POETIC FORMS EMBRACING MATHEMATICS
Nature is a wondrous thing—science tries to capture its design in mathematical formulas, for example, the Möbius strip, Fibonacci sequence, Golden Ratio, Phi poem (the design based upon the Golden Ratio),* etc—many being eponymous.
Golden Spiral
Run with the idea while hot;
fun—
stretch your imaginary pun.
For a pie in the sky it is not:
PHI
© Suzette Richards (2021)
As described in mathematical literature, a Möbius strip is a surface with a boundary, whereas a Klein bottle (pictured below) has none. The properties of the Klein bottle were first described by the German mathematician, Felix Christian Klein (1849–1925), in 1882.
The term Klein bottle is the more widely accepted and commonly used name in mathematics and topology. Klein's Vase, though less common, is sometimes used metaphorically or in artistic contexts to describe the same concept, particularly when its visual or sculptural aspects are emphasised—a preference adopted in this article.
Introducing the new, innovative Klein’s Vase poem – a poetic form inspired by the boundless flow of Klein's Vase; where silence rivals the spoken word in significance and ambiguity weaves a seamless narrative, flowing in infinite cyclical movement. It is a poetry style liberated from rigid structures, guided instead by subtle, intuitive principles.
KLEIN’S VASE POEM
The integration of Klein’s Vase as both a structural inspiration and thematic metaphor, is deliberate. It embraces ambiguity as a creative lens, not only challenging the reader’s perceptions but inviting them to explore infinite interpretations. The guidelines transcend conventional formats, paving the way for multidimensional narratives.
More free than free verse! Introducing the new, innovative Klein’s Vase poem – a poetic form inspired by the boundless flow of Klein's Vase; where silence rivals the spoken word in significance and ambiguity weaves a seamless narrative, flowing in infinite cyclical movement. It is a poetry style liberated from rigid structures, guided instead by subtle, intuitive principles.
Defining Features
Klein’s Vase is not merely a metaphor but an embodiment of ambiguity; a symbol representing the abstract components inherent in its shape—the design properties of the Klein bottle/Klein’s Vase expressed in mathematical terms. Ambiguity is not just confusion but also possibility—where multiple meanings exist simultaneously rather than simply being unclear.
Guidelines
The lack of any formal structure.
- Liberated from Structure: Inspired by the boundless flow of the Klein’s Vase’s topology it is liberated —but not advocating formlessness—from rigid structures found in most poetry design formats, for example, rhyme, metre, syllabic counts, number of lines, prescribed presentation, etc. An organic responsiveness to meaning would ensure the poem retains intentional fluidity rather than randomness.
- Perspective: The Klein’s Vase has no definable boundary (no inside or outside). This duality in perspective is reinforced by an objective view (wide lens view), juxtaposed with a subjective view (introspection).
- Flow: It aims for a natural sinuous flow to the text with unforced energy permeating the poem, creating a pleasing cadence. Variation in rhythm (through subtle disruptions or pauses) can enhance the impression of movement.
- Subtlety: It is guided by subtlety, where poetic devices don’t overpower the poem. Since some types of tropes depend upon an element of subtle repetition, for example, a common motif, it can provide a rhythmic undercurrent to a poem.
- Themes: It ideally keeps to a single common theme per poem, with the vocabulary sympathetic or complimentary to the topic, and not jarring (pun intended) as it would be contrary to the harmonious ambience being aimed for.
- Keep an Open Mind: Don’t overthink it as you might lose yourself, like in the maze of the planes of the Klein’s Vase—rather rely on organic flow of ideas.
Unique Elements
Klein’s Vase poem embraces ambiguity as a creative lens.
- Silence: It is as important as the words. Silence (the caesurae/pauses) in the lines forms an integral part of the Klein’s Vase poem, imitating the void in the Klein’s Vase. The pause(s) may involve negative space (white space), typographical symbols such as ellipse, etc.
- The Echo: Distorted repetition not only mimics echoes, but also reinforces layered perception, much like the way Klein’s Vase alters space, The distorted repetition of words and phrase, relying on synonyms and antonyms, and the misquoting of phrases (even paraphrasing the earlier text), conveys the characteristics of echoes.
- Fragmented Syntax: It uses fragmented syntax that interacts with coherence—whether meaning coalesces over multiple readings or remains unstable—it is not in preordained phrases (as recommended in free verse), to underscore the fragmented view and freedom of form of the Klein’s Vase.
- Line Breaks: Liberated from structural restraints, it is guided by intuitive principles, for example, the line breaks—opposed to the prescribed, formalistic approach found in poetic forms such as Suzette Prime which favours line breaks in line with prime number syllable counts per line.
Criteria to Obtain Objectives
- Cyclical Repetition: The natural, organic flow of the poem reinforces the feeling of looping by incorporating the cyclical repetition of words/phrases/thoughts, emulating the plane of the Klein’s Vase. Motifs are revisited at irregular, undefined intervals.
- Oscillate Elements: Whereas the poetic device of juxtaposition—which places contrasting images, situations, or thoughts side by side for the purpose of comparison—oscillation between opposites, like sincerity and irony, not merely contrast but displays a continuous interplay; ambiguity itself shaping the poem’s rhythm.
- Tropes: Repeated and revisited topes oscillate throughout the poem with unpredictable regularity. All tropes work to evoke a mood, emotion, or physical sensation. A literary trope is the use of figurative language, via word, phrase or an image, for artistic effect such as using a figure of speech.
- A Rest Stop: Your eyes need a place to REST—best achieved just before the punch line. This might be stylistically achieved by extending the negative space before the end of the poem.
- The Finale: The openness of the final verse (meaning both a line, or a stanza) is a standout feature of the Klein’s Vase poem, carrying ambiguity beyond the poem—its meaning remaining porous even after reading.
Some Recommended Literary Devices
- Figures of Speech: The element of ambiguity is achieved by using figures of speech that embraces opposing interpretations, for example, syllepis (also known as zeugma), puns, double entendre, etc.
- Metaphor & Simile: Figures of speech such as extended metaphor as well as recurring metaphor, is encouraged. A metaphor is often poetically saying something is something else; a direct relationship where one thing or idea substitutes for another, whereas a simile is saying something is like something else.
- Synecdoche is similar to a metaphor, but it uses related concepts to help illustrate meaning. For example, introducing children as ‘mouths to feed’ is part-metaphor and part synecdoche.
- Analogy: An analogy, by using for example, metaphor or simile, can be a spoken or textual comparison between two words (or sets of words) to highlight some form of semantic similarity between them.
- Symbolism: A symbol must be something tangible or visible, while the idea it symbolises must be something abstract or universal. This
- Explored Different Elements: Exploring other aspects of the Klein’s Vase such as the audio and visual elements of imagery:
- Create a concrete poem (graphic poem) using the above guidelines to honour the topology of the Klein’s Vase, or depicting a single chosen aspect, depending on its physical orientation.
- Onomatopoeia is where sounds are spelled out as words; when words describing sounds actually sound like the sounds they describe. It, in effect, adds a sound track to your poem. I might be fun to coin new words to lend some zing to your poem.
- Poets weave euphonious words into their poems when they wish to achieve a harmonious mood. These words usually contain lots of consonants with soft or muffled sounds (like L, M, N, and R) instead of consonants with harsh, percussive sounds (like T, P, and K).
- Et cetera.
MY EXAMPLE POEM
Starlight Eyes
viewing life
through the fingers
of a facepalm
an unhealthy
obsession
to broaden the mind
with the
help from social media
jumbled up in jargon
no more useful than a Word of the Day:
excired: (n) meaning exhilaration and desire
—or—
whenever …
bombarded with unrelated
f.a.c.t.s
as pertinent as
school level algebra
the mind’s ‘nothing box’
teaming with possibilities
inexpressible
visions dancing to an inaudible jukebox
a child’s
toy
kaleidoscope
charting the stars
given way to ‘Stars Foretell’
how we should feel
and think
nowadays
by naming the planets
the stardust
the very essence of existence
we escape categorisation
life views back at me
through the cosmic lens
of perceptions:
starlight eyes
of
hope
shines …
© Suzette Richards (1/5/2025)
CONCLUSION
- Infinite Lines: Use enjambment to create a flowing, endless feel as lines spill over into one another.
- Negative Space: Incorporate deliberate pauses and fragmented lines to evoke the idea of voids and silence.
- Inward-Outward Movement: Balance expansive metaphors with introspective ones to simulate simultaneous contraction and expansion.
- Circular Themes: Repeat ideas, phrases, or motifs cyclically to mimic the looping nature of the Klein’s Vase.
- Layered Perspectives: Include multiple viewpoints within the poem, reflecting the complexity and ambiguity of the form.
- Recurring Tropes: Revisit motifs and themes throughout the poem, reflecting the endless planes within and without the Klein’s Vase.
- Open Interpretation: Use metaphorical and open-ended language, allowing the reader to project their own meanings.
- Breaking with Tradition: Never be didactic. Eschew conventional design formats of introduction, plot development, and conclusion. Embrace fragmenting lines at unexpected points, i.e. it isn’t organic.
- The Finale: The finale is left open-ended, carrying ambiguity beyond the poem.
- Coin New Words: Thinking outside the box is encouraged—even coining new words, as I did with excired.
The indentation of various lines, paired with negative space, is a matter of personal taste – it might, or might not enhance the poem.
The final verse of a poem usually carries significant weight in that it provides a sense of conclusion, wrapping up the poem’s themes and ideas. However, in the Klein’s Vase poem, the finale is intentionally left open-ended. After all, without the participation of readers, poetry is nothing.