Nazmus Saquib's PhD dissertation from the MIT Media Lab centered around embodied math. Simply stated, this is the idea that real-world, relatable representations of math can help create a simpler and more enjoyable language for doing math, compared to the status quo symbol pushing. He proposes a sketch-based medium to create embodied representations, and demonstrates how both elementary and advanced math can fit within this model. Like many hypotheses that examine such fundamental behavior, this thesis combined theory from multiple fields, such as, math, cognitive science, design, and computation. You can read more about Saquib's thesis here.
The Requirements and Constraints
Saquib wanted his dissertation to reflect the amalgamation of math and art that is a key theme in his dissertation, and wanted to incorporate some math-art inspiration in his thesis. He and I spoke at length about his ideas and theories, which helped me empathize strongly with his vision. Two disclaimers here:
I am not an artist and the content I created is not art. But it's also not not-art. So I've decided to call it math-art.
Full disclosure, Saquib and I happen to be married, which also made the empathizing easier!
Based on my conversations with Saquib, my interpretation of the key requirement was to create math-art that shows how math and art are everywhere and are intertwined. The math-art needed to represent diverse settings and needed to capture the reader's imagination.
A key constraint was that the artwork needed to incorporate elements from the developed sketch interface. Also because the thesis was heavy in mathematical theory, the math-art was intended to be more art than math.
An early decision that Saquib and I collaboratively made after some of my preliminary work was to create math-art that looked less like conventional art and were either hand-drawn sketches or were collages of eclectic components. This was to reinforce the idea that math can be playful and also to mirror the artwork often produced by young schoolchildren.
I put together several pieces of math-art that were incorporated into Saquib's thesis, but the one shown above was my favorite. Using an EE Cummings poem as the base layer, I wanted to create a design that would reinforce it's message through math-art. EE Cummings is known for playing with word and punctuation placement to create a desired effect. In this poem, he uses imagery "a leaf falls" and also structures the layout of the words to resemble the trajectory of a falling leaf and to signify loneliness.
I thought adding a math-art layer on top of this could extend and enrich the analogy in the poem while also adding a mathematical angle - how far does a leaf fall; what path does it take to its destination; where, in fact, does its destination lie?
Initially, my idea was to build a tree trunk around the poem with the bottom of the trunk fanning out to represent roots and also accommodating the wider line of letters. A leaf would then be shown falling to the ground with an obvious mathematical relationship between its distance traveled and the height of the tree. But after a few drafts, I realized this visualization was too rigid to be able to capture the evocation of emotion I wanted. Also, few leaves take a straight path from the tree to the ground; most dance about in the wind for a few seconds before embracing obscurity.
These thoughts inspired me to create the visual that is pictured above. I added leaves to the bottom both for its poetic connotation and also because it juxtaposed well with the wider collection of letters at the bottom. The red dotted line represents the path of the falling leaf, intentionally messy, through the gaps in the text. The red dotted line also resembles the object brush strokes from the sketch interface, which can be used to sketch and measure distances.
One of the foundational ideas in math is grouping and lists. Saquib's sketch interface addresses this need using a "list" brush, represented by dashed blue lines. In the world of embodied math, lists don't need to resemble Venn diagrams - an apartment can be seen as a grouping of dwellers, a bus is a grouping of passengers, a nest is a grouping of birds. I've played with representations of groupings in many of the other math-art made for the dissertation. But because it's such an important and playful concept, I wanted to add a simple list here too, which I have done by grouping the letters "leaf" within a drawn leaf.
Overall, I thought this was a very different design challenge and thoroughly enjoyed the process of creating math-art. Leave me a note and let me know what you think or have any feedback!