Ed Schenk Predestination / Karma / Reincarnation

The following text are expressions by the Dutch Mathematical Poet, Ed Schenk

Predestination / karma / reincarnation

Some agnostics define death as:
death = life – life axiom 1)

In many religions the believe is there is something after or above death. This could be written as:
death ≠ 0 axiom 2)

Now if axiom 1 and axiom 2 are simultaneous valid, this leads to the postulate:
life ≠ life

This looks contradictory, however if we introduce the element time, axiom 1 could be written as:
death = life(n+1) – life(n),
where n is the current life. Moving variables yields: life(n+1) = life(n) + death. This could be written as:

next life = this life + death (predestination)

or

this life = next life – death This formula looks a bit strange, however this is due to semantics. If we take into account that time is not necessarily linear we could replace the word ‘next’ by the word ‘another’.

This leads to: this life = another life – death (karma)

My Response To a Critic

I would like to address a comment made in reference to the piece “Peano’s String; A History of Spiritual Stories”(displayed above) … the following (text in green) is a copy of a comment from my blog entry “New Work Accepted At The Bridges Show In Leeuwarden Netherlands Aug 2008”:

This is a strange place. Im all for maths, dont get me wrong. Anyone who's any good at maths needs to make it part of themself but democrats? Abraham? maths is made a cliche with these comparisons. Everything can be expressed in maths but some things shouldnt. Just make a billboard with euler's formula

My response:

I appreciate you giving me some feedback to my blog and I would love to engage you in discourse on any concerns that you may have. I am certainly not going to imply that I am always correct in my assumptions of anything. Furthermore I consider myself a student.

I want to note that I may not defend mathematical poems made by others so if you wish to criticize the axiomatic poem concerning Barack Obama and the democrats you may wish to address your concerns to its author. I also wish to make this same disclaimer concerning any mathematical poetry posted on this blog that is not authored by me. However, I will be happy to address any concerns or criticism involving my work. My Job at this blog is to promote interest in mathematical poetry not criticize it. Yet, I may someday express criticism of someones work if I feel “the discipline” of mathematical poetry is being subverted.

To get to your concerns let’s look at the term cliché and what Wikipedia has to say about it:

A cliché (from French, pronounced [klɪ'ʃe]) is a phrase, expression, or idea that has been overused to the point of losing its intended force or novelty, especially when at some time it was considered distinctively forceful or novel. The term is most likely to be used in a negative context.

It seems that you have applied this term ‘cliché’ to my axiomatic poem titled, “Peano’s String; A History of Spiritual Stories”. So I can only assume that there is something about this mathematical poem that you would consider overused. It is hard to imagine that you may be referring to mathematical poetry in general since there is so little of it. What is it that is overused here? Is your concern related to my references to biblical history? Are you feeling that I have taken biblical references out of context in jest? I can only say that while I can see how one may find this mathematical poem humorous, the root of it can be taken very serious. Maybe, what you may really be trying to say, is that mathematical poetry is aesthetically trivial. This may be is a little more difficult for me to defend due to my belief that just because I find something beautiful I can never assume that anyone else would find it such. However, I do find mathematical poetry extremely beautiful especially in its use of dual aesthetics. My fear is that you, or anyone else for that matter, will discard this entire proposition and never really answer the following questions.

1. From a cognitive scientific point of view what is a metaphor, what are the parts within the structure of a metaphor and what are their relationship to mathematics in general and mathematical equations in particular?

2. What is the difference between connotation and denotation and how do they apply to the language of mathematics?

3. When looking at the structure of a mathematical equation how does that structure relate to other phenomena that can be described with that same mathematical structure?

4. Are the commonalities between identical mathematical structures purely linguistic? Or are they physical?... Or maybe spiritual? Could there be something such as archetypical equations?

5. What are the differences between the aesthetics of mathematics and the aesthetics of poetry or art? How can those differences be delineated when analyzing a mathematical poem?

6. How does mathematical poetry relate to the history of art, poetry and applied mathematics? Can mathematical poetry be considered a legitimate field of applied mathematics?


And now let’s address this mathematical poem in particular:


7. What is the relationship of Natural numbers to linear historical events?

8. What do the descendents of Abraham have to do with current cultural events especially ones that concern the military of the United States of America? Who are the children of Abraham and what is the historical and spiritual relationship that they share.

9. How are cultural stories passed from generation to generation?

10. How are mytho-spiritual (religious) stories created? How does deities and deification come to be? What is the source of the ‘so called’ divine inspirations that create works of poetry and art? And what is their relationship to this piece of art in particular.

11. What is the relationship of cats in mytho-spiritual literature? What is the meaning of cat when applied to a human being? What is the meaning of a cat when applied to a God?

12. When looking at the proofs using these axioms what can be said poetically from the proofs.

13. What are the proofs that can be created from Peano’s axioms?

14. How do questions 7 through 13 relate to questions 1 through 6?

I am not going to discount that you may provide an argument to the idea that my work is cliché and trivial but I would hope you address the latter questions within your argument.

Thanks!

Kaz

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"

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)

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

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?