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.
