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Sunday, February 23, 2020

Book Review-Mathematics for Human Flourishing


There are moments in one’s reading life where one come across an unexpected book which gives one pleasure in absorbing the text and revelation in ruminating about the message. This was my feeling after I finished Mathematics for Human Flourishing by Frances Su.

This is a book that I discovered when I saw Thomas Lin, the editor of Quanta Magazine touting it on Twitter. Being curious and being as that the author gave me a code which gave me 25% off on the purchase of the book, I jumped at the chance.

It was one the best chance that I have ever taken.

Professor Su is a mathematician at Harvey Mudd College in California. He was also the President of the mathematical Association of America; this book came out of an address that he made in 2014 as the president of MAA. I have not read the address, but I have read the book and the book is an amazing amalgam of intellectual wonderings about life and what humans hold to be noble and mathematics of course. The author asks question, many questions. Illuminating questions that is much beyond quick and facile answers. He also lays himself out honestly and courageously, sharing with the readers his quest to becoming a mathematician, on his insecurities about growing up Asian in the United States, his feelings about being in an over achieving family culture, and working in an art form that America does not appreciate or value. He also introduces his friend Christopher Jackson, an inmate in the penal law system of Georgia. Chris had committed a crime when he was very young, aged 19,  and he's has been in the penal system for what he had done. While he was in prison he also started to dabble in mathematics, soon discovering that he a passion for mathematics and also that he was adept at mathematics, enough to be a researcher, per Prof. Su’s estimation. Prof. Su shared some of his correspondence with Chris Jackson. The correspondences were about math, but also about many things beyond math, which helped illustrate the main thesis of the exposition.

Prof. Su chose thirteen concepts, words, and ideas to delineate his feelings about mathematics. He uses them to dive deeply into the ideas that mathematics enhances and improves, he uses these concepts to expound on what it means for him to be doing mathematics. The structure of the book is completely non-traditional, and it is breathtaking in its scope.

The central tenet of the book of course is laid out in the title: Mathematics for Human Flourishing. The author’s thesis is that mathematics is the path towards making humans flourish in their reality, to give us humans a path towards reaching realms that are beyond our initially meager imaginations, that doing math is not just a task or chore or a talent but a necessary spiritual practice to advance our society, to feed our naturally fecund imaginations, to sate our very human yearning for meaning in this life and in this world.

This thesis a giant leap for those who are math phobic, but it is a heroic declaration for those who are passionate about mathematics. Professor Su does yeoman’s work in using those concepts to illuminate his thesis: flourishing, exploration, meaning, play, beauty, permanence, truth, struggle, power, justice, freedom, community, and love to flesh out his argument that not only is mathematics a practical and beautiful practice, but it is also a critical necessity for human thriving in our internal lives. The doing of mathematics makes us better people, it makes us kinder, more patient, more cognizant of the world around us, it makes us more curious, it makes us learn that our world is more than just what we see in front of us.

Ever the detailed technician, Prof. Su carefully lists the virtues that comes through each of the concepts he chose to highlight in each chapter. He assiduously frames his chapters to clearly illustrate each of the virtues and connects them to each of the words he used to name the chapters. He also lists them all at the end of the book, to make sure the readers understood his point.
The completeness of his authorly duties does not end there, he provides discussion questions at the end, as well as hints and solutions to the puzzles he provides at the end of his chapters. He was very complete in pursuing his mission.

Unlike many of the books regarding mathematics, this one goes into the reasons why mathematicians become mathematicians, more importantly, the book amply demonstrates the point that mathematics is not only a magnificent art to pursue, it is also one that is desirable one to pursuit. This book is enlightening, inspirational, and gives hope to everyone who is willing to read it.

Wednesday, February 19, 2020

Volleyball Coaching Life-Freedom

I was reading a book by mathematician Francis Su, he was the president of the Mathematical Association of America and the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College. His book is titled: Mathematics for Human Flourishing (Su, 2020).  In the book, Prof. Su lays out his case that doing mathematics exemplifies the best of human endeavors and is worthy of the struggles. Each chapter is centered around a word, a concept, or a value that he holds dear, and he goes into detail to discuss the relationship between mathematics and those words, concepts, and values.

What does this have to do with volleyball?

I found his chapter on the topic of freedom very compelling. Unsurprisingly, my mind went off into the wild blue yonder and I thought that the freedoms that Prof. Su discussed could fit universally into many realms, but I started thinking specifically into what we are doing in coaching volleyball. I felt that the five freedoms he named are ideally suited to describe what we strive to do for the teams and the players that we coach.

If, by serendipity, the discussion on the concept of freedom can also make coaches pause and think about what they are doing a little differently than the usual dogma, so much the betterThe five freedoms of mathematics that Prof. Su cited are:
·       Freedom of knowledge
·       Freedom to explore
·       Freedom of understanding
·       Freedom to imagine

·       Freedom of welcome.

Taking these same freedoms, we can delve into the details and generate some ideas as to what those freedoms mean in terms of volleyball.

Freedom of Knowledge

In volleyball terms, there are plenty of volleyball related knowledge to be taught: skills, techniques, systems, tactics, strategies, etc.

So does this mean that freedom of knowledge is a no-brainer?

Just do what we are doing and what we have been doing since there was such a thing as volleyball coaching? Are there more to this?

How about the non-volleyball knowledge that are tangentially related to what we do but are also impactful, knowledge like statistical analysis, psychology, cognitive sciences, leadership qualities, ability to communicate, ability to build teams, kinesiology, skill acquisition, decision making, …the list does seem to go on and on. Do we just stop at the volleyball knowledge? Or do we give them as much as they can handle, giving them all the knowledge that we can to bolster their knowledge base?
Just as there are many ways to look at and play volleyball, and all can be valid for specific situations and circumstances; all the knowledge listed have validity for different situations and players. The idea then is to decide on which knowledge do we want to have in our toolbox? Which tools will be the most useful for most situations? We can’t dig deeply into everything about everything, so which ones are the most optimal for me? Which ones can I understand, use, and implement? It is good to know what you have many tools available, but the world being uncertain and random, “what you don’t know” and “what you don’t know you don’t know” could be critical.

My take on this is to give them as many ideas, opinions, and options as possible. Some might be on a shallow level, but at least make them aware of it and understand the limitations each tool has and leave the deep dives for when they feel the interest or need to implement the concept to solve problems.

As a coach, we need to give our players that freedom, of teaching our players all that we know and more in order to give them that complete toolbox to go out and play the game.

Freedom to Explore

The idea of the freedom to explore may seem anomalous if we think in terms of a practice environment where we are giving the players strict instructions in the practices and an environment of discipline under which the players have perform. Indeed, the argument should be made that the freedom to explore gives the players the ethos to stimulate creativity, imagination, and enchantment in themselves. It allows the players to interact, question, and seek answers on their own motivation, on their own schedule, and in their own ways. Their interpretation of the game might be different from our interpretation, as the oft quoted mantra, albeit in a completely different sense: the games teaches the game. The exploration of the game on an intellectual as well as on a physical level creates that tension between regimentation and freedom to explore which will stimulate the intellectual impulse of the player while also giving them a chance to test out their impulses in real time..
As coaches we need to give our players space to explore, room to fail, opportunities to come to wrong conclusions and then correct those conclusions; all to serve their freedom to knowledge, because knowledge gained through personal experience are much more meaningful, easier to recall, and be called upon to use in a meaningful way.

Freedom of Understanding

From the freedom of understanding, we know that we have tools in the toolbox, but having the tools does not mean that we know when or where to use those tools. This is where the freedom of understanding comes in. You can give them all the knowledge, but they need to know the answer to the question: Why? Why do we pass with this technique versus another? Why do we hit with this technique versus another? Why do we play this defense versus that defense? Why is the tempo of our sets fast versus slower? Why do we serve this zone versus that zone?

Freedom of understanding allows the players to make connections as a natural progression of action. It gives them a causal link from one action to the reasonable following action. It gives them a bigger picture that everything you do in volleyball is connected and fit together meaningfully.
For the players to achieve mastery of the knowledge of the game of volleyball, they need to have a deep understanding of the underlying structure of the physical, tactical, psychological, and emotional responses that we humans employ during the game. Freedom of understanding also enables the freedom to knowledge to flourish, it gets the innate curiosity that is the hallmark of human nature to take the players where they can fill in their own blanks, which serves to satisfy their own sense of wonder, enables them to be  responsible for their intellectual yearnings, as well as we question the self-imposed envelope of how we see our game, maybe even expand that envelope.

Freedom of Imagination

Imagination is one of the most exalted ideals in our pantheon of ideals, for good reason. It is result of letting our minds run free and exploring all our knowledge and through our understanding of the fundamental tenets of our game. I believe it is the logical follow-up to our study and practice of the game of volleyball. Yet we coaches, to a large extent, shut down this natural inclination in deference to performance and to the procedural execution of playing the game. The urge is understandable: we cannot be discovering, exploring, and using our conceptual processes all the time while playing the game: the game is a game of reactions and counter-reactions. Yet as we defer to the procedural, we are turning off our players’ natural curiosity to explore and come to different conclusions because we have labeled any ideas that are different from our preferred orthodoxy counterproductive and forbidden. We have, unintentionally, killed off some of that natural curiosity and we have also relegated the search for new ideas to the domain of the coach.

I will admit that the game of volleyball is severely limited in its scope in many areas mainly because of the rules of the game as well as the limits of human ability to perform. Indeed, we can argue that the beginning player will inevitably repeat the same mistakes as those that came before them in previous generations and make the same discoveries only to be told that the idea has been attempted previously. So what. Personally earned experience serves to harden the lesson, much more so than oral instructions. There are, of course, limits to that idea. We don’t want every player to personally relive every volleyball innovation throughout history in order to learn the limits of the game. We also don’t want to make the sport to be dead and without room for imagination, we have erred excessively towards one end of the argument, to the detriment of the sport.

Another way to think of this comes in a phrase: “making space for the divine.” Actors talking about acting have this phrase to remind themselves to not becoming too regimented, that the idea of acting is an exercise in creation, reacting to and allowing the other performers to perform and in being spontaneous; the admonishment is: “You don’t want to end up acting like robots.” In other words, “leaving room for the divine” means to leave room for the spontaneous, the moment of dealing with the unknown, whether the spontaneity is due to something mundane, i.e. the situation, or whether the spontaneity is due to impulse.

In volleyball, “leaving room for the divine” means that you don’t want the players to play like robots, i.e. to breakdown the free-flowing game into digestible bites of movements. We want instead to leave room for the spontaneous play. We want our players to be able to deal with and succeed in dealing with the unknowns of the uncertainty of play. It doesn’t matter whether the spontaneity is due to something mundane or due to impulse. Free flowing wu-wei, or flow is the desirable goal.

Freedom of Welcome

The freedom of welcome is perhaps the one freedom that will confuse. The idea is that volleyball is and should always be welcoming to all who come and seek. While that idea has been ingrained in our pluralistic society, the actual implementation of the ideal is sketchy.

I remember when I was playing pick-up ball in my college gym, and I was ostracized and shunned because I was a terrible player, the worst. I was the game-killer. It was embarrassing to be waiting to play and never be selected to play. Fortunately for me there were people at the open gyn who selected me, showed me the skills, encouraged me to try things out on the court. Unsurprisingly, they were all also the best players in the gym. Their generosity and the sense of welcome made me a better player. They used their status to bring me into the cult of volleyball, my life was changed forever because of their welcome.

Some would think that that is the way it should be, always. But is never is. We so value the quality of our playing time that we forget to be kind, generous, and welcoming.

This is a freedom that is perhaps the most challenging for everyone involved, because it asks us to suspend our rabid competitiveness for the sake of being kind, for allowing others into our private club. For growing the game.

Freedom of welcome also means to be welcoming to ideas and opposing opinions. It means to be patient and listen to the opinions of others and to welcome debate amongst friends. We can live and prosper together even if we disagree on the details.

To be welcoming needs to be a freedom given to all of our players, to indoctrinate in their minds that volleyball at least, is and needs to always be a pluralistic enterprise.

The Virtues

We, of course, do not give our players these freedoms without getting something in return. We gain more, in my estimation, than we give.

The freedom of knowledge gives the player sense of resourcefulness, a sense that they have the freedom to do what they need to do to accomplish their goals because they have the tools.

The freedom to explore gives the players the virtue of fearlessness in asking the difficult questions. It gives them the virtue of independent thinking as well as the virtue of viewing failure as an opportunity

The freedom of understanding gives the players the virtue of having confidence in knowledge.

The freedom of imagination gives the players the virtues of inventiveness, joyfulness, and a sense of the confidence to deal with uncertainties.

The freedom of welcome gives us the virtue of kindness, generosity, and the chance to serve our vast volleyball community. We are indeed growing the game.

As I described these freedoms and all the good that are a part of the gift, we must also be incisive enough to emphasize to the players that: true freedom comes with many costs, responsibilities, and relationships. Freedom does not imply nihilism, that by itself could be the most important lesson of all.

References

Su, F. (2020). Mathematics for Human Flourishing. Yale: Yale University Press.