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.