An overview of emeritus math professor William Byers' newest work, "The Blind Spot," a book more for the general science reader, but having philosophical application to mathematics as well, and not an easy book to give justice to in a review!:
Many years ago I didn't have much patience for philosophy of science, but since reading the ideas of Godel and Cantor, and more generally about uncertainty, the underlying tenets of mathematics and science have fascinated me. I've previously mentioned that William Byers' book "How Mathematicians Think" is my favorite book about mathematics. With the usual admonition that we all have different tastes, I can now add that I love this new book wherein he adapts the ideas from that earlier volume to the broader realm of science.
The new volume is a relatively short, 180+ pages, for such a broad topic, but very rich, even if at times wordy or redundant. And I'd call it a heavier, denser, sloggier read, than the earlier math book covering similar material. I've sometimes remarked that I think our educational system would benefit if we threw Shakespeare in the trash bin, but required all high-schoolers to read Godel and Cantor (well, their interpreters)... or perhaps now, just substitute Byers! (I may be biased though, as I've never encountered a volume that more precisely matched my own take on science than this offering -- it's uncanny how often some of the phrases and examples he uses mimic those I've employed myself at times.)
Byers' theme is laid out in the Preface... the rest of the book fleshes out, from different angles and sometimes in subtle, nuanced ways, the same message and ideas over and over. I understand Byers' need to keep repeating things in different ways (almost to the point of redundancy) to make us consider basic points that are easily overlooked or taken for granted. We are entrenched in a viewpoint and bias that he is trying to penetrate and overcome.
The Preface opens this way:
"This book is about science, what it is as opposed to what people say it is; what scientists do as opposed to what most people believe they do...But actually the best summary of the book, perhaps, comes from this longer passage toward the end:
"The popular belief in scientific certainty has two aspects: first, that a state of objective certainty exists and second, that scientific kinds of activities are the methods through which this state can be accessed. Yet I will make the case that absolute certainty is illusory and that the human need for certainty has often been abused with noxious consequences."
"It is certainly conceivable that the clarity we perceive in the world is something we bring to the world, not something that is there independent of us. The clarity of the natural world is a metaphysical belief that we unconsciously impose on the situation. We consider it to be obvious that the natural world is something exterior of us and independent of our thoughts and sense impressions; we believe in a mind-independent reality. Paradoxically, we do not recognize that the belief in a mind-independent reality is itself mind-dependent. Logically, we cannot work our way free of the bubble we live in, which consists of all of our sense impression and thoughts. The pristine world of clarity, the natural world independent of the observer, is merely a hypothesis that cannot, in principle, ever be verified.Byers argues through these pages that there is both a "science of certainty" (that most people recognize or assume) and a "science of wonder," which is closer to what science ought be -- in fact he calls the former a "simplistic misinterpretation of the latter." What differentiates the two is whether or not what he calls "the Blind Spot is acknowledged." It is because subjectivity and objectivity CANNOT be consistently or definitively separated, that the science of certainty is illusory. Ambiguity, not certainty, is the true central element of science and is recognized by the 'science of wonder.' In turn, the reason for this is because we cannot escape the bubble of self-reference that all our thought and reason is trapped in, never permitting true certainty to prevail. This is our blind spot (metaphorically similar to the blind spot in our visual system, that we're usually unaware of, but is there nonetheless). There are in his words "limits to reason, to deductive systems, to certainty, and to objectivity." He is often echoing the work/thought of Gregory Chaitin.
"To say that the natural world is ambiguous is to highlight this assumption. It is to emphasize that the feeling that there is a natural world 'out there' that is the same for all people at all times, is an assumption that is not self-evident. This is not to embrace a kind of solipsism and to deny the reality of the world. It is to emphasize that the natural world is intimately intertwined with the world of the mind. In consequence, the natural world is a flow just like the inner world. By stabilizing the inner world through language, logic, mathematics, and science, we simultaneously stabilize the outer world. The result of all this is the recognition that the clarity we assume to be a basic feature of the natural world merely masks a deeper ambiguity.
"One of the functions of mathematics and science is precisely to deny this ambiguity. This is really the motivation behind the science of certainty." Yet, as he writes at another point, "...in the deepest and most profound sense, the things that make up the world cannot be defined, nor can they be understood or pinned down in any definitive way."
Further, "Human beings have a basic need for certainty. Yet since things are ultimately uncertain, we satisfy this need by creating artificial islands of certainty. We create models of reality and then insist that the models are reality."
This is easily seen in the areas of religion and finance (and not always to positive outcomes) as Byers alludes to, but is endemic to science as well.
In the world of science there are 'participants' (or actors) and 'observers' (the scientists) who are considered to be more detached and objective, and thus have a more accurate view of things. But the observers themselves are participants in the larger scale (participating in the act of observing/recording -- the observers could be observed by other observers, who could be observed by....). The dichotomy is itself ambiguous or self-referential, or as Byers writes: "...it is impossible to definitively separate the objective from the subjective; they are joined in a unity whose complexity arises from the inevitability of self-reference."
Some may confuse Byers' viewpoint as "postmodernistic," but he is not at all a postmodernist. The postmodern view would have it that one's science outlook is molded by the culture and environment one is embedded in. For Byers (and me) it has little to do with culture or society, but the weakness or blind spot of science stems from the very intrinsic nature of our human cognition... it would be the same for all humans even if we all shared identical cultures and background. The human mind cannot get outside of itself, and science, as a product of that mind, can't achieve the objectivity it seeks or claims. At times (and this may bother some readers), Byers is almost slightly "mystical" (my term, not his, although he might settle for the descriptor "transcendental"). This will trouble some hard-nosed science-types but I find it quite appropriate for what he is driving at, and something that science (and math), for all its self-aggrandizement, simply can't escape from.
Ambiguity and self-reference though are slippery subjects, by their very nature difficult to get a firm handle on. I've long been interested in self-reference, both in language and in science, and had hoped the creative, fertile thinker Douglas Hofstadter would have something profound to say about it in his 2007 book "I Am a Strange Loop"... but I find Byers' approach here more satisfying. Still, ambiguity is itself ambiguous, and self-reference is indeed a kind of endless loop, neither lending themselves to the empiricism of "science" -- which I think is sort of Byers' point: that empiricism is just one element in science; it ought not be seen as the equivalent (or even central factor) of science, and uncertainty is the rule, not the exception. Indeed, it becomes dangerous, when science is perceived as certainty.
How does this all apply to math... well for starters of course, math underlies science; the sense of pattern and order that is intrinsic to math is heavily impacted by the ambiguities and uncertainty Byers addresses. So too are the axioms which are the most fundamental components/assumptions of mathematics and logic. Even basic concepts of "number," "quantity," and "measurement," are far more difficult to pin down than our everyday usage would lead one to expect. The dichotomy drawn between discrete and continuous numbers is just one example of concepts in conflict that pervade mathematics.
If philosophy bores you, as it once did me, you might take a pass on this volume... but personally, I believe it should be read and contemplated by every scientist... and even applied to their own endeavors.
Anyway, another review of Byers' book here: