Just as I was about to submit this book for broader review, I realized that I had taken the steps necessary to illustrate exactly how a theory concerning experience as sense in biophysics fits into the physical sciences in general. And it seemed to me that this really needed to be elaborated in this first book. So the book will now appear in two volumes since the changes will need to be propagated through the related work I have on the tensors and functors involved. The second volume will focus on details in this regard, presenting a comparison of my experimental approach with standard complex analysis.
I am happy with this approach and feel the first volume will now be more accessible, and make a stronger argument. Hopefully, the delay will be no more than a month or, maybe, two of writing and then a broader review - subject to the mundane matters of life staying out of my way.
In the meantime I will be reading from the first volume at Stanford University on November 13th, 2013. In that lecture I will read the first part of the book. I expect between 7000 and 9000 words that layout the new form (about an hour in length), and then 15 minutes or so of Q&A. The lecture will be streamed live and recorded, available subsequently through Stanford's usual channels on iTuneU and YouTube.
You can find details of the lecture here on FaceBook. You can find the Stanford University page for my lecture at Stanford, with bio. Here is are the first few paragraphs:
ON THE ORIGIN OF EXPERIENCE: THE SHAPING OF SENSE AND THE COMPLEX WORLD
Institute for Advanced Science & Engineering
"In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks." Benjamin Peirce, Linear Associative Algebra, 1870.
How are we to explain the presence of our experience in the world and its many forms? This book is the product of a research journey to answer this question that begins for me in the corridors of the University of Arizona in conversations with Oxford mathematician Roger Penrose. In March of 2003 we participated in a meeting that asked whether advances in quantum mechanics and biophysics informed us concerning the nature of the mind.
Relying primarily upon the work of Kurt Gödel (1906-1978) and Alan Turing (1912-1954), Penrose argues that a mathematical solution to the problem of describing experience in nature is impossible, more precisely he says the solution deals with the “non-computable.”
It has always been my intuition, however, that the limits of logical description he refers to are not limits of the world or failures of mathematics in general. They are, rather, indications of a failure in the foundations of mathematical logic, they are failures of a particular method. It seemed to me, therefore, most likely that resolution could be found by an inquiry into the nature of computation.
I am especially concerned that the immediate continuous transformation of structure, as holistically conceived by a mathematician and evident throughout biophysics, is not reflected naturally in any of Turing's methods of systematic computation. This fact passes unnoticed at the scale of computing familiar to most of us. And this has seduced many to believe that computation is invincible. But it is now clear that the efficiency of Turing computation decreases as the problem size increases with physically limiting consequences at large-scales. These consequences will ultimately lead me to exclude Turing's models of computation from biophysics.
As a keen scholar of recent biophysical results, funded for other causes often far from basic research, I had long suspected that the attempt to mathematize biophysics promised to inform the foundations of logic. It seemed to me impossible for biophysics to make progress without an exact account of experience as sense. And so as I listened to Penrose's ideas and concerns a contrary approach to the problem came to mind.
My approach then is simple to state, it is to ask what methods are required to enable a mathematical description of the different forms of sense, how they are modified, and the role that these actions play in the operation of biophysical structure. Sense in this case is simply the variety of experience.
Specifically, the goal of such an approach is to illustrate how a particular sensation is formed and modified in biophysical structure and the role that this action plays in the selection and performance of directed and non-directed response. And further, to describe how this basic mechanism combines to construct the entire experience of individuals and the operations of the familiar mind.
Such an approach is the first step toward reasoning about the many forms of experience, its place in nature, and its place in the considerations of physical science. It leads us to ask what may be missing from our physical conceptions and models of mathematical computation. With respect to these conventions, in terms of mathematical logic, it asks “What remains for the living mind?”
In addressing this question I illustrate in exact terms how my solution takes its place in the physical sciences.
The purpose here is to present the theory in sufficient detail to a broad audience, across disciplines. It includes the mathematical framework of the theory and its immediate implications to physics in general, logic, and computation. In the process I treat logic as a natural science whose mandate is to construct the bridge between pure mathematics and the physical sciences.