Book Review-Infinite Powers By Steven Strogatz

After having been trained in the dark arts of engineering, I considered myself, if not a full-blown expert, at least well versed in calculus: what it is, what the idea can be used for in my engineering specialty, and some of the history about calculus through my classes. I now happily admit to my unreasonable hubris. Steven Strogatz is the master of all that is calculus, what it was, how it came into being, where it is now, and possibly where it is going to be in the future.

My initial arrogance concerning my knowledge on the subject made the initial chapters of the book flow by quickly, I read the historical notes that Strogatz included as a sidelight to the main discussion — something to entertain the less informed of the general reader — I wondered why we would need to know the arcana of ancient mathematics, even I also fancied myself a nerd for history of mathematics? Little did I realize how important these historical notes will be: to drive later discussions as well as to form the foundations of the macro view of calculus.

Strogatz frames the story of calculus in ten chapters, creating the intricate scaffolds that allows the readers to follow the technical developments through history with added notes on the mathematicians that originated the ideas which drove calculus to where it is now. An eleventh chapter serves as his own peering-into-the-crystal-ball statement on what he believes will come in the future. He carefully builds up the structure of the development of calculus and seamlessly build the connections between subjects and shows the open questions that was left at the end of the previous chapters and how the topics covered in the new chapters serves to answers those open questions. It is this attention to the many loose ends and how they were resolved that held my interest.

As Strogatz observed, the teaching of calculus had been subdivided into many subtopics for the sake of convenience, but in so doing, the students had been sold a myth that these subtopics are standalone topic because it suited the purposes of teaching logistics rather than suiting the purposes of gaining a holistic view of what mathematicians throughout history had wrought, continuously.

Chapters 8, 9, and 10 were the chapters that had me holding my breath, for it is in these chapters that Strogatz pulled together all the work from the previous seven chapters, integrated them and brought the story to a denouement, for the moment. It brought together the differential and integral halves of calculus, showed the true powers of the calculus. True to the title of the book, he also forcefully made the point of just how the powerful idea of infinity allowed the method to flourish in the minds of mathematicians, scientists, engineers, and so many more specialties.

One cannot discuss calculus without discussions — many times heated ones — about the two men who are recognized as the progenitor of the largest leaps forward in the calculus: Newton and Leibnitz. Strogatz recognition of each, while nicely put their contributions into the historical context of calculus without delving into the bickering that happened between proponents of either men, which is as it should be, even though the human smallness in me wanted some juicy stories about the two.

Strogatz introduced us to the important women mathematicians which made contribution to the art and science of calculus, their contributions were most often ignored and if recognized, their works were slighted. He gave them credit where it was due, and the book is much better for the recognition.

As I was taking my time reading and enjoying the narrative, I thought about how this book should be made an integral part of the teaching of calculus, a required text taught in parallel with the technical aspects of calculus; a book that answers the “why” and “how did it get this way” questions in parallel with the technical training that answers the “how to do it” questions. I then realized that the reasons that I appreciated this book so much are not the same reasons that the young students in AP Calculus or in college level calculus would appreciate. It took me years of working with the calculus to ask those questions that Strogatz had sought to answer. It takes a certain level of maturity and appreciation for the context of the methods which built up the citadel that is the calculus. I still think that the material in this book has a critical role to play in motivating the understanding of the “how” while also building an appreciation for what our forebears had wrought. As Newton had said: We Stand on the Shoulders of Giants. This book would nicely illumnate that blind spot.

One note of interest. I was reading Mortimer Adler and Charles Van Doren’s book How To Read a Book (Adler 1972) when it was brought to my attention that until the end of the nineteenth century, scientific books were written for the layman, that the habit of having specialists writing only for specialists was necessitated by the increasing complexities that comes with the expansion of knowledge in each scientific topic, so that the necessary knowledge needed to understand scientific books became so broad as to be covered in a single tome. Which I thought was a shame, but I understand how daunting the task of writing science and mathematics books has become. Which makes this tome that much more impressive in that, whether Strogatz realizes it or not, he had accomplished a rare and difficult feat — to communicate this very specialized and complex topic to the general public — a general public that has varying levels of a priori knowledge to draw upon to aid in their comprehension. He has joined the pantheon of authors which serves the knowledge of everyone, if they chose to read the book. He has served the role of the public intellectual by writing this book.

This is a remarkable book from my perspective, it filled in the gaps of my knowledge, technical, historical, and conceptual, without losing my interest nor overwhelmed me.

References

Adler, Mortimer. "How to Read Science and Mathematics." In How To Read A Book, by Charles Van Doren Mortimer Adler, 255-269. New York: Touchstone, Simon and Schuster, 1972.

 

 

 

 

Volleyball Fan’s Life-The VNL

I was finally persuaded to invest in a Volleyball World account to watch the VNL. I am kicking myself for not having done so earlier. I logged in to the various volleyball groups in the virtual world after the match against Türkiye to see what others had to say. It was, I must say, amusing and disconcerting at the same time.

So here is some history and some realities for the sake of context.

Volleyball Nations League was inaugurated in 2018. It is a revamping of the World League and World Grand Prix, both of which are tournaments put on by the FIVB for the top teams in the world. The VNL replaced the World Grand Prix. These tournaments take place every year except for Olympic years. They charge big bucks to each nation who want to participate but also payoff in big bucks for those finishing atop the league.

One thing to remember is that the Olympic sports places the premium on the Olympics, all the other tournaments are ways to build up to the Olympic competition. Cycle time is four years, just as the Soccer World Cup, International basketball, and any other sport whose biggest competition is the Olympics. Unlike the popular sports that we follow in the US, where there is a payoff and champion every year. The VNL is NOT the be all and end all for international volleyball. None of these countries would play to lose, it costs too much. But the impetus is much different.

Looking from the athletes’ point of view, they are playing overseas in a single year cycle so that they can distinguish themselves for the national team on the four-year cycle. Playing professionally overseas is very trying: physically and emotionally.  There are injuries, home sickness, language, and culture issues etc. Why do it? Some thrive on the adventure of the experience while others do it because they know this is the only way they can get experience in  the international game while playing against the best competition, all done to enhance their chances at making the team every quad.  The schedule though, works against them. The players need to rush home after their pro season is over to practice in the national team gym for a very short time, then it is off to four weeks of playing and traveling. This year Hentz and Hancock were the only two that went on all four legs of the VNL. Others were on and off the rosters as the weeks rolled by.

The reason for that musical roster is because they have to give the veteran players time off to heal and to rest from their professional seasons. But there is also a broader and more long term focused purpose. The national team roster is ever evolving, even though most fans get fixated on the roster each week of the VNL as their focus. Coaches are dealing with a fluid roster. Karch said that he considers all 24 on the training roster members of the national team after the USA won the gold. He is not just being kind; it is a reality. The selection of the final Olympic roster is an arduous and emotional experience for everyone involved. More on that later.

All the countries who are contenders for the Olympic title treat the VNL in various contexts: as a competition, as a period of assessment, and most importantly, as a laboratory to experiment with everything — tactics, strategy, players, player interaction, team makeup, individual and team ability to withstand game pressure and being able to make good decisions under game pressure. They don’t pretend that winning the VNL is the ultimate prize for the national team. Winning is important, but it is not the most important. The most important thing is to learn about the disparate parts: players, coaches, and staff; the humans involved and figuring out ways to melding them into a team.

The coaching staffs needs to know about how much the veterans have left in their batteries, whether they are performing up to the highest of international standards, their ability to make the best decisions under pressure, and whether they are still as motivated as they were from the last quad. They also need to know where the young players are at: how the pipeline of players are developing, whether they are playing overseas or are in college. The international game is very different and much more demanding, physically, emotionally, and mentally than the collegiate game. Competing against wily veterans from other countries, even the non-competitive countries in the international scene, is not the same as competing with other 18 to 22-year-olds. International coaches leverage the changing rosters for the VNL to work groups of young players in and out of their roster decision every two weeks to not only expose the young players to the level of play but to also observe how well the young players mesh with the veterans and how they are able to “solve problems” as Karch noted in the comments between sets against Türkiye. Digging into the granularities, coaches will want to know which players play better together, which players seem to not do well when on the court with one another. The coaches need to be the alchemists of team chemistry.  Coaches also need to let the players play themselves into and out of trouble. I see many comments about the coaches being too slow with the subs. I believe that this is deliberate, they want to see whether the veterans have lost their edge and whether the young players have learned to develop that edge. This is the time for the coaching staffs to be patient and experimental, not during the Olympics.

There are many countries who treat the World Grand Prix and now the VNL in a very controlled manner, many will only send the next level of players, to get them seasoning. They will also play a plain vanilla game, not showing any of their new strategies, preferring to save them for the Olympics. Partly to play a cat and mouse game, partly to lull the opposing team’s scout into thinking that this is all there is. I am not sure how much of that is going on right now, but that was the way it was.

The decisions for the USA women’s team is made particularly difficult because the USA has never won a gold medal in the Olympics until the last quad. The reason for that is convoluted and complex. I wrote about it in one of my other blogs immediately after the gold medal match. (https://polymathtobe.blogspot.com/2021/08/an-appreciation-of-karch-kiraly.html) I have been a fan since the 1980 team, and quad after quad, I was disappointed. The USA team is the illustration of the adage: “Men battle to bond, and women bond to battle.”  The difference with the gold medal winning team and Karch as head coach is that he pays attention to the relationships, building trust, convincing the players to work on themselves, their relationships with one another, and their own altruistic motivations when playing with the national team. In order to have a roster of 14 players who can step in when needed, they must be unselfish about their roles. The coaches need to put the players through the gauntlet so that they have knowledge of their players when it comes time to actually pick the members of the squad, and work with them to help resolve issues. As alluded to before, the selection is for the last pre-Olympic roster and not just the final Olympics roster.  There must also be trust between those that made the final Olympic roster and those that did not, the coaching staff need to make sure that everyone on the pre-Olympic roster is 100% on board with the Olympic team, no petty jealousies, no selfish petulance, nothing that would detract from the drive to the gold.

This is not something that all other national teams go through, and some may say that this is just another case paralysis by analysis, but we have one gold medal to show for this method and 40 years of frustrations otherwise.

I wanted to put all that context out there for everyone’s consideration. To call attention to the fact that what we are seeing in the final weekend of VNL competition, or for the month of VNL competition is just a snapshot in time of the very large national team roster as we know it, a year away from the actual Olympics. There are many players with many different levels of experience, physical shape, emotional welfare, and maturity levels. Each member of that expanded roster will have individual and collective interactions and couplings with one another, some tenable and some not. The coaching staff will have to sort through all of that, the VNL is their testing ground, their sandbox to play in so that they have all that information. Of course, the process is imperfect, but when they, the coaching staff, make the decisions, they need to have as much information based on different scenarios on the actions and reactions of the team to reference, if that means being patient with players when they are on court so be it, you don’t learn much about how they will play if they are on the bench.

It is a marathon folks, not a sprint.