure can identify with West's experiences
>and thinking style a lot better than what I was reading from Davis. Now that
>is a dyslexic that I feel on the same wavelength with. I had just about
>exactly the same kinds of aptitudes as he did in school. He even had trouble
>with the same kinds of sports as I did. It was totally uncanny reading that.
>I was certainly much less extreme at least in the academic things in that I
was
>never at the bottom of my class in anything, but I was very mediocre and
>those 'easy' things that you learn in elementary school and didn't excel at
>anything until I got to university.
Shelley, I think it might be interesting to further compare your definitions of
"abstract" and "concrete" with those of some other people.
This could result in an interesting philosophical debate in itself, because the
medium of thought and the perceptions involved in the symbology used may not
determine the level of "abstration" so much as the way they are employed. You
are obviously a fairly verbal thinker (math being also a language of written
symbols), even though you describe your thought as non-linear.
Tom West in his book makes the example of people who make a mental 3-D chart or
graphic, for instance (like those pretty helical models made with Mathematica,
the computer program). Then they mush around the curves of the graphic in their
heads and extract numeric values and formulas from the new shape. This is how
Einstein thought, and he had a terrible time transating his conclusions into
written form.
This is a little like sculpting isn't it? So is it "conc rete" because it
deals with form? Or is it another variety of abstraction?
>I would guess him to be fairly abstract. He was good at philosophy. Well, he's
certainly more dyslexic than I am, but he did learn to read on his own somehow.
>
I think Tom West learned to read OK because he had an extremely supportive
family. Writing a long, scholarly book was an effort for him, though, and he
didn't do it without some assistance. He is extremely 3-D visual, and computer
graphics are his field.
Your comment about the German school system is interesting. As an aside on that
topic, German dyslexics are the ones who require a lot more
grammatical/syntactical work on sentence structure. When confused, they tend to
scramble entire words around within sentences more than students of English,
but have less trouble with word definitions. Seemingly this happens because
German is such a rigidly linear language. (In the sense that one must the verb
on the end of the sentence put.)
Students in other languages with more varied sentence structure options will
tend to mix up letters within words more frequently and make spelling/homynym
errors. And this despite the German convention of stringing together compound
words that are a mile long.
It is almost perverse in a sense that when something is considered "important"
in a particular language, that is exactly what people will tend to mix up when
they are confused. I suspect it may be at least partly due to conditioning
inflicted by educators who accentuate the negative by concentrating on
students' weaknesses rather than their strengths.
jip
>
> You on the other hand from what you have written appear
> to be not at all that way. You appear from what you have
> written to be reasonably comfortable with the abstract,
> so the appropriate question relevant to this thread seems
> to be, how would you rate your dyslexia?
>
I don't think dyslexics (like me) have problems with
abstract ideas. My theory is that dyslexics have a different
way of making asociations. The 'logical' steps I take to find
the answer of a problem, may seem illogical to the rest of
the world. And to memorise things I had to create my own
system which is very different to non-dyslexics.
I considder myself very dyslexic. Not because of my reading
or writing but because it made the person I am today.
Because I'm 23 and was diognosed when I was 12, I have already
developed a lot of my own methodes to overcome a lot of problems
caused by dyslexia. I know when it is useful to put energy
into something and when it is not.
I'm a trained reader and writer so that's not a big problem.
I don't care much about the few spelling errors I make as long
as I pass my school exams (which I didn't last year). When texts
(or tables) are really unreadable for me (because or the font
or the backgroundcoler) I don't read then or ask someone to read
it for me.
School is sometimes very hard for me. I still run into new
problems sometimes (I discoverd only last year that I made reading
and writing errors in mathemathical notations as wel. Before than
I had always thought that I just didn't understand it) Memorizing
facts is really difficult and frustrating. But because I enjoy
learning so much I am very motivated. School is just a big
challenge for me.
>
> Another possibly relevant question for you:
> Were words that you couldn't associate a picture with
> like 'the' and 'a' ever a major reading problem for you?
>
Words like 'the' and 'a' are to me from the same group as
'one', 'two', 'a lot' and 'that', 'those' and 'my' 'yours' etc.
(I don't know the English words for it) The are nessesary to
view the picture in the right context.
There is a huge difference between 'a computer' and 'that computer'
or 'your computer'. To visualize the meaning or 'your computer'
a picture of a (universal) computer alone isn't enough.
It's harder to memorise the difference between June and July.
In Dutch it is 'juni' and 'juli' this sounds almost the same.
When I name all the months of the year in Dutch, I generally
call both June and July: ju-i. I sometimes even forget if it is
the first ju-i or the second. To remeber this I have to use
the birthday of my nephew, on the last day of June:
When it is ju-i and my nephews birthday hasn't happend
yet the next month is the other ju-i. If it is ju-i and the
birthday was last month the next month will be August.
But this still doesn't end here, because how can I remember
if my nephews birthday was on the first or the second ju-i ?
Luckelly my boyfriends birthday is on the 30th of the other
ju-i. I can somehow remember that my nephews birthday is before
my boyfriends. I love birthday-parties but it's still not much fun
to write down the date in June or July. :-)
I think a lot of dyslexics would recognize this way of
remembering stupid illogical defenitions.
Pamela Fitzpatrick
I have been watching this exchange -- enjoying it actually. Something that
you wrote struck a heart string here for me <G>.
When I was learning to read (way long ago) I was placing as much importance
on each and every word. My daughter was doing the same thing *and*
struggling to make sense of that one particular word. When I taught her to
read them together "a cup", "the house" this all started to make sense. The
school was doing the phonics thing and *each* and *every* word was
analysised to death. So, she took it that each and every word has to have
the same level of importance attached to it. I still read this way too --
and most would assume that I would be a very slow reader -- that was
commented on by someone recently. I'm not a slow reader <G>. I'm very lucky
though. I figured out how to compensate for the "teach the averages"
instruction.
I will be working on the labels for the words here with my daughter this
next year. Verbs, adverbs, adjectives and the whole mess. I never learned
these...but found that when my daughter receives an explanation about a
words purpose, the confusion goes away. I don't believe any of this is
"officially" taught until around 6th grade -- for my daughter that would be
too late. It was for me.
And yes, she wants to learn this...I'm not forcing her to do something
because of a lack on my part <sheesh, hate to do those disclaimers for that
one person that will jump down my throat>.
-Pam
jip <ji...@geocites.com> wrote in article
<35D449F1...@geocites.com>...
> Shelley Walsh wrote:
Shelley Walsh
> Shelley, I think it might be interesting to further compare your definitions of
> "abstract" and "concrete" with those of some other people.
Well, I think I'm going to have to think about this. Actually I'm not sure if
I really understand what abstract is in the first place. But the first time I
ever was highly praised for anything in school seemed to have to do with it.
When I was in high school physics and was interested in finding out more about
relativity than was taught in our textbook, the teacher loaned me Feynmann's
Lectures. In spite of the fact that I had had less mathematics than many of
the people in the class, with a little work I could understand it. When I
asked why we could use that book in class, the teacher said that I could
understand it because I have a talent for abstract thinking that the others
didn't have. To this day I haven't the slightest idea of what was so abstract
about it. I certainly didn't do it by any kind of phenomenal 3D sort of
thinking. You know in spite of the awe we hold Einstein in, special relativity
is surprisingly simple. Once you have the daring to think the unthinkable, it
all comes out with fairly simple algebra from the Michelson Morely experiment.
The second time I was told I was good at abstract thinking was when I couldn't
figure out why everyone was falling apart at the seams when I took linear
algebra. I suppose it had something to do with dealing with an arbitrary
vector space rather than examples of them. It seems that there is a distinct
class of people are totally unbothered by this sort of thing, but the majority
totally freak out. And those you don't freak out can't figure out what the
fuss is all about, and the instructors all said that it had something to do
with abstraction. But perhaps they were mistaking formalism for abstraction
for all I know.
> This could result in an interesting philosophical debate in itself, because the
> medium of thought and the perceptions involved in the symbology used may not
> determine the level of "abstration" so much as the way they are employed.
What kind of surprises me here is how much pride people take in being
abstract.
>You
> are obviously a fairly verbal thinker (math being also a language of written
> symbols), even though you describe your thought as non-linear.
Tell that to my verbal GRE score. I'm kind of meta-verbal. I was always better
at foreign languages than at English. I didn't learn to enjoy writing until I
learned to do it in a foreign language, because then it became clear to me
that there was a conscious art to putting thoughts into words. I struggle a
lot for the right word to express my thoughts. I don't really know whether I
think linearly or nonlinearly, but again others seem to see me as thinking
nonlinearly. I doubt if anyone truly thinks totally one or the other. As far
as spatial things, I probably think better in 2D than in 3D and more
topologically than geometrically.
> Tom West in his book makes the example of people who make a mental 3-D chart or
> graphic, for instance (like those pretty helical models made with Mathematica,
> the computer program). Then they mush around the curves of the graphic in their
> heads and extract numeric values and formulas from the new shape. This is how
> Einstein thought, and he had a terrible time transating his conclusions into
> written form.
>
> This is a little like sculpting isn't it? So is it "conc rete" because it
> deals with form? Or is it another variety of abstraction?
From the little idea that I have about what abstract means, I would think
whether it comes from a 3D chart or graphic has little to do with its
abstractness, but certainly the fact that it is visual as apposed to verbal
doesn't make it abstract either. I think it is the mushing around that would
determine that. But I would say that for some funny reason it is precisely the
people who have fantastic senses of 3D geometry that are often the ones who
totally freak out in a linear algebra class, and one of these people who was a
very good friend of mine was far from being dyslexic.
> >I would guess him to be fairly abstract. He was good at philosophy. Well, he's
> certainly more dyslexic than I am, but he did learn to read on his own somehow.
> >
> I think Tom West learned to read OK because he had an extremely supportive
> family. Writing a long, scholarly book was an effort for him, though, and he
> didn't do it without some assistance. He is extremely 3-D visual, and computer
> graphics are his field.
But if he studied philosophy, then I was capable of dealing with intangibles.
I suppose this means that my definition of abstract has to do with the ability
to deal with things that are not accesible through the 5 senses. In this sense
being visual spatial neither implies nor contradicts it. And yet I must say as
I have hinted at above, that a lot of times it seems to have a way of getting
in its way. It's like this very vivid imagery for all its advantages is almost
too heavy to fly with.
jip
>
> When I taught her to read them together "a cup", "the house"
> this all started to make sense.
>
If you ever find the logic of where to put all those 'h's
in English words, or when to use 'ea', 'ee' or 'ie', 'au' or 'ou'
etc please tell me. :-)
Jeb
jip wrote in message <35D4CA53...@geocites.com>...
>Pam wrote:
>>
>>
>
>If you ever find the logic of where to put all those 'h's
>in English words, or when to use 'ea', 'ee' or 'ie', 'au' or 'ou'
>etc please tell me. :-)
>
I think it is more important to be able to read these sounds in words with
automaticity, than to be able to know which one to use in a specific
instance (spelling). Even non-dyslexic people have difficulty remembering
whether it is ei or ie or ee etc. (spelling) -- they use the dictionary.
If you know that ea, ee ei and ie all have the long e sound at least you are
able to find it by process of elimination and that is how it is done. - eg.
you look up neet and neat.
Structured phonetic teaching means that the sounds are introduced in a
specific order so they are easier to learn.
Anyway I am always looking up words for spelling now, because it is a few
years since I went to school. Angela
Shelley Walsh
> Tom West in his book makes the example of people who make a mental 3-D chart or
> graphic, for instance (like those pretty helical models made with Mathematica,
> the computer program). Then they mush around the curves of the graphic in their
> heads and extract numeric values and formulas from the new shape. This is how
> Einstein thought, and he had a terrible time transating his conclusions into
> written form.
Believe it or not, there is nothing really unusul about this. Everybody does.
Even experienced writers struggle for just the right word to express the
inexpressible. A little while ago I watched a movie about a certain famous
literary critic who taught at Cambridge. I can't think of his name right now,
but there is this lovely scene where his wife, also a literary critic finally
came to the realization of why she does it, and it was just that struggle to
express in this limited medium of language that which it doesn't express well.
There is an interesting thing that goes on particularly in mathematics and the
sciences, which is that practically nobody thinks when they are discovering
something the way they write it up. Why this is done is something that has
often puzzled me. This is also why in the humanities at conferences you often
see people reading a paper that they have written, but this is totally unheard
of in mathematics, because nobody would listen to it if they did. Instead they
make presentation about it, often with a lot of pictures and gesturing and a
much more informal spoken style that you would never get away with in a formal
write up.
An extreme example of this sort of thing is the development of calculus. In
some sense Newton's work on calculus wasn't properly written up until a couple
hundred years after his time. Orginally calculus was developed by using
numbers smaller than any number but larger than zero, called infinetesmals,
sort of ghosts of departed quantities, and in fact they were ridiculed by
theologists as just that. Mathematicians got all kinds of useful results using
these in spite of the fact that they were never properly defined. It wasn't
until toward the end of the 19th century before mathematicians managed to
formalize what they were doing, so it is not surprizing that this
formalization is precisely what drives mathematics students nuts when they try
to understand it. Some people think there is a great beauty to the
formalization, but the last time I taught calculus I started really wondering
if there isn't a better way to do things. Nonstandard analysis attempts to do
this but in the end it is even more complicated.
The subject of mathematical logic was born primarily out of long term
consequences of the standard formalization of calculus. There is a story that
a certain mathematician told an allegorical story about an old house full of
spider web and somebody coming to clean up and clear out the spider webs, but
the spiders cried out that they mussn't do that because it was the spider webs
that were keeping the house from falling down. In the allegory, the spiders
represent the logicians, and there are indeed times when I think that this
allegory does make some sense and that I too would like to clear out the
spider webs. But also to some extent they are holding up the building, because
those mathematicians before the formalization of calculus did make some really
wild mistakes too, that were only discovered after the formalization.
And also it wasn't really the teasing that from the theologians that prompted
mathematician to work out the foundations of calculus, it was the need to
teach. Yes, believe it or not those deltas and epsilons and the convoluted
logic with the sequence of three quantifiers really were invented to make
something simple enough that you can read it on your car speedometer easier to
understand. Sounds strange pretty, doesn't it? And yet the kind of intuition
for the subject that 18th c. mathematicians had for calculus and Einstein had
for his subject takes--yes, a certain knack for it--but probably more
importantly just plain a lot of experience and emmersion in it that the
average nonspecialist simply doesn't have the time for. The reality is that
students would complain as badly as the theologian did if you taught them
about the ghosts of departed quantities. Perhaps dyslexics can find a better
way. And yet if they could have, why with all the influence that Einstein had
didn't he?
EldonB123
the history of math, and my mind is boggled. I will be thinking about your post
for the next five years, and I'm not kidding. This is the kind of thing that
makes newsgroups intersting.
Frank
^ Boy, you sure gave me something to think about. Shelley, you definitely know
^ the history of math...
That message didn't show up on my server, could someone please reply to it and
leave the entire message intact?
Thanks,
Frank
EldonB123
>and
>leave the entire message intact?
>
>Thanks,
>
>Frank
>
incredibly lousy 3.0 news reader. However,. here is a recent exchange between
Shelley and me...my reply to excerpts from an e-mail I just received from her,
which I assume she doesn't mind me posting. --Eldon
-------------------------
In a message dated 98-08-24 10:36:38 EDT, Shelley writes:
<< One of reasons I think we get confused about what 'abstract' means is that
the
word has been contaminated by its specific meaning associated with art to
suggest something having to do with forms and geometry. But even with respect
to art, this is a corruption of its original meaning. The orginal idea behind
abstract art was an isolating out or abstracting of certain chosen aspects of
a
picture, like if you take an ordinary realistic scene and reduce it down to
its horzontal and vertical lines, or represent its colors broken up into
primary colors. When you take this sort of thing to the extreme, the orginal
picture is no longer recognizable and you get something like Mondrian's
'Composition in Red, Yellow, and Blue'. Taken to the furthest extreme maybe
the ultimate in abstract art would be a blank sheet of paper--it's been done
in music, Cage's 4 minutes and 33 seconds (4 minutes and 33 seconds of
silence). But even a blank sheet of paper is limiting because you are
restricted in your imagination to art that will fit on that piece of paper,
and 4'33" is certainly limiting in specifying the time, so really the ultimate
in abstract art is simply to have something of totally arbitrary form to
represent all art. But we already have such a thing. It is the word 'art.'
-------------------------------------------------------
Correct. There was a funny play a few years ago--I don't remember the name, but
it was big in London and Paris--about a man who had bought a white-painted
canvas as the ultimate work of abstract art. Most of the play was an argument
about whether it really was art, and whether he had been duped. Of course, he
had bought it as an investment, which added to the dilemma. It was a pretty
funny concept--everyone arguing about whether it was "art" or just something
someone could have done with a paint roller.
It seems to me that abstraction is at the very core of language and symbolic
thinking, and I am not so sure if they really can be totally separated.
Even for a word that represents a concrete thing like a chair, to
think of the word 'chair' or perhaps more accuately the concept behind it, can
never really be the same as picturing a chair, because to picture a chair with
any kind of accuracy or detail, you must choose a specific chair to picture,
and once you have done that, the generality of the word is gone. I have a
vague recollection from when I was a small child imagining some specific kind
of chair, either an overstuffed sort of living room one or a simple straight
back one, I'm not sure which, and then having a slight amount of trouble with
the fact that the other kind was a chair as well. When I now think about what
I imagine when I hear or see the word chair, I find it is mostly a very
simplified version of a chair that looks like an unrounded letter 'h'. When I
think about why I visualize it like that, I am inclined to think that this
isn't just because I am too bad an artist to draw it better. It is
also because that shape is more general and accomodates itself better to all
chairs. Once you have such an image for chair, though, you are right on the
path to forming language and thinking verbally. In fact isn't that just about
exactly the way written languages were originally formed in the first place? I
seem to recall learning that even the letters used for writing our language
originally came from simplifications, or abstractions of pictures.
------------------------------------------------
Yes, all languages are thought to have derived from pictographs. In some of
them, such as Egyptian and the ancient Mayan and Aztec langauages, phonic word
play has been detected, which would have eventually perhaps led to a phonetic
language.
Would we be better off if we had stayed closer to the pictures like Chinese
did? Maybe in some ways but not in others, because even that 'h' shape that I
imagine for a chair is prejudicial. If I were to form my own written language
that used a straightened 'h' to represent 'chair', and someone were to invent
a new kind of chair, like for example that one that you kneel on an lean into
that is supposed to be better for your back, would it not be possible that my
symbolism would cause me to be less openminded about the invention? The
abstraction here is the process of forming the concept of 'chair' apart from
any
individual chair. It is a process of forming a group of things with something
in common.
---------------------------------------------------------------
It is also a matter of convenience. Chinese, Japanese and the other mainly
pictographic languages with a few thousand characters are really hard to use on
a keyboard. You have to start with a root word and go down a tree of meanings
to get to the particular one you want. Their mechanical typewriters were really
a mess--they would go pick up loose pieces of type from bins, strike a letter
and then replace the type.
Perfect abstraction is by means the holy grail, though. Look at what it does
to art. Cage's 4'33" could only be done once. And speaking of the holy grail
reminds
me of an overuse of abstraction that really annoyed me. Joseph Campbell was
speaking about myth and spoke of Tristan merely in terms of something like
achetypal hero figure. Yes the common elements of the heroic myth is an
interesting and useful thing to do. But Tristan of all heros, to see merely
his similarity with other heros is to miss so much. It is to miss some really
individual features that say something about the culture that created him,
namely that he was a hero artistically as well as a warrior.
-- >>
---------------------------------------------------------
An interesting new art form is one I saw as a cover story in Time or Newsweek
several months ago, and my stupid memory won't remember the name of the artist.
However, this person basically makes a face portrait out of a whole bunch (as
in a thousand or more) of pictures. They are scanned by a computer program
which organizes their respective colors and composition to turn them into
individual little pixels that might be 1/4" square. Then the little pictures
are cropped and arranged to form pixels. They are used to form the big picture,
which looks photographic from a distance. While closeup, you can still see the
litttle ones. It's a mind-boggling effect of representation.
Eldo...@aol.com
Shelley Walsh
>
> >That message didn't show up on my server, could someone please reply to it
> >and
> >leave the entire message intact?
> >
> >Thanks,
> >
> >Frank
> >
> Frank, I don't know where that exact exchange went, and I am hampered by AOL's
> incredibly lousy 3.0 news reader. However,. here is a recent exchange between
> Shelley and me...my reply to excerpts from an e-mail I just received from her,
> which I assume she doesn't mind me posting.
No, not at all. I messed up with Netscape's response button. I meant to post
that to the newsroup. I noticed the mistake later and posted another one, but
somehow it didn't get through. So here is the message again in its entirety so
that you know what the response is about.
EldonB123 wrote:
>
> Boy, you sure gave me something to think about. Shelley, you definitely know
> the history of math, and my mind is boggled. I will be thinking about your post
> for the next five years, and I'm not kidding. This is the kind of thing that
> makes newsgroups intersting.
Thanks. That made my day. About the knowledge of history of math, I don't
really that well, but I have heard a bit of lore from my time spent as a math
grad student. Don't trust it to be perfectly exact, it's just stuff that I
remember from repeated tellings to students. But to quote Scott Beach, "A
story doesn't have to be true to be good."
Here's another response to keep you busy.
EldonB123 wrote:
> Shelley, I think it might be interesting to further compare your definitions of
> "abstract" and "concrete" with those of some other people.
>
> This could result in an interesting philosophical debate in itself, because the
> medium of thought and the perceptions involved in the symbology used may not
> determine the level of "abstration" so much as the way they are employed. You
> are obviously a fairly verbal thinker (math being also a language of written
> symbols), even though you describe your thought as non-linear.
This verbal/pictorial, linear/non-linear dichotomy which has at least the
potential of becoming a they/we sort of thing kind of bothers me. When I ask
myself whether I think in words or in pictures I end up finally coming to the
conclusion that I think in thoughts. There are those who would say this is not
possible and they we need some kind of thing to associate with those thoughts.
There may be some truth to that, but it seems that both words and pictures are
only imperfect models, and to make full use of one's thinking ability one
cannot restrict oneself to one or the other. Most really great minds--and I've
spent too much time as a small fish in a big pond to claim to be one of them--are
flexible in their way of thinking and use every resource they can find. Words
and pictures are not the only ways that thoughts can be expressed either, what
about music or motion or who knows what else?
Somebody in this newsgroup once suggested that Richard Feynmann might be
dyslexic because he seems to think so visually. Well, I have met the man, and
I have heard him speak, and I have read some of his writings, and I have seen
no lack of verbal ability there. He writes beautifully. And I have an
interesting story to tell about Feynmann too. An English teacher who I knew
used to know him fairly well when she was a student at I believe Long Beach
State University--and now this isn't quite making sense because Long Beach and
Cal Tech are at opposite sides of Los Angeles, so maybe it wasn't Long Beach.
But anyway there was a group of English people and Physics people who got
together regularly for drinks and socializing and they played various games.
And of course the physics crowd always stomped the English crowd in chess and
the English crowd always stomped the physics crowd in scrabble. All except
Feynman-- who beat everybody at everything.
There are many things that pictures express very well, but the evidence of
Davis' trigger words suggests there are other things that words express
better. When I look over this list abstraction, seems to be what these words
have in common. Abstraction in its root word meaning means draw or pull away.
Think of the similar word, extract, which is more commonly used in its purely
physical sense. When you extract a tooth, for example you pull it out. Davis'
trigger words are for the most part words that are difficult to make sense of
outside of their sentential context, that is difficult to abstract their
abstract meaning.
Generality is at the essence of abstraction. It is interesting to note that
the word 'everything' is on the list. I have been thinking lately about
whether I picture anything when I think of the word 'everything', and actually
I think I do. When I think of 'everything' I imagine some kind of picture with
a bunch of rounded squiggly lumps, and it is a real wide picture with some
really big things in it. But at the same time I know full well that no picture
can possibly represent everything, so I make the picture deliberately fuzzy, I
suppose to make sure that I don't forget that. This, of course, is all going
on on a level that I am not normally conscious of and it takes a good amount
of effort to bring it into consciousness, so I'm not really sure that I have
it right.
One of reasons I think we get confused about what 'abstract' means is that the
word has been contaminated by its specific meaning associated with art to
suggest something having to do with forms and geometry. But even with respect
to art, this is a corruption of its original meaning. The orginal idea behind
abstract art was an isolating out or abstracting of certain chosen aspects of a
picture, like if you take an ordinary realistic scene and reduce it down to
its horzontal and vertical lines, or represent its colors broken up into
primary colors. When you take this sort of thing to the extreme, the orginal
picture is no longer recognizable and you get something like Mondrian's
'Composition in Red, Yellow, and Blue'. Taken to the furthest extreme maybe
the ultimate in abstract art would be a blank sheet of paper--it's been done
in music, Cage's 4 minutes and 33 seconds (4 minutes and 33 seconds of
silence). But even a blank sheet of paper is limiting because you are
restricted in your imagination to art that will fit on that piece of paper,
and 4'33" is certainly limiting in specifying the time, so really the ultimate
in abstract art is simply to have something of totally arbitrary form to
represent all art. But we already have such a thing. It is the word 'art'
It seems to me that abstraction is at the very core of language and symbolic
thinking, and I am not so sure if they really can be totally separated.
Even for a word that represents a concrete thing like a chair, to
think of the word 'chair' or perhaps more accuately the concept behind it, can
never really be the same as picturing a chair, because to picture a chair with
any kind of accuracy or detail, you must choose a specific chair to picture,
and once you have done that, the generality of the word is gone. I have a
vague recollection from when I was a small child imagining some specific kind
of chair, either an overstuffed sort of living room one or a simple straight
back one, I'm not sure which, and then having a slight amount of trouble with
the fact that the other kind was a chair as well. When I now think about what
I imagine when I hear or see the word chair, I find it is mostly a very
simplified version of a chair that looks like an unrounded letter 'h'. When I
think about why I visualize it like that, I am inclined to think that this
isn't just because I am too bad an artist to draw it better. It is
also because that shape is more general and accomodates itself better to all
chairs. Once you have such an image for chair, though, you are right on the
path to forming language and thinking verbally. In fact isn't that just about
exactly the way written languages were originally formed in the first place? I
seem to recall learning that even the letters used for writing our language
originally came from simplifications, or abstractions of pictures.
Would we be better off if we had stayed closer to the pictures like Chinese
did? Maybe in some ways but not in others, because even that 'h' shape that I
imagine for a chair is prejudicial. If I were to form my own written language
that used a straightened 'h' to represent 'chair', and someone were to invent
a new kind of chair, like for example that one that you kneel on an lean into
that is supposed to be better for your back, would it not be possible that my
symbolism would cause me to be less openminded about the invention? The
abstraction here is the process of forming the concept of 'chair' apart from any
individual chair. It is a process of forming a group of things with something
in common. It is certainly possible to do this without using symbols, because
the symbols only come when you name it, but naming concepts is a very useful
mental tool. What the name is doesn't really matter, but the fact that you use
a name for it does, because it turns a class of objects into a single entity
and allows generalization.
Perfect abstraction is by means the holy grail, though. Look at what it does
to art.
Cage's 4'33" could only be done once. And speaking of the holy grail reminds
me of an overuse of abstraction that really annoyed me. Joseph Campbell was
speaking about myth and spoke of Tristan merely in terms of something like
achetypal hero figure. Yes the common elements of the heroic myth is an
interesting and useful thing to do. But Tristan of all heros, to see merely
his similarity with other heros is to miss so much. It is to miss some really
individual features that say something about the culture that created him,
namely that he was a hero artistically as well as a warrior.
--
Shelley Walsh
Eldon, I was just thinking about this on the way to work, and I think I see
the beginnings of an answer to my puzzle. It has to do with what you said
earlier and apologized for its Freudian nature, getting stuck in an earlier
stage of development. Stuck is a very bad word for it, because it sounds too
negative and it is also far too strong, but for now I can think of a better
one.
I'm sure it is much more complicated than this, but perhaps the key is that we
develop our language skills in somewhat of a similar way as this historic
development. In the beginning we all think nonverbally, and purely nonverbally
without the category making of abstraction. The development of the abstraction
that allows us to think verbally is a stage between thinking verbally and
thinking nonverbally/visually/sensually, sort of a proto-verbal thinking.
People get stuck at the purely nonverbal stage think in a VERY different way
from people you get stuck at the proto-verbal stage. They are maybe even
stages where they basic thinking style is essentially oposite in nature. Stuck
is bad word, because it isn't really stuck, because there is further
development at that stage that those who go on probably don't get. Once
'normal' people have learned their language skills, they lose most of their
visual and their abstract skills. This would explain why many people who are
good at abstraction are mildly dyslexic, and yet why at least some dyslexics
seem to be totally abstraction disabled. They are stuck in the purely
nonverbal stage are we are stuck in the proto-verbal stage. It would also
explain why I am better than most nondyslexic people at foreign language in
spite of the fact that many dyslexics complain of having trouble with them. I
have retained skills from the language attaining phase rather than the
pre-language phase, so my elements of language are there but not as cemented
to my native language as much as most people's are.
Again, I'm sure the whole thing is a lot more complicated than this, I'm
talking totally off the top of my head with virtually no knowledge about how
language acquisition works, so perhaps someone with more knowledge can fill in
the details
Shelley Walsh
>They are stuck in the purely
> nonverbal stage are we are stuck in the proto-verbal stage.
Further to this, apart from any right or wrong theories about language
development, it seems that this goes along with what we--or at least I--think
of abstract thinking as the least tangible--or perhaps more accurately the
most difficult kind of thinking to communicate--because it falls between the
crack between visual and verbal. For visual thinking there is the picture that
can be drawn or sculpted, for verbal thinking there is the word that can be
spoken or written, in the crack there is only imperfect grasping at straws
taken form both realms. Once you have the word it becomes concrete as in the
opening line of the gospel according to John, "In the beginning there was the
word and the word was made flesh." Once the word is made flesh visual thinkers
and verbal thinkers have a lot more in common than abstract thinkers, who fall
between the cracks.
This could explain why mild dyslexic can think in a seemingly opposite style
from severe dyslexics. People who live in the crack are use to dealing with
blanks, because they live with them all of the time. They even get to the
point of finding them fun. Blanks are where all is possible.