산신 의 선물

Here is the Korean version of the Similar Triangle Poem titled “The Gift of San Shin / 산신 의 선물

” shown in the previous post.

The Gift of San Shin 산신

Here is another Similar Triangles Poem inspired by the Korean Mountain spirit San Shin 산신

Gregory Vincent St Thomasino Interviews Kaz Maslanka

Gregory Vincent St Thomasino Interviews Kaz Maslanka

I am happy to announce that my interview with The Poet/Philosopher Gregory Vincent St Thomasino has now been published at Word For/Word. I was fortunate enough to have met Gregory last summer in his home town of NYC and really appreciate the effort he made for this interview. I also want to thank Jonathan Minton at Word For/ Word for being kind enough to publish it.

If you are interested in who I am and what drives me then this interview will answer most of your questions. It also explains much of the theory behind mathematical poetry. Check it out here

New Work Accepted At The Bridges Show In Leeuwarden Netherlands Aug 2008

"Peano’s String; A History of Spiritual Stories" has been accepted into the Bridges show in Leeuwarden Netherlands Aug 2008.

For the theory on this piece please check out "Axiomatic Poems"

Ego Pride

Here is a new similar triangles poem titled “Ego Pride”

Heisenberg and Pablo Kagioglu

Pablo Kagioglu sent me a few slides showing some Mathematical Paradigm Poems. I am extremely limited in my understanding of Quantum Mechanics so I am sure there will be much reflexive didactic that I will miss however, I do find it interesting that he has substituted the idea of "quanta" for “self” in our human identity. I am interested in pondering these further I hope you do as well.

Boundaries? Thierry Brunet

Here is an orthogonal space Poem submitted to us by Thierry Brunet via France.

a+b+c Does Not Equal c+b+a

In Delancyplace's excerpt for 4/16/08 --as discussed by political advisor Frank Luntz, the sequential arrangement of information often creates the very meaning of that information:

"[In film, when] two unrelated images are presented, one after the other, the audience infers a causal or substantive link between them. A shot of a masked killer raising a butcher knife, followed by a shot of a woman opening her mouth, tells us that the woman is scared. But if that same image of a woman opening her mouth is preceded by a shot of a clock showing that it's 3 a.m., the woman may seem not to be screaming, but yawning. The mind takes the information it receives and synthesizes it to create a third idea, a new whole. ...

"The essential importance of the order in which information is presented first hit home for me early in my career when I was working for Ross Perot during the 1992 presidential campaign. I had three videos to test: a) a Perot biography, b) testimonials of various people praising Perot, and c) Perot himself delivering a speech. Without giving it much thought, I'd been showing the videos to various focus groups of independent voters in that order--until, at the beginning of one session, I realized to my horror that I'd failed to rewind the first two videotapes. So I was forced to begin the focus group with the tape of Perot himself talking.

"The results were stunning.

"In every previous focus group, the participants had fallen in love with Perot by the time they'd seen all three tapes in their particular order. No matter what the negative information I threw at them, they could not be moved off their support. But now, when people were seeing the tapes in the opposite order, they were immediately skeptical of Perot's capabilities and claims, and abandoned him at the first negative information they heard. ... I repeated this experiment several times, reversing the order, and watched as the same phenomenon took place. Demographically identical focus groups in the same cities had radically different reactions--all based on whether or not they saw Perot's biographical video and the third-party testimonials (and were therefore predisposed and conditioned to like him) before or after the candidate spoke for himself.

"The language lesson: A+B+C does not necessarily equal C+B+A. The order of presentation determines the reaction."

Dr. Frank Luntz, Words that Work, Hyperion, Copyright 2007 by Dr. Frank Luntz, pp. 40-41

A Math Art Moment #11

Delineation #11

Mathematics, among other things, is a language.
Art, among other things, uses language.

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On The Dangers of Spiritual Art

Karl Kempton sent me the piece (shown above). It, as well as other works of his spawned the following essay.

I feel that one of the most dangerous areas of contemporary art comes when the artist makes him/herself a target by embracing spiritual concerns. Our society enjoys pointing fingers at the inadequacies of institutionalized religion (there are many) and ignoring the archetypical ideas of the spirit that have brought us the wonderful icons of the past. These spiritual metaphors have manifested themselves throughout history in many forms always relating to the culture of the artist. Many of the ideas of religions are obsolete and don’t function well in societies as diverse and ever-changing as ours. The artistic challenge of spirit is an extremely difficult task especially when trying to use historically loaded iconography of current dominant religions. I think many of the artistic phobias associated with the spirit are due to our experience of so many ‘so-called’ spiritual artists, who have created cliché kitsch or dogmatic concepts that accent the hypocritical ideas of the church or yet have forged an audaciously different direction aligning themselves with likes of aliens from other planets. Also to note, there seems to be a direct conflict between science and the spirit, which is anxiously evident when scientific minds address spiritual matters. I believe the problem is based in the illusiveness of Truth in both arenas. There are many that think that Truth is defined by science using the language of mathematics. Others believe Truth is beyond logic and only evoked through the metaphoric language of a spiritual ritual. Then there is my personally distasteful category of those who think that Truth is defined by their particular religion or should I say defined by their particular church. Focusing on the later idea we see that human nature tends to have many conflicts and from a historical perspective, one of the most destructive is the religious “us versus them conflict.” I see churches tending to promote this kind of behavior due to its doctrine being fed through so many egos. On the same line of thinking, the testosterone of the self righteous seems to have made its way into religion and spiritual matters to set up so many of the conflicts that we humans engage in. Many have died and continue to die in spiritual wars created by the religious intolerant.

The fact that the conflicts exist, illustrate how illusive Truth is. It seems to me that science is no better when it comes to Truth. The eminent scientist David Boehm points out that science does not find Truth, its purpose is to correlate experience. Also in this vein, we can see that there are those who provide great arguments against the platonic nature of mathematics pointing out numerous problems with using mathematics as a true model for reality. I see the bottom line being that the terra firma of veracity is constantly shifting; therefore, we must accept this fact and move on. The eastern mystics use the metaphor, “form is emptiness and emptiness is form”.

I believe it is the function of special artists to assimilate as much information as possible from the diverse cross-planet cultural ideas not limited to including the concepts of science so that they can re-contextualize, synthesize and synergize their metaphors to be acute and pertinent to the global culture today. They must fully embody the ideas of love and tolerance as if the ideas were new so as to debride the cliché skins attached to them. As impossible this task seems, it is the challenge of those artists to reconnect the loose strands of past archetypical works and re-contextualize them to breathe new life in today’s world. Their job is not to run from the spiritual confusion that permeates the ever-changing cultures on this globe by hiding in some self-conceived scientific illusion of truth without spirit. That is not to say that science cannot be the new religion … it can. However, the spiritual scientist must connect the magical and irrational mind to scientific metaphors so that our spiritual understanding can be flexible as science metamorphoses. The past mytho-spiritual ideas were always based in the science of the times. It takes courage to navigate through the mental minefield of past ‘truths’ finding new veracity that resonates in ones psyche as they express it and expose themselves to the ridicule of being an irrational kook.

I believe the special artist/poets should focus their efforts to make metaphors current to our historical and sociological condition. The purpose of a metaphor is to bridge the infinite to the concrete. Many people feel that past mytho-spiritual/religious metaphors are absolute in the notion that they permanently point to the infinite. Personally speaking, I see the veracity of metaphors being temporal with their cultural relevance having different half-lives. What can confuse matters is that the half-life in some metaphors have existed for such a long time that they seem absolute. There is an argument that the Bastian elemental ideas and Jungian archetypes are absolute. Even if this is true, the metaphors employing those elemental ideas always need recontextualizing to be relevant to the current cultural thought. The frustrating aspect for the artist is having so little control over the fertility of the inspiration process. I wish I could say that artists had full control over the source and production of their metaphors. However, it seems to me that their strength, viability and temporality are a function of graciousness, imparted from the muses. I believe it is though the struggle and success with life that these special artists acquire the molecular building blocks of a vocabulary that becomes the means of their expressions. These ideas logically coagulate around an infinite idea provided to them by the unknown.

A Math Art Moment #10

Delineation #10

Mathematical creations are not unique in the sense that they could be discovered by anyone.

Artistic creations are uniquely invented by individuals.

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The Muses

Here is another similar triangles poem

Bravery

Here is the orthogonal space poem "Bravery" realized as a polyaesthetic work.

Is Pure Mathematics Poetic?

I receive a very important comment the other day from Jonathan who uses the JD2718 to identify himself on his blog. His comment was in reference to axiomatic mathematical poetry. However, I think his question is much broader.

Jonathan expressed the following:

Abraham, cats, Gods.

One, numbers, successors.

Which is really more poetic?

This is a sticky question because I want to avoid slipping into the bottomless void of the “What is poetry? What is art?” question However; I can discuss elements of poetry from which my idea of poetics is derived. I also want to add the following statements are not a value judgment on the aesthetics of mathematics. The mathematical aesthetic is one of the most wonderful experiences one may realize.

To answer Jonathans question; I am assuming that his question implies that pure mathematics is poetic. It is my view that pure mathematics is not poetic. Furthermore, the quick and dirty response to this question is that pure mathematics is different from poetics the same as pure mathematics is different from physics. Physics and Mathematical poetry, although vastly different, live in the realm of applied mathematics. Even when we ‘feel’ that pure mathematics is poetic, we are applying mathematics to some preconceived notion of what we believe poetry is without actually applying it. We may choose to argue that mathematics contains elements of poetry such as rhythm and pattern. Yet one may argue that it is not maths that has poetic elements but poetry that has mathematical elements. For the sake of argument, let us say that poetry possesses the mathematical element of pattern. I would like to make the point that it is difficult to get excited about these metric patterns when taken out of the context of poetry and view in only the light of mathematics. I know we are starting to get away from the intention of our question however, the point I want to make is that the aesthetics of mathematics is much different from the aesthetics of poetry and poetics. The ‘polyaesthetic experience’ that we are discussing is a vector sum experience of the aesthetics of art/language poetry and the aesthetic of mathematics. (They are different aesthetics) If we were to separate the mathematical aesthetic from a language poem how beautiful is it? Now let us look at the aesthetics of mathematical pattern by comparing the beauty of the pattern in iambic pentameter (or any other meter for that matter) to the beauty of self-similar patterns in a mathematically generated fractal. Which is more beautiful? Is the ‘isolated’ metric pattern in poetry more beautiful than a fractal? How about asking, “Is the fractal poetic?” If so what are the elements of poetry in the fractal. Is it the concept of rhythm that makes maths poetic? Are all things displaying rhythm poetic? The point I am trying to produce is that mathematical poetry, makes the structure of mathematics poetic only by application of poetics within that structure. Pure mathematics is not poetic by itself.

When addressing the metric beauty in language poetry; the metric beauty is not relevant to the mathematical pattern per se. It is relevant to the aesthetics involved in the relationship of the pattern to the words and the sounds of the words with its synesthetic energy igniting the meaning of the words as they point further to the cultural and historical relationships within the poem. The mathematical aesthetic devoid of the poetic aesthetic plays an extremely limited role in the aesthetics of language poetry. Yes, there is maths in the poetry however, break it out of the poetry, isolate it and I believe it becomes aesthetically trivial.

Let us look at metaphor – Does pure mathematics express metaphor? How could it? for pure mathematics is more about illuminating the logical structure of thinking. The key word that I want to stress is “logical”. Metaphor requires logical tension if not paradox to function as a concept to bridge the infinite to the concrete. However, I must say that mathematics does provide us with the linguistic structure to express metaphor. Again, this is the issue of pure mathematics relative to applied mathematics. To express metaphor you have to have an application of poetic concepts. You need a source domain and a target domain. (see the section on metaphor structure at Wikipedia) Pure mathematics does not have these metaphoric domains until we apply the poetic idea to the structure of maths as we do in mathematical poetry. The essay “Polyaesthetics and mathematical poetry” goes into more detail on this matter as well as an interview conducted by poetic aesthetician Gregory Vincent St. Thomasino. The interview will soon be published at “word for/word” an online journal of new poetry. I hope to announce the interview soon at this blog.

Axiomatic Poems

This is a page devoted to collect information on axiomatic poems.

Introduction to axiomatic poems -- Peano’s string; a history of spiritual stories.

Axiomatic Poems part two -- More structure added to Peano’s string; a history of spiritual stories.

The addition of another stanza and creating a metamorphic poem.

Proof that no cat is the God of itself (Peano’s proof by Professor Ray Balbes)

Download Polyaesthetics and Mathematical Poetry

In March of 2007 I announced “Polyaesthetics and Mathematical Poetry.” published by Taylor and Francis in the Journal of Mathematics and the Arts Edited by Professor Gary Greenfield. This paper outlines many of the basic principles of mathematical poetry and polyaesthetics.

The contents of the paper are available for downloaded free at this link.

Journal of Mathematics and the Arts published “Polyaesthetics and Mathematical Poetry” March 2007 Volume 1 Number 1 ISSN 1751-3472

The published paper can be purchased at this link.

Proof That No Cat Is The God Of Itself

The Mathematician, Professor Ray Balbes will prove to you that “No Cat Is The God Of Itself”.

At the end of my blog entry for Axiomatic poems dated January 29, 2008 I asked the question, “Can these axioms create interesting theorems?” And the answer is definitely yes! Professor Balbes has shown us four theorems that are proven from the Peano’s axioms. Due to the poetic nature of the new axioms, not only are the four theorems poetic but even the proof of theorem #1 is poetic. Furthermore, the choices Professor Balbes made for the terminology in his proof shows his perceptions of how the poetic nature of the axioms should extend. Therefore, there can be uncountable variations of poetic form in the proofs one could make for the theorems. I find this very exciting.

Kaz

The Professor Ray Balbes wrote the following text:

For reference, here is what we have so far.

The Peano Axioms

1. One is a number
2. If x is a number, the successor of x is also a number.
3. One is not the successor of any number.
4. If two numbers have equal successors, they are equal.
5. If a set of numbers contains the number one and it contains all the successors of its members then the set contains all the numbers.

Let us replace “number” with “cat” and let us also replace “successor” with “God”. Lastly, I am going to replace “One” with “Abraham”.

The Poetic Peano Axioms

1. Abraham is a cat
2. If x is a cat, the God of x is also a cat.
3. Abraham is not the God of any cat.
4. If two cats have equal Gods, they are equal.
5. If a set of cats contains the cat Abraham and it contains all the Gods of its members then the set contains all the cats.

OK, now to make the theorems more succinct, lets set up some conventions. With regard to the Peano Axioms, let us call the set of all numbers N and let us denote by n’, the successor of n

Also let:

1₁ = 1’

1₂ = 1’’

1₃ = 1’’’

etc.

We will refer to 1’ by the name of 2, 2’ will be called 3, etc.

Axiom 3 says that there is no n such that n’=1.

Axiom 4 says that if m’ = n’ then m=n.

Axiom 5 says that if S is a non-empty subset of N with these 2 properties:

i) 1 is in S

ii) If n is in S then n' is in S.

Then S = N.

Here are three theorems that lead up to the Well Ordering Principle. First, I will state them in terms of the Peano Axioms, next in terms of the Poetic Peano Axioms and finally I will prove something.

Theorem 1. For every n in N, n’≠n.

Theorem 2. If n ≠ 1 then n=m’ for some m.

We will say that m ≤ n provided that m = n or m_p = n, for some p

Theorem 3. For every n in N, 1 ≤ n

Theorem 4 (The Well Ordering Principle) If S is any non empty subset of N then there is a number m in S such that m ≤ n for all n in S.

Here are the theorems in terms of the Poetic Peano Axioms. We will say that m is the source of n provided that m ≤ n. In other words, a finite number of Gods of m, yields n.

Theorem 1 No cat is the God of itself.

Theorem 2. Every cat, other than Abraham is the God of some other cat.

Theorem 3. Every cat has Abraham as a source.

Theorem 4 (The Well Ordering Principle) In any (non-empty) set of cats, there is one that is the source of all the others.

Here is the proof of Theorem 1 in terms of the Peano Axioms

Let S = {n| n’ ≠ n}. We will show that S satisfies the conditions i) and ii) of Axiom 5. By Axiom 3, 1 is in S so i) is true. To prove ii), suppose that n is in S then n’≠n. But if n’’=n’ then, by Axiom 4, we would have n’=n, a contradiction, so n’’<>n’. Hence n’ is in S. This means that S satisfies the conditions of Axion 5 and therefore S= N. So that n’<>n for all n in N.

Here’s the proof of Theorem 1 in terms of the Poetic Peano Axioms. Note that in the proof, I am referring to the Poetic Peano Axioms, not the Peano Axioms.

Consider the set S of all cats that are not Gods of themselves. We will show that S satisfies the conditions i) and ii) of Axiom 5. By axiom 3, Abraham is a member of S so i) is true. To prove ii), suppose that Isaac is a cat in S then Isaac is not the God of Isaac. Suppose the God of Isaac is Moishe. Now if the God of Moishe is Moishe then by Axiom 4, Moishe would be Isaac; that is the God of Isaac would be Isaac, a contradiction. Hence Moishe is in S. Since Moishe is the God of Isaac, we have shown that the God of Isaac is in S; in other words, the condition ii) of Axiom 5 is satisfied and thus S is the set of all cats. This means that all cats satisfy the property that they are not Gods of themselves.

The proofs of the other theorems are similar to this.

Ray

Axiomatic Poems Part Two

I have been having some wonderful conversations with the mathematician Ray Balbes. Ray has been asking some very important questions concerning the axiomatic poem. Ray has also helped me by correcting mathematical errors in my nomenclature.

Ray also has had concerns with the idea of God being a viable substitute for successor within the Peano axioms. For God in this sense must be comparable to a mathematical function. I personally have no problem with this idea for my understanding of the word God is metaphorical anyway. Therefore, I can see this metaphoric structure of “God IS mathematical function” as being nested e.g. metaphors within metaphors. The question then would be is God a mathematical function? Alternatively, can we say God functions mathematically? Historically God is described beyond language so I would not try to convince anyone otherwise. I personally do not see God functioning mathematically as a mathematical Platonist would however, I do see the accessibility of ideas mathematically expressed as phenomena attributed to a deity. I believe if you denote phenomena with words, you can do the same with math. Furthermore, I would go on to say that if you can be inspired to connote it with words you can do the same with math for those type of inspirations fuel mathematical poetry.

Therefore, the poem addresses the dichotomy of God being created by men or men being created by God.

To help anyone see how the logic in Peano’s axioms is functioning correctly in the Blog entry of January 29^th, I created another axiomatic poem to show some more structure. The disadvantage to creating another ‘equal’ poem is that the new poem focuses the semantics in such a way that limits the metaphorical content. The advantage is that it gives more semantic structure, which enables one to see the Peano logic with ease. So in essence, we now have an axiomatic poem, which has metamorphic qualities. We see that the Peano axioms function as the underlying paradigm for the poem however, it could be viewed as the source domain with the other two ‘axiomatic stanzas’ as the target domains for the ‘overall metaphor’. In this case, we have three structures separated by two equal signs.

The Peano Axioms

1. One is a number
2. If x is a number, the successor of x is also a number.
3. One is not the successor of any number.
4. If two numbers have equal successors, they are equal.
5. If a set of numbers contains the number one and it contains all the successors of its members then the set contains all the numbers

Poem #1 -- Peano’s string; a history of spiritual stories

1. Abraham is a story
2. If x is a story, the unique inspiration of x is also a story.
3. Abraham is not the unique inspiration of any story
4. If two stories have equal unique inspiration, they are equal.
5. If a set of stories contains the story Abraham and it contains all the unique inspirations of its members then the set contains all the stories.

Poem #2 -- Peano’s string; a history of spiritual stories

1. Abraham is a cat
2. If x is a cat, the God of x is also a cat.
3. Abraham is not the God of any cat.
4. If two cats have equal Gods, they are equal.
5. If a set of cats contains the cat Abraham and it contains all the Gods of its members then the set contains all the cats.

Poem #1 = Poem#2

The Metamorphic Mathematical Poem

From Poems 1972-1997 Copyright © 1997 by Scott Helmes

"Philosophic cocktails" by Thierry Brunet 2007

I would like to introduce a new term for a technique used in mathematical poetry. The first person I know to have used this technique is Scott Helmes. His poem from 1997 (upper image) illustrates the technique well. One can see that it has five structures separated by four equal signs. What occurs is that the mathematical poem contains several structures (equations) all set equal to each other. In effect, the poem reads as a series of statements that metamorphose into each other through the duration while reading the poem.

The lower image, by Thierry Brunet, titled “Philosophic cocktails” is also a metamorphic mathematical poem as you can see three structures separated by two equal signs.

A metamorphic mathematical poem could possess unlimited structures and equal signs however; it must contain at least three structures separated by two equal signs to be considered metamorphic.

The aesthetically interesting thing about these poems is that the target domain and the source domain for the ‘overall whole’ metaphor bounces and shimmers in ones mind as you swap or rotate the domains around each other. This is due to there being multiple domains for the target and source. **

**The metaphor nomenclature borrowed from the cognitive scientist George Lakoff can be viewed in more detail at this link.

Axiomatic Poems

Peano’s string; a history of spiritual stories (Image above)


Axiomatic Poems

I would like to introduce a new mathematical structure to be used with mathematical poetry.

I understand that for two thousand years Euclid’s axioms stood alone as a meaningful axiomatic system. However, in 1889 Italian mathematician Giuseppe Peano created a new axiomatic system based on two primitive notions and the five following statements:

1. One is a number
2. If x is a number, the successor of x is also a number.
3. One is not the successor of any number.
4. If two numbers have equal successors, they are equal.
5. If a set of numbers contains the number one and it contains all the successors of its members then the set contains all the numbers.

What is interesting is that this system does not have to be limited to number. Calvin C. Clawson in his book “Mathematical Sorcery: Revealing the Secrets of Numbers” gives us the same five statements in the following form:

1. Heinsforth is a gelb
2. If x is a gelb, the ranker of x is also a gelb.
3. Heinsforth is not the ranker of any gelb.
4. If two gelbs have equal rankers, they are equal.
5. If a set of gelbs contains the gelb Heinsforth and it contains all the rankers of its members then the set contains all the gelbs.

Clawson has substituted the number “one” with Heinsforth, the term “number” with “gelb” and used “ranker” in place of successor. The point that Clawson is trying to make is that we need not be concerned with the primitive notions per se. What we need to be concerned with is the relationship of these notions within the axiomatic structure. From what I understand there could be incalculable different ways to describe the primitive notions however, only one way to logically relate them to each other. After reading Clawson’s axioms, I became aware of the ability of this structure to create metaphor. The source domain of the metaphor is the Peano axioms. The target domain is the same set of axioms with poetic substitutions placed inside the axioms. Therefore, I have created the axiomatic poem shown below:

Let us replace “number” with “cat” let us also replace “successor” with “God”. Lastly, I am going to replace “One” with “Abraham”.

1. Abraham is a cat
2. If x is a cat, the God of x is also a cat.
3. Abraham is not the God of any cat.
4. If two cats have equal Gods, they are equal.
5. If a set of cats contains the cat Abraham and it contains all the Gods of its members then the set contains all the cats.

Now the next interesting idea is:

Can these axioms create interesting theorems?