Ruminations-Acatalepsy

The word acatalepsy appeared on my radar a few weeks ago. I looked it up and the definition from Merriam Websters is as follows: 

Acatalepsy (Noun): 

1: an ancient Skeptic doctrine that human knowledge amounts only to probability and never to certainty 2: real or apparent impossibility of arriving at certain knowledge or full comprehension 

Chambers's Twentieth Century Dictionary attribute the word to the sceptic school of Carneades (214-129/8 BCE) 

The reason the word caught my attention is that it perfectly describes my present belief regarding my own philosophical outlook; that my perception of now is probabilistic in nature and the certainty of what I know and see are uncertain and subject to randomness and any inference that I make about the future is uncertain and subject to that randomness. 

It hasn’t always been this way. As with most children, my worldview comes from my faith in the people around me, that they are giving me the straight dope; what they believe and what they tell me is certain and unwavering. Most adults are insightful enough to know that explaining the uncertainties of life to children will inevitably end up in frustration, for both the explainer as well as for the explained to. The fluid state of reality is such that the inevitable follow up questions tend to grow exponentially as the uncertainties concatenate and the naïve and innocent minds will inevitably find the loopholes in our explanations gaping. 

It is easier for adults to give young minds a set of absolute beliefs and dogmas to follow temporarily so that they can at least manage to live in this limited reality long enough to learn about uncertainties; we also hope that young minds can achieve a level of critical thinking which will allow them to question their first beliefs and dogmas intelligently as they gain more experience. 

Some can navigate this journey into the world of critical thinking as they gain more experience and come to understand the complexities and nuances of the real world; others hold steadfastly to their very first beliefs: some do it because it is just easier, while other cannot fathom the idea of randomness and uncertainty being the primary state of being. 

Historical lessons became set in stone and no amount of nuance or interpretational ability was allowed because it was easier to teach. The math and sciences became a recitation of accepted facts and figures. Of course, the way math was taught gave the students no recourse: if there is a number, then that number is correct according to the tradition. Math is never that way, the creativity and wonders of mathematics became lost in our desire to be deterministic. 

 My formal education reinforced this deterministic viewpoint. As an engineering student, my belief in determinism hardened into stubborn dogma. I became enamored with the idea that the world is certain, that the errors from my calculations and experimentation comes from unwanted noise — which is minimal— i.e. the signal to noise ratio is very large, so the introduced errors are inconsequential and negligible. My initial foray into probability reinforced my dogma, we wrestled with coin flipping, die tossing, and Polya’s urn problems until we were blue in the face. These seem to be childish games that are distracting our attention from the important work of engineering. The importance of how measurement errors, quantization errors, and approximation errors in simulations were lost on me. I took Einstein’s quote: “God does not play dice” to heart and was in denial about the role that randomness play in the physical world. As I worked away at my control system classes in gradual school, I became more predisposed to the optimal control course that I took because I did not have to disturb my beautiful solutions with small signals; while at the same time was much less predisposed to the optimal estimation course that I had to take at the same time, where I had to go through great lengths to filter out the randomness. Kalman filtering was just some mental gymnastics that I had to work my way through to get rid of those pesky noise that are predetermined to be large enough to be a nuisance and small enough to be handled efficiently. 

As I entered the work force, where I had to measure real signals, not signals cooked up by my professor to fit into an exam problem, reality intruded. It became apparent that the noise that we are measuring as a part of our experiment was many times greater than the signal that we were wanting to measure. First thing that occurred to us was that our measuring equipment was crap; so, we bought better, more expensive equipment, but even then, the relative magnitude of the noise was beyond what I was expecting. This was a cataclysmic shock to my philosophical foundational beliefs regarding reality. 

As I came to terms with the way reality really behaves, I became more interested in those things that I had subconsciously rejected as perturbations on reality. Probability and statistics became grudgingly interesting and important. As I progressed through the bastardized corporate versions of statistics in the form of Statistical Process Control (SPC), Quality Control, Six Sigma etc. I became better acquainted with the ideas of statistics. I read through some of the introductory texts of statistics with interest as I became a convert to SPC. The ideas of being in control and out of control, special and common cause variations crept into my vocabulary; run charts became a natural part of my subconscious. I took the SPC view of engineering processes into my outside life and looked at my real world reality in those terms, much as I had taken the dynamical systems vocabulary and framework into the way I looked at reality when I was introduced to control theory. 

 Even as I came to value the understanding the uncertainties in the physical world, I clung on to the old paradigm that is best expressed by the Michaelangelo quote. 

“Every block of stone has a statue inside it and it is the task of the sculptor to discover it.” - Michelangelo 

My belief was that reality existed under all the noise and randomness, much like the sculpture under the stone that Michaelangelo referred to. As such, I felt that it was possible to completely decouple the uncertainties and randomness structurally from the “reality”. Which is how I came to the belief that we can use the SPC tools in volleyball. The idea was to treat each player or each team as an industrial process, that we can identify the underlying physical process of the player or the team by applying the SPC and inferential statistical tools to identify the human capabilities of an individual or a team. I was hoping to gain an understanding of the essential ability of the athlete or the team so that I can devise training regimens which directly addresses the performance weakness identified by the SPC analysis. It was a naïve and simple-minded approach, one that I undertook because of my adherence to my rigid world view: randomness and uncertainties can be readily filtered and reality made whole by proper application of statistical tools, and we can make good decisions based on incomplete statistical information because of the previously stated belief. 

Yet, as I investigated further, I realized the immensity of the data set needed for each athlete and each player just so that I can indulge in my fantasy of consistently inferring and identifying training needs from pure statistical analysis. 

 A critical mistake I made was to underestimate the complexity and the deep coupling between the various parts of the process I was trying to measure, i.e. I underestimated human complexity, I assumed that we can easily decouple and measure parameter within humans and that the assumptions we make to measure isolated parameters would be simple and leave the parameters unaffected: I assumed that humans are as simple as machines and industrial processes. I realized quickly that I was on the wrong path as the complexity of human reaction forced me to rethink my ideas. 

 In addition, I had approached the measurement process in an open loop manner, I assumed that if I gathered enough data the numbers will tell me where to look, what to look for, that the calculated data will cause rational conclusions to jump out. Not adequately setting expectations meant that the data had little or no meaning. I did not know the question that I wanted to ask, so the answers that I got had no meaning. The data can and will mislead us unless we knew what we are looking for. 

 All my thinking does not, however, lead to the conclusion that the Moneyball idea is fundamentally flawed, it is saying that reliance on just numbers is as silly as relying on just “gut feel”. I cringe when I hear managers in corporations say: what does the numbers say, or the numbers will tell us the truth, or our decision is decided by the metrics that we can measure and not what we should measure. I also cringe when I hear coaches say: the numbers determine who plays and who doesn’t, or our numbers are why we lost, or we need to train to improve these numbers rather than improving our skills or our game play. 

“The world cannot be understood without numbers. But the world cannot be understood with numbers alone.” —Hans Rosling  

We mistakenly rely on numbers as the bulwark for our arguments because people tend to substitute numbers for their lack of expertise: i.e. I am not sure of what I am saying, but I have lots of numbers to prove it. 

There should be a hybrid approach which takes advantage of the salient qualities of both experiential knowledge while backing up the experience with good Design of Experiments practices. Being biased one way or the other will inevitably introduce fallacies and biases into the decision-making process, which leads to bad decisions. 

As my experience with uncertainty and randomness evolved, I changed my beliefs, I adjusted my assumptions about the role that randomness plays. I no longer look at the physical world as having a pure truth, i.e. I no longer see the statue in the stone that will inevitably be uncovered through my efforts. I see the randomness as part of the reality rather than as noise that we can filter out. I do believe that there are some noises that can be filtered out, but not all of it. I see our role as being able to discern and identify those noises that can be filtered and those that cannot; our more important role is to make better decisions DESPITE having those pesky random events constantly obfuscating our understanding of our processes, be they in the sciences or in sports. I now see reality as the parable of the blind men trying to describe an elephant. We “see” different parts of the whole and we come to an understanding of what we see, but our perception should be changing as we learn more by perceiving more of the elephant through our experience and measurements, even as the elephant is constantly changing. We must continue to gain experience and take measurements just to keep up. 

 So, this was a very long way to explain why the word acatalepsy describes my view of reality.

Book Review-Do Dice Play God: The Mathematics of Uncertainty

By Ian Stewart

This is the book that I was very eager to read because of the subject: the mathematics of uncertainty. I read it in parallel with The Art of Statistics by David Spiegelhalter because I felt the combination of the two books on similar topics from two different directions would make the reading experience more complete as the two books should complement one another. It was mentally challenging to read both books together, but I am glad I did because my goal was accomplished: they were indeed complementary. There were certain areas where the books overlapped but it was good retrieval practice to go over some of those areas at spaced intervals.

The book comprises of 18 chapters. The first two chapters sets the tone for Stewart.  By defining the six ages of uncertainty in Chapter One, Stewart proceeds to converse about some of the things that humankind has been using to deal with uncertainty and to predict the future. He follows that initial setting of the stage with a qualitative discussion of the idea of probability and statistics. It is a difficult task because it is easier to discuss probability and statistics in terms of the equations. Even with that caveat, Stewart did an excellent job of explaining quantitative concepts qualitatively, it takes someone who deeply understands the ideas, in all their glory, to be able to pull it off, and Stewart did so. This is not to say that the book is completely devoid of numbers and figures, but it was enlightening to be reading about these concepts without equations and mathematics.

The book then proceeds into many topics about uncertainty and randomness. He shares an abundance of examples and evidence which demonstrates the idea. It sometimes feel like an unrelenting onslaught of different cases in different areas, regarding different problems. The examples  come from mathematics, biology, medicine, physics, numerical systems, and many more, which gives proper perspective to the reader as well elicits an understanding about the universality of uncertainty in our reality.  The main topics that I had struggles with,  and that is true of Spiegelhalter's book as well, is the section on the Bayesian probability, even though Stewart did a masterful job of explaining it. I understand Baysian ideas after having read both but I am still easily confused when trying to apply the idea.

Stewart lost me with his explanation of quantum mechanics and the counter intuitive ideas from quantum mechanics. It was a difficult section to read, even though I was exposed to the idea when I was a young engineering student. On the other hand, when Stewart expounded on the ideas of  dynamical systems, he made perfect sense, as I was thinking about  Lorenz attractors when I was studying dynamical systems as a graduate student.  Since I had understood those equations as equations,  it was not much of a leap for me to understand them as applications which made the mathematics more sensible.

As the reader work their way through the book, they will find themselves doing many mental gymnastics with the mathematics that he does present, but he does an excellent job of explaining  why these concepts are so important to us.

The last chapter is the magnum opus chapter that Professor Stewart uses as his platform to summarize his intention with the book. His key intent is to make the general audience become aware and comfortable with the fact that uncertainty is a normal part of life. Professor Stewart has work diligently throughout the book to chip away at our enduring and grossly erroneous belief that our lives are deterministic, and that any uncertainty that we admit or accept is not something that we overcome easily or can be disregarded because the uncertainty plays a very large role in how our lives will often result.

A quick summary of all the topics that that had been discussed ends the book. In returning to these topics while reading these short pages, the reader realizes the extensive number of  topics that Professor Stewart had discussed; more importantly, the reader finally understands the lessons that Professor Stewart is trying to teach us. He started with the basic ideas of how human beings dealt with uncertainty. As humanity progressed along the timeline, we got better at rationalizing some of the uncertainties, and we thought we were able to minimize the uncertainties. We invented tools like statistics and probability; we deliberately tested and  experimented to arrive at what we thought was the truth. Even though this book is not the definitive history of uncertainty in our world, this book does very well in filling some of the obvious gaps in our thinking and dispels enough biases to make the readers at least accept the fact that life itself is uncertain and full of mystery.

I thought the book was a marvelous read even though it was particularly challenging. Professor Stewart explained many different concepts very well, some better than others, but the overall effect is that the reader can gain a much better understanding of how little and how much we know about our world and appreciate how much guessing we are doing on a daily basis.