Danuta
Błaszak
With my
mathematical background and serious poetry awards, I’ve been thinking how we
get our understanding of the world, via axioms or via poetry.
I have honor to
present here my interviews with great scientists
Tame Fowe
Włodzimierz
Holsztyński
Włodzimierz
Kuperberg
David
Jou
For me,
mathematics’s never been numbers. Rather ways to various infinities or ways to
find out that something is really close us even we don’t see it.
I will also
present poetry inspiraed by mathematics. Is there exist any piece of
mathematics inspired by poetry?
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Danuta
Blaszak talks with Tame Fowe
1. Why did you decide to become a mathematician?
I was doing well in Math. My parents and professors encouraged me to continue.
2. You are a mathematician. For many people mathematic means numbers,
fractions, bad grades, and other painful things. What does it mean to you?
Math means logic. It’s so amazing to me that simple lemmas evolve and flow into
intricate concepts with such a beautiful coherence and logics.
3. Math terms should be well-defined. Can you go to infinity using strict
axioms and definitions?
No one can go to infinity, one can only get close. Infinity is a time and space
concept hard to grasp. One can only have a vague feeling of it. My response is
therefore no.
4. There are some fields of understanding where axioms and definitions don’t
work. While a math term has exactly one meaning matching the definition, poetic
metaphors are read with all the possible meanings. What do you think about the
metaphorical description of the world? Does poetry complete math formulas? Is
poetry more general (better?) while leading to understanding of infinity?
I think poetry is more for enjoyment of the mind and the ear. Poetry is beauty
expressed through words. Math is the gymnastics of the neurons and fulfills a
more scientific purpose as it is the foundations of many fields that require
analytical theories and applications
5. Somebody told me great mathematicians are poets. Do you agree with that?
If we want to draw a similarity between both fields, we can say that
mathematicians are artists trying to understand the mechanisms the world
through numbers and theorems whereas as a poet does it with words juggling.
6. Can you give me some examples of applying math in art?
Math Modeling has PDE equations with space and time representation produce
three-dimensional marvelous figures that are characteristics of art.
7. Can you find numbers in poetry?
I think so. Numbers are utilized for various reasons in literature in general.
As an illustration they can be used to ordering multiple objects, referring to
specific entities, etc... Poetry is no exception.
8. What do you think watching stars on the sky at night? Would you describe it
using math and poetry?
When heeding the sky at night, my mind wanders about what does exist in the
confinements of our universe that is probably beyond our wildest imagination.
Science has proved to be limited in explaining certain happenings. Reason why
I’ll probably use poetry to describe such a thing since poetry gives you
freedom to express yourself and feeling. Math already have set rules and
logical steps which force you to follow instead of lead.
9. Have you ever tried to describe dreams?
No unfortunately but I will try one of these days. Usually I attempt instead to
look for an interpretation or a hidden message.
10. What do you think about the metaphorical description of the world in the
Bible or Qur’an or Tora? Didn’t God use the axioms or definitions for His message?
The metaphorical description of the world in the Bible seeks more a pedagogic
purpose.
If we consider axioms or definitions in a more open sense, then God used His
axioms and definitions that definitely are way above our understanding. In the
mathematical concept, axioms and definitions will not be applied to God deeds
since they are humanly fabricated (created by a human brain).
Those were interesting questions
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Danuta Blaszak talks with Wlodzimierz Kuperberg
1. Why did you decide
to become a mathematician?
I did not make this decision. In high school I liked solving mathematical
problems, then I studied mathematics, and then, gradually, mathematics became
my passion. I did not seem to have a choice.
2. You are a mathematician. For many people mathematics means numbers,
fractions, bad grades, and other painful things. What does it mean to you?
What I find most attractive in mathematics is the element of ingenuity and
elegance, when a problem that appears extremely difficult is solved in a flash
of understanding as if a bright light has been turned on inside a dark room
hiding a mystery. The pleasure of mathematical discovery can be compared to the
pleasure of finding a beautiful gem well hidden from sight, and finding it not
by chance, but by the pure power of mind. Often methods created for use in the
process of mathematical discovery are just as valuable as, or even more
valuable than, the discovery itself. In this sense mathematics is not much
different form any other area of human creative activity, be it science, music
or art. The only difference lies in the fact that mathematics deals with the
idealized "universe" of axioms, precise notions, well-defined
objects, definitions, and theorems, and with its own language that includes
formulas, equations, graphs and diagrams (it is perhaps this formal, rigorous,
artificial language that is the main cause of so much "pain" to many
people who declare their aversion to or fear of mathematics), but it does not
deal not with human emotions, dreams, aspirations or desires, which most people
can recognize and appreciate naturally.
3. Mathematical terms should be well-defined. Can you go to infinity using
strict axioms and definitions?
The expression "go to infinity" is defined in mathematical analysis
quite precisely. But the term "infinity" itself has many meanings in
mathematics, each described and studied according to the usual principles of
rigor and precision. One should realize, however, that just because a notion is
well-defined, it does not mean that the notion is well understood, let alone
completely understood. To the contrary: it is easy to define a new notion, but
to understand it deeply can be quite difficult, and understanding it completely
may even be impossible.
4. There are some fields of understanding where axioms and definitions don’t
work. While a mathematical term has exactly one meaning matching the
definition, poetic metaphors are read with all the possible meanings. What do
you think about the metaphorical description of the world? Does poetry complete
math formulas? Is poetry more general (better?) while leading to understanding
of infinity?
Metaphorical descriptions of the world are many, and they differ from each
other significantly. They aim to affect our interpretation of the world and our
feelings about it, but not to describe the world itself. Poetry does not
compete with mathematics or other sciences in studying the physical world.
Poetry deals with, and appeals to, the human mind, its emotions, dreams,
relations with others, etc. Poetry will not help you with computing the
trajectory of a comet, but may help you express your feelings when you see one
in a dream. Poetry will not define infinity, but may describe your elation or
your feeling of being overwhelmed while looking at the midnight sky filled with
unimaginably many, unimaginably distant stars.
5. Somebody told me great mathematicians are poets. Do you agree with that?
Both poet and mathematician seek truth and beauty, though of a different kind.
Both poet and mathematician create things, though of a different nature, and
both dig deep in their minds in their creative acts. In this sense
mathematician and poet are alike. I would say that, because of these
similarities, it is possible for a great mathematician to be a poet too, but I
would also say that most of them are not, unless one counts beautiful,
significant mathematical creations as a kind of poetry.
6. Can you give me some examples of applying mathematics in art?
The connection between mathematics and music has been proclaimed so often, that
it became an old truism already in antiquity (see, for example,
http://en.wikipedia.org/wiki/Music_and_mathematics). Architecture is an obvious
place where mathematics and art connect. I cannot give you any first-hand
examples of such applications, however. I would say instead that mathematics,
at a certain level, IS ITSELF a kind of art.
7. Can you find numbers in poetry?
Yes, but only if you look for them there. In poetry, I believe, you can find
anything you want or expect to find.
8. What do you think watching stars on the sky at night? Would you describe it
using mathematics and poetry?
The analytical part of my brain thinks about the difference between what stars
appear to be (tiny specks of light arranged in constellations or crowded
together in lumps) and what they really are (immensely huge balls of nuclear
fire incredibly far from each other). But the other part just enjoys the
feeling of "infinite" space, the "friendly" twinkles from
far away, their quietness and tranquility... Mathematics has its say and so
would poetry, if I only were a poet.
9. Have you ever tried to describe dreams?
I know my own dreams only. A story told about a dream is not the same as the
dream. One can easily describe an event in reality, but not a dream, at least
not well enough to make another person see the same things and feel the same
way as seen and felt while dreaming. Because a dream is not at all like any
event in reality. Perhaps in the future one will be able to record the images
and sounds of a dream by decoding one's own brain waves emitted in sleep and
turning them into a "video", but that alone will tell us very little
about the emotions of the dreamer. I suppose everything can be described with
words, but it takes a true artist to be able to describe something as unreal as
a dream.
10. What do you think about the metaphorical description of the world in the
Bible or Qur’an or Tora? Didn’t God use the axioms or definitions for His
message?
I cannot assume that these descriptions were intended to be metaphorical. My
limited knowledge about these writings prevents me from voicing my opinion on
them.
Music and mathematics - Wikipedia, the free encyclopedia
en.wikipedia.org
Music theorists often use mathematics to understand music. Indeed, mathematics
is "the basis of sound" and sound itself "in its musical
aspects... exhibits a remarkable array of number properties", simply ...
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Danuta
Błaszak talks with Włodzimierz Holsztyński
1. Why did you decide
to become a mathematician?
I didn't. I simply was.
2. You are a mathematician. For many people mathematic means numbers,
fractions, bad grades, and other painful things. What does it mean to you?
The Art of Thinking.
3. Mathematical terms should be well-defined. Can you go to infinity using
strict axioms and definitions?
Mathematical language grasps infinity--several aspects of it--formally. This
does not mean that we control infinity. On the contrary, infinity is mostly
unruly. It is a source of excitement, beauty and profoundness. The main role of
infinity is to simplify the complex finite situations by stressing their most
important features. (Infinity, like many other good ideas, can be also abused
to produce a low quality research, which misuses infinity to complicate things
for no good reason).
4. There are some fields of understanding where axioms and definitions don’t
work. While a mathematical term has exactly one meaning matching the
definition, poetic metaphors are read with all the possible meanings. What do
you think about the metaphorical description of the world? Does poetry complete
math formulas? Is poetry more general (better?) while leading to understanding
of infinity?
It is not true that mathematical terms have exactly one meaning. They may have
several seemingly different meanings (interpretations). Actually, they always
do or else it is not mathematics. In poetry, haiku is like this.
In my opinion poetry does not deal with infinity, not seriously. It only brings
infinity to your mind in a vague way. Poetry considers infinity only on the
emotional level. When a poem includes also certain intellectual analysis of
infinity then it goes beyond poetry. If it does so well then so much better.
Most of the intellectual poems are poor both as poems and as an intellectual
exercise; they tend to be muddy, and snobbish or preachy.
It's not the goal of poetry to describe the whole world (be it in a metaphoric
or in any other way). That's physics in the case of physical world, and, say,
sociology in the case of the human world. A poem may use the notion of the
world as a pretext to do poetry. The main goal of such a poem will be to create
an artistic text. A single poem may study just one or two aspects of the world.
Different poems may contradict each other. Even a single poem may include
contradictions. Poetry may occasionally provide a mnemonic, or it may confirm
what we already know, or may open our eyes on this or that, but it is not a a
way to study the world, to build knowledge about the world, to discover new
truths. When a poem does so then it goes beyond poetry.
5. Somebody told me great mathematicians are poets. Do you agree with that?
They are so within mathematics. Otherwise, no, not necessarily. I don't know
even a single instance of an outstanding mathematician who at the same time
would be a strong poet (one song writer is known to the public also as a
mathematician but only because he was a popular artist; without his songs he
would not be publicly known as a mathematician).
6. Can you give me some examples of applying mathematics in art?
• Mathematics contributes to the art via technology, which uses mathematics.
Occasionally, mathematics provides artists with new techniques.
• Projective geometry has contributed to progress in architecture and paintings
(the theory of perspective). One can even claim the opposite direction: the
architecture and the theory of painting have provided a stimulus to develop
projective geometry.
• Salvador Dali and M.C.Escher used geometric transformations and symmetry
groups in their paintings.
• Mathematical elements may appear in art or poems. Durer featured a magic
square in at least one of his painting. There is a poem which features an
integer or two in each of its lines--this has worked as artistic means (like
rhyme, metaphor, etc).
• The world of mathematics, like any domain of human activity, provides
inspiration and material for poetry and art.
7. Can you find numbers in poetry?
Literary style can be studied statistically, in terms of numbers: the average
length of words, lines, phrases, ...; the frequency of certain sounds or
grammatical elements, etc.
Poems may feature numbers. For instance, Chinese around the eight century used
the "ten thousand miles" phrase. I know of one poem only which used
integers both intensively and artistically.
8. What do you think watching stars on the sky at night? Would you describe it
using mathematics and poetry?
One could.
Most every poet has the night sky and stars in some of their poems.
Celestial Mechanics is one of the classical fields of mathematics. It's a
difficult one. Several top mathematicians from different times have obtained
outstanding results. Deep. Nevertheless this research field is wide open to the
new generations of great mathematicians.
When at night I see stars straight above my head but not in the lower parts of
the sky, due to pollution, then I feel claustrophobic. *)
9. Have you ever tried to describe dreams?
It's common among poets. Several of my poems involve dreams or different stages
of being asleep.
10. What do you think about the metaphorical description of the world in the
Bible or Qur’an or Tora? Didn’t God use the axioms or definitions for His
message?
Unfortunately, I am not an expert on Bible nor Qur'an nor Tora.
****
Note:
*) In order to reach me the light ray from a star above the head has to cross a
shorter distance through the Earth atmosphere than in the case of a star lower
above the horizon.
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Danuta Blaszak
talks with David Jou
1. Why did you
decide to become a mathematician?
I wanted to study literature, but I also enjoyed physics. I thought that it
would be easier to go back from physics to literature than from literature to
physics, so eventually, in font of my hesitation, I decided to study physics,
which combines the observation of nature with the mathematical analysis.
2. You are a
mathematician. For many people mathematic means numbers, fractions, bad grades,
and other painful things. What does it mean to you?
It means one of the underlying forms of order of the universe, may be the
subtler one. It means, thus, a way towards the heart of reality, and a way
towards beauty.
3. Mathematical terms should be well-defined. Can you go to infinity using strict
axioms and definitions?
Mathematics tries to grasp infinity, as theology tries to grasp God. Axioms and
dogms may be a part of the logical way, but it seems that these realities
-infinity, God- really transcend our understanding.
4. There are some
fields of understanding where axioms and definitions don’t work. While a
mathematical term has exactly one meaning matching the definition, poetic
metaphors are read with all the possible meanings. What do you think about the
metaphorical description of the world? Does poetry complete math formulas? Is
poetry more general (better?) while leading to understanding of infinity?
I enjoy the contrast between univocal meaning in science and multiplicity of
meanings and suggestions in poetry. In our communication with nature, both ways
may be useful and exciting. Reason and emotion, each of them are a source of
enoyment. In some occasions, reason and emotion, analysis and intuition, go
along the same way, and this produces wonderful moments.
5. Somebody told me great mathematicians are poets. Do you agree with that?
In some sense, yes. They look for beauty and understanding through language. Of
course, language, in their case, is a very symbolic and strictly codified language.
Poets invent words and open new ways to the sensibility. This is also true for
mathematicians. Creating new mathematical techniques is creating new languages
which make more accessible and ituitive some aspects of reality.
6. Can you give me
some examples of applying mathematics in art?
The golden ratio is found in many classical paintings and buildings. It has
been a source of proportions with much esthetical appeal. Since I am a Catalan
poet, I cannot forget the architect Antoni gaudí, and the painter
Salvador Dalí, both of them Catalan: Gaudí combined mathematics -paraboloids,
hyperboloids- with structures found in biology -tress, branches, snail to prove
their buildings with surprising structures; Salvador Dali was passionated of
physics and mathematics, which are present in many of his paintings, especially
after the Second World War. Their last passion in life was catastrophe theory.
Nuclear physics, relativity theory, molecular biology, were sources of
inspiration for him.
7. Can you find numbers in poetry?
Numbers are as present in poetry as in music. In fact, in poetry they are more explicit:
the number of syllables, the rhythm of accents... One can also find numbers as
organizing the books -for instance, the number of poems of the several sections
of some books reflect symmetries at the level of the concept of the book. Finally,
one may find poems on numbers. There are several poems on the number pi
-myself, I have a poem on the number pi which has some tree hundred verses,
about the history and the esthetical and philosophical appeal of this
fascinating number.
>
> 8. What do you think watching stars on the sky at night? Would you
describe it using mathematics and poetry?
>
>
I have described it in both ways. Using mathematics, I have woked on some
cosmological problems, or astrophysical problems-; astronomy makes a very
precise use of numbers. But numbers do not describe your feelings, they do not
convey the admiration, the fear, or other sensations you may feel when looking
at the stars.
9. Have you ever tried to describe dreams?
In my poems I have described several dreams. Dreaming I have had access to the
first verses of a considerable number of my poems. To not forget this magic verses,
which give the thrust of the whole poem, I write these verses in some paper and
I go back to the bed.
10. What do you
think about the metaphorical description of the world in the Bible or Qur’an or
Tora? Didn’t God use the axioms or definitions for His message?
I consider the first chapter of the Genesis as an exciting combination of
poetry and numerology: an essay to organize the world and time. Today, we see
it as poetry, but when it was written for the first time, this description was
one of the most accurate scientific descritpion of the structure of the
reality. But, of course, science changes when your means to observe it change.
In any case, the intention of the writer was to celebrate the greatness and
power and existence of God, rather than to give the scientific details about
nature.
Orlando 2010