Basho (Specific Condition)

After some more (noisy mind) thoughts about not thinking; I feel the poem from the last blog entry should be considered as a relationship stated in a general condition (without direct value or value in a positive or negative sense) furthermore, I think the poem would be easier read in the specific condition. So I have a new version in the specific condition. (see above)

The mathematical structure remains the same as the last poem and can be seen on the last blog entry.

The Poem is derived as such:

Starting with the ideas that the Splash is to the Waveless Old Pond as Frog is to No Self and as Noisey mind is to clear Mind. Which is set up mathematically as:

Splash/Waveless Old Pond = Frog/No Self = Noisy Mind/Clear Mind

and arbitrarily choosing to use flavor five from the expanded similar triangles poem examples we can see that the next line can be set up as g/h = a-d/b-e

Which translates as:
Splash / Waveless Old Pond = (Frog - Noisy Mind)/( No Self- Clear Mind)

The variables are as such:

Frog =a

No Self =b

Noisy Mind=d

Clear Mind= e

Splash=g

Waveless Old Pond=h

An aesthetic decision to solve for a and using the third example from flavor five yields: a= g(b-e)/h + d

Therefore:
Frog = (Splash(No Self – Clear Mind)/ Waveless Old Pond) + Noisy Mind

Basho

Everyone seems to have had their way with poor Basho’s poem. I am not going to be pretentious enough to call this ‘haiku’ however, this expanded similar triangles poem was inspired by the wisdom that I have gleaned from my experience with Basho's poem.

The Poem is derived as such:

Starting with the ideas that the Frog is to The Self as Noise is to The Mind and as Splash is to the Old Pond Which can be set up mathematically as:

Frog/The Self = Noise/The Mind = Splash/Old Pond


and choosing (aesthetic decision) to use flavor five from the expanded similar triangles poem examples we can see that the next line is set up as g/h = a-d/b-e

Or:

Splash / The Old Pond = (Frog - Noise)/( Self- The Mind)

The variables are as such:

Frog =a

The Self =b

Noise=d

The Mind= e

Splash=g

The Old Pond=h

Furthermore, to solve for a or choosing to use the third example from flavor five yields: a= g(b-e)/h + d

Therefore:
Frog = (Splash(The Self – The Mind)/ The Old Pond) + Noise

After some more (noisy mind) thoughts about not thinking; I feel that I should mention that the poem above is stated in a general condition furthermore, I think the poem may be seen easier in the specific condition. So I have a new version in the specific condition. Please see the next blog entry for the specific condition.

Bogus Science

Here is an Expanded Similar Triangle Poem in all six synonymous syntactical permutations from group six.

Poincaré's House

The expression above is an expanded similar triangles poem. Inspired by the musings of Henri Poincaré

Flavor one h = (b(d+g)/a) - e

L'anxieux

Thierry Brunet has kindly translated “The Insecure” into French. This is an expanded similar triangles poem. Flavor three: h = ((e(a+g))/d)-b

Foul Of Pray

The mathematical poem above is an example of a expanded similar triangles poem.

Flavor two: a = (g(b+e)/h)-d

The Expanded Similar Triangles Poem

The similar triangles method for constructing mathematical poems easily enables us to manipulate a logical structure for metaphoric expression. What this pedagogical blog entry is trying to accomplish is the introduction and showing of the expanded version of the similar triangles poem. This poetic structure is logically more complex however, still easy to manipulate.

Before you read further, please be familiar with the similar triangles poem. You may read about it here.

The 'regular' similar triangles poem only utilizes two similar triangles and is defined as an expression of two ratios. The expanded similar triangles poem utilizes ‘n’ number of ratios and is able to create very large (infinite) complex mathematical poems and still have a logical structure to act as a source domain for our metaphoric expression.



I am going to create an expanded similar triangle poem made of three similar triangles to serve as our example.
The following image shows three similar triangles with three different sets of relationships:‘a is to b’ as ‘c is to d’ and ‘e is to f’

The trick in the construction of the poem is to add or subtract the numerators of two of the relationships and also add or subtract the two corresponding denominators of the same two relationships. The next image shows us how we construct our three ratios and associated them differently with subtraction and addition to form six flavors. There are actually 12 flavors possible however; I wish to focus on these six, which I consider the best ones to give us a good understanding of what is occurring in this method.

Each flavor yields a group of six equations after the flavor is solved for each variable. The next six images show the six syntactical arrangements for each flavor. There are at least seventy-two different syntactical arrangements however; I wish to focus on what I feel to be the thirty-six most important ones. The next six images show each of the six groups created by each flavor.

FLAVOR ONE YIELDS:
FLAVOR TWO YIELDS:

FLAVOR THREE YIELDS:

FLAVOR FOUR YIELDS:

FLAVOR FIVE YIELDS:

FLAVOR SIX YIELDS:

Lets now create a poem using the following text.

a = Love Lies
b = The Lonely
d = Sugar
e = The Starving
g = Sexual Conquests
h = The Insecure

The structure follows as thus: ‘Love Lies’ is to ‘The Lonely’ as ‘Sugar’ is to ‘The Starving’ as ‘Sexual Conquests’ are to ‘The Insecure’

We then substitute the variables with the poetic phrases to yield thirty-six poems in six groups relating back to the flavors shown above.

I find it interesting to savor each syntactical permutation to get a ‘feel’ for each poetic expression.

GROUP ONE CONSTRUCTED FROM FLAVOR ONE:

GROUP TWO CONSTRUCTED FROM FLAVOR TWO:

GROUP THREE CONSTRUCTED FROM FLAVOR THREE:

GROUP FOUR CONSTRUCTED FROM FLAVOR FOUR:

GROUP FIVE CONSTRUCTED FROM FLAVOR FIVE:

GROUP SIX CONSTRUCTED FROM FLAVOR SIX:


Many of the links below are examples of the expanded similar triangles poem.

Similar Triangles Poems

Similar Triangles Poems / Proportional Poems

I would like to map out the structure and show examples of what I call "Similar Triangles Poems"or "Proportional Poems". Let me use the example of Similar Triangles to help visualize the proportional relationship in this mathematical structure.

Let us first look at two similar triangles with sides labeled ‘a’ ‘b’ ‘c’ and the second with sides labeled ‘d’ ‘e’ and ‘f’ Notice the laws of geometry state that a/b is equal to d/e as shown below. I am going to call this latter equation "The Similar Triangles Relationship".

Also let us note that we can solve for any or all of the variables. This will give us four synonymous variations of the similar triangles relationship in terms of one variable – examples shown in the next slide:

Now let us look at the logical structure of the following comparison: Apples are to apple butter as peanuts are to peanut butter. Furthermore, let us also look at how we can map the latter statement into the similar triangles relationship.
The following slide shows us a good example of how metaphor can be applied to the relationship of similar triangles.

Now let us substitute the terms of our logical comparison into the all of the similar variations to create four similar triangles poems.

We now have four poems that are logically equivalent but syntactically different. Each poem says the same thing only with a different flavor much like playing a piece of music in four different keys.

The pedagogical example above uses rather mundane subject matter. To see more poetic examples, please click on the lablel for "Similar Triangles Poems" (below)