Re: The abstract realm that lies between the 9x13 pan and the 9x9 pan
Joan
> > What or where is this realm which is mostly indirectly connected to the world I know?This is really neat, Diane.
>
> This realm is in the recipe that makes a 9x13" pan and you have a 9x9" pan; it
> connects the two. It's in the difference between fixed expenses and variable expenses
> in running a household or business.
It seems that the wonder of many things lies somehow in what seems to be empty space. Whether the space is between differently sized pans or people, it's in the space that our imagination and creativity work.
Decorators work on the space between objects arranged on a table or in a room; painters with the space surrounding images on a canvas.
When I perform, either in a play or reading, or when I used to dance, there's an experience I've always had, usually after plenty of rehearsal, when I know we're in a good place.....All of a sudden there's a sensation of there being air between the words or movements and people. It just feels airy. And that's a good show.
Joan
[email protected]
<< Decorators work on the space between objects arranged on a table or in a
room; painters with the space surrounding images on a canvas. >>
In music, the silences and the lack of harmony are as much a part of the
music as the busy runs and big loud chords.
Because of school and such traditions (music lessons) we get the prejudicial
idea that once one has "completed" a step or level, they should never look
back, but keep on moving upward and onward, to harder, bigger, more complex
things. Things with less airy space. More solid/hard.
The ideas of baby books and "too easy" and "beginning things" are a danger to
unschoolers too. To prevent falling into the same vortex, we shouldn't
discourage kids from revisiting their wonder at an elegant, simple beginning
piece, whether it's music or magic or math. Just because a child can make a
cake from scratch doesn't mean she should be ashamed ever after for making a
bowl of ramen. One of the principles of spirituality (Eastern and Western
and probably all outside those two big-to-us groups) is to be present in the
moment, to dedicate small actions to God, to be mindful.
Sometimes mindfulness works best with simple tasks. So priests and nuns
clean floors and woodwork, they pull weeds or arrange sand and rocks. They
don't say "Okay, I've mastered that task; I can only do hard things I don't
know how to do well."
It's okay for a teenager or an adult to play with arithmetical patterns and
see how fun it is that "times nine" makes a pattern where the numbers add up
to nine. It's more than okay. It's okay for someone to make a mobius strip
even though it's not news to him or her.
Before someone asks, here:
http://www.theriver.com/mobiusjewelry/tms.html
And don't be surprised: It talks about "sacred geometry," among other
interesting things.
Sandra
room; painters with the space surrounding images on a canvas. >>
In music, the silences and the lack of harmony are as much a part of the
music as the busy runs and big loud chords.
Because of school and such traditions (music lessons) we get the prejudicial
idea that once one has "completed" a step or level, they should never look
back, but keep on moving upward and onward, to harder, bigger, more complex
things. Things with less airy space. More solid/hard.
The ideas of baby books and "too easy" and "beginning things" are a danger to
unschoolers too. To prevent falling into the same vortex, we shouldn't
discourage kids from revisiting their wonder at an elegant, simple beginning
piece, whether it's music or magic or math. Just because a child can make a
cake from scratch doesn't mean she should be ashamed ever after for making a
bowl of ramen. One of the principles of spirituality (Eastern and Western
and probably all outside those two big-to-us groups) is to be present in the
moment, to dedicate small actions to God, to be mindful.
Sometimes mindfulness works best with simple tasks. So priests and nuns
clean floors and woodwork, they pull weeds or arrange sand and rocks. They
don't say "Okay, I've mastered that task; I can only do hard things I don't
know how to do well."
It's okay for a teenager or an adult to play with arithmetical patterns and
see how fun it is that "times nine" makes a pattern where the numbers add up
to nine. It's more than okay. It's okay for someone to make a mobius strip
even though it's not news to him or her.
Before someone asks, here:
http://www.theriver.com/mobiusjewelry/tms.html
And don't be surprised: It talks about "sacred geometry," among other
interesting things.
Sandra
[email protected]
The picture they're talking about below, Escher's transformation from birds
to fish, is at the website listed at the bottom. I found this following
links from the mobius strip page, and I'll probably get Marty the t-shirt for
Christmas, but the commentary there was so much like what's been being
discussed here I had to share it, mostly because of this line: "Any
scientist who uses a print to illustrate a theory selects one or more
elements from the print that are analogous to components of the theory, and
in this way the print becomes a model for the theory."
That, and the title of this thread, and the idea that between the fish are
the birds. Where birds aren't, fish are.
---------------------------
"In the horizontal center strip there are birds and fish equivalent to
eachother. We associate flying with sky, and so for each of the black birds
thesky in which it is flying is formed by the four white fish which
encircleit. Similarly swimming makes us think of water, and therefore the
fourblack birds that surround a fish become the water in which it swims.
M.C.E.
Reprinted from the text M.C. Escher - The Graphic Work; with the kind
permission of Benedikt-Taschen Publishers.
------------------------------------------------------------------------
This print has been used is physics, geology, chemistry, and in psychology
for the study of visual perception. In the picture a number of visual
elements unite into a simple visual representation, but separately each forms
a point of departure for the elucidation of a theory in one of these
disciplines.
The basis of this print is a regular division of the plane consisting of
birds and fish. We see a horizontal series of these elements - fitting into
each other like the pieces of a jigsaw puzzle - in the middle, transitional
portion of the print. In this central layer the pictorial elements are equal:
birds and fish are alternately foreground or background, depending on whether
the eye concentrates on light or dark elements. The birds take on an
increasing three-dimensionality in the upward direction, and the fish, in the
downward direction. But as the fish progress downward they gradually lose
their shapes to become a uniform background of sky and water, respectively.
We can think of a number of paired concepts applying to this picture:
light-dark, top-bottom, flat-rounded, figure-background, interlocking
pictorial elements-independent pictorial elements, geometric
structure-realistic form; and, with respect to the subject of the print,
birds-fish, sky-water, immobility-movement. Any scientist who uses a print to
illustrate a theory selects one or more elements from the print that are
analogous to components of the theory, and in this way the print becomes a
model for the theory. C.H.A. BROOS
Reprinted from the text of M.C. Escher - 29 Master Prints; with the kind
permission of Harry N. Abrams, Inc., Publishers
http://www.worldofescher.com/gallery/SkyAndWater.html
to fish, is at the website listed at the bottom. I found this following
links from the mobius strip page, and I'll probably get Marty the t-shirt for
Christmas, but the commentary there was so much like what's been being
discussed here I had to share it, mostly because of this line: "Any
scientist who uses a print to illustrate a theory selects one or more
elements from the print that are analogous to components of the theory, and
in this way the print becomes a model for the theory."
That, and the title of this thread, and the idea that between the fish are
the birds. Where birds aren't, fish are.
---------------------------
"In the horizontal center strip there are birds and fish equivalent to
eachother. We associate flying with sky, and so for each of the black birds
thesky in which it is flying is formed by the four white fish which
encircleit. Similarly swimming makes us think of water, and therefore the
fourblack birds that surround a fish become the water in which it swims.
M.C.E.
Reprinted from the text M.C. Escher - The Graphic Work; with the kind
permission of Benedikt-Taschen Publishers.
------------------------------------------------------------------------
This print has been used is physics, geology, chemistry, and in psychology
for the study of visual perception. In the picture a number of visual
elements unite into a simple visual representation, but separately each forms
a point of departure for the elucidation of a theory in one of these
disciplines.
The basis of this print is a regular division of the plane consisting of
birds and fish. We see a horizontal series of these elements - fitting into
each other like the pieces of a jigsaw puzzle - in the middle, transitional
portion of the print. In this central layer the pictorial elements are equal:
birds and fish are alternately foreground or background, depending on whether
the eye concentrates on light or dark elements. The birds take on an
increasing three-dimensionality in the upward direction, and the fish, in the
downward direction. But as the fish progress downward they gradually lose
their shapes to become a uniform background of sky and water, respectively.
We can think of a number of paired concepts applying to this picture:
light-dark, top-bottom, flat-rounded, figure-background, interlocking
pictorial elements-independent pictorial elements, geometric
structure-realistic form; and, with respect to the subject of the print,
birds-fish, sky-water, immobility-movement. Any scientist who uses a print to
illustrate a theory selects one or more elements from the print that are
analogous to components of the theory, and in this way the print becomes a
model for the theory. C.H.A. BROOS
Reprinted from the text of M.C. Escher - 29 Master Prints; with the kind
permission of Harry N. Abrams, Inc., Publishers
http://www.worldofescher.com/gallery/SkyAndWater.html
Dan Vilter
> In music, the silences and the lack of harmony are as much a part of theTheatre can work in the same way.
> music as the busy runs and big loud chords.
A good friend of mine asked me about Harold Pinter's Homecoming - what I
thought of it. She had seen a production of it I didn't like it. If I
remember correctly, it is a story of emotional violence and sexual power
struggle between a mother and son. I was at a loss to explain that the
substance of the play is in what is NOT there. That characters are often
not people, that people are often just ideas or emotion or instincts. The
actors stand there (like the numbers in an equation) delivering carefully
crafted dialogue that has been reduced to only the necessary syllables,
empty of emotion, that is the reality of the situation that isn't physically
there. The son may be interpreted as the mother's sexual and emotional
dysfunction. Her life might exist outside the characters and time we see on
the stage. That the world happens in the [pause] indicated in the script.
It felt easier to explain this with something as abstract as math.
I think Pinter would define the world as existing *between* the 9x9 and the
9x13 pans
In 1958 Pinter wrote the following:
"There are no hard distinctions between what is real and what is unreal, nor
between what is true and what is false. A thing is not necessarily either
true or false; it can be both true and false."
I think once you get past the computational functions Pam equates to
phonics, math can be a Pinter play.
And Sandra, I didn't do drugs in the 60s. <G>
And 2+2 doesn't necessarily add up to 4.
-Dan Vilter
[email protected]
<< And 2+2 doesn't necessarily add up to 4.>>
The first time I used this sort of math language on Marty, he said "two
WHAT?" I remember he was really little, and he had no interest in the idea
that you could add two numbers without it being numbers of actual things.
And it makes sense. One army plus one army is...
Well are they on the same side? If so, it's one bigger army. If not, it
could be a battle.
Is there enough food for them all? If not, it might be anarchy.
I argued with everyone here for a week (and lost to the mathies, and won to
the verbals) that 0x0 is "something."
Keith said "that's set theory." I said fine.
We'd been through all the other zero factors.
zero plus one is one
zero minus one is zero or negative one (depending if it was money or not)
something divided by zero is not divided, it's whole.
zero times a something is nothing.
zero times a nothing must be a something. You have NO nothing, therefor
something.
It is the stuff of headaches.
Sandra
The first time I used this sort of math language on Marty, he said "two
WHAT?" I remember he was really little, and he had no interest in the idea
that you could add two numbers without it being numbers of actual things.
And it makes sense. One army plus one army is...
Well are they on the same side? If so, it's one bigger army. If not, it
could be a battle.
Is there enough food for them all? If not, it might be anarchy.
I argued with everyone here for a week (and lost to the mathies, and won to
the verbals) that 0x0 is "something."
Keith said "that's set theory." I said fine.
We'd been through all the other zero factors.
zero plus one is one
zero minus one is zero or negative one (depending if it was money or not)
something divided by zero is not divided, it's whole.
zero times a something is nothing.
zero times a nothing must be a something. You have NO nothing, therefor
something.
It is the stuff of headaches.
Sandra
zenmomma *
>When people say, "My son just sits and stares out the window, unschoolingThis brings to mind Ch. 11 of the Tao Te Ching:
>isn't working" it's hard to explain that this is unschooling, as much as
>reading or writing or building or breathing is, no more, no less, and that
>it's working just fine.
Thirty spokes share the wheel's hub;
It is the center that hole that makes it useful.
Shape clay into a vessel;
It is the space within that makes it useful.
Cut doors and windows for a room;
It is the holes which make it useful.
Therefore benefit comes from what is there;
Usefulness from what is not there.
After I read this the first time I felt like I had been blinded by the
light. I'll admit I had never thought about it that way before. Now it all
makes perfect sense and I can't understand how I missed it before. It's the
space between. The German's call it zwischenraum. In Zen painting they refer
to the impotance of negative space. It all serves a purpose.
~Mary
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Cindy
SandraDodd@... wrote:
70s book!
--
Cindy Ferguson
crma@...
>Have you read _Godel, Escher, Bach : An Eternal Golden Braid_? It's a
> The picture they're talking about below, Escher's transformation from birds
> to fish, is at the website listed at the bottom. I found this following
> links from the mobius strip page, and I'll probably get Marty the t-shirt for
> Christmas, but the commentary there was so much like what's been being
> discussed here I had to share it, mostly because of this line: "Any
> scientist who uses a print to illustrate a theory selects one or more
> elements from the print that are analogous to components of the theory, and
> in this way the print becomes a model for the theory."
>
70s book!
--
Cindy Ferguson
crma@...
Tia Leschke
>I have it and have started it several times. So far that's as far as I've
>Have you read _Godel, Escher, Bach : An Eternal Golden Braid_? It's a
>70s book!
gotten. One of these times I'm going to get it out again.
Tia
Tia Leschke leschke@...
On Vancouver Island
********************************************************************************************
It is the answers which separate us, the questions which unite us. - Janice
Levy