Afterthought - Putting it all together

This is a post to help me consolidate my thoughts. 

I feel like I am on to something.

A connection I just made was about Amy Alznauer's obsession with following people with obsessions. Individuals who have an obsession and perpetually engage in an activity that would take all their time away (probably without realization) and that they would find extremely rewarding are individuals who have experienced flow.

Csikszentmihalyi (1988) writes about the development of the human consciousness leading to the identify and perpetuity of self. The sense of self cannot be solely focused on fulfilling the goals written into our biology (eat, reproduce, etc). Our consciousness acts as a buffer between what our biology dictates and our social emotional environments in which we must navigate to reach our 'goals' (social goals, cultural goals, biological goals) that we consciously or subconsciously determine for ourselves. Csikszentmihalyi talks about psychic entropy in our information-processing system that is experienced as fear, anxiety, confusion; but there is a balance called psychic negentropy that is the optimal state of flow that provides feelings of exhilaration, and fulfillment leading to higher levels of complexity.

We choose to seek out and engage in activities that draw us into a state of flow because it allows our consciousness to experience new emergent structures in our sense of self regardless of a final goal in mind. It becomes pleasure in doing. To obtain this state that differs for everyone it depends on a number of factors: 

1) personality of the individual - namely the ability to recognize challenge commensurate to their skill level.

2) the activity must be balanced in challenge and skill of the individual, as the skill of the individual rises, so must the challenge.

3) the activity must have clear goals.

4) the activity must provide quick and unambiguous feedback so the individual can know if they are rising to the challenge. 

Understanding Vygotsky's Zone of Proximal Development (ZPD), as an educator, I would need to engineer an activity at the boundary of capability that an individual can do alone, but JUST... and it must constantly be able to move away as the student understands more. 

If the skills exceed the challenge... the student experiences bordeom. 

If the challenge exceeds the students' skills... the students experience anxiety. 

This balance is extraordinarily hard to achieve as everyone is different and providing quick and unambiguous feedback to 30 students is impossible!... UNLESS the student understands just enough for other systems of understanding to provide the feedback. This is where the introduction of art in mathematics class makes sense. 

When writing mathematical poetry - a linguistic meaning making system can act as an immediate feedback provider for the underlying mathematical concepts. For example, the syllables don't rhythmically fit. 

When drawing/painting mathematical pieces - the visual meaning making system can act as an immediate feedback provider. For example, the pattern breaks or there's an inconsistent spot that draws attention.

When sculpting/constructing mathematical pieces - the physical (and visual) meaning making system can act as an immediate feedback provider. For example, the pieces don't fit.

When dancing/playing music - the auditory and kinesthetic meaning making systems can act as an immediate feedback provider. For example, there's too many beats and too few movements, or the rhythm doesn't add up. 

In each of these cases, no instructor is needed to assess and provide prompt feedback. The creation of the art itself is under continuous assessment by the student creator ensuring its development matches or exceeds the visualization towards the goal of completion. It produces a "merging of activity and awareness" so total that "one simply does not have enough attention left to think about anything else" (Csikszentmihalyi, 1988, p.32).

When mathematics is taught abstractly and without context, art may be the bridge back to meaning making and identity that is needed for students. When mathematics is taught practically and contextually, art may enhance student understanding and identity by bringing them into a state of flow developing their sense of self. The self-imposed challenge of adding complexity to artwork keeps a students' actions, concentration, awareness and memory at the expanding boundary of ZPD always within their capability for as long as they maintain a drive toward their goal.  

The experience of flow is autotelic. It is done to experience itself; an intrinsic reward. The best most enjoyable experiences become preserved and transmitted throughout generations as cultural experiences. Huizinga ([1939]1970 as cited in Csikszentmihalyi, 1988) realized that all institutions that constitute society all started as games where participants could experience the joy of goal-directed action. 

So, now that I have my blueprints and mindset, I guess it's time to find the fun/flow.

References: 

Csikszentmihalyi, M. (1988). The flow experience and its significance for human psychology. In M. Csikszentmihalyi & I. S. Csikszentmihalyi (Eds.), Optimal Experience (1st ed., pp. 15–35). Cambridge University Press. https://doi.org/10.1017/CBO9780511621956.002

McLeod, S. (2024). Vygotsky’s Zone of Proximal Development.

Bridges 2026 - Aug. 8th (Day 4)

 This was the final day of the conference. The agenda for the day was to:

1. attend the two plenary talks, 
2. watch the four short mathematical plays, 
3. participate in the free math community event with my family,
4. read my poem in the poetry open mic along with my partners.
5. attend the Poets dinner and socialize with the other mathematician/poets.
6. attend/participate in the informal music night after I put my children to bed.

(I haven't written the agenda for the other days, but this was the shortest list of them all so far!)

Matt Zucker was the first speaker talking about Reaction-diffusion Truchet Tiles. Reaction-diffusion patterns are complex spatial structure that emerge naturally when two or more chemical substances interact locally and spread through space at different rates (wiki) yielding organic-looking structures responsible for patterns like coral patterns, leopard sports, zebra stripes, and fish skin patterns (Fig. 2 from Zucker, 2026). My first stop came when Zucker reveals this project was inspired by Sabetta Matsumoto who asked a question about Matt Zucker's 2025 Bridges talk about his Squiggly Orbs - since that point he was inspired to use Reaction-diffusion patterns to tile. I think this interaction embodies the type of supportive, inspiring interactions that arise from a community of like-minded individuals. I really felt at home in this curious, excited, generative/creative, mathematical community. 

My second stop came at the end of Zuckers talk when he tried to generalize his artwork for the audience: good math art is a good riddle! His argument was that it invites the audience to ask "what are the rules that produce this pattern/shape/art?" This invitation to participate was also communicated by Lester and Ryan in my blog post of Aug. 7th creating a very strong point of entry for mathematical engagement.

This statement connects deeply with me as this mentality created a dramatic shift in my success as a mathematics student in highschool; I wasn't very successful with all the traditional drill-type questions used to hone my skills, but I absolutely loved puzzles, riddles, sudoku, etc. When I came to the realization that each drill-type question was just another daily sudoku, I started enjoying "trying out" each puzzle to see if I could get it, so it really took the pressure off of trying to get the solution for every single one. This connection absolutely reflects the foundation of thinking echoed across the presentations I've seen: 

• Gary Lester saying that artistic sculptures invite conversations and interpretation. 
• Georgina Ryan saying that the artwork (embroidery) invited curiosity through known media (or format... connecting to Nick Sayers below).
• Kerry Mitchell saying his subtle artwork reveals hints of a pattern, but you must work for it. Only then will connections jump out at you over time reigniting motivation to keep digging.
• Saad Mneimneh saying you must be able to engage with math art to achieve the aha! moment.
• Britt Kaufmann saying students receive a hit of dopamine from discovering connections on their own and to give them time to do so.
• Nick Sayers saying math as medium - not the message. I interpret this as trying to tell a riddle with the math, not just presenting the format of the riddle and saying "see? the format? see it? that's all"

The second plenary talk of the morning was by electrical engineer/fibre artist Amy Wendt whose work I've had the pleasure of wearing during the Math/Art Fashion show the night before. Her talk was titled Modular Kirigami Knitting where kiri = cut, gami (kami) = paper. Her work extended beyond paper to materials like Ultrasuede and Kevlar. Wendt represented each line of a knitted piece (visualized as back-and-forth loops like a meandering river system) as a two dimensional pathway, then weaved them together creating surface-covering approximations that were not only 2D but also 3D allowing conforming to body parts like shoulders (Fig.10 below from Wendt, 2026). 

The next stop came during the poetry reading: Jim Wolper likened teaching math to being a jazz musician who is playing the 'hits' in yet another club alongside hundreds of other jazz musicians each night. Motifs foreshadow connections to related theorems that are interspersed throughout the melodies. I absolutely feel this alternative perspective of teaching. Being anchored by the curriculum, the roots run deep with connections and all good teachers (musicians) must know them, but they improvise based on reactions from the audience, how they feel, whatever inspired them recently, their techniques and capabilities, etc. What a fantastic metaphor for teaching. 

Reading my poem about my daughter, meteorology and its comparison to prophetic fortune telling.

The final stop came when Duston Wetzel read a poem that he titled Many Faces that captures his feelings of inclusion in this mathematics community that truly echoes my own. 

References: 

Wendt, A. (2026) Modular Kirigami Knitting. Proceedings of Bridges 2026: Mathematics and the Arts.

379–386.

Zucker, M. (2026) Reaction-Diffusion Truchet Tiles. Proceedings of Bridges 2026: Mathematics and the Arts. 157–164.

Bridges 2026 - Aug 7th (Day 3)

Today started with a plenary talk from Amy Alznauer on Why We Tell Stories. Her main argument was that we tell stories because our lives are stories, and we have questions of which we long for answers. The stories themselves are simply vehicles for council: my first stop. Alznauer introduced a quote from Walter Benjamin: "Council is less an answer to a question than a proposal concerning the continuation of a story which is just unfolding." This makes sense and connects with my experiences and discussion with Coast Salish educators on the topic of parenting; stories are often told as a means of council rather than prescriptive commands that lead to power-struggles. The stories then become a vehicle for self-reflection and introspection; the same story may be told many times with the child pulling a new message from it due to their developing experiences in life. A story becomes a way for a teller to process occurrences of cause and effect, making clearer for themselves relations in time.  

My second stop was when Alznauer brought up the idea (through quotes of Edward Shils, Wendell Berry and Doris Schattscheider) of being at the centre and alternatively (or simultaneously) at the periphery. Each location comes with benefits. As math artists, mathematics is at the periphery of fine art, and art is at the periphery of mathematics. The peripheral relation promotes beneficial qualities of engaging in generative (genius) power as an originator, with freedom and passion of a lover/amateur, with the wonder of a child. Perhaps this is why cross-curricular interdisciplinary projects offer such exciting opportunities; just by engaging simultaneously in two different disciplines, you get to access all the benefits of peripheral qualities.

My third stop was when Alznauer mentioned the tombstone of Lucy Joan Slater which read Computer Pioneer. Alznauer stated that Lucy was homeschooled and that it was a huge benefit to her as she was able to have the time to pursue whatever interested her. This connects with thoughts that I've been having about the rapid pace of 21st century life, time-pressures of government curriculum and the school system, and focused downtime for hobbies (aka boredom that leads to discovery). As Hannah Fry stated in a youtube short, "Time [pressure] - the killer of all things good." to which I absolutely agree. I'm not sure if "fear" is the right word that accompanies time-pressures, but I certainly have made many choices in my classroom out of "fear" (linguistically, perhaps literally) that I will run out of time - condensing instructions for important activities, cutting activities short ruining experiences, reducing exploration, or skipping concepts to name a few. The uninterrupted free mind that can take the time to obsess and wander and pursue imaginative ideas really makes all the difference to a creative (not just creative but generative) individual. I now wonder how I can structure my classroom to have more of this uninterrupted free time where they can pursue what interests them in mathematics, then choose how they wish to represent it... perhaps in more of a Montessori style such that students may have agency to explore several concepts all at once and spend the most time on what is most challenging to them. 

My fourth stop came from Clare Moriarty on Semiotics, Ease and Elegance: Oliver Byrne's Elements of Euclid. Moriarty drove home the fact that Byrne was obsessed with accessibility of mathematics trying to build in many ways/systems for understanding and accessing knowledge. Byrne therefore used red, yellow, blue and black in his print on Elements of Euclid freeing up mental space for geometrical reasoning by rendering each shape/angle/object/ etc in colour, then referencing it in colour during the proofs. This connects deeply with me as a math educator and - before that - a tutor trying to explain or draw things in ways that allowed my students to grasp the concepts. This monumental effort of printing a coloured book in the 1800s that tanked the printing company shows the kind of dedication (obsession) Byrne had in trying to make math accessible.

On the topic of making math more accessible, my fifth stop came during Gary Lester's talk on Art as Math Representation: A practice-based Investigation of Cognition and Pedagogy. Lester wanted to investigate why the notion of "I'm not a math's person" was socially acceptable leading him to develop an art-based sculptural approach with embedded mathematical concepts as a way to invite discussion. Lester found that the same scupture presented a very different message to very different audiences with their interpretation largely reflected by the background knowledge they brought in to the experience. Lester reminded us that when teachers teach what they already know, they fail to communicate complex mathematical ideas from the viewpoint of a novice using their vocabulary and their experiences from which to scaffold. So, how can we extract a math concept's core idea and introduce them from the viewpoint of the novice? Lester finished with two more leading questions that are thought provoking: What are the differing cognitive processes taking place between experts and novices? And, can artistic forms be used as avenue for greater engagement? This becomes another point of entry towards accessibility of complex math ideas.

Quick aside: On Aug 8th (the following day) I had the pleasure of meeting up with Georgina Ryan in the art gallery as I wanted to have a discussion with her about the differences between her findings and that of Gary Lester's. Ryan has created a website called Threaded Theorems in which she shares unique self-made embroidery patterns of advanced mathematical ideas as an accessible entry point for women to become introduced and curious. 

An example of Ryan's free patterns found on her website. What a curious shape this is! Why does every branch break into two? It looks like every part is a smaller and smaller part of the original! Interested?  Go google "Binary Tree" and "Fractals" then combine the two in a search :) 

Where Lester's findings showed that people only cognitively engage with art at the level of their background prior knowledge, separately Ryan's idea feels like a hopeful attempt to introduce and advance mathematical knowledge. These two ideas work together and become driven by curiosity. In the beginning, embroidery enthusiasts would only engage with the artistic qualities of the math ideas, but then find out more about their embroidered concepts through inquiry. I believe as long as we don't let the curious walk away and miss out on an opportunity to engage, then this could be a strong point of entry in education. 

OK, back to Aug. 7th. I attended Saad Mneimneh's talk on The Poetry of Math. This talk was a beautiful perspective shift looking at the provocation of thought stimulated by engagement with math (and poetry). Mneimneh's main argument was that both math and poetry were very similar in that they are both imaginative, use metaphor, deal with abstraction, convey deep consequences, make statements, and even provide plot twists that can excite a reader. Mneimneh likened the Collatz conjecture (google it, it's worth it!) to the poem called "The Red Wheel Barrow" by William Carlos Williams because they were both simple, elegant, basic, unusual, and had an emerging structure without needing to be complex.

Mneimneh left off with my sixth stop: every poem + math concept has a certain level of engagement (similarly to the message by Lester and Ryan the following day) that must occur for a while to be able to receive the aha! moment of realization - this is on the part of the student/receiver/witness/listener/audience. This brings me to a conversation with another poet at the conference, Britt Kaufmann, author of Midlife Calculus, about allowing the engagement on the position of the educator/presenter/performer/speaker:: "If you don't wait [as an educator] the students never receive their own dopamine hit from the joy of discovery, and the learning is truncated... waiting is so hard when you have an agenda."

A seventh stop came when Mneimneh mentioned teaching math without being creative with it is like learning the alphabet but never being allowed to write any words. Ryan furthered this analogy by saying (paraphrased) that you finish your alphabet in grade 1, then for the rest of your life you practice generating more and more complex ideas with this alphabet for the rest of your life... whereas, in mathematics, you don't stop learning the alphabet until you become an undergraduate in university... so the earlier you can shift between being a consumer of mathematics towards being a creator, the faster we will be able to see its place in our life. 

The last talk I attend that day was Susan Gerofsky's Artists Re-storying their Relationship with Math and Art. The participants of Susan's project have all experienced shame, fear, embarrassment and trauma from negative experiences in math class. Through this process of re-storying their relationship with math through embodied means, they have given themselves an opportunity to recognizing and maybe even acknowledging and utilizing mathematics in their lives and artwork. I found Gerofsky's inquiry question to be quite related to Lester's: "How do we break this intergenerational transmission of trauma?" The individuals affected by these negative experiences develop an aversion to math and claim to not be math people. My eighth stop came during her retelling of participant Carole's journey. Carole was a ceramics artist who said that the creation of a mug 24 times isn't creative but creating. It's not generative. This shift in vocabulary for me was interesting because in my classroom I always ask my students to be "creative" when doing their math projects... but perhaps, I need to re-specify that just the act of putting math somewhere other than paper is not enough, but they need to generate something with it. Our experiences in life are limited by our vocabulary to express them. 

Euler's Vision by Tom Petsinis
A dramatic reading by Susan Gerofsky (e), Kristie McClellan (i), Eveline Pye (pi), Oliver Podwysocki (+), Jim Wolper (1), Lisa Lajeunesse (=), Britt Kaufmann (0), and Tom Petsinis (Euler)

The two groups of symbols fighting over zero. 

 

I was invited to participate in the Math + Art Fashion Show in the evening. Here is me wearing a raindow truchet tile t-shirt created by electrical engineer/fibre artist Amy Wendt (seen over my left shoulder) sporting another arrangement of the same truchet tiles on her t-shirt! It was a wonderful experience. 

References: 

Alznauer, A. (2026) Lunar Music, Lost Notebooks, Pentagons, and Paralysis: How the Hidden Stories of Amateurs – of Those Who Love – Offer Vital Counsel to Both Mathematicians and Artists.    Proceedings of Bridges 2026: Mathematics and the Arts. 3-3.

Gerofsky, S., Nicol, C., Li, Z., Leung, A., and Omonade, C. (2026) Artists Re-Storying Their Relationship with Math and Art. Proceedings of Bridges 2026: Mathematics and the Arts. 427–434.

Lester, G. (2026) Art as Mathematical Representation: A Practice-Based Investigation of Cognition and Pedagogy. Proceedings of Bridges 2026: Mathematics and the Arts. 553–556.

Moriarty, C. M. (2026) Semiotics, Ease, and Elegance: Oliver Byrne’s Elements of Euclid. Proceedings of Bridges 2026: Mathematics and the Arts. 1–1

Mneimneh, S. (2026) The Poetry of Math. Proceedings of Bridges 2026: Mathematics and the Arts. 419–426.

Ryan, G. (2026) Threaded Theorems: Hand Embroidery as Mathematics Outreach. Proceedings of Bridges 2026: Mathematics and the Arts. 541–544.

Bridges 2026 - August 6th (Day 2)

Starting off my post with a fibble about my journey on August 4th-5th. The poetic form is based on the first 8 digits of the golden ratio: 1.6180339

Pack.
Westjet steals our prep time.
Call.
Eight hours forty minutes on phone.

Re-booked flight.
Reunite.
Thankful we arrived in Ireland.

----------------------------------------------------------------------------------------

I arrived at the mathematical art gallery absolutely floored with the pieces displayed. Here's a small glimpse:

Today, we started with a plenary talk by Nick Sayers on Math-Art with Meaning. I particularly loved his emphasis on meaning which he gave the examples of poetry, societal relevance, ambiguity, universality and transcendence. Sayers uses math as a medium, not the message itself. This was my first stop. I believe that my most successful lessons have been when I've used math as a means of developing an idea (ie. graphing function art, angles, shapes and geometry) instead of as an abstract end in itself learning it for the sake of learning it. Before i dig into planning my future units, I will need to remember this brief and powerful idea of "math as medium, not as message". This is impactful because when it is used as a tool to work something into existence through a means of self-expression, then the creator feels the utility and importance of the tool - especially when it improves the quality of their life. 

Sayers foreshadowed aside ties in with his final inquiry question for us: What is the meaning of your math-art? Art for the sake of art was lost to me until a few days ago, when I read through Saad Mneimneh's presentation proceedings about "The Poetry of Math" and the thoughts that arise when we engage with poetry in the same way as a mathematical formula regardless of the creators original meaning. When the process itself brings about new thought pathways that become the keys to meaning-making for the individual, the making of the art (not necessarily the art itself) becomes meaningful to the creator. This would infer that the world is full of human-slop (not AI-slop) and that not all art is meaningful to everyone (or anyone), but the process of making it helped to transform the creator themself. Mneimneh reiterated that, "meaning is in the journey and the process" during the Q&A period. 

Throughout each of Sayers' math-art pieces, he demonstrates his positionality and intersectionality as mathematician, artist, eco-activist, father, programmer, and pro-cyclist. This brings me to my second stop: Find the intersection where all your passions, values, and skills meet. Sayers has found a unique niche where each of these pieces of his being unite and mutually strengthen each other while contributing to the betterment of society. I think this is one of the prime functions that teachers are capable of due to our unique positions of constantly and rigorously introducing new ideas, tools and experiences to our students. I keep thinking about helping students develop a relationship (and making-meaning) with others and their environments, but I keep forgetting that they need to be able to develop the strongest relationship with their own self through noticing, recognizing, and reflecting.

Our second plenary talk was with Dave Whyte on Bees + Bombs, his webpage is https://beesandbombs.com/ where he highlights his journey in developing short looping geometric animations (gifs). Listening to his journey of growth as an artist, mathematician and programmer was very inspiring as it required observation, experimentation, excitement, reiteration, and playfulness. My third stop came when he introduced a simple idea that the symbol for nothing is 0, and the symbol for everything is ♾️... so everything is nothing with a twist. This cheekily became one of his frequently used tools in his bag of tricks but the concept is profound. I visualize the twist being the flip of a zero from the numerator to a denominator. I imagine it like a mindset going from a thought of scarcity to one of gratitude. It is a really appealing metaphor of life for me. 

During the Q&A, someone asked about Whyte's creative process: he jokingly declares that he thinks things, writes them down, and then creates them... but there's so much more than that. Whyte has a vague idea about the kind of effect that would be visually attractive to him, then he experiments and tries many things. Sometime he comes up with something that he absolutely loves, an intricate visual pattern with hidden seams. Sometimes he comes up with nothing and throws it away. This brings me to my four stop of the day: Both Sayers and Whyte have exceptionally explorative (or playful) attitudes towards creative projects. McClellan helped me to connect this idea even with the talks from Aug. 5th of which I was absent. She said each presenter was extremely playful and wouldn't stop tinkering and reiterating and exploring and tweaking just for fun or out of curiosity! These examples have solidified my belief that playfulness is one of the most important qualities of a successful creator and mathematician. 

I attended six more presentations today. Surprisingly my fifth stop is the most important things I've learned have come from the Q&A sections regarding the artists preferences or creative processes. This makes me want to come to the next presentations with some pre-written generic questions all related to their creative process, or meaning-making because, as stated in stop one, the creation of the art is most transformative for the artist themself! So who better to report out on it than them of what they learned?

An example of this was during Kerry Mitchell's presentation on Creating Art with Space-filling Curves. He mentioned his favourite part of creating these pieces (ie. Fig 11 below) is that the Hilbert curve is subtly embedded in this abstract artwork, it doesn't jump out at you but you have to work to reveal it. I appreciate Mitchell's response as I feel the same way about my artwork. I subtly embed or hide easter eggs in my artwork so that it has layers of meaning for those who engage with it. There's a saying for this: "if you know, you know" abbreviated "IYKYK" online. When digging or revealing new layers within artwork, it re-ignites a viewer's interest and helps them further develop an expectation for success and discovery that motivates them to keep exploring/digging. The same happens in mathematics!

This reminds me of Aharoni's (2014) discussion of an unexpected twist in poetry (and mathematics) where one level of meaning is made while the details of a poem or story are read until the unexpected twist occurs that forces the reader to take all that accumulated data at once and re-interpreting it with a new meaning giving the reader a sensation of transcendent beauty (Su & Jackson, 2020) - giving the reader a glimpse into a larger truth by comprehending a great deal all at once. 

That's all for now!

References: 

Aharoni, R. (2014). Mathematics, poetry and beauty. Journal of Mathematics and the Arts, 8(1–2), 5–12. https://doi.org/10.1080/17513472.2014.943490

Mitchell, K. (2026) Creating Art with Space-Filling Curves. Proceedings of Bridges 2026: Mathematics and Arts. 45-52.

Sayers, N. (2026) The Mathematical Art of Bikes and Children's Toys: Using Bicycles and Everyday Materials for Geometric Drawing. Proceedings of Bridges 2026: Mathematics and the Arts. 5-12.

Su, F. & Jackson, C. (2020). Mathematics for human flourishing. Yale University Press.

Whyte, D. (2026) Bees & Bombs: My Gifs. Proceedings of Bridges 2026: Mathematics and 

        the Arts. 2-2.

Poetic Development - Modulor Poem "Crystal-ball Bath-time"

This poem was by far the most challenging to create. After e-mailing the form creator, Lisa Lajeunesse, and asking for a few pro-tips for how to think to develop such a poem, I was successful in creating a poem about my daughter and other things I'm passionate about: Earth Science & magical fantasy.

The modulor poem form was tricky for me because, like the Miura-Ori poem form from earlier blog posts, the separate sections need to be able to be read together, but also be capable of standing alone; not only that but they should be able to be shifted into different positions and still retain (or enhance!) meaning - but maybe not the same meaning as it would create an entirely different thought provoking experience.

My process started with meteorology (tile 1: upper LHS), then after filling the space with its own unique poem, I tried to compare being able to witness and predict the forecast on the planet with magical fortune tellers peering into crystal balls. So line by line, I wrote a similar poem as tile 2 (upper RHS) with a magical twist while cross-checking for meaning and coherence with tile 1. Finally, thematically starting with large-scale global viewing and prediction, zooming into small-scale crystal-ball viewing and prediction (despite both processes looking similar where one is staring into a glowing glass sphere, the other stares into backlit glass rectangular prism with a keyboard), we zoom out (and simultaneously in) to my daughter's bath time and the microcosm of her toys experiencing the changes in environmental conditions invoked by her.

Tile 3 was written separately only needing coherence in inspiration from tiles 1 and 2. The whole poem - once inspired - was a joy to write, but until inspiration struck was quite a daunting challenge! I am hoping to read this at Bridges Conference 2026.

Side note with consistent spelling issue:

I keep writing/typing modular poem because I think of the parts (or tiles) as modules that can be shifted, replaced, and/or removed. I've been corrected several times with the spelling being modulor consistent with the spelling of the title of the book Modulor by Le Corbusier the inspiration for the poetic form. So this is more of a note-to-self for future recollection.

Poetic Development - A Series of Goldies related to Experiences of Stress

Struggle

Growth.

Also known as Learning.

Thrive:

When struggle becomes a hobby.

The good stress;

A teacher.

Experience for life-long learners.

-----------------------------------------------------------------------------------------------------------------

Push

Stress.

Imagined perceived threat.

Help

push boundaries to new limits.

Too much push,

no support:

Affectual effect of trauma.

------------------------------------------------------------------------------------------------------------------

Pain

"Fight"

"Time to dissociate"

"Hide"

Subconscious responses to stress.

We can't run.

We can't fight.

Endorphins prepare us to receive. 

---------------------------------------------------------------------------------------------------------------------

Hope

Add

one more thing to your list.

Gain

control with snowball-momentum.

Overwhelm/

Panic-mode;

action combats ambiguity.

- Olly

Poetic Development - Miura-Ori Template + Golden Fibble Process

I have been working on templates to try and simplify the process of creation for myself. 

Here is the Miura-Ori foldable template: 

And the paper template with rules and shaded boxes to assist in breaking down which parts of the poem would be written in order. Even through an 8.5 x 11 inch piece of paper can produce an 8 (words) x 11 (rows) form. Bigger might not necessarily mean better. 

Creating a 8x8 would work just as well (but unless folded to obtain exactly 8 rows, you'd need to cut the paper). Here's another template. 

Some tips I've found help:

• If the subject in NE boxes is singular, it helps if the subject in the NW boxes is singular too so that verb tenses line up appropriately and one doesn't have to add or subtract 's' when switching between singular/plural conjugations. 
  
  
• Write with space in mind for adjectives and double meanings. Break larger words with a single meaning into two with a hyphen for additional flexibility and meanings (Example: takeaway = take + away, eavesdrop = eaves + drop)  
  
  
• Thank goodness for the repetition of words in the English language that function as both a noun and a verb depending on the em-PHA-sis! (Example: pro-DUCE (verb), PRO-duce (noun))

I'm working on developing a poem with this in mind. It is quite challenging! If anyone reading this makes their own, please share your creation. Art inspires more art!

 

And now for something completely different: 

A Golden Fibble (8 lines/144 syllables; 5 lines/89 syllables) about Astronomy (Attempt 1)

Another dawn Sun arises slowly (10) traversing the darkness. (6)

Rotations of place denotes time. (8)

Experiences frame it.(7)

Eight-light minutes to travel one AU. (10)

The energy loss: a glorious treasure (11) that we squander. (4)

Just five billion (5) more years of solitude (6) before our star runs out of patience needing attention. (14)

Wanting to be closer after (8) tinkering for billennia (an eon) (11) making heavier products in the (9) energy factory. (6)

Will the human experience get to (10) witness a planetary nebula (10) form from a distance?(5)
Currently 140 syllables

Will we get to participate? (8)

I heard you get ribbons for that. (8)

I might attend if I can get over (10) the loss of our monthly nightlight (8) and timekeeper. (4)

It has really stilled my seas. (7)

I might be late. (4)

Currently 49 syllables

---------------------------------------------------------------------------------------------------------------------

A Golden Fibble (8 lines/144 syllables; 5 lines/89 syllables) about Astronomy (Attempt 2)

Another dawn Sun arises slowly (10) traversing the darkness reluctantly. (10)

Rotations of place denotes time. (8)

Experiences frame it.(7)

Eight-light minutes to travel one AU. (10)

The energy loss: a glorious treasure (11) that we squander. (4)

Just five billion (5) more years of solitude (6) before our star runs out of patience needing attention. (14)

Wanting to be closer after (8) tinkering for billennia (an eon) (11) making heavier products in the (9) energy factory. (6)

Will the human experience get to (10) witness a planetary nebula (10) form from a distance?(5)
Currently 144 syllables

Will we get to contribute to its creation? (12)

I heard you get ribbons for participation (12), and that showing up is half the battle. (10)

What would be written in my orbit-uary? (12) Could this make me a Mars-tyr? (7)  

I might attend if I can get over (10) the loss of my nightlight (8) and monthly timekeeper. (4)

It has really stilled my seas, (7) so I might be late. (4) Don't wait up. (3)

Currently 89 syllables

-----------------------------------------------------------------------------------------------------------------------

(Final) Title: Five yawns.

Another dawn Sun arises slowly traversing the darkness reluctantly. 

Rotations of place denotes the time.

Experiences frame it.

Eight-light minutes to travel one AU. 

The energy loss: a glorious treasure that we squander. 

Just five billion more years of solitude before our star runs out of patience needing attention. 

Wanting to be closer after tinkering for billennia (an eon) making heavier products in the energy factory.

Will the human experience get to witness a planetary nebula form from a distance?

Will we get to contribute to its making? 

I heard you get ribbons for participation, and that showing up is half the battle. 

What would be written in my orbit-uary? Could this make me a Mars-tyr?

I might attend if I can get over the loss of my nightlight and monthly timekeeper.

It has really stilled my seas, so I might be late. Don't wait up.

Poetic Development - The Beginning

April 4th, 2026: The Beginning

Some interesting thoughts came to mind after attending the Math/Art Manifesto discussions with Fumiko Futamura. Susan Gerofsky described Dadaist automatic poetry (which was completely new to me), and I visualized placing types of words on each coordinate of a Cartesian plane (instead of shaking random words and drawing them from a hat).

The origin being a proper noun, then expanding out in concentric circles we would have adverbs, verbs, adjectives, and more adjectives, more adjectives, then another noun (ex. (0,0) = Olly, and (3,5)=quietly, (3,-5)=quickly, (-3,-5)=sneakily, (3,-5)=briskly and (5,7)=read, (-5,-7)=biked, (-5,-7)=hiked, (-5,7)=travelled, etc. with other values filling in all the integer coordinates). Then depending on the graphical equations used, we would produce a different iteration of a poem. This is still in its development as an immediate flaw would be vertical and horizontal translations whose graphs do not cross the origin. Regardless, I’m hoping to brainstorm by troubleshooting with AI to tackle the structural issue. Perhaps concentric circles are not the answer for parts of a sentence.

April 6th, 2026: Update

With the help of Claude.ai, it developed an experimental version of the Dadaist-type graphical poem generator. I asked it to lay different types of words in concentric circles around the origin, varying the qualities of the words based on the quadrant type (example: positive bright words = positive quadrants).

• Proper noun (0,0)
• common nouns (radius of 1-2)
• adverbs (radius of 3-4)
• verbs (radius 5-6)
• adjectives (radius 7-8)
• abstract noun (9-10)

Next, I asked it to create a series of basic equations that could be clickable to generate a poem with an option of adding in your own equation. I asked the poem generator to only pull 9 words as that is pretty typical of a regular descriptive sentence despite the radius being 10 which would give the linear poems a maximum wordcount of 20. It has been a very interesting experiment so far! 

Here is the link to try it yourself! 

I'm not quite satisfied with my exploration. I will continue developing.

 

Now for something total different, I wanted to combine the idea of the Miura-Ori origami fold and write a poem onto it. Due to its mountains and valley's, imagining that the creased/folded sheet of paper itself was the landscape and your head was the sun arching overtop of it there would be times when one of the faces wouldn't be visible, then then entire poem would open up at high-noon, then as you set on the other side of the landscape the opposing side of the poem would not be visible. I want to develop a poem that transforms as you pass through these three positions. 

(image created with ChatGPT to visualize this idea)

This idea should be similar to the old holographic lenticular prints where we, the viewer, change position and see a moving image.

(Source: https://cdn11.bigcommerce.com/s-c6093/images/stencil/1280x1280/products/714/849/Lenticular-Printing-Animation-Card-3D010-__53167.1733308668.jpg?c=3)

Counting the folded paper facets from a previous experiment with the Miura-Ori, I believe there would be an 8x11 grid that I could use to develop this poetry. That means, every "east" facet needs to create a stand-alone poem with meaning, while every "west" facet must do the same. Combining both "east" and "west" together should create yet another poem that gives a fuller picture altogether. 

Lines 1,3,5,7,9,11 = positive? hopeful? 

Lines 2,4,6,8,10 = negative? sad? hopeless?

...WAIT. Thinking more about this, I am simplifying the Miura-ori too much by thinking about it in only two orientations; the lenticular hologram idea needs just two facets (east & west), and the folds would not be particularly interesting in the shape of a zigzag. However, the facets that are presented in a Miura-Ori fold have angles facing a "northern" or "southern" direction as well adding complexity not only to shape but also to the potential structure of the poem. I may be able to create five separate poems by using each north-eastern face, north-western face, south-eastern face, south-western face, and finally high noon positions to develop unique poetry in one. This poetic form may be an interesting linguistic challenge. Here's a diagram of what I'm thinking: 

Each face is labelled so you can see how many words would appear while in a view orientation. 

Kristie T & Olly P: The Geometry of the Blade

Here are the links to our final project in our course on Teaching Mathematics with the Body and through the Arts - a presentation that features four lessons, swordplay concepts with spotlighted mathematical principles, a review f our piloted lesson in the classroom and links to our lessons, teaching slide deck, and connections to academic research (it's 22 minutes long).

Photo by Lance Reis on Unsplash

• Canva presentation includes videos that will auto play as you progress through.
• YouTube video of our presentation. (Same as the Canva, but allows for rewinding or skipping forward in the presentation). 
• Lesson plans
• Teaching slides view only and template link.

Week 10 Readings: Math & Traditional and Contemporary Practices of Making and Doing

Reference: Kallis, S. (2014). Common threads: Weaving community through collaborative eco-art. New Society Publishers. 

Summary: In this excerpt from Kallis, she poses questions about a future where we centralize our society on producing for ourselves once again - a means to shelter, clothe and feed ourselves. The movement requires a different set of values and ways of thinking that brings consciousness, self-esteem and empowerment.

I see value in so many of the things Kallis writes in her book. Here are a few that connect personally:

"From outsourcing to local factories, then national factories, and finally to developing nations, we have happily divested the responsibility of taking care of ourselves" (Kallis, 2014, p. 21).

"...the process of meeting our own needs provides opportunity for relearning lost skills; un-venting ancestral knowledge and technologies we are otherwise at risk of losing" (Kallis, 2014, p. 21).

"The act of learning to make for personal use what we have previously purchased is perhaps the most fundamentally important gift we as individuals can give to ourselves" (Kallis, 2014, p. 21). 

"...we must find ways to see change from the perspective of what we are gaining (strengthened community resources), not what is being lost (ease of global consumerism). ...No matter how truthful what is being said, environmental doomsday lectures scare many people away" (Kallis, 2014, p. 22). 

This way of thinking has been abandoned in favour of cheap and easy influenced greatly by a much faster-paced lifestyle. Unless these arts of clothing oneself is a hobby that you can invest countless hours into outside of your 'normal life', we're giving into the abundance of availability of potentially cheap and easy. 

These ideas of being self-sufficient with my own hands have crossed by mind many times in my life, and I have always been attracted to hand-made crafts found in local markets with artisans. A few places that really piqued my interest has been Granville Island shops, Saturday-morning markets in Penticton and more recently, Etsy! The ideas in Vogelstein et al (2019) about foraging, dissecting and re-enacting (or recreating in my case) is something I've done for fun given my self-imposed financial constraint I discussed in a previous post.

A bustling market in Japan full of hand-made items (Photo: Oliver Podwysocki).

I've always wanted to participate in a Christmas market (Photo: Oliver Podwysocki).

I wanted to learn leatherwork to be able to develop skills with these materials and tools. Then, I realized that outside of making durable clothing items and gear, I could make shoes! Shoes being an absolute necessity in our daily life, developing skills of a cobbler was really exciting and I finished my first pair in 2023.

As described by Kallis, there is a sense of heightened self-esteem (or better yet, self-efficacy) knowing that I can provide for myself (and family) and not need to rely on an external system. I have a goal of trying to learn all self-sustaining skills so that I will not need the consumer structures in place to - at the very least - clothe and feed myself and my family. 

This post doesn't have a central mathematical thread tying it to the rest of the course, but broadens the view of how we can provide opportunity to generate this kind of back-sourced (opposite of outsourced, as used by Kallis) thinking and doing to develop a healthier community, social identity and sense of self. Having these goals in mind should help to guide our choices to engineer experiences for our students (and self) by manipulating/modifying our local community environments in a way that will provide mathematical experiences that develop a healthier Western culture. 

Wonders: 

• Can we manipulate the pace of life so as to accommodate the production of self-made items? 
• What does the cyclical timeline look like for planting, harvesting and processing nettle, dogs bane and milkweed for cordage, rope, or spinning? (This I can google. I plan on using a seasonal round template to document these timelines in planning to develop a school community specifically for fibre arts).
• How many of these processes can happen within a semester?
  (ie. deciding on crop, planting, harvesting, processing, and creating)
  (ie. will the past semester need to "gift" the future semester with a decision of a crop-type such that the future semester can reap the benefits of crafting with it?)
• How can I develop a Pro-D workshop to teach my math department (who are VERY traditional) and colleagues to lead by example?
• Are there mathematical papers that demonstrate these inherent principles that can help justify these choices to administration, parents and - most importantly - my (traditional-math) students, similarly to Bohr & Olsen (2011) and Astrom & Astrom (2021)? 

That's all for now.

Week 10 Activities + Connections: Interview with Lisa Lajeunesse

Our final week creating a blog post. This week, we have several bonus activities to engage with and I'm going to do my best to make some final connections. With that said, this week is a bonus and no one needs to read this :) Skip to stop 7 if you want to try the Eratosthenes Poem generator I asked Claude.ai to develop.

Interview Link to Lisa Lajeunesse video (2026): https://vimeo.com/1173500795/9c65fde7a1?share=copy&fl=sv&fe=ci 

Summary: Lajeunesse presents his many artistic mathematical examples of symmetry types found in the arts using the image below as her foundation. 

Stop 1: @ timestamp 11:39 Lajeunesse brings up a quote by Henri Poincare. "Mathematics is the art of giving the same name to different things." 

My reading group this week had a discussion about a founding theme in mathematics and whether to include this idea as part of the criteria for a Math/Art Manifesto. It is the idea that mathematics is the imposition of rules, categorization and structure on natural observations or as creation. Lajeunesse interprets Poincare's idea as categorizing two different experiences or events with the same name if you can recognize it as the same concept. Mathematics may be the right language for being able to articulate similarities between seemingly different experiences. 

In addition, musicians have terms for their techniques of composition that are similar to mathematicians.

Musician	Mathematician
Pattern	Melody
Horizontal Reflection (Reflection about the Y-axis)	Retrograde
Vertical Reflection (Reflection about the X-axis)	Inversion
180° rotation	Retrograde Inversion

Stop 2: @ timestamp 30:48 Lajeunesse uses the film Memento (2000) by Christopher Nolan to describe a retrograded (reversed in order) conversational (back-and-forth) crab-canon (normal & reverse played simultaneously) based on symmetrical reflection. 

This was one of my favourite movies growing up due to its unique structure, interesting ideas and tragic storyline. When I was in my twenties, I didn't have the vocabulary to describe the structure of this movie with terminology, but those who described it would say that the whole movie is "played backwards" which doesn't accurately describe its complexity. 

This is a screenshot from Lajeunesse's interview showing the complexity of the shot list.

Stop 3: @ timestamp 41:32 Lajeunesse explains a musical movement called Serialism where composers wanted to rebel against the current cultural 'sound' and break the mould with more dissonance. In Serialism, they needed to play all twelve notes within the octave before they could repeat the same note again. To assist their composition process, they developed the Serial Matrix (below) that has a similar structure to a Latin Square (or similarly, Sudoku).

Stop 4: @ timestamp 1:11:01 Lajeunesse challenges us to write a Goldie or a Golden Fibble. Both styles were developed by American mathematical poet, Sarah Glaz.

A goldie is an eight line poem written with syllable count the same as the digits of the golden ratio. 

A golden fibble uses two pairs of consecutive Fibonacci numbers to construct a two stanza poem.

Here is my attempt at a Goldie: 

See?

Subjective perception.

How?

Vocabulary defines us.

We filter

and ignore

that which we cannot describe in words.

Stop 5: @ timestamp 1:15:34 Lajeunesse and Gerofsky converse over the origins of the names of Latin squares and Greco-Latin squares which I have been wondering about myself. But once Lajeunesse describes the Greco-Latin square feature of two categories overlaid with each combination appearing exactly once - this connected directly to De Vries's (2016) video on Mathematical Quilting where I've heard the term "mutually orthogonal" before when describing combinatorics of quilting patterns (De Vries video @ timestamp 0:43:35).

The Greco-Latin Square from Lajeunesse's (2026) video

The Latin Square Pattern used for making the quilt of a projective plane of order 4. (De Vries, 2016). De Vries mentions stacking the different squares at the top of the image overtop of each other to achieve this mutual orthogonality.

So, Greco-Latin squares = Mutually Orthogonal Latin Square.

   

Stop 6: @ timestamp 1:17:53-1:31:02 Lajeunesse describes a literary work by OULIPO member George Perec (1936-1982) called "La Vie mode d'emploi" (1978). The setting, structure, and constraints in writing this book are absolutely fascinating. 

A diagram of the setting of the book to help Perec organize the structure of the chapters and movements between them using a 'knight's tour' - the movement of a chess knight across the entire chessboard visiting exactly each square once. 

The list of constraints for the chapters. Choosing the constraints are a little bit fuzzy to me as I'm not exactly sure why there are this many ordered in this way. Regardless, this process of using a mathematical foundation with constraints is a really interesting way to generate a story!

Stop 7: @ timestamp 1:48:22 Gerofsky inquires about how Lajeunesse generated the Sieve of Eratosthenes poem. This got me curious as to how to create one myself because my first attempt became absolute gobbledygook. I went through He Heard the Snow and analyzed the parts of the sentence. Here is my data:

So following this template, it would be possible to create a poem with the same parts of a sentence structure even if using random words. With this structure in place, one would create this: 

Pronoun verb noun, article adjective noun conjunction adjective adjective adjective noun, adverb conjunction noun, adjective preposition noun, article adjective adjective adjective noun verb.

Noun adjective conjunction adjective noun conjunction adjective noun adjective adjective verb.

Pronoun verb article noun adjective adjective adverb noun preposition article adjective noun.

Adjective noun adjective.

Pronoun verb article noun adjective adverb preposition article noun.

Definitely not as catchy as Lajeunesse, but it would be interesting to set some word values to substitute for "adjective 6" and "adjective 9", etc. Then, see what it would become just like a Mad Libs.

For fun, I developed a Sieve of Eratosthenes poem generator using the skills I developed from EDCP 585 (teaching and learning with GenAI), Claude.ai and the structural template from Lajeunesse. 

Here is my poem, and a link to the generator if you would like to give it a try yourself! (It's not perfect nor pretty and could do with some tweaks, but there is an option to go back and edit your words to make the poem flow more smoothly, which I appreciate)

Our Home

I wander Moon, the pale home but deep endless free space, quietly like puddle winking across penumbra the limitless unappreciated invisible Earth cycles.

Moon pale but endless space like winking penumbra limitless invisible cycles.

Deep puddle unappreciated.

I wander the home, free, quietly across the Earth.

In the construction of this poem, Gerofsky and Lajeunesse describe starting at the end and working backwards towards the beginning. However, part of the fun/surprise is to surprise myself with what's being created, so if I were to write poetry for others I would definitely use the process of starting with the 9 key prime words and work backwards... but to surprise myself - I used the generator so I can feel the surprise along with the reader. 

Stop 8: @ timestamp 1:52:09 "The first exercises that we had were highly constrained otherwise just the presentation of the blank page can be overwhelming for someone just starting out and doesn't have a lot of confidence and doesn't have an artistic direction in a sense...it can be really intimidating...constraints can be really helpful" (Lajeunesse, 2026). 

About 12 years ago when I first started my PDP, I was told of a study where children played in a field without a fence and due to the vastness of this space, they all stayed very close together. Then, they put up a fence and the children ventured right to the edges of the fence to play covering a space far greater than that with the field limitlessly presented. This idea blew my mind, and upon further personal reflection is exactly how I function as a human as well. 

I am paralyzed by choice and possibility because before I make a choice, I need to prioritize and ensure that the task I'm doing is appropriate for the time allotted, the space provided and I won't be interrupted just to name a few thoughts. This is an added layer of decision making that doesn't aid in a relaxing activity unless there are a whack-load of constraints that force a direction. Frequently, I must impose my own constraints in my creative direction or else... paralysis. So, one of the easiest ways has been imposing a financial constraint in my life and in my classroom - this usually helps to limit, time, resources, effort and waste. 

I understand that this isn't the same process for everyone and children see threat when choices are taken away, but I see limitless freedom in playing up to, on, around and within the fence incorporating the crossing of the fence into the artistic direction that is presented. I need the balance of restriction to feel freedom; this is a profound and paradoxical concept.

Thank you Lajeunesse and Gerofsky for the intriguing discussion, and for the thoughts that you've inspired.