Verticality, Triangle, Circle, Square, and Lessons from Aikido for Academia: Class Assignments, Research, and More

In my last offering of CSE 484, the undergraduate computer security course at the University of Washington, a student asked me how I cultivated my teaching philosophy. My answer: Through martial arts and yoga. While one new to these arts might think that they are all about physical movements, they are — or at least can be — so much more. Martial arts and yoga can teach us how to approach our lives and our relationship with everything around us.

In addition to being a computer science professor, I am an aikido student of Barrish Sensei and the Kannagara Earth Shinto Dojo. In this post, I provide an interpretation of the principles of “verticality” and “triangle, circle, square” from aikido, as taught to me by Barrish Sensei, to academia — namely, to class assignments and research. The question I explore is: What should one do if they find themselves in a challenging situation, e.g., if they encounter a challenging homework assignment or a difficult research question?

The intended audience of this post is any student working on challenging course assignments or PhD students (or other students) or researchers focused on scholarly research projects.

Note: While I attempt to make this post accessible to those who do not practice aikido, it is somewhat challenging to describe these aikido concepts in words. I hope what I provide here is still useful to non-aikido practitioners. I structure this post such that the more accessible parts come first.

Calligraphy of “Triangle, Circle, Square” hanging in the Rising Sun Dojo in Kissimmee, Florida. I first felt the power of this calligraphy and its lessons while training Kannagara Aikido with Barrish Sensei in Granite Falls, Washington.

Overview of Recommendations: A Short Summary for Both Aikido and Non-Aikido Practitioners

I provide a short summary of my aikido-inspired recommendations here.

When faced with a challenging situation — a challenging homework assignment, a challenging research question, and more, one might consider:

• Verticality: Pause, feel a powerful vertical connection between the earth below and the sky above, and breathe deeply. Establish and maintain a sense of calmness and perspective that is both aware of and detached from the challenge at hand.
• Triangle: With that sense of verticality, calmness, and sense of perspective, feel a detached connection with the challenge at hand. Then, with a sense of kindness, curiosity, and openness, determine an initial point of entry — an initial approach for tackling that challenge. The triangle represents the finding of (or arrival at) an initial entry point.
• Circle: Again with a sense of kindness, curiosity, and openness, begin to tackle the challenge. The circle captures the movement of the mind and the body as it navigates that challenge, changing directions as needed as the challenge evolves or new insights about the challenge arise. Continue to maintain your verticality, calmness, breath, and detached awareness. The circular movement is part of the technique or method you will use, but is also involved in preparing you for the decisive application of your technique or method (square, below).
• Square: The circular movements above are not erratic but, rather, are built on the strong foundations that you have established or are establishing. These strong foundations — the techniques — are represented by the square. In courses and in research, the foundations are whatever materials you are learning as well as all the materials you have learned before. As you tackle the challenge, with both confidence and openness to new insights and discoveries, apply the techniques that you have established or are establishing.

While each bullet has a distinct label, the concepts are also all quite related. For example, the foundations and known techniques (square) help one determine the initial point of entry (triangle). The verticality enables fluidity and agility of movement (circle). And, as one explores the problem and positions themselves (circle) to applies the technique (square), new elements of the challenge may arise, in which case one may need to adapt and explore new entry points (triangle).

In an aikido training session, we learn how to apply the above principles in challenging combat situations. But a challenging combat situation is in many ways just like any other challenging situation and, hence, the principles we learn in aikido — and try to incorporate into the fabric of our being — apply far beyond combat situations.

The Opposite: A Short Summary for Both Aikido and Non-Aikido Practitioners

To better understand what the above is, it might be worth also articulating what it is not. In a challenging combat situation — or any other challenging situation in life — it may be tempting to “jump right into the fight” or “completely disengage”.

“Jump right into the fight” might mean moving without fully thinking. Or, it might mean focusing all of one’s energy on the opponent, directly, such that they are not aware of whatever else is around them and they become stuck if the opponent moves or changes their technique. If you’ve ever seen an incredibly angry person, you might notice that all their energy appears to be on the front side of their body. All of these are examples of not having verticality and of not using the triangle-circle-square approach for navigating a challenge.

In coursework, an example of “jump right into the fight” might be reading a problem statement and then starting to solve it in the “most obvious way” without taking the time to make sure one understood the problem correctly or without asking whether there might be other solutions.

In research, an example of “jump right into the fight” might be tackling a research problem without first asking whether it is the right research problem to be working on. Or, maybe there is a different and better approach for solving the problem. A variant of “jump right into the fight” is not taking a step back after working hard on a problem for multiple months; by taking a step back — and establishing verticality and applying the triangle-circle-square principles — one may realize that there are other ways to tackle the problem or, perhaps, that one should shift to working on a different problem.

“Completely disengage” might mean giving up and not fighting. In a combat situation, if one is frozen or becomes stiff, then they have disengaged from the fight and it is hard (if not impossible) to regain control of oneself or the situation. And, if one simply gives up, then the fight is over.

In coursework, an example of “disengagement” might be to procrastinate on working on an assignment. It is good — if not essential — to have work-life balance, and it is my belief that one should not have to work on course work all the time. So, this paragraph is really about the following situation: When it is time to work on the assignment, if one can’t bring themselves to do so, then that is an example of “disengagement”. Establishing verticality, and moving through the triangle-circle-square methodology can help.

In research, an example of “disengagement” might also be spending a significant amount of time trying to figure out “the perfect and exactly right” methodology to use for one’s research before beginning the research process, rather than finding an initial entry point (triangle), making some progress (circle and square), and then adapting (new triangle) as one learns more. That initial entry point (triangle) and the initial efforts (circle and square) may not be what you ultimately use in the final research problem. But, through establishing verticality and by applying the triangle-circle-square methodology even when the final direction is unclear, one can make initial progress, and that initial progress can lead to new insights and understanding that then, later, provide a foundation for the final methodology.

On the above and related topics, readers might also be interested in my post on The PhD Process, Measuring Progress, Procrastination, and Unlocking the Next Research Step.

Aiki Taisai and the Rest of this Post

I recently returned from Aiki Taisai, an aikido retreat hosted by Barrish Sensei and the Kannagara Earth Shinto Dojo in Kissimmee, Florida. I always learn so much every time I have a chance to study under Barrish Sensei, and this time was no exception.

I could write volumes on Barrish Sensei’s teachings alone — and someday I would like to! I was inspired to write this post after realizing how fully aikido training has impacted my approach to many challenges in academia.

In the rest of this post, I explore the principles outlined in this article in a little more depth.

The Vertical Column

In Barrish Sensei’s aikido classes, we have been working at establishing our vertical column — a vertical connection of our bodies with the earth below and the sky above. We have been cultivating this vertical connection primarily through our jo (short staff) and bokutō (wooden sword) training. In our training, we reach high into the sky with the tip of our jo/sword while feeling our breath enter deep into our bellies and feeling the ground beneath our feet. This is a place of stillness, and a place where we can move instantaneously in any direction. Even though physically still and calm, this is a very energetic, powerful, and alive state.

It is from this position of verticality — and calmness, awareness, and detachment — that one can objectively assess the challenge at hand. It is also from this place of verticality that one can have decisiveness of movement.

Triangle, Circle, Square

Sign hanging under the “Triangle, Circle, Square” calligraphy in the Rising Sun Dojo in Kissimmee, Florida. It reads: (1) Triangle— Sankaku — Lit.- 3 angles (Tai wa san men — Body is 3-sided). The stance prior to contact. Establishment of angle and radius of entry. Irimi — Entry. (2) Circle — Maru — Lit.- circle (Kokoro wa maru — mind/technique are circular). Circular movement (omote and ura) of technique. Tai sabaki — Body Movement. (3) Square — Shikaku — Lit.- 4 angles (Ashi wa shikoku gen — Basic rules of feet are foundation). Basic rule of footwork to provide explosive power of technique, and expanding echo (zanshin). Waza — Technique.

The above sign hangs under the “Triangle, Circle, Square” calligraphy shown in the first figure of this post. There is significantly more depth to the discussion of triangle, circle, and square. Here, I draw more on Barrish Sensei’s teachings as well as his 2009 post on AikiWeb. Of course, my post here still only scratches the surface.

In aikido, the aiki happens before the initial contact. Before the first contact, the triangle establishes the point of contact, at which point the circle manifests and the technique is applied (square). This process is similar to a gas (triangle) becoming a liquid (circle), and a liquid becoming a solid (square). And, just like elements can transition from solid to liquid to gas, extensive training in technical foundations (the techniques, square) leads to fluidity of movement and the ability to apply the technique in any situation (circle) and gives one the ability to control the fight before the initial contact ever happens (triangle).

In academia, an interpretation of the above is that one should develop strong technical foundations (square) and learn how to apply them in different situations (circle) such that they know how to apply the technical foundations as they encounter new situations (triangle).

The triangle also means mission (future), the circle means life (present), and the square means destiny (as a function of karma and the past and influenced by the purification of the present). While this view is about life as a whole, one can still draw connections between this broad view and academia. For example, for research, what is the vision of the project (triangle), how does one make progress on that vision (circle), and what place will that research ultimately take in the broader field (square)?

More on Aikido and Academia

I make other connections between aikido, Barrish Sensei’s teachings, and academia in my post on Lululemon, Life Directions, and the PhD Process and my post on Research Projects are Like Fractals.

Acknowledgements.

Thank you to Koichi Barrish Sensei of the Kannagara Earth Shinto Dojo for all the wisdom and insights that echo throughout this post. Thank you also to Reggie Townley for the photos used in this post.