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## symmetry, asymmetry, mathematics

### elizabeth priddy on sat 18 dec 99

mathematics is at the heart of this subject.

If you can dredge up the parabola from your
youth, you will recognize your pots cut in half.

all symmetrical pots are based on parabolas.

now we get to harder math, asymmetry. Calculus
and piecewise fuctions describe the non regular
forms. And Chaos theory can describe the
amorphous.

Beauty is in the capacity of the mind of the
beholder, to coin a phrase.

If the mind has the capacity for a parabola,
the golden mean, the basics of radial or
bi-lateral symmetry, that is all they will find
beautiful and desirable.

If they have it in their consciousness to enjoy
the mathematical options that are glorified in
irregular forms, then they will love those too.

Not everyone can appreciate these works and very
rare individuals can describe it with math.
And you don't need to know the math to know and
appreciate the beauty it delineates.

Form is mathematics. And intuition about the
math is all it takes to appreciate beauty.

Unfortunately, they don't grade on the
intuition, or I would have become a
mathemetician.

Instead I am a philosopher, a lover of beauty, not a quantifier.

---
Elizabeth Priddy

email: epriddy@usa.net
http://www.angelfire.com/nc/clayworkshop
Clay: 12,000 yrs and still fresh!

On Fri, 17 Dec 1999 16:56:54 I.Lewis wrote:
>----------------------------Original message----------------------------
>------------------
>First, some questions. Are spirals symmetrical? If they are, what are their
>symmetries? If not, why do they attract our attention so strongly? Why do they
>occur so frequently in the natural world?
>
>Perhaps care should be taken to distinguish between meanings before forming
>value judgements or assigning feelings of personal prejudice by calling things
>which have been disfigured, deformed or mutilated Asymmetric.
>
>Symmetry is concerned with measures and proportions which relate to each other
>in ways which achieve harmony and balance. It is a word which suggests equality
>regularity, correspondence, conformity, and uniformity. Moreover, symmetry
>asserts mathematical rules encompassing reflection, rotation, radiation, patter
>and periodicity.
>
>By way of contrast, asymmetry is in opposition to these things. Asymmetry
>denotes relationships which cannot be readily quantified, which are
>disproportionate, may be devoid of rhythm, do not repeat, coordinate or map.
>They are often converge in on themselves or diverge to infinity.
>
>Neither rightness nor wrongness should be assigned to either symmetry or
>asymmetry. Do not equate them with beauty or ugliness. They embody no sense of
>aesthetic. They serve us in processes of ideation. Their value comes from the
>way we employ them when we arrange conceptual, formal and structural elements o
>design. I would like to believe they are elemental structures which are made
>manifest when we make our artefacts.
>
>Ivor Lewis. Inquisitive about Art and Design. Knowledgeable about Salt, Ice and
>Water.
>

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Share what you know. Learn what you don't.

### Vince Pitelka on sun 19 dec 99

>mathematics is at the heart of this subject.

This strikes me as a very strange response. Mathematics has nothing to do
with this subject. I suppose it is possible to interpret asymmetry and
symmetry in mathematical terms, but that is after the fact.

>all symmetrical pots are based on parabolas.

Huh? What about the cylinder? There are plenty of beautiful, symmetrical
pots that do not contain parabolas.

>And you don't need to know the math to know and
>appreciate the beauty it delineates.

The math does not delineate the beauty, thank god.

>Form is mathematics. And intuition about the
>math is all it takes to appreciate beauty.

Sorry to be so contrary, but this is indeed a strange interpretation. As I
said, mathematics may provide a way of interpreting form, but the form was
there before the math. Intuition about math has nothing to do with
appreciating beauty unless you happen to love math.

Best wishes -
- Vince

Vince Pitelka
Home - vpitelka@DeKalb.net
615/597-5376
Work - wpitelka@tntech.edu
615/597-6801 ext. 111, fax 615/597-6803
Appalachian Center for Crafts
Tennessee Technological University
1560 Craft Center Drive, Smithville TN 37166

### Barney Adams on mon 20 dec 99

Hi,
>From what I know of the recent study (which isn't alot) They have
determined a way to calculate a value of a person's face or body
to measure the overall symmetry. The lower the value the more
symmetrical. The idea is that the symmetrical features are heathier
and thus the more symmetrical a mate looks the chances of producing
strong heathy offspring.

Barney

Vince Pitelka wrote:

> ----------------------------Original message----------------------------
> >mathematics is at the heart of this subject.
>
> This strikes me as a very strange response. Mathematics has nothing to do
> with this subject. I suppose it is possible to interpret asymmetry and
> symmetry in mathematical terms, but that is after the fact.
>
> >all symmetrical pots are based on parabolas.
>
> Huh? What about the cylinder? There are plenty of beautiful, symmetrical
> pots that do not contain parabolas.
>
> >And you don't need to know the math to know and
> >appreciate the beauty it delineates.
>
> The math does not delineate the beauty, thank god.
>
> >Form is mathematics. And intuition about the
> >math is all it takes to appreciate beauty.
>
> Sorry to be so contrary, but this is indeed a strange interpretation. As I
> said, mathematics may provide a way of interpreting form, but the form was
> there before the math. Intuition about math has nothing to do with
> appreciating beauty unless you happen to love math.
>
> Best wishes -
> - Vince
>
> Vince Pitelka
> Home - vpitelka@DeKalb.net
> 615/597-5376
> Work - wpitelka@tntech.edu
> 615/597-6801 ext. 111, fax 615/597-6803
> Appalachian Center for Crafts
> Tennessee Technological University
> 1560 Craft Center Drive, Smithville TN 37166

### elizabeth priddy on mon 20 dec 99

Math isn't worth fighting over, really.

Some people, philosophers to be specific,
believe that beauty can actually be quantified.

Its an odd notion, to be sure, but it is none
the less a real thought.

and its relationship to symmetry and asymmetry.

Like it or not, math is one way to describe and
approach the subject.

And a cylinder is a piecewise function, which I
mentioned before, and is of questionable beauty
in and of itself.

A blind mathemetician, when addressing a group
of formulae will look for balance and symmetry
to locate the beauty. It is an inherent beauty,
a rational beauty, not a superficial one. In
that there lies the point. For all the
superficial beauty of the piece, when you pick
it up, if the balance is off and it feels "top
heavy" of "off" in some other way, you will
notice, and a mathematical model of the piece
will have noted it also.

You don't have to know math to feel the balance
of a piece, but you and the math will come to
the same conclusions, that is the intuition we
speak of. Some people, namely me, believe that
the intuition we feel about things is actually
quantifiable, just not yet.

You don't have to be on talking terms with your
intuition about a subject in order to be in tune
with it. You can truly love mathematical
symmetry (sociologists say we can't help it)
and not know what zero is. That is why babies
prefer symmetrical faces and harmonic tones,
but they don't know math from their rattles.
They don't have to, to feel their intuition.

Chemistry and physics are essentially math
also, so glaze and physics of firing, beautiful
in their own right are related to math. A bad
release compared to oxygen ratios make for bad
reduction. These are math based relationships.

This maybe should go off group as a discussion,
because I doubt that others are interested.
Aesthetic Philosophy Theory is not for the
light of heart or the sober. And probably not
for a pottery group discussion. I only brought
it up as a thing to roll about in your mind for
a minute and then let go, not to chew too
thoroughly.

Maybe the approaching new year is making me
wax philosophical or maybe the upcoming BIG
moon is beginning to affect me.

Either way, Happy Holidays!

---
Elizabeth Priddy

email: epriddy@usa.net
http://www.angelfire.com/nc/clayworkshop
Clay: 12,000 yrs and still fresh!

On Sun, 19 Dec 1999 10:52:45 Vince Pitelka wrote:
>----------------------------Original message----------------------------
>>mathematics is at the heart of this subject.
>
>This strikes me as a very strange response. Mathematics has nothing to do
>with this subject. I suppose it is possible to interpret asymmetry and
>symmetry in mathematical terms, but that is after the fact.
>
>>all symmetrical pots are based on parabolas.
>
>Huh? What about the cylinder? There are plenty of beautiful, symmetrical
>pots that do not contain parabolas.
>
>>And you don't need to know the math to know and
>>appreciate the beauty it delineates.
>
>The math does not delineate the beauty, thank god.
>
>>Form is mathematics. And intuition about the
>>math is all it takes to appreciate beauty.
>
>Sorry to be so contrary, but this is indeed a strange interpretation. As I
>said, mathematics may provide a way of interpreting form, but the form was
>there before the math. Intuition about math has nothing to do with
>appreciating beauty unless you happen to love math.
>
>Best wishes -
>- Vince
>
>Vince Pitelka
>Home - vpitelka@DeKalb.net
>615/597-5376
>Work - wpitelka@tntech.edu
>615/597-6801 ext. 111, fax 615/597-6803
>Appalachian Center for Crafts
>Tennessee Technological University
>1560 Craft Center Drive, Smithville TN 37166
>

--== Sent via Deja.com http://www.deja.com/ ==--
Share what you know. Learn what you don't.

### Don Goodrich on mon 20 dec 99

Elizabeth, I love it when you talk mathematics that way ;)

So when I admire my favorite pitcher, its sinuous curves reminiscent of my
lover's body, it's the mathematically defined pure form common to them both
that's the source of their beauty.
Similarly, I stare in awe at my orange/black/white shino teabowl whose
chaotic irregularities make it look like it grew out of living stone and only
happens to be shaped to hold liquid. It's the mathematical laws of physics
that determined how it looks and feels. The character of this cup reflects
the power of the natural laws that completed its making when the artist
consigned it to the fire.
You're saying ( I think) that a person's perception of beauty is a measure
of intuitive perception of the math behind the object. There's a
dissertation in psychology here if anyone's looking for a thesis. If I were
in grad school I'd consider it.

By the way, having been a math major in an earlier life I agree with you.

Yule cheer to all of you,
Don Goodrich
goodrichdn@aol.com
http://members.aol.com/goodrichdn

Elizabeth wrote:
>>..If the mind has the capacity for a parabola,
the golden mean, the basics of radial or
bi-lateral symmetry, that is all they will find
beautiful and desirable.

>>If they have it in their consciousness to enjoy
the mathematical options that are glorified in
irregular forms, then they will love those too.

>>Not everyone can appreciate these works and very
rare individuals can describe it with math.
And you don't need to know the math to know and
appreciate the beauty it delineates.

>>Form is mathematics. And intuition about the
math is all it takes to appreciate beauty.<<

### madwa on tue 21 dec 99

Elizabeth!

I'm so glad you brought these mathematical thoughts to our table - I throw
and work instinctively with clay, but in most other areas in life am largely
practical and logical. I have found these particular discussions
stimulating and they have given me lots to think about and most certainly,
another tool for my work. Thank you!

>From Sweet New Zealand

### Vince Pitelka on tue 21 dec 99

>Math isn't worth fighting over, really.

Elizabeth -
I truly appreciate your "waxing philosophical" and it was never my intention
to "fight" over it. I simply stated my responses in straightforward terms,
as I always do.

>Some people, philosophers to be specific,
>believe that beauty can actually be quantified.

I know that they do, but somehow the concept horrifies me a bit, because it
denies the ultimately subjective component of beauty.

>Like it or not, math is one way to describe and
>approach the subject.

I don't mind it a bit, but as I said, the subject (beauty or symmetry or
asymmetry) was there before the mathematical interpretation.

>And a cylinder is a piecewise function, which I
>mentioned before, and is of questionable beauty
>in and of itself.

I find that a cylinder can be extraordinarily beautiful. You have perhaps
seen the large Sumerian clay cylinders inscribed with cunieform script. Or
an even better example - the classical Mayan cylindrical vessels covered
with that exquisite caligraphic painting. There are examples of very
beautiful cylindrical vessels in so many cultures. If you are discussing
the purity of unembellished form, then the cylinder is certainly less
interesting than an articulated ceramic form based on intersecting
parabolas, but it certainly does not preclude the beauty of the simple cylinder.

>You don't have to know math to feel the balance
>of a piece, but you and the math will come to
>the same conclusions, that is the intuition we
>speak of.

That's one place where I do disagree. Intuition is not universal, and one's
response to a work of art arises from an infinitely complex combination of
psychological and emotinional forces. To say that the subjective response,
based on ituition, will come to the same conclusion as the quantifiable,
mathematical response denies the infinitely complex, unpredictable nature of
subjective response.

>You can truly love mathematical
>symmetry (sociologists say we can't help it)
>and not know what zero is.

This just indicates how little sociologists apparently know about art and
the human response to art. As I said in an earlier post, in some cultures
symmetry in art is seen as unimaginative and tedious.

>That is why babies
>prefer symmetrical faces and harmonic tones,
>but they don't know math from their rattles.
>They don't have to, to feel their intuition.

This is true, but I believe that this intuition has to do with survival, and
nothing to do with beauty. Babies intuitively like symmetry and harmonic
tones because those qualities symbolize balance, stability, and safety.

>light of heart or the sober. And probably not
>for a pottery group discussion. I only brought
>it up as a thing to roll about in your mind for
>a minute and then let go, not to chew too
>thoroughly.

Seems entirely appropriate for a pottery/sculpture discussion group, and I
am sure that many would be dissappointed if we chased it off line.

>Maybe the approaching new year is making me
>wax philosophical or maybe the upcoming BIG
>moon is beginning to affect me.

I think the combination of the two is affecting all of us, at least I damn
well hope it is!

Best wishes and happy holidays -
- Vince

Vince Pitelka
Home - vpitelka@DeKalb.net
615/597-5376
Work - wpitelka@tntech.edu
615/597-6801 ext. 111, fax 615/597-6803
Appalachian Center for Crafts
Tennessee Technological University
1560 Craft Center Drive, Smithville TN 37166

### Norman van der Sluys on wed 22 dec 99

I'm surprised thaeree are so many potters out there with so little knowledge of
art history. Those lovely Greek pots are a product of mathematics, just as are
those fabulous male nudes and the Parthenon. That doesn't mean you have to
understand the math to appreciate them, but the creators of these objects sure
did.
By the way, The Greeks tempered their mathematical purity. There is almost
always an intentional devience from the pure mathematical for, which is what
brings those sculptures to life and adds warmth to the proportions of a Greek
temple. So the Greek Ideal contains both symmetry and asymmetry in the same
work! So where is the argument?

Norman van der Sluys
in Western Michigan, where the worst thing about winter isn't the cold, it's the
dark!

elizabeth priddy wrote:

> ----------------------------Original message----------------------------
>
> Math isn't worth fighting over, really.
>
> Some people, philosophers to be specific,
> believe that beauty can actually be quantified.
>
> Its an odd notion, to be sure, but it is none
> the less a real thought.
>
> and its relationship to symmetry and asymmetry.
>
> Like it or not, math is one way to describe and
> approach the subject.
>
> And a cylinder is a piecewise function, which I
> mentioned before, and is of questionable beauty
> in and of itself.
>
> A blind mathemetician, when addressing a group
> of formulae will look for balance and symmetry
> to locate the beauty. It is an inherent beauty,
> a rational beauty, not a superficial one. In
> that there lies the point. For all the
> superficial beauty of the piece, when you pick
> it up, if the balance is off and it feels "top
> heavy" of "off" in some other way, you will
> notice, and a mathematical model of the piece
> will have noted it also.
>
> You don't have to know math to feel the balance
> of a piece, but you and the math will come to
> the same conclusions, that is the intuition we
> speak of. Some people, namely me, believe that
> the intuition we feel about things is actually
> quantifiable, just not yet.
>
> You don't have to be on talking terms with your
> intuition about a subject in order to be in tune
> with it. You can truly love mathematical
> symmetry (sociologists say we can't help it)
> and not know what zero is. That is why babies
> prefer symmetrical faces and harmonic tones,
> but they don't know math from their rattles.
> They don't have to, to feel their intuition.
>
> Chemistry and physics are essentially math
> also, so glaze and physics of firing, beautiful
> in their own right are related to math. A bad
> release compared to oxygen ratios make for bad
> reduction. These are math based relationships.
>
> This maybe should go off group as a discussion,
> because I doubt that others are interested.
> Aesthetic Philosophy Theory is not for the
> light of heart or the sober. And probably not
> for a pottery group discussion. I only brought
> it up as a thing to roll about in your mind for
> a minute and then let go, not to chew too
> thoroughly.
>
> Maybe the approaching new year is making me
> wax philosophical or maybe the upcoming BIG
> moon is beginning to affect me.
>
> Either way, Happy Holidays!
>
> ---
> Elizabeth Priddy
>
> email: epriddy@usa.net
> http://www.angelfire.com/nc/clayworkshop
> Clay: 12,000 yrs and still fresh!
>

### Ray Aldridge on wed 22 dec 99

At 02:42 PM 12/21/99 EST, you wrote:
>>Like it or not, math is one way to describe and
>>approach the subject.
>
>I don't mind it a bit, but as I said, the subject (beauty or symmetry or
>asymmetry) was there before the mathematical interpretation.
>

Not to be argumentative, but I'm not sure this is a settled question. If
you asked a pure astrophysicist, he might say that the math predates the
object, in the sense that the universe may have existed as a mathematical
template before the Big Bang.

It's true that most of us see mathematics as a descriptive language. But
some folks see the universe as a web of linkages so infinitely intertwined
that it could all be described in some uberequation that continuously
updates itself to reflect the position of every particle and energy vector
in the universe.

In the more specific sense, I've often had the sense that a number of
mathematically quantifiable processes are occurring as I form the clay.
Certainly the physical characteristics of a given clay exist in this form
prior to forming-- the plasticity and strength of the body, the percentage
of water, and so forth. And the skills of the individual potter, the size
of her hands, the speed of the wheel, etc., are all quantifiable elements
of the finished form, in the most subtle sense. The hemispherical bowl I
throw today will be different from the one I throw tomorrow and very
different from the hemispherical bowl thrown by another potter, even though
the descriptive mathematics are roughly the same. Can these subtler
mathematical factors be said to antedate the object, when they were all in
place before the object existed?

Okay, I know this is a load of wild mountain meadow muffins, but I love
these sorts of discussions-- not because anything will ever be settled
because of them, but because they make my neurons link in new ways, and
it's that brain-itch that I live for.

Everyone, I hope you have a wonderful holiday, and that we all become
masters of the clay universe in the New Millenium. I've really enjoyed my
time on Clayart-- long may we natter.

Ray

Aldridge Porcelain and Stoneware
http://www.goodpots.com

### Tom Wirt on wed 22 dec 99

> >You can truly love mathematical
> >symmetry (sociologists say we can't help it)
> >and not know what zero is.
>
> This just indicates how little sociologists apparently know about art and
> the human response to art. As I said in an earlier post, in some cultures
> symmetry in art is seen as unimaginative and tedious.
>

I should note here, that there is getting to be quite a bit of evidence that
the mathematical mind and the way it seems to operate is very similar to the
"creative", artistic mind and how it operates.....especially among
musicians.

Tom Wirt

### Janet Kaiser on wed 22 dec 99

Thanks Vince,

I could not have put it better and quite agree. Mathematicians tend to
forget that mathematics are a construct there to interpret and explain. They
are a "man-made" set of rules and conventions. Whether pure or applied, the
advanced user finds beauty in the maths alone. I am married to a number
lover, who can go into raptures about all sorts of statistics and other
mathematical convolutions which leave me cold.

On the whole I think this maths and appreciation of symmetry/asymmetry
thread is a bit like "which came first? The chicken or the egg?" IMHO maths
can only explain what is symmetry/asymmetry in a logical mathematical way.
Is it not therefore rather preposterous to say that we are appreciating what
we see because of our innate mathematical abilities and "inner eye"? If that
were true, everyone would have the same subjective taste. This is clearly
not the case.

Janet Kaiser

-----Original Message-----
From: Vince Pitelka
To: CLAYART@LSV.UKY.EDU
Date: 20 December 1999 03:27
Subject: Re: Symmetry, Asymmetry, mathematics

----------------------------Original message----------------------------
>mathematics is at the heart of this subject.

This strikes me as a very strange response. Mathematics has nothing to do
with this subject. I suppose it is possible to interpret asymmetry and
symmetry in mathematical terms, but that is after the fact.

>all symmetrical pots are based on parabolas.

Huh? What about the cylinder? There are plenty of beautiful, symmetrical
pots that do not contain parabolas.

>And you don't need to know the math to know and
>appreciate the beauty it delineates.

The math does not delineate the beauty, thank god.

>Form is mathematics. And intuition about the
>math is all it takes to appreciate beauty.

Sorry to be so contrary, but this is indeed a strange interpretation. As I
said, mathematics may provide a way of interpreting form, but the form was
there before the math. Intuition about math has nothing to do with
appreciating beauty unless you happen to love math.

Best wishes -
- Vince

Vince Pitelka
Home - vpitelka@DeKalb.net
615/597-5376
Work - wpitelka@tntech.edu
615/597-6801 ext. 111, fax 615/597-6803
Appalachian Center for Crafts
Tennessee Technological University
1560 Craft Center Drive, Smithville TN 37166

### Vince Pitelka on thu 23 dec 99

>I'm surprised thaeree are so many potters out there with so little knowledge of
>art history. Those lovely Greek pots are a product of mathematics, just as are
>those fabulous male nudes and the Parthenon. That doesn't mean you have to
>understand the math to appreciate them, but the creators of these objects sure
>did.
>By the way, The Greeks tempered their mathematical purity. There is almost
>always an intentional deviance from the pure mathematical for, which is what
>brings those sculptures to life and adds warmth to the proportions of a Greek
>temple. So the Greek Ideal contains both symmetry and asymmetry in the same
>work! So where is the argument?

Symmetry and asymmetry in the same work of art is certainly nothing unusual.
The above does not negate the argument in any way, and in fact it proves my
point as well as anything, because among Classical Greek art there is
certainly plenty of bad art, illustrating that creating art purely from
mathematical principles doesn't work. Artists like Exekias, one of the
greatest of vase-painters, made great art specifically because they paid
attention to the mathematical principles, had a good sense of formal design,
and deviated from the math wherever the principles did not work. Those who
did not have a good sense of formal design and attempted to make art purely
on the basis of the mathematical principles made bad art. The mathematical
principles may be a fascinating way of interpreting or evaluating art, and
no doubt there are qualities of art which sometimes have a mathematical
regularity, but the best art is still made from experience and intuition
independent of ANY sort of externally imposed generalizations or principles,
other than those the individual artist chooses to draw into the content and
narrative of his/her own work.

I love Greek art, but I recognize that the Greek infatuation with pictorial
realism and mathematical principles was something of an anomaly in world
art, and when the Classical Greek ideal was grabbed up by Italian
Renaissance Christians and converted to a religious ideal, it became the
standard of Western civilization. Greek art is wonderful, but the idea of
judging world art by comparison to Greek art is absurd.
Best wishes -
- Vince

Vince Pitelka
Home - vpitelka@DeKalb.net
615/597-5376
Work - wpitelka@tntech.edu
615/597-6801 ext. 111, fax 615/597-6803
Appalachian Center for Crafts
Tennessee Technological University
1560 Craft Center Drive, Smithville TN 37166

### Edward Wright on thu 23 dec 99

------------------
A symmetrical vessel may be considered a demonstration of simple design =
skills
or the presentation of a 'perfect' world. That is if you understand the =
vessel
as an isloate, not part of a larger frame. Imagine a vessel on a table with
other things and a person working nearby, or on a pedestle in a room with =
other
things and people moving about. Then the whole experience is asymmetric, if
this symmetrical vessel is understood in relationship to its surroundings: =
what
it sits on, what's next to it, the light in the room, and the people viewing=
it,
etc. If the frame around the art is large, then symmetry and asymmetry are
always present in the experience.

Edward Wright

### Ray Aldridge on fri 24 dec 99

At 02:04 PM 12/23/99 EST, you wrote:
>----------------------------Original message----------------------------
>To all,
>
>Just wondering with all of these speculations on math and appreciation of
>symmetry/asymmetry what the group thinks about the fact that most of the
>really significant mathematical discoveries have come from relatively young
>persons < age 30 while those who produce art continue productive and
>creative well into older age?
>

Tom, you've raised a very interesting question, and one I've given way too
much thought to, myself. It distresses me to say so, because I'm fairly
ancient, but it's probably true that we all reach our intellectual peak
early in life, which may account for the fact that most leading edge work
in the pure sciences occurs in relative youth. It's probably also the case
for those who labor in the High Arts, though the effect is masked somewhat
by the Fame Effect. For example, it's my opinion that Picasso did his best
work before he was thirty. But thereafter, he was Picasso, and everything
he did was golden.

On the other hand, certain art forms depend heavily upon experience for the
basic substrate on which they are built. Writing is one such form, which
is why we have relatively few enfants terible in the writing biz. Writers
tend not to start doing their best work until they've reached their thirties.

It's my perhaps optimistic belief that making functional pottery is another
such art form, in which experience can become more important that raw brain
power and creative energy. It takes time to learn what works, in an
internalized sense. I take as evidence for this position the observation
that old functional potters still seem able to do vital work, but old clay
sculptors often seem to fall into the trap of repeating old triumphs or
wandering off down weedy byways that the visual art establishment sucked
dry many years ago-- abstract expressionism in clay comes to mind.

Then there's another way of looking at the matter. It's a commonplace
among writers to say that every writer has just so many good books in him,
and that it doesn't matter whether you write them all in 5 years or fifty.
When you're done, you're done. It may be true in other creative fields as
well, that every artist has just so many tricks up her sleeve, and so even
if we start later in life, we can still have a career with an arc similar
to the one we might have had if we'd started sooner. Look at Grandma Moses.

Anyway, very interesting idea to think about.

Ray

Aldridge Porcelain and Stoneware
http://www.goodpots.com

### Don & Isao Morrill on sat 25 dec 99

At 12:32 12/24/99 EST, you wrote:
>----------------------------Original message----------------------------
>At 02:04 PM 12/23/99 EST, you wrote:
>>----------------------------Original message----------------------------
>>To all,
>>
>>Just wondering with all of these speculations on math and appreciation of
>>symmetry/asymmetry what the group thinks about the fact that most of the
>>really significant mathematical discoveries have come from relatively young
>>persons < age 30 while those who produce art continue productive and
>>creative well into older age?
>>
>
>Tom, you've raised a very interesting question, and one I've given way too
>much thought to, myself. It distresses me to say so, because I'm fairly
>ancient, but it's probably true that we all reach our intellectual peak
>early in life, which may account for the fact that most leading edge work
>in the pure sciences occurs in relative youth. It's probably also the case
>for those who labor in the High Arts, though the effect is masked somewhat
>by the Fame Effect. For example, it's my opinion that Picasso did his best
>work before he was thirty. But thereafter, he was Picasso, and everything
>he did was golden.
>
>Tom, Prof. Ward Whalling of Cal Tech once in a personal conversation with
this writer gave as his opinion that "You'd best achieve your doctorate
before you are 30...after that,the information explosion has passed you
by." I believe he was correct. Young persons MAKE history as older persons
WRITE history. Since al of us at advanced age work out of our experience,we
cannot avoid working out of history. All teaching is history,but its
reception by the student may make this history NEW. Unfortunatly,the very
nature of our accquisitive system make a really 'free' science nearly
impossible. of what passes as science today,is engineering and innovation
based upon virtually 'ancient' basic discoveries. Raising the question of
the relationships of age and discovery is not simply appropriate but,also
frightening since virtually ALL new work in the sciences carries
proprietory secrecy making it impossible for the Scientist to share
discovery freely in the public domain. Galileo recanted before the
Inquisition and prevented the new world from coming to full fruition.
Today,we have patent law and "prior Right."
Don Morrill
Don & Isao Sanami Morrill
e-Mail:

### Reid Harvey on sun 26 dec 99

After working as a practicing artist for ten years or so I took a number
of engineering, science and math courses. As a result I believe that the
first mathematician was God, and that we have simply been interpretting.
My brain weighed heavily in the opposite direction I was never I great
student in these subjects, but courses like Crystal Chemistry and Optics
and Waves, to name just a few, have clued me in that there is something
in math and science just a little deeper than anything a mere man could
come up with.

Look at crystals and their geometry, or a crytal lattice, and tell me
you see chaos. Yes their are voids and imperfections in the lattice, but
so what? First and foremost is amazing order. Or try optic waves. As
with a lot of other math we can't see waves but they are there.

It is hard for me to imagine that even pure math, say Calculus, is man
made. The equations are too elegant, and simple when one really
understands them. Can someone explain to me how it is that a triangle
with sides equal to 3, 4 and 5 just happened to have a right angle? Was
this something a man came up with?

We know that entropy is the tendency to disorder, kind of like Murphy's
Law. If there can be a void in a crystal lattice there will be. Life
would be kind of boring otherwise.

Reid Harvey
Abidjan, Cote d'Ivoire,
where there is a lot of disorder at the moment, and we have been holed
up at home for three days, listening to sporadic machine gun fire. Those
going out with cars are having these comandeered by soldiers. We are
told there are lots of abandoned cars throughout the city, where
soldiers ran out of gas, no gas stations open to serve them. We feel
safe and secure inside.

### Martin A. Arkowitz on mon 27 dec 99

hi- i have been reading this thread on *symmetry, asymetry, mathematics* for
several days and even my husband has looked on, as these many messages have
been sent forward to the group. we have been bothered by some of the thoughts
written and wish to add our two cents.

I think people are confusing abstraction with artificiality or non-naturalness
with regard to mathematics. Mathematics is abstract, but not artificial. For
example, the number pi exists: it is the ratio of circumference to diameter of
*any* circle. Just because no one can draw a perfect circle and measure the
circumference and diameter exactly does not imply that pi is an imperfect or
artificial construction. In fact, the closer one comes to drawing a perfect
circle and the more precisely one measures it, the better one approximates pi.
I think the best way to think of mathematics is as an idealization which is an
abstraction from the physical world.

One other comment (on age): it is a stereotype that mathematicians do their
best work before the age of thirty. There are of course many examples of this,
but until recently people did not live to a ripe old age. Now there are many
instances of great work done after the age of thirty. The most striking
example is Andrew Wiles who proved the 350 year old Fermat Theorem when he was
in his forties.

martin arkowitz

eleanor arkowitz

marty1@dartmouth.edu

### Norman Vandersluys on wed 19 jan 00

Mathematics is an abstract concept, a product of the human mind.
The fact that we perceive a one-to-one correlation between
mathematics and "reality" speaks more to the nature of human
perception than to the nature of existance.

Could it be that there is a range of responses to an object,
common to all humans, but that individual taste varies widely within
that range?

Merry Christmas all

Norman van der Sluys
jackpottery.tripod.com
. . in Western Michigan where the day has been sunny and a crisp
20oF. What a day for rakuing!!!

### Peter T. Wang on mon 24 jan 00

Hmm.... As a mathematician I would have to disagree that mathematics is a
product of the human mind. For instance, suppose humanity never came to
be on this planet--does that mean that the planets in our solar system
would cease to travel in elliptical orbits? Would this mean gravity could
not be described by an inverse square law? I would hardly think so; to be
sure, I am of the school of thought which says that simply because we are
not present to observe an event, does not mean the event did not occur.

And while I admit this discussion is a bit off topic, as a potter I also
believe that a ceramic form exists as a previsualized ideal before it is
made from clay, much as Michaelangelo once said a block of marble already
contains the masterpiece within it, and that all he did was remove the
excess. I think it's a very interesting commentary on the role of the
artist, as well as the idea of form existing without realization.

Therefore, it seems evident to me that mathematics, like form, is not so
much a product of the mind but much more like a block of marble, which
mathematicians in their humble, careful ways, chip away at, layer by
layer, revealing ever so carefully the beauty and truth which was there
all along. And as potters, why should we be so self-centered to believe
that we make the clay what it is, rather than the other way around?

-Peter
http://www.ugcs.caltech.edu/~peterw/

On Wed, 19 Jan 2000, Norman Vandersluys wrote:

> ----------------------------Original message----------------------------
> Mathematics is an abstract concept, a product of the human mind.
> The fact that we perceive a one-to-one correlation between
> mathematics and "reality" speaks more to the nature of human
> perception than to the nature of existance.
>
> Could it be that there is a range of responses to an object,
> common to all humans, but that individual taste varies widely within
> that range?
>
> Merry Christmas all
>
> Norman van der Sluys
> jackpottery.tripod.com
> . . in Western Michigan where the day has been sunny and a crisp
> 20oF. What a day for rakuing!!!
>

### Norman van der Sluys on tue 25 jan 00

To me, mathematics is a way of expressing the "music of the spheres" to use an
old fashioned term. The fact that you can correlate mathematical principals
with physical phenomenon is wonderful, an indication that man's expression
contains truth. but it remains an expression of this reality. Art can be seen
as another kind of expression of the "music of the spheres." and it can be as
true to the essence of existence as the mathematical expression.
We certainly don't make clay what it is, but we do form it in a goss sense,
thus expressing ouselves and the nature of existence. I don't think it is a
putdown to say mathematics is a human expression.
If you paint a picture of the solar system as it apeared from a specific
vantage point at a specific point of time, using a given spectrum, would that
be mathematics? would it be nature? or would it be a human expression of the
mechanics of the solar system?

Peter T. Wang wrote:

> ----------------------------Original message----------------------------
> Hmm.... As a mathematician I would have to disagree that mathematics is a
> product of the human mind. For instance, suppose humanity never came to
> be on this planet--does that mean that the planets in our solar system
> would cease to travel in elliptical orbits? Would this mean gravity could
> not be described by an inverse square law? I would hardly think so; to be
> sure, I am of the school of thought which says that simply because we are
> not present to observe an event, does not mean the event did not occur.
>
> And while I admit this discussion is a bit off topic, as a potter I also
> believe that a ceramic form exists as a previsualized ideal before it is
> made from clay, much as Michaelangelo once said a block of marble already
> contains the masterpiece within it, and that all he did was remove the
> excess. I think it's a very interesting commentary on the role of the
> artist, as well as the idea of form existing without realization.
>
> Therefore, it seems evident to me that mathematics, like form, is not so
> much a product of the mind but much more like a block of marble, which
> mathematicians in their humble, careful ways, chip away at, layer by
> layer, revealing ever so carefully the beauty and truth which was there
> all along. And as potters, why should we be so self-centered to believe
> that we make the clay what it is, rather than the other way around?
>
> -Peter
> http://www.ugcs.caltech.edu/~peterw/
>

### Morris S. Davis on mon 31 jan 00

Certainly mathematics and the laws of physics are constructions of the
human mind. The fact is that the planets do not travel in elliptical
orbits around the sun. That is only an approximation to Newton's laws. The
actual paths are ellipses that are perturbed by the gravitational action of
all the other bodies in the solar system, some consequential and others
not, depending on the degree of accuracy. In the case of the inner
planets, Newton's Law of Gravity does not explain the motion fully for it
is necessary to apply Einstein's General Theory of Relativity in that case.
In the microcosmic world quantum mechanics applies, in the macrocosmic
world Einstein's theory applies.

Nature is described by models (constructions of the human mind) which best
are able to understand and predict behavior. The history of science is one
of constantly improving models in the sense that as our observations become
more and more refined, it becomes necessary to improve the models if that
is possible (epicycles are added to epicycles in the Ptolemaic theory, for
example), or discard the model and introduce a new one (Einstein
replaces Newton, for example).

Peter Wang is suggesting that the laws of nature exist outside the human
mind. Obviously, that is not the domain of science or mathematics. All
scientists can do is explain nature by evolving mathematical models. All
mathematicians can do is to discover constructions of the mind that have no
relation to nature but must satisfy certain internal rules of consistency.

If the masterpiece resides in the block of stone as Michelangelo is quoted
as having said, how come I, and most people, cannot carve the Pieta? That
is because the mind of the artist has constructed the model on the basis of
his training and experience. It is not there independent of the mind.
If the masterpiece were inherently there, all sculptors would produce the
same masterpiece.

Apart from all of this, I can still enjoy a pot by David Frith, or a
Concerto Grosso by Handel without concern about their underlying existence.

Morris Davis
(astronomer and potterspouse)

On Mon, 24 Jan 2000, Peter T. Wang wrote:

> ----------------------------Original message----------------------------
> Hmm.... As a mathematician I would have to disagree that mathematics is a
> product of the human mind. For instance, suppose humanity never came to
> be on this planet--does that mean that the planets in our solar system
> would cease to travel in elliptical orbits? Would this mean gravity could
> not be described by an inverse square law? I would hardly think so; to be
> sure, I am of the school of thought which says that simply because we are
> not present to observe an event, does not mean the event did not occur.
>
> And while I admit this discussion is a bit off topic, as a potter I also
> believe that a ceramic form exists as a previsualized ideal before it is
> made from clay, much as Michaelangelo once said a block of marble already
> contains the masterpiece within it, and that all he did was remove the
> excess. I think it's a very interesting commentary on the role of the
> artist, as well as the idea of form existing without realization.
>
> Therefore, it seems evident to me that mathematics, like form, is not so
> much a product of the mind but much more like a block of marble, which
> mathematicians in their humble, careful ways, chip away at, layer by
> layer, revealing ever so carefully the beauty and truth which was there
> all along. And as potters, why should we be so self-centered to believe
> that we make the clay what it is, rather than the other way around?
>
> -Peter
> http://www.ugcs.caltech.edu/~peterw/