Digital Reality: Knowledge as Set Construction

By George Towner

At every juncture during the evolution of digital technology, computer architects intuitively or consciously incorporated truths about human functioning into their designs. So although computers operate digitally, they are intended to act like human beings. Software, in particular, is specifically written to accomplish humanlike tasks and to be understood in human terms. Yet unlike human life, computer operations can be analyzed in detail because we build machines that execute them and know the decisions that went into their construction.

Digital Reality: Knowledge as Set Construction is the final report of a thirty-year study of how computers are designed. Author and philosopher George Towner shares his research and uncovers these truths hidden in digital architectures, assembling them into a new explanation of human knowledge. In addition, he includes an analysis of computing architectures that provides insights into some of the great questions of traditional philosophy, because much of digital technology is now dedicated to creating new realities.

A new theory based on emerging digital realities can offer another way of understanding human knowledgehow it functions, how it is related to what it knows, and what its natural limitations may be. Unlike many theories, digital reality theory is not expressed in laws and formulas; it just explains how human knowledge works.

• Language: English
• Publisher: Archway Publishing
• Release date: Jun 29, 2018
• ISBN: 9781480863262

George Towner

George TowneRtrained at Berkeley as a logician and philosopher, and he started his career as assistant director of the Kaiser Foundation Research institute, working on the biology of primitive organisms. During the computer revolution, Towner switched to information technology and spent thirty years on the senior technical staff at Apple; he also dug into the bare metal of computing and analyzed how these machines evolved from number crunchers into todays smart digital assistants. The result of his study was three books that analyzed human knowledge. Digital Reality, Towners final book in the series, presents a completely new explanation, based in set theory, of how knowledge works in both people and computers.

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Copyright © 2018 George Towner.

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ISBN: 978-1-4808-6327-9 (sc)

ISBN: 978-1-4808-6325-5 (hc)

ISBN: 978-1-4808-6326-2 (e)

Library of Congress Control Number: 2018907155

Archway Publishing rev. date: 06/29/2018

Life, like a dome of many-colored glass,

Stains the white radiance of Eternity …

(Shelley, Adonais, stanza 52)

CONTENTS

Preface

1   How Knowledge Works: Digital Reality Theory

Understanding how we know the world around us is not just a matter of better physics or higher mathematics. We must rediscover the basic interactions between life and reality.

2   Connecting to the World: Existence and Reality

Existence is what it is and we’re part of it. But the realities that we know, while based on existence, are not identical with it. Life makes them different.

3   Understanding Reality: Analog and Digital Knowledge

Analog and digital are two ways of knowing things. We deal with existence through analog interactions, and from those interactions we construct digital realities to support our everyday knowledge.

4   Explaining Human Knowledge: Set Construction

The best way to analyze digital reality is through set theory. Within its toolset, the powerset axiom provides an effective way to explore the complexity of human knowledge.

5   The Structure of Knowledge: Orders of Reality

When we examine typical digital realities using set theory, we find three kinds of objects of knowledge: behavioral, physical, and ideal. They populate a hierarchy of powersets. This structure makes knowledge work.

6   Constructing New Realities: Digital Categorization

Digital reality construction enlarges common sense by creating new categories. These new categories help us theorize and frame concepts of error in knowledge.

7   Using New Knowledge: Social Realities

Knowledge affects social norms and institutions. Our social behavior undergoes regular patterns of change in response to the evolution of our digital understandings.

8   The Future: Beyond Ideals

Using set theory, it is possible to envision future kinds of human knowledge and predict how they may alter our digital realities.

Acknowledgments

Notes

PREFACE

T his book describes a new way to understand how knowledge works. The details are based on observations I recorded in three earlier books: The Architecture of Knowledge (1980), Processes of Knowledge (2001), and The Reality of Knowledge (2011). What’s new are the explanations of why knowledge works the way it does, accompanied by commentaries that are simple and logical.

I did not originally plan to write this book. It seemed to me that my job was finished when I had traced out the major ways that people (1) discover what the world is like and (2) figure out how they can make sense of it. I regarded the mechanisms of knowledge that I had found in my earlier books as given, in the sense that they were just the way things happened to be. Describing these mechanisms of knowledge had raised old and seemingly intractable philosophical questions, such as the famous mind-body problem, but I could not imagine any way even to begin to address such questions.

Then I began to think about the axioms of set theory that I had worked with in the philosophy department at Berkeley. It occurred to me to apply these axioms to what I had subsequently learned about storing and accessing digitized knowledge while working with the senior technical staff at Apple. The final result was one of those happy Aha! moments, and this book was born.

My Aha! was partly about mathematics versus set theory. Schools since Newton’s time have taught that mathematics holds the key to understanding reality. In 1963, for instance, Nobel physicist Paul Dirac, who inherited Newton’s professorship at Cambridge, wrote that it seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it.¹ Yet as I analyzed what computers do, I found that far from being number-crunchers, computers spend most of their time manipulating sets. Moreover, engineers usually understand the inner workings of these machines as set operations. Computers are machines that process data, and data are the units of knowledge: so, was set theory, not mathematics, the key to understanding reality?

Set theory is a fairly recent addition to the logical tools that can be used to handle abstractions. It was launched by a single paper published in Germany in 1874, and an agreed-upon set of axioms wasn’t formulated until the 1920s. Yet during the twentieth century logicians discovered that the foundations of mathematics, including both numbers and functions, can be defined in terms of sets. The converse is not true: the foundations of set theory cannot be defined in mathematical terms. Thus set theory is arguably more basic to human thought than mathematics is.

Modern set theory is based on its own axioms, a dozen or so rules of procedure that make set manipulations work. It seemed to me that if one were to search for a tool to explain human knowledge, the axioms of set theory might be a good place to start. This line of thought wound up inspiring the subtitle of my book: Knowledge as Set Construction.

In its widest definition, a set is a collection of zero or more elements of any kind, taken as a whole. The essential idea here is that every set is a new, real thing, distinct from its elements. This is what makes digital computers work. When a sequence of memory cells is loaded with bits—zeros or ones—that sequence takes on a meaning as a set that is different from the meaning of any one bit. A set of bits in memory may become a language character, a picture, a sound, a movie, or even a complex virtual reality. It all depends on the values of the bits, and if you change just one bit, the set may become something quite different.

When you think about it, set construction appears to be the kind of miracle that life is good at. A group of separate things, taken together, becomes a new, different thing with its own independent reality. Only living things (including us humans) seem to construct sets, and only living things possess knowledge. The problem is that the relation (if any) between these two facts is far from obvious.

So whether knowledge depends on set construction—and if so, how—became the primary questions I wanted to resolve. The answer to the first question, as you may guess, is yes. The route by which I arrived at that conclusion and discovered how it happens is mapped out in this book.

George Towner

Sunnyvale, California

June 2018

1

How Knowledge Works: Digital Reality Theory

I believe that the best way to present a new theory is all at once and up front. So while this book is primarily about knowledge, it is also about a lot of other things. It discusses existence, reality, digitizing, set theory, categorization, and theorizing. It presents a coherent analysis of certain threads that weave through these disparate topics, linking them in ways that are novel and make sense.

This book is a work of philosophy. When I told my nonacademic friends that I was writing such a thing, they rolled their eyes. One even quoted the late Stephen Hawking’s pronouncement that philosophy is dead. What Hawking went on to say is less inflammatory, but it bears directly on my work:

Philosophy has not kept up with modern developments in science, particularly physics. Scientists have become the bearers of the torch of discovery in our quest for knowledge.²

Hawking’s book The Grand Design makes it obvious that he believed the primary bearers of the torch were physicists. He seemed to agree with Ernest Rutherford’s quip, made nearly a century ago, that all science is either physics or stamp collecting. Yet it